School of Mathematics and Statistics

Mathematics and Statistics

613-520-2155

http://math.carleton.ca

This section presents the requirements for programs in:

**Mathematics B. Math. Honours****Mathematics with Concentration in Stochastics B. Math. Honours****Computational and Applied Mathematics and Statistics with Concentration B.Math. Honours****Concentration in Applied Analysis****Concentration in Applied Statistics and Probability****Concentration in Discrete Mathematics****Statistics B. Math. Honours****Statistics with Concentration in Actuarial Science B. Math. Honours****Mathematics B. Math.****Computer Mathematics B. Math.****Statistics B. Math. General****Computer Science and Mathematics: Concentration in Computing Theory and Numerical Methods B. Math. Combined Honours****Computer Science and Mathematics: Concentration in Statistics and Computing B. Math. Combined Honours****Mathematics and Physics B.Sc. Double Honours****Economics and Mathematics B.Math. Combined Honours****Economics and Statistics B.Math. Combined Honours****Mathematics (Combined B.Math./M.Sc.) B.Math.****Statistics (Combined B.Math./M.Sc.) B.Math.****Minor in Mathematics****Minor in Statistics**

### Program Requirements

### Course Prerequisites

The following courses central to B.Math. programs have grade requirements in their prerequisites:

- MATH 2000 requires C+ in (MATH 1002(no longer offered) or MATH 2052) , or B+ in (MATH 2007 or MATH 1005), and C+ in (MATH 1102(no longer offered) or MATH 2152), or B+ in (MATH 1107 or MATH 1104).
- MATH 2100 requires C+ in (MATH 1102(no longer offered) or MATH 2152), or B+ in MATH 2107.
- MATH 2454 requires C+ in (MATH 1002(no longer offered) or MATH 2052 or MATH 2007or MATH 1005), and C+ in (MATH 1102(no longer offered) or MATH 2152 or MATH 2107).
- STAT 2655 requires C+ in (MATH 1002(no longer offered) or MATH 2052 or MATH 2007 or MATH 1005), and C+ in (MATH 1102(no longer offered) or MATH 2152 or MATH 1107 or MATH 1104).
- MATH 2007 requires MATH 1004 or C- in (MATH 1007 or MATH 1009).
- MATH 2107 requires MATH 1104 or C- in MATH 1107

### Course Categories for B.Math. Programs

2000-level Honours Sequence | ||

The following courses constitute the 2000-level Honours Sequence: | ||

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2100 [1.0] | Algebra | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

MATH 2907 [0.5] | Directed Studies (Honours) |

3000-level Honours Sequence | ||

The following courses constitute the 3000-level Honours Sequence. Courses in the 3000-level Honours Sequence have grade levels in their prerequisites | ||

MATH 3001 [0.5] | Real Analysis I (Honours) | |

MATH 3002 [0.5] | Real Analysis II (Honours) | |

MATH 3003 [0.5] | Advanced Differential Calculus (Honours) | |

MATH 3057 [0.5] | Functions of a Complex Variable (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3106 [0.5] | Introduction to Group Theory (Honours) | |

MATH 3158 [0.5] | Rings and Fields (Honours) | |

MATH 3306 [0.5] | Elements of Set Theory (Honours) | |

MATH 3355 [0.5] | Number Theory and Applications (Honours) | |

MATH 3806 [0.5] | Numerical Analysis (Honours) | |

MATH 3807 [0.5] | Mathematical Software (Honours) | |

MATH 3855 [0.5] | Discrete Structures and Applications (Honours) | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) |

Natural Science Electives | ||

All courses with the following subject codes: | ||

BIOC, BIOL, CHEM, ENSC, ERTH, ISCI, NSCI, PHYS |

APPROVED ARTS OR SOCIAL SCIENCES ELECTIVES | ||

All courses offered by the Faculty of Arts and Social Sciences and the Faculty of Public Affairs are acceptable as Arts or Social Sciences Electives except for the following courses, which are only accepted for credit as free electives in any program of the School. See item 3 under Prohibited and Restricted Courses below concerning Computer Mathematics programs. | ||

Business | ||

BUSI 1001 [0.5] | Principles of Financial Accounting | |

BUSI 1002 [0.5] | Management Accounting | |

BUSI 1004 [0.5] | Financial Accounting for Business Students | |

BUSI 1005 [0.5] | Managerial Accounting for Business Students | |

BUSI 1402 [0.5] | Introduction to Business Information and Communication Technologies | |

BUSI 2001 [0.5] | Intermediate Accounting I | |

BUSI 2002 [0.5] | Intermediate Accounting II | |

BUSI 2402 [0.5] | Business Applications Development | |

BUSI 3001 [0.5] | Accounting for Business Combinations | |

BUSI 3008 [0.5] | Intermediate Management Accounting and Control | |

Economics | ||

ECON 4005 [0.5] | Operations Research II | |

Geography | ||

GEOG 3102 [0.5] | Geomorphology | |

GEOG 3103 [0.5] | Watershed Hydrology | |

GEOG 3105 [0.5] | Climate and Atmospheric Change | |

GEOG 3108 [0.5] | Soil Properties | |

Field Studies | ||

Directed Studies in Geography | ||

GEOG 4101 [0.5] | Two Million Years of Environmental Change | |

Water Resources Engineering | ||

GEOG 4104 [0.5] | Microclimatology | |

GEOG 4108 [0.5] | Permafrost | |

Geomatics | ||

GEOM 2007 [0.5] | Geographic Information Systems | |

GEOM 3002 [0.5] | Introduction to Remote Sensing | |

GEOM 3005 [0.5] | Geospatial Analysis | |

GEOM 3007 [0.5] | Cartographic Theory and Design | |

GEOM 4003 [0.5] | Remote Sensing of the Environment | |

GEOM 4008 [0.5] | Advanced Topics in Geographic Information Systems | |

GEOM 4009 [0.5] | Applications in Geographic Information Systems | |

Psychology | ||

PSYC 2700 [0.5] | Introduction to Cognitive Psychology | |

PSYC 3506 [0.5] | Cognitive Development | |

PSYC 3700 [1.0] | Cognition (Honours Seminar) | |

PSYC 3702 [0.5] | Perception | |

PSYC 4001 [0.5] | Special Topics in Psychology |

### Prohibited and Restricted Courses

- MATH 1805/COMP 1805 can be counted only as a half-credit free elective in Mathematics and Statistics programs.
- The following courses may not be counted for academic credit (even as free electives) in any program offered by the School of Mathematics and Statistics: BIOL 3604, COMS 3001, CRCJ 3001,ECON 1401, ECON 1402, ECON 2201 (no longer offered), ECON 2202 (no longer offered),ECON 2210, ECON 2220, ECON 2400 (no longer offered), ECON 3001, ECON 4001, ECON 4002, ECON 4004, ECON 4025, ECON 4706, ECON 4707, ECON 4713, ECOR 2606, GEOG 2006, GEOG 3003, NEUR 2001, NEUR 2002, NEUR 3001, NEUR 3002, PSCI 2702, PSYC 2001, PSYC 2002, PSYC 3000 [1.0], SOCI 3000, SOCI 3002, SOCI 4009, SOWK 3001, SYSC 2510.

Students who have completed ECON 2201 (no longer offered) and ECON 2202 (no longer offered) and enter a B.Math. General program may be exempted from taking STAT 2507 and STAT 2509 only with permission of the School of Mathematics and Statistics, and provided the grade in ECON 2201 (no longer offered) and ECON 2202 (no longer offered) is B- or higher in each. - BUSI 1402, BUSI 2402 and COMP 1001 may not count for credit in the Computer Mathematics Honours or General program, even as free electives.
- Only one of MATH 3806, COMP 3806 (no longer offered), CMPS 3800 (no longer offered) or MATH 3800 may count for credit in a B.Math. program.

### Mathematics

B. Math. Honours (20.0 credits)

A. Credits Included in the Major CGPA (11.5 credits) | ||

1. 2.5 credits in: | 2.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2152 [0.5] | Introductory Algebra II | |

2. 3.5 credits in: | 3.5 | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2100 [1.0] | Algebra | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

3. 2.0 credits in: | 2.0 | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

MATH 3057 [0.5] | Functions of a Complex Variable (Honours) | |

MATH 3106 [0.5] | Introduction to Group Theory (Honours) | |

MATH 3158 [0.5] | Rings and Fields (Honours) | |

4. 0.5 credit from: | 0.5 | |

MATH 3002 [0.5] | Real Analysis II (Honours) | |

MATH 3003 [0.5] | Advanced Differential Calculus (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

5. 1.0 credit from 3000-level Honours Sequence | 1.0 | |

6. 1.5 credits in MATH or STAT at the 4000-level or higher | 1.5 | |

7. 0.5 credit in: | 0.5 | |

MATH 4905 [0.5] | Honours Project (Honours) | |

B. Credits Not Included in the Major CGPA (8.5 credits) | ||

8. 4.0 credits not in MATH, STAT or COMP, consisting of: | 4.0 | |

a. 1.0 credit in Natural Science Electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

9. 4.5 credits in free electives | 4.5 | |

Total Credits | 20.0 |

### Mathematics with Concentration in Stochastics

B. Math. Honours (20.0 credits)

Items 3, 4, 5 and 6 in the Mathematics degree requirements are replaced by:

3. 3.0 credits in: | 3.0 | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

STAT 4501 [0.5] | Probability Theory (Honours) | |

4. 0.5 credit from: | 0.5 | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

MATH 3801 [0.5] | Linear Programming | |

5. 0.5 credit in STAT at the 4000-level | 0.5 | |

6. 1.0 credit in MATH or STAT at the 4000-level or higher | 1.0 | |

Total Credits | 5.0 |

### Computational and Applied Mathematics and Statistics with Concentration

B.Math. Honours (20.0 credits)

A. Credits included in the Major CGPA (14.0 credits) | ||

1. 7.0 credits in: | 7.0 | |

COMP 1405 [0.5] | Introduction to Computer Science I | |

COMP 1406 [0.5] | Introduction to Computer Science II | |

COMP 2401 [0.5] | Introduction to Systems Programming | |

COMP 2402 [0.5] | Abstract Data Types and Algorithms | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2152 [0.5] | Introductory Algebra II | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

2. 6.5 credits in one of the concentrations described below, also included in the Major CGPA: | 6.5 | |

3. 0.5 credit in: | 0.5 | |

MATH 4905 [0.5] | Honours Project (Honours) | |

B. Credits Not Included in the Major CGPA (6.0 credits) | ||

4. 1.0 credit in Natural Science electives at the 1000 level or above | 1.0 | |

5. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | 3.0 | |

6. 2.0 credits in free electives | 2.0 | |

Total Credits | 20.0 |

#### Concentration in Applied Analysis (6.5 credits)

Requirements: | ||

2a. 3.0 credits in: | 3.0 | |

MATH 2100 [1.0] | Algebra | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3057 [0.5] | Functions of a Complex Variable (Honours) | |

MATH 3806 [0.5] | Numerical Analysis (Honours) | |

MATH 3855 [0.5] | Discrete Structures and Applications (Honours) | |

2b. 1.0 credit from: | 1.0 | |

MATH 4700 [0.5] | Partial Differential Equations (Honours) | |

MATH 4701 [0.5] | Topics in Differential Equations (Honours) | |

MATH 4703 [0.5] | Dynamical Systems (Honours) | |

MATH 4708 [0.5] | Asymptotic Methods of Applied Mathematics (Honours) | |

MATH 4806 [0.5] | Numerical Linear Algebra (Honours) | |

MATH 4816 [0.5] | Numerical Analysis for Differential Equations (Honours) | |

2c. 0.5 credit in MATH at the 4000 level | 0.5 | |

2d. 2.0 credits in MATH or STAT at the 3000 level or above | 2.0 | |

Total Credits | 6.5 |

#### Concentration in Applied Statistics and Probability (6.5 credits)

Requirements: | ||

2a. 2.5 credits in: | 2.5 | |

MATH 3107 [0.5] | Linear Algebra III | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

2b. 1.5 credits from: | 1.5 | |

STAT 4500 [0.5] | Parametric Estimation (Honours) | |

STAT 4502 [0.5] | Survey Sampling (Honours) | |

STAT 4503 [0.5] | Applied Multivariate Analysis (Honours) | |

STAT 4504 [0.5] | Statistical Design and Analysis of Experiments (Honours) | |

STAT 4506 [0.5] | Nonparametric Statistics (Honours) | |

STAT 4508 [0.5] | Stochastic Models (Honours) | |

STAT 4509 [0.5] | Advanced Mathematical Modeling (Honours) | |

STAT 4555 [0.5] | Monte Carlo Simulation (Honours) | |

STAT 4601 [0.5] | Data Mining I (Honours) | |

STAT 4603 [0.5] | Time Series and Forecasting (Honours) | |

STAT 4604 [0.5] | Statistical Computing (Honours) | |

2c. 2.5 credits in MATH or STAT at the 3000 level or above | 2.5 | |

Total Credits | 6.5 |

#### Concentration in Discrete Mathematics (6.5 credits)

Requirements: | ||

2a. 3.0 credits in: | 3.0 | |

MATH 2100 [1.0] | Algebra | |

MATH 3801 [0.5] | Linear Programming | |

MATH 3802 [0.5] | Combinatorial Optimization | |

MATH 3806 [0.5] | Numerical Analysis (Honours) | |

MATH 3855 [0.5] | Discrete Structures and Applications (Honours) | |

2b. 1.0 credit from: | 1.0 | |

MATH 4109 [0.5] | Fields and Coding Theory (Honours) | |

MATH 4801 [0.5] | Topics in Combinatorics (Honours) | |

MATH 4802 [0.5] | Introduction to Mathematical Logic (Honours) | |

MATH 4803 [0.5] | Computable Functions (Honours) | |

MATH 4805 [0.5] | Theory of Automata (Honours) | |

MATH 4807 [0.5] | Game Theory (Honours) | |

MATH 4808 [0.5] | Graph Theory and Algorithms (Honours) | |

MATH 4811 [0.5] | Combinatorial Design Theory (Honours) | |

2c. 0.5 credit in MATH at the 4000 level | 0.5 | |

2d. 2.0 credits in MATH or STAT at the 3000 level or above | 2.0 | |

Total Credits | 6.5 |

### Statistics

B. Math. Honours (20.0 credits)

A. Credits Included in the Major CGPA (12.5 credits) | ||

1. 2.5 credits in: | 2.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2152 [0.5] | Introductory Algebra II | |

2. 1.0 credit in: | 1.0 | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

COMP 1006 [0.5] | Introduction to Computer Science II | |

3. 6.0 credits in: | 6.0 | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3806 [0.5] | Numerical Analysis (Honours) | |

MATH 4905 [0.5] | Honours Project (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

STAT 4500 [0.5] | Parametric Estimation (Honours) | |

4. 1.0 credit from: | 1.0 | |

MATH 2100 [1.0] | Algebra | |

or | ||

MATH 3107 [0.5] | Linear Algebra III | |

and 0.5 credit from: | ||

3000-level Honours Sequence, or: | ||

MATH 3705 [0.5] | Mathematical Methods I | |

MATH 3801 [0.5] | Linear Programming | |

MATH 3807 [0.5] | Mathematical Software (Honours) | |

MATH 3809 [0.5] | Introduction to Number Theory and Cryptography | |

or Mathematics or Statistics at the 4000-level or higher | ||

5. 0.5 credit from the 3000-level Honours Sequence or MATH or STAT at the 4000-level or higher | 0.5 | |

6. 1.5 credits in STAT at the 4000-level | 1.5 | |

B. Credits Not Included in the Major CGPA (7.5 credits) | ||

7. 4.0 credits not in MATH, STAT or COMP, consisting of: | 4.0 | |

a. 1.0 credit in Natural Science Electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

8. 3.5 credits in free electives | 3.5 | |

Total Credits | 20.0 |

### Statistics with Concentration in Actuarial Science

B. Math. Honours (20.0 credits)

A. Credits Included in the Major CGPA (13.0 credits) | ||

1. 2.5 credits in: | 2.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2152 [0.5] | Introductory Algebra II | |

2. 1.0 credit in: | 1.0 | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

COMP 1006 [0.5] | Introduction to Computer Science II | |

3. 6.5 credits in: | 6.5 | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3806 [0.5] | Numerical Analysis (Honours) | |

MATH 4905 [0.5] | Honours Project (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

STAT 2660 [0.5] | Mathematics for Finance (Honours) | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

STAT 4500 [0.5] | Parametric Estimation (Honours) | |

4. 1.0 credit in: | 1.0 | |

MATH 3107 [0.5] | Linear Algebra III | |

and 0.5 credit from: | ||

3000-level Honours Sequence, or: | ||

MATH 3705 [0.5] | Mathematical Methods I | |

MATH 3801 [0.5] | Linear Programming | |

MATH 3807 [0.5] | Mathematical Software (Honours) | |

MATH 3809 [0.5] | Introduction to Number Theory and Cryptography | |

or Mathematics or Statistics at the 4000-level or higher | ||

5. 1.0 credit in: | 1.0 | |

STAT 3661 [0.5] | Life Contingent Risk Modelling I | |

STAT 3662 [0.5] | Life Contingent Risk Modelling II | |

6. 1.0 credit in: | 1.0 | |

STAT 4508 [0.5] | Stochastic Models (Honours) | |

STAT 4603 [0.5] | Time Series and Forecasting (Honours) | |

B. Credits Not Included in the Major CGPA (7.0 credits): | ||

7. 3.0 credits in: | 3.0 | |

BUSI 1001 [0.5] | Principles of Financial Accounting | |

BUSI 1002 [0.5] | Management Accounting | |

ECON 1001 [0.5] | Introduction to Microeconomics | |

ECON 1002 [0.5] | Introduction to Macroeconomics | |

ECON 2020 [0.5] | Intermediate Microeconomics I: Producers and Market Structure | |

ECON 2102 [0.5] | Intermediate Macroeconomics I | |

8. 2.5 credits in: | 2.5 | |

BUSI 2504 [0.5] | Business Finance I | |

BUSI 2505 [0.5] | Business Finance II | |

BUSI 3500 [0.5] | Applied Corporate Finance | |

BUSI 3502 [0.5] | Investments | |

BUSI 3512 [0.5] | Derivatives | |

or | ||

ECON 2030 [0.5] | Intermediate Microeconomics II: Consumers and General Equilibrium | |

ECON 3050 [0.5] | Introduction to Financial Economics | |

ECON 4051 [0.5] | Financial Asset Pricing | |

ECON 4052 [0.5] | Corporate Financial Economics | |

and one of: | ||

ECON 2103 [0.5] | Intermediate Macroeconomics II | |

ECON 3607 [0.5] | Monetary and Financial Institutions | |

ECON 4053 [0.5] | Financial Market Modeling | |

9. 1.0 credit in Natural Science electives | 1.0 | |

10. 0.5 credit in free electives | 0.5 | |

Total Credits | 20.0 |

### Mathematics

B. Math. (15.0 credits)

A. Credits Included in the Major CGPA (7.5 credits) | ||

1. 0.5 credit in: | 0.5 | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

2. 1.0 credit in: | 1.0 | |

MATH 1007 [0.5] | Elementary Calculus I | |

or MATH 1004 [0.5] | Calculus for Engineering or Physics | |

MATH 2007 [0.5] | Elementary Calculus II | |

or MATH 1005 [0.5] | Differential Equations and Infinite Series for Engineering or Physics | |

3. 1.0 credit in: | 1.0 | |

MATH 1107 [0.5] | Linear Algebra I | |

or MATH 1104 [0.5] | Linear Algebra for Engineering or Science | |

MATH 2107 [0.5] | Linear Algebra II | |

4. 2.0 credits in: | 2.0 | |

MATH 2008 [0.5] | Intermediate Calculus | |

MATH 2108 [0.5] | Abstract Algebra I | |

MATH 2404 [0.5] | Ordinary Differential Equations I | |

STAT 2507 [0.5] | Introduction to Statistical Modeling I | |

5. 3.0 credits from: | 3.0 | |

STAT 2509 [0.5] | Introduction to Statistical Modeling II | |

MATH or STAT at the 3000-level or higher | ||

Excluding: | ||

MATH 3101 [0.5] | Algebraic Structures with Computer Applications | |

STAT 3502 [0.5] | Probability and Statistics | |

B. Credits Not Included in the Major CGPA (7.5 credits) | ||

6. 4.0 credits not in MATH, STAT or COMP, consisting of: | 4.0 | |

a. 1.0 credit in Natural Science Electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

7. 3.5 credits in free electives. | 3.5 | |

Total Credits | 15.0 |

### Computer Mathematics

B. Math. (15.0 credits)

A. Credits Included in the Major CGPA (10.5 credits) | ||

1. 0.5 credit in: | 0.5 | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

2. 1.0 credit in: | 1.0 | |

MATH 1007 [0.5] | Elementary Calculus I | |

or MATH 1004 [0.5] | Calculus for Engineering or Physics | |

and | ||

MATH 2007 [0.5] | Elementary Calculus II | |

or MATH 1005 [0.5] | Differential Equations and Infinite Series for Engineering or Physics | |

3. 1.0 credit in: | 1.0 | |

MATH 1107 [0.5] | Linear Algebra I | |

or MATH 1104 [0.5] | Linear Algebra for Engineering or Science | |

and | ||

MATH 2107 [0.5] | Linear Algebra II | |

4. 2.5 credits in: | 2.5 | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

COMP 1006 [0.5] | Introduction to Computer Science II | |

COMP 2401 [0.5] | Introduction to Systems Programming | |

COMP 2402 [0.5] | Abstract Data Types and Algorithms | |

COMP 2404 [0.5] | Introduction to Software Engineering | |

5. 2.5 credits in: | 2.5 | |

MATH 2008 [0.5] | Intermediate Calculus | |

MATH 3804 [0.5] | Design and Analysis of Algorithms I | |

MATH 3825 [0.5] | Discrete Structures and Applications | |

STAT 2507 [0.5] | Introduction to Statistical Modeling I | |

STAT 2605 [0.5] | Probability Models | |

6. 0.5 credit from: | 0.5 | |

MATH 2108 [0.5] | Abstract Algebra I | |

MATH 3101 [0.5] | Algebraic Structures with Computer Applications | |

7. 1.0 credit from: | 1.0 | |

MATH 3801 [0.5] | Linear Programming | |

MATH 3802 [0.5] | Combinatorial Optimization | |

MATH 3800 [0.5] | Mathematical Modeling and Computational Methods | |

MATH 3807 [0.5] | Mathematical Software (Honours) | |

MATH 3809 [0.5] | Introduction to Number Theory and Cryptography | |

8. 1.0 credit in MATH or STAT at the 3000 level | 1.0 | |

9. 0.5 credit in MATH or STAT at the 2000 level or higher | 0.5 | |

B. Credits Not Included in the Major CGPA (4.5 credits) | ||

10. 4.0 credits not in MATH, STAT or COMP, consisting of: | 4.0 | |

a. 1.0 credit in Natural Science Electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

11. 0.5 credit in free electives. | 0.5 | |

Total Credits | 15.0 |

### Statistics

B. Math. General (15.0 credits)

A. Credits Included in the Major CGPA (7.5 credits) | ||

1. 0.5 credit in: | 0.5 | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

2. 1.0 credit in: | 1.0 | |

MATH 1007 [0.5] | Elementary Calculus I | |

or MATH 1004 [0.5] | Calculus for Engineering or Physics | |

MATH 2007 [0.5] | Elementary Calculus II | |

or MATH 1005 [0.5] | Differential Equations and Infinite Series for Engineering or Physics | |

3. 1.0 credit in: | 1.0 | |

MATH 1107 [0.5] | Linear Algebra I | |

or MATH 1104 [0.5] | Linear Algebra for Engineering or Science | |

MATH 2107 [0.5] | Linear Algebra II | |

4. 4.0 credits in: | 4.0 | |

MATH 2008 [0.5] | Intermediate Calculus | |

STAT 2507 [0.5] | Introduction to Statistical Modeling I | |

STAT 2509 [0.5] | Introduction to Statistical Modeling II | |

STAT 3503 [0.5] | Regression Analysis | |

STAT 3504 [0.5] | Analysis of Variance and Experimental Design | |

STAT 3507 [0.5] | Sampling Methodology | |

STAT 3508 [0.5] | Elements of Probability Theory | |

STAT 3509 [0.5] | Mathematical Statistics | |

5. 0.5 credit from: | 0.5 | |

BUSI 1402 [0.5] | Introduction to Business Information and Communication Technologies | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

ECOR 1606 [0.5] | Problem Solving and Computers | |

6. 0.5 credit in MATH or STAT at the 2000 level | 0.5 | |

B. Credits Not Included in the Major CGPA (7.5 credits) | ||

7. 4.0 credits not in MATH, STAT or COMP, consisting of: | 4.0 | |

a. 1.0 credit in Natural Science Electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

8. 3.5 credits in free electives. | 3.5 | |

Total Credits | 15.0 |

### Computer Science and Mathematics:

Concentration in Computing Theory and Numerical Methods

B. Math. Combined Honours (20.0 credits)

A. Credits Included in the Major CGPA (16.0 credits) | ||

1. 4.5 credits in: | 4.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2100 [1.0] | Algebra | |

MATH 2152 [0.5] | Introductory Algebra II | |

2. 6.0 credits in: | 6.0 | |

COMP 1405 [0.5] | Introduction to Computer Science I | |

COMP 1406 [0.5] | Introduction to Computer Science II | |

COMP 2401 [0.5] | Introduction to Systems Programming | |

COMP 2402 [0.5] | Abstract Data Types and Algorithms | |

COMP 2404 [0.5] | Introduction to Software Engineering | |

COMP 2406 [0.5] | Fundamentals of Web Applications | |

COMP 2804 [0.5] | Discrete Structures II | |

COMP 3000 [0.5] | Operating Systems | |

COMP 3004 [0.5] | Object-Oriented Software Engineering | |

COMP 3005 [0.5] | Database Management Systems | |

COMP 3804 [0.5] | Design and Analysis of Algorithms I | |

COMP 3805 [0.5] | Discrete Structures and Applications (Honours) | |

3. 0.5 credit from: | 0.5 | |

COMP 4905 [0.5] | Honours Project | |

MATH 4905 [0.5] | Honours Project (Honours) | |

Concentration in Computing Theory and Numerical Methods | ||

4. 3.0 credits from: | 3.0 | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

MATH 3801 [0.5] | Linear Programming | |

MATH 3806 [0.5] | Numerical Analysis (Honours) | |

COMP 4804 [0.5] | Design and Analysis of Algorithms II | |

5. 0.5 credit from: | 0.5 | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

MATH 3002 [0.5] | Real Analysis II (Honours) | |

MATH 3003 [0.5] | Advanced Differential Calculus (Honours) | |

MATH 3057 [0.5] | Functions of a Complex Variable (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

6. 1.0 credit from: | 1.0 | |

MATH 4109 [0.5] | Fields and Coding Theory (Honours) | |

MATH 4801 [0.5] | Topics in Combinatorics (Honours) | |

MATH 4802 [0.5] | Introduction to Mathematical Logic (Honours) | |

MATH 4803 [0.5] | Computable Functions (Honours) | |

MATH 4805 [0.5] | Theory of Automata (Honours) | |

MATH 4806 [0.5] | Numerical Linear Algebra (Honours) | |

MATH 4807 [0.5] | Game Theory (Honours) | |

MATH 4808 [0.5] | Graph Theory and Algorithms (Honours) | |

MATH 4811 [0.5] | Combinatorial Design Theory (Honours) | |

MATH 4816 [0.5] | Numerical Analysis for Differential Equations (Honours) | |

MATH 4821 [0.5] | Quantum Computing (Honours) | |

MATH 4822 [0.5] | Wavelets and Digital Signal Processing (Honours) | |

7. 0.5 credit in COMP at the 3000 level or above. | 0.5 | |

B. Credits Not Included in the Major CGPA (4.0 credits) | ||

8. 4.0 credits not in MATH, STAT, or COMP consisting of: | 4.0 | |

a. 1.0 credit in Natural Science electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

Total Credits | 20.0 |

Note: | ||

The following courses offered by the School of Business and the Faculty of Engineering are treated as Computer Science courses in this program: | ||

Business | ||

BUSI 2400 [0.5] | Foundations of Information Systems | |

BUSI 4400 [0.5] | IS Strategy, Management and Acquisition | |

BUSI 4406 [0.5] | Business Analytics | |

Engineering | ||

SYSC 3303 [0.5] | Real-Time Concurrent Systems | |

SYSC 4005 [0.5] | Discrete Simulation/Modeling | |

SYSC 4507 [0.5] | Computer Systems Architecture |

### Computer Science and Mathematics:

Concentration in Statistics and Computing

B. Math. Combined Honours (20.0 credits)

A. Credits Included in the Major CGPA (16.0 credits) | ||

1. 4.5 credits in: | 4.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2100 [1.0] | Algebra | |

MATH 2152 [0.5] | Introductory Algebra II | |

2. 6.0 credits in: | 6.0 | |

COMP 1405 [0.5] | Introduction to Computer Science I | |

COMP 1406 [0.5] | Introduction to Computer Science II | |

COMP 2401 [0.5] | Introduction to Systems Programming | |

COMP 2402 [0.5] | Abstract Data Types and Algorithms | |

COMP 2404 [0.5] | Introduction to Software Engineering | |

COMP 2406 [0.5] | Fundamentals of Web Applications | |

COMP 2804 [0.5] | Discrete Structures II | |

COMP 3000 [0.5] | Operating Systems | |

COMP 3004 [0.5] | Object-Oriented Software Engineering | |

COMP 3005 [0.5] | Database Management Systems | |

COMP 3804 [0.5] | Design and Analysis of Algorithms I | |

COMP 3805 [0.5] | Discrete Structures and Applications (Honours) | |

3. 0.5 credit from: | 0.5 | |

COMP 4905 [0.5] | Honours Project | |

MATH 4905 [0.5] | Honours Project (Honours) | |

Concentration: | ||

4. 3.0 credits in: | 3.0 | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3806 [0.5] | Numerical Analysis (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

5. 0.5 credit from: | 0.5 | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

6. 1.0 credit in STAT at the 4000 level | 1.0 | |

7. 0.5 credit in COMP at the 4000 level | 0.5 | |

B. Credits Not Included in the Major CGPA (4.0 credits) | ||

8. 4.0 credits not in MATH, STAT, or COMP consisting of: | 4.0 | |

a. 1.0 credit in Natural Science electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

Total Credits | 20.0 |

### Mathematics and Physics

B.Sc. Double Honours (21.5 credits)

Note that the following courses have minimum grade requirements in their prerequisites. Refer to the section Course Prerequisites under the Mathematics and Statistics programs sections of the calendar. | ||

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2100 [1.0] | Algebra | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) |

A. Credits Included in the Major CGPA (17.0 credits) | ||

1. 7.5 credits in: | 7.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2100 [1.0] | Algebra | |

MATH 2152 [0.5] | Introductory Algebra II | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3057 [0.5] | Functions of a Complex Variable (Honours) | |

MATH 3705 [0.5] | Mathematical Methods I | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

2. 0.5 credit from: | 0.5 | |

MATH 3002 [0.5] | Real Analysis II (Honours) | |

MATH 3003 [0.5] | Advanced Differential Calculus (Honours) | |

MATH 3106 [0.5] | Introduction to Group Theory (Honours) | |

PHYS 3007 [0.5] | Third Year Physics Laboratory: Selected Experiments and Seminars | |

PHYS 3606 [0.5] | Modern Physics II | |

3. 1.0 credit in 4000-level or higher MATH, STAT | 1.0 | |

4. 1.0 credit from: | 1.0 | |

Foundations of Physics I Foundations of Physics II (recommended) | ||

Introductory Mechanics and Thermodynamics Introductory Electromagnetism and Wave Motion | ||

Elementary University Physics I Elementary University Physics II (with an average grade of B- or higher) | ||

5. 2.0 credits in: | 2.0 | |

PHYS 2202 [0.5] | Wave Motion and Optics | |

PHYS 2305 [0.5] | Electricity and Magnetism | |

PHYS 2401 [0.5] | Thermal Physics | |

PHYS 2604 [0.5] | Modern Physics I | |

6. 3.0 credits in: | 3.0 | |

PHYS 3308 [0.5] | Electromagnetism | |

PHYS 3701 [0.5] | Elements of Quantum Mechanics | |

PHYS 3802 [0.5] | Advanced Dynamics | |

PHYS 4409 [0.5] | Thermodynamics and Statistical Physics | |

PHYS 4707 [0.5] | Introduction to Quantum Mechanics I | |

PHYS 4708 [0.5] | Introduction to Quantum Mechanics II | |

7. 1.0 credit in PHYS at the 4000-level | 1.0 | |

8. 1.0 credit from: | 1.0 | |

b. PHYS 4909 [1.0] | ||

B. Credits Not Included in the Major CGPA (4.5 credits) | ||

9. 1.0 credit from: | 1.0 | |

Foundations of Biology I Foundations of Biology II | ||

General Chemistry I General Chemistry II | ||

Elementary Chemistry I Elementary Chemistry II | ||

Exploring Planet Earth The Earth System Through Time | ||

10. 0.5 credit in: | 0.5 | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

11. 0.5 credit from: | 0.5 | |

NSCI 1000 [0.5] | Seminar in Science | |

Approved courses outside the faculties of Science and Engineering and Design | ||

12. 1.5 credits in approved courses outside the faculties of Science and Engineering and Design | 1.5 | |

13. 1.0 credit in free electives | 1.0 | |

Total Credits | 21.5 |

### Economics and Mathematics

B.Math. Combined Honours (20.0 credits)

A. Credits Included in the Major CGPA (15.5 credits) | ||

1. 7.5 credits in: | 7.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2100 [1.0] | Algebra | |

MATH 2152 [0.5] | Introductory Algebra II | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

2. 0.5 credit from: | 0.5 | |

MATH 3002 [0.5] | Real Analysis II (Honours) | |

MATH 3003 [0.5] | Advanced Differential Calculus (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

3. 0.5 credit in: | 0.5 | |

MATH 4905 [0.5] | Honours Project (Honours) | |

4. 1.0 credit in MATH or STAT at the 4000-level | 1.0 | |

5. 4.0 credits in: | 4.0 | |

ECON 1001 [0.5] | Introduction to Microeconomics | |

ECON 1002 [0.5] | Introduction to Macroeconomics | |

ECON 2020 [0.5] | Intermediate Microeconomics I: Producers and Market Structure | |

ECON 2030 [0.5] | Intermediate Microeconomics II: Consumers and General Equilibrium | |

ECON 2102 [0.5] | Intermediate Macroeconomics I | |

ECON 2103 [0.5] | Intermediate Macroeconomics II | |

ECON 4020 [0.5] | Advanced Microeconomic Theory | |

ECON 4021 [0.5] | Advanced Macroeconomic Theory | |

6. 2.0 credits in ECON at the 4000-level | 2.0 | |

B. Credits Not Included in the Major CGPA (4.5 credits) | ||

7. 1.0 credit in: | 1.0 | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

COMP 1006 [0.5] | Introduction to Computer Science II | |

8. 1.0 credit in Natural Science Electives | 1.0 | |

9. 2.5 credits in free electives | 2.5 | |

Total Credits | 20.0 |

**Notes:**

- An Honours Essay (ECON 4908 [1.0]) may be written by students with Overall and Major CGPAS of 9.50 or higher. In cases where a grade of B- or higher is earned on this essay, it may count for 1.0 credit in ECON at the 4000-level. Qualified students who choose to pursue the Honours Essay option must first complete an Honours Essay prospectus to the satisfaction of both their adviser and the Department of Economics Undergraduate Supervisor.
- The following courses do not count for credit in this program: ECON 1401, ECON 1402, ECON 2201 (no longer offered), ECON 2202 (no longer offered), ECON 2210, ECON 2220, ECON 2400 (no longer offered), ECON 3001, ECON 4001, ECON 4002, ECON 4004, ECON 4025, ECON 4706, ECON 4707, and ECON 4713.

### Economics and Statistics

B.Math. Combined Honours (20.0 credits)

A. Credits Included in the Major CGPA (15.5 credits) | ||

1. 8.5 credits in: | 8.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2152 [0.5] | Introductory Algebra II | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3107 [0.5] | Linear Algebra III | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

STAT 4502 [0.5] | Survey Sampling (Honours) | |

STAT 4503 [0.5] | Applied Multivariate Analysis (Honours) | |

2. 0.5 credit in: | 0.5 | |

MATH 4905 [0.5] | Honours Project (Honours) | |

3. 0.5 credit in STAT at the 4000 level | 0.5 | |

4. 4.0 credits in: | 4.0 | |

ECON 1001 [0.5] | Introduction to Microeconomics | |

ECON 1002 [0.5] | Introduction to Macroeconomics | |

ECON 2020 [0.5] | Intermediate Microeconomics I: Producers and Market Structure | |

ECON 2030 [0.5] | Intermediate Microeconomics II: Consumers and General Equilibrium | |

ECON 2102 [0.5] | Intermediate Macroeconomics I | |

ECON 2103 [0.5] | Intermediate Macroeconomics II | |

ECON 4020 [0.5] | Advanced Microeconomic Theory | |

ECON 4021 [0.5] | Advanced Macroeconomic Theory | |

5. 2.0 credits in ECON at the 4000 level | 2.0 | |

B. Credits Not Included in the Major CGPA (4.5 credits) | ||

6. 1.0 credit in: | 1.0 | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

COMP 1006 [0.5] | Introduction to Computer Science II | |

7. 1.0 credit in Natural Science Electives | 1.0 | |

8. 2.5 credits in free electives | 2.5 | |

Total Credits | 20.0 |

**Notes:**

- An Honours Essay ECON 4908 [1.0] may be written by students with Overall and Major CGPAs of 9.50 or higher. In cases where a grade of B- or higher is earned on this essay, it may count for 1.0 credit in ECON at the 4000-level. Qualified students who choose to pursue the Honours Essay option must first complete an Honours Essay prospectus to the satisfaction of both their adviser and the Department of Economics Undergraduate Supervisor.
- MATH 2100 [1.0] may replace MATH 3107 and 0.5 credit in free electives in this program.
- The following courses do not count for credit in this program: ECON 1401, ECON 1402, ECON 2201 (no longer offered), ECON 2202 (no longer offered), ECON 2210, ECON 2220, ECON 2400 (no longer offered), ECON 3001, ECON 4001, ECON 4002, ECON 4004, ECON 4025, ECON 4706, ECON 4707, and ECON 4713.

### Program Requirements for Combined B.Math./M.Sc.

This "fast-track" program combines the requirements for Bachelor of Mathematics in Mathematics or Statistics, and Master of Science in Mathematics, into a sequence that will enable exceptional students to complete in four years of study.

Entry to this program directly from an Ontario High School requires both of the following:

- an average of 90 per cent or better on Grade 12 Mathematics: Advanced Functions and Grade 12 Mathematics: Calculus and Vectors;
- an average of 85 per cent or better over six credits in Grade 12 courses of University or University/College type.

Admission, continuation and graduation from the undergraduate portion of the program requires a Major CGPA of 11.0 or better and Overall CGPA of 10.00 or better.

Before entry into the fourth year of this program, students must: obtain a recommendation from the School of Mathematics and Statistics to continue, apply to graduate with a B.Math. General degree, by the end of January of their third year, and submit an application for graduate studies to the School by mid-February.

### Undergraduate Portion

Students may apply for admission to either the Mathematics or the Statistics versions of the program.

### Mathematics (Combined B.Math./M.Sc.)

B.Math. (15.0 credits)

A. Credits Included in the Major CGPA (10.0 credits) | ||

1. 7.5 credits in: | 7.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2100 [1.0] | Algebra | |

MATH 2152 [0.5] | Introductory Algebra II | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

MATH 3057 [0.5] | Functions of a Complex Variable (Honours) | |

MATH 3106 [0.5] | Introduction to Group Theory (Honours) | |

MATH 3158 [0.5] | Rings and Fields (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

2. 0.5 credit from: | 0.5 | |

MATH 3002 [0.5] | Real Analysis II (Honours) | |

MATH 3003 [0.5] | Advanced Differential Calculus (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

3. 0.5 credit from 3000-level Honours Sequence or MATH or STAT at the 4000-level or higher | 0.5 | |

4. 1.5 credits at the 4000-level or higher in MATH or STAT | 1.5 | |

B. Credits Not Included in the Major CGPA (5.0 credits) | ||

5. 4.0 credits not in MATH, STAT or COMP, consisting of: | 4.0 | |

a. 1.0 credit in Natural Science Electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

6. 1.0 credit in free electives | 1.0 | |

Total Credits | 15.0 |

Students wishing to specialize in Stochastics may, with the permission of the School, replace **Credits Included in the Major CGPA** of the Mathematics version with:

1. 6.0 credits in: | 6.0 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2100 [1.0] | Algebra | |

MATH 2152 [0.5] | Introductory Algebra II | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

2. 2.0 credits in: | 2.0 | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

3. 0.5 credit from: | 0.5 | |

MATH 3002 [0.5] | Real Analysis II (Honours) | |

MATH 3003 [0.5] | Advanced Differential Calculus (Honours) | |

MATH 3057 [0.5] | Functions of a Complex Variable (Honours) | |

MATH 3008 [0.5] | Ordinary Differential Equations (Honours) | |

4. 1.5 credits at the 4000-level or higher in MATH or STAT | 1.5 | |

Total Credits | 10.0 |

### Statistics (Combined B.Math./M.Sc.)

B.Math. (15.0 credits)

A. Credits Included in the Major CGPA (10.0 credits) | ||

1. 8.5 credits in: | 8.5 | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

MATH 1152 [0.5] | Introductory Algebra I | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

MATH 2000 [1.0] | Multivariable Calculus and Fundamentals of Analysis | |

MATH 2052 [0.5] | Calculus and Introductory Analysis II | |

MATH 2100 [1.0] | Algebra | |

MATH 2152 [0.5] | Introductory Algebra II | |

MATH 2454 [0.5] | Ordinary Differential Equations (Honours) | |

MATH 3001 [0.5] | Real Analysis I (Honours) | |

STAT 2559 [0.5] | Basics of Statistical Modeling (Honours) | |

STAT 2655 [0.5] | Introduction to Probability with Applications (Honours) | |

STAT 3506 [0.5] | Stochastic Processes and Applications (Honours) | |

STAT 3553 [0.5] | Regression Modeling (Honours) | |

STAT 3558 [0.5] | Elements of Probability Theory (Honours) | |

STAT 3559 [0.5] | Mathematical Statistics (Honours) | |

2. 1.5 credits in MATH or STAT at the 4000 level or above | 1.5 | |

B. Credits Not Included in the Major CGPA (5.0 credits) | ||

3. 4.0 credits not in MATH, STAT, or COMP consisting of: | 4.0 | |

a. 1.0 credit in Natural Science Electives | ||

b. 3.0 credits from Natural Science, or Approved Arts and Social Sciences electives | ||

4. 1.0 credit in free electives | 1.0 | |

Total Credits | 15.0 |

### Graduate Portion - M.Sc.

During the graduate portion of the "fast-track" program, the student is registered as a graduate student and is covered by the regulations of the Faculty of Graduate Studies.

5. 1.5 credits at the 5000-level or higher in MATH or STAT | 1.5 | |

6. 1.0 credit at the 5000-level or higher in mathematics or statistics or from another department or school | 1.0 | |

7. Either: | 2.0 | |

MATH 4905 and 1.5 credits in MATH or STAT at the 5000-level or higher | ||

or | ||

an M.Sc. thesis in Mathematics | ||

Total Credits | 4.5 |

### Minor in Mathematics (4.0 credits)

This minor is open to students in all undergraduate programs except programs of the School of Mathematics and Statistics.

Requirements | ||

1. 1.0 credit from: | 1.0 | |

Elementary Calculus I Elementary Calculus II | ||

or | ||

Calculus for Engineering or Physics Differential Equations and Infinite Series for Engineering or Physics | ||

or | ||

Calculus and Introductory Analysis I Calculus and Introductory Analysis II | ||

2. 1.0 credit from: | 1.0 | |

MATH 1107 [0.5] | Linear Algebra I | |

or MATH 1104 [0.5] | Linear Algebra for Engineering or Science | |

MATH 2107 [0.5] | Linear Algebra II | |

or | ||

Introductory Algebra I Introductory Algebra II | ||

3. 0.5 credit from: | 0.5 | |

MATH 1800 [0.5] | Introduction to Mathematical Reasoning | |

or | ||

0.5 credit in MATH at 2000-level | ||

4. 1.0 credit in MATH at the 2000-level or higher | 1.0 | |

5. 0.5 credit in MATH at the 3000-level or higher | 0.5 | |

6. The remaining requirements of the major discipline(s) and degree must be satisfied. | ||

Total Credits | 4.0 |

Note: As a prerequisite, MATH 1800 opens more options at the 2000-level and above. It is recommended that students taking MATH 1800 do so as early as possible.

### Minor in Statistics (4.0 credits)

This minor is open to students in all undergraduate programs except programs of the School of Mathematics and Statistics.

Requirements: | ||

1. 0.5 credit from: | 0.5 | |

MATH 1004 [0.5] | Calculus for Engineering or Physics | |

MATH 1007 [0.5] | Elementary Calculus I | |

MATH 1009 [0.5] | Calculus: with Applications to Business | |

MATH 1052 [0.5] | Calculus and Introductory Analysis I | |

2. 0.5 credit from: | 0.5 | |

MATH 1104 [0.5] | Linear Algebra for Engineering or Science | |

MATH 1107 [0.5] | Linear Algebra I | |

MATH 1119 [0.5] | Linear Algebra: with Applications to Business | |

MATH 1152 [0.5] | Introductory Algebra I | |

3. 1.0 credit from: | 1.0 | |

Introduction to Statistical Modeling I Introduction to Statistical Modeling II | ||

or | ||

Probability and Statistics Introduction to Statistical Modeling II | ||

or | ||

Business Statistics I Business Statistics II | ||

or | ||

Introductory Statistics for Economics Introductory Econometrics | ||

4. 1.5 credits in: | 1.5 | |

STAT 3503 [0.5] | Regression Analysis | |

STAT 3504 [0.5] | Analysis of Variance and Experimental Design | |

STAT 3507 [0.5] | Sampling Methodology | |

5. 0.5 credit from: | 0.5 | |

BUSI 1402 [0.5] | Introduction to Business Information and Communication Technologies (Business students only) | |

COMP 1005 [0.5] | Introduction to Computer Science I | |

ECOR 1606 [0.5] | Problem Solving and Computers (Engineering students only) | |

6. The remaining requirements of the major discipline(s) and degree must be satisfied. | ||

Total Credits | 4.0 |

**Notes:**

- With approval an alternate introductory statistics course may be used to satisfy Item 3 above.

### Mathematics (MATH) Courses

**Note:**

• See also the course listings under Statistics (STAT) in this Calendar.

**Prerequisites for First-year Mathematics Courses in B.Math. Programs**

Students who do not have the required Ontario Grade 12 Mathematics courses or equivalents may take MATH 0005 Precalculus: Functions and Graphs and MATH 0006 Precalculus: Trigonometric Functions and Complex Numbers in lieu of Advanced Functions, MATH 0107 Algebra and Geometry in lieu of the algebra component of Calculus and Vectors. These 0000-level mathematics courses serve as alternate prerequisites for MATH 1052 Calculus and Introductory Analysis I and MATH 1152 Introductory Algebra I. These courses would be in addition to the minimum 15.0 credits required in General programs, or 20.0 credits required in Honours programs.

**MATH 0005 [0.5 credit]**

Precalculus: Functions and Graphs

Precalculus: Functions and Graphs

Review of algebraic manipulations. Polynomials: the remainder theorem, and the factor theorem; graphing. Real and Complex roots. Absolute values. Inequalities. Functions, including composition of functions, and Inverse functions. Logarithmic and exponential functions.

Prerequisite(s): Grade 11 Functions (University/College Preparation), or equivalent.

Lectures three hours a week, tutorial one hour a week.

**MATH 0006 [0.5 credit]**

Precalculus: Trigonometric Functions and Complex Numbers

Precalculus: Trigonometric Functions and Complex Numbers

Angles and the unit circle, radian measure. Definitions of trigonometric functions. Fundamental relations, Law of Sines and Cosines. Analytic trigonometry, graphs, inverse functions. Trigonometric identities and equations. Applications in science and engineering. Complex numbers in polar form, de Moivre's Theorem, n-th roots of complex numbers.

Lectures three hours a week, tutorial one hour a week.

**MATH 0009 [0.5 credit]**

Calculus and Vectors

Calculus and Vectors

Limits and continuity. Differentiation rules. Trigonometric, logarithmic, and exponential functions, and their derivatives. Curve sketching. Optimization problems. Introduction to vectors. Dot and cross products. Projections. Equations of lines and planes. Intersection points and distances between points, lines, and planes.

Prerequisite(s): Grade 12 Mathematics (Advanced Functions); or both MATH 0005 and MATH 0006; or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 0107 [0.5 credit]**

Algebra and Geometry

Algebra and Geometry

Vectors in the plane and in 3-space. Linear combinations and linear independence. Equations of lines and planes in space. Solution of systems of linear equations. Proofs by induction. Binomial Theorem. Logic.

Lectures three hours a week, tutorial one hour a week.

**MATH 1004 [0.5 credit]**

Calculus for Engineering or Physics

Calculus for Engineering or Physics

Limits. Differentiation of the elementary functions. Rules of differentiation. Inverse trigonometric functions. Applications of differentiation: max-min problems, curve sketching, approximations.Definite and indefinite integrals, techniques of integration. Applications to areas and volumes.

Prerequisite(s): Ontario Grade 12 Mathematics: Advanced Functions, or MATH 0005 and MATH 0006, or equivalent. Restricted to students in the Faculty of Engineering, or in certain B.Sc. and B.A.S. programs where specified.

Lectures three hours a week, tutorial one hour a week.

**MATH 1005 [0.5 credit]**

Differential Equations and Infinite Series for Engineering or Physics

Differential Equations and Infinite Series for Engineering or Physics

First-order differential equations. Second-order linear equations with constant coefficients, undetermined coefficients, variation of parameters. Sequences and series, convergence tests, estimation of sums. Power series, Taylor series, remainders. Fourier series.

Prerequisite(s): i) MATH 1004; and ii) MATH 1104 (or MATH 1107), either previously or concurrently; or equivalents; or permission of the School.Restricted to students in the Faculty of Engineering, or in certain B.Sc. programs where specified.

Lectures three hours a week, tutorial one hour a week.

**MATH 1007 [0.5 credit]**

Elementary Calculus I

Elementary Calculus I

Limits. Differentiation of the elementary functions, including trigonometric functions. Rules of differentiation. Applications of differentiation: max-min problems, curve sketching, approximations. Introduction to integration: definite and indefinite integrals, areas under curves, fundamental theorem of calculus.

Prerequisite(s): Ontario Grade 12 Mathematics: Advanced Functions; or MATH 0005 and MATH 0006; or equivalent.

Lectures three hours a week, tutorial one hour a week.

**MATH 1009 [0.5 credit]**

Calculus: with Applications to Business

Calculus: with Applications to Business

Applications of mathematics to business. Limits. Differentiation of the elementary functions. Rules of differentiation. Max-min problems, curve sketching. Functions of several variables, partial differentiation, constrained max-min. Definite and indefinite integrals.

Prerequisite(s): Ontario Grade 12 Mathematics: Advanced Functions, or MATH 0005, or equivalent.

Lectures three hours a week, tutorial one hour a week.

**MATH 1052 [0.5 credit]**

Calculus and Introductory Analysis I

Calculus and Introductory Analysis I

Properties of the real numbers. Limits. Sequences and series. Elementary functions. Continuity. Derivatives. Extreme values. Mean Value Theorem. L’Hospital’s rules. Antiderivatives. An emphasis is placed on proofs and theory.

Prerequisite(s): i) Grade 12 Mathematics: Advanced Functions, and Grade 12 Mathematics: Calculus and Vectors, with grades of at least 75% in each; or MATH 0005 and MATH 0006 with grades of at least B in each; or equivalents; and ii) MATH 1800 (may be taken concurrently); or permission of the School of Mathematics and Statistics.

Lectures three hours a week, tutorial one and one half hours a week.

**MATH 1104 [0.5 credit]**

Linear Algebra for Engineering or Science

Linear Algebra for Engineering or Science

Systems of linear equations. Matrix algebra. Determinants. Invertible matrix theorem. Cramer’s rule. Vector space R^n; subspaces, bases. Eigenvalues, diagonalization. Linear transformations, kernel, range. Complex numbers (including De Moivre’s theorem). Inner product spaces and orthogonality. Applications.

Prerequisite(s): Ontario Grade 12 Mathematics: Advanced Functions, or MATH 0005, or equivalent, or permission of the School. Restricted to students in the Faculty of Engineering, the School of Computer Science, or in certain B.Sc. and B.A.S. programs where specified.

Lectures three hours a week and tutorial one hour a week.

**MATH 1107 [0.5 credit]**

Linear Algebra I

Linear Algebra I

Systems of linear equations; vector space of n-tuples, subspaces, bases; matrix transformations, kernel, range; matrix algebra and determinants. Dot product. Complex numbers (including de Moivre's Theorem, and n-th roots). Eigenvalues, diagonalization and applications. Note: MATH 1119 is not an acceptable substitute for MATH 1107.

Prerequisite(s): Ontario Grade 12 Mathematics: Advanced Functions, or MATH 0005, or equivalent, or permission of the School.

Lectures three hours a week and tutorial one hour a week.

**MATH 1119 [0.5 credit]**

Linear Algebra: with Applications to Business

Linear Algebra: with Applications to Business

Introduction to systems of linear equations, geometric interpretation in two and three dimensions, introduction to matrices, vector addition and scalar multiplication, linear dependence, matrix operations, rank, inversion, invertible matrix theorem, determinants. Use of illustrative examples related to business.

Prerequisite(s): Ontario Grade 12 Mathematics of Data Management; or Ontario Grade 12 Mathematics: Advanced Functions, or MATH 0005, or equivalent, or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 1152 [0.5 credit]**

Introductory Algebra I

Introductory Algebra I

Properties of numbers. Modular arithmetic. Fields, including complex numbers and finite fields. Vector spaces. Matrix algebra. Solutions of linear systems. Linear dependence. Spanning sets. Bases. Subspaces. The rank-nullity theorem. Linear transformations. An emphasis is placed on proofs and theory.

Prerequisite(s): i) Grade 12 Mathematics: Advanced Functions, and Grade 12 Mathematics: Calculus and Vectors, with grades of at least 75% in each; or MATH 0005, MATH 0006, and MATH 0107 with grades of at least B in each; or equivalents; and ii) MATH 1800 (may be taken concurrently); or permission of the School of Mathematics and Statistics.

Lectures three hours a week, tutorial one and a half hours a week.

**MATH 1401 [0.5 credit]**

Elementary Mathematics for Economics I

Elementary Mathematics for Economics I

Functional relations: functional forms and error terms. Graphing economic magnitudes: scatter diagrams, time-series graphs, functional relationships. Applied calculus: mechanics of differentiation and integration, elasticity, consumer/producer surplus. Applied algebra: solving systems of linear equations and Keynesian national-income analysis. Problem solving approaches.

Precludes additional credit for BIT 1000, BIT 1001, BIT 1100, BIT 1101, BIT 1200, BIT 1201; MATH 1007, MATH 1009, MATH 1052, MATH 1104, MATH 1107, MATH 1119, MATH 1152.

Prerequisite(s): Ontario Grade 12 U Advanced Functions, or MATH 0005, or equivalent; and ECON 1000 or FYSM 1003, which may be taken concurrently with MATH 1401/ECON 1401.

Lectures three hours a week, tutorial one hour a week.

**MATH 1402 [0.5 credit]**

Elementary Mathematics for Economics II

Elementary Mathematics for Economics II

Calculus: including partial differentiation, definite and indefinite integrals, techniques of integration, and unconstrained optimization. Vectors and matrices: scalar multiplication, inner product, linear dependence, matrix operations, rank, invertible matrix theorem, and determinants. Economic applications such as profit maximization, comparative statics, and the Leontief input-output model.

Precludes additional credit for BIT 1000, BIT 1001, BIT 1100, BIT 1101, BIT 1200, BIT 1201; MATH 1007, MATH 1009, MATH 1052, MATH 1104, MATH 1107, MATH 1119, MATH 1152.

Prerequisite(s): ECON 1000 or FYSM 1003 with a grade of C- or higher, and ECON 1401/MATH 1401 with a grade of C- or higher.

Lectures three hours a week, tutorial one hour a week.

**MATH 1800 [0.5 credit]**

Introduction to Mathematical Reasoning

Introduction to Mathematical Reasoning

Elementary logic, propositional and predicate calculus, quantifiers, sets and functions, bijections and elementary counting, the concept of infinity, relations, well ordering and induction. The practice of mathematical proof in elementary number theory and combinatorics.

Prerequisite(s): Ontario Grade 12 Mathematics: Advanced Functions, or MATH 0005, or equivalent.

Lectures three hours a week, tutorial one hour a week.

**MATH 1805 [0.5 credit]**

Discrete Structures I

Discrete Structures I

Introduction to discrete mathematics and discrete structures. Topics include: propositional logic, predicate calculus, set theory, complexity of algorithms, mathematical reasoning and proof techniques, recurrences, induction, finite automata and graph theory. Material is illustrated through examples from computing.

Also listed as COMP 1805.

Precludes additional credit for MATH 1800.

Prerequisite(s): one Grade 12 university preparation Mathematics course; and one of: COMP 1005 or or COMP 1405 or SYSC 1100 (which may be taken concurrently).

Lectures three hours a week, tutorial one hour a week.

**MATH 2000 [1.0 credit]**

Multivariable Calculus and Fundamentals of Analysis

Multivariable Calculus and Fundamentals of Analysis

Higher dimensional calculus, chain rule, gradient, line and multiple integrals with applications. Use of implicit and inverse function theorems. Real number axioms, limits, continuous functions, differentiability, infinite series, uniform convergence, the Riemann integral.

Prerequisite(s): i) MATH 1002 with a grade of C+ or higher, or (MATH 2007 or MATH 1005 with a grade of B+ or higher and permission of the School); and ii) MATH 1102 with a grade of C+ or higher, or MATH 1107 or MATH 1104 with a grade of B+ or higher; and iii) MATH 1800 with a grade of C+ or higher; or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 2004 [0.5 credit]**

Multivariable Calculus for Engineering or Physics

Multivariable Calculus for Engineering or Physics

Curves and surfaces. Polar, cylindrical and spherical coordinates. Partial derivatives, gradients, extrema and Lagrange multipliers. Exact differentials. Multiple integrals over rectangular and general regions. Integrals over surfaces. Line integrals. Vector differential operators. Green’s Theorem, Stokes’ theorem, Divergence Theorem. Applications.

Prerequisite(s): i) MATH 1005 or MATH 2007; and ii) MATH 1104 or MATH 1107; or permission of the School. Restricted to students in the Faculty of Engineering, or in certain B.Sc. programs where specified.

Lectures three hours a week, tutorial one hour a week.

**MATH 2007 [0.5 credit]**

Elementary Calculus II

Elementary Calculus II

Techniques of integration, improper integrals. Polar coordinates, parametric equations. Indeterminate forms, sequences and series, Taylor's formula and series.

Prerequisite(s): i) MATH 1004, or a grade of C- or higher in MATH 1007; or MATH 1052 and permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 2008 [0.5 credit]**

Intermediate Calculus

Intermediate Calculus

Partial differentiation, chain rule, gradient, line and multiple integrals with applications, transformations of multiple integrals.

Prerequisite(s): one of MATH 1002, MATH 1005 or MATH 2007, and one of MATH 1102, MATH 1104 or MATH 1107.

Lectures three hours a week and one hour tutorial.

**MATH 2052 [0.5 credit]**

Calculus and Introductory Analysis II

Calculus and Introductory Analysis II

Definite, indefinite integrals. Improper integrals. The fundamental theorem of calculus. An introduction to differential equations. Sequences and series of functions. Power series. Taylor’s formulae. Uniform convergence. An emphasis is placed on proofs and theory.

Prerequisite(s): (i) MATH1052 with a grade of C- or higher or (MATH1007 or MATH1004 with a grade of B+ or higher and permission of the School), and (ii) MATH1800 with a grade of C+ or higher; or permission of the School.

Lectures three hours a week, tutorial one and one half hours a week.

**MATH 2100 [1.0 credit]**

Algebra

Algebra

Introduction to group theory: permutation groups, Lagrange's theorem, normal subgroups, homomorphism theorems. Introduction to ring theory: ring of polynomials, integral domains, ideals, homomorphism theorems. Hermitian forms, spectral theorem for normal operators, bilinear and quadratic forms, classical groups.

Prerequisite(s): i) MATH 1102 with a grade of C+ or higher, or (MATH 2107 with a grade of B+ or higher and permission of the School); and ii) MATH 1800 with a grade of C+ or higher; or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 2107 [0.5 credit]**

Linear Algebra II

Linear Algebra II

Finite-dimensional vector spaces (over R and C), subspaces, linear independence and bases. Linear transformations and matrices. Inner product spaces (over R and C); Orthonormal bases. Eigenvalues and diagonalization. Bilinear and quadratic forms; principal axis theorem.

Prerequisite(s): i) MATH 1104, or a grade of C- or higher in MATH 1107 or MATH 1109; and ii) a grade of C- or higher in MATH 1007 or equivalent; or MATH 1152 and permission of the School. Note: in item i), MATH 1119 is NOT acceptable as a substitute for MATH 1109.

Lectures three hours a week and one hour tutorial.

**MATH 2108 [0.5 credit]**

Abstract Algebra I

Abstract Algebra I

Sets and relations, number theory, group theory, ring theory, cardinal numbers.

Prerequisite(s): i) MATH 1102 or MATH 2107; and ii) MATH 1800 (MATH 1800 may be taken concurrently, with permission of the School); or COMP 1805 or MATH 1805; or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 2152 [0.5 credit]**

Introductory Algebra II

Introductory Algebra II

Linear transformations. Determinants. Eigenvalues and eigenspaces. Diagonalization and other canonical forms. Inner products. An emphasis is placed on proofs and theory.

Prerequisite(s): (i) MATH1152 with a grade of C- or higher or (MATH1107 or MATH1104 with a grade of B+ or higher and permission of the School), and (ii) MATH1800 with a grade of C+ or higher; or permission of the School.

Lectures three hours a week, tutorial one and a half hours a week.

**MATH 2210 [0.5 credit]**

Introduction to Geometry

Introduction to Geometry

An introduction to classical geometry; Euclidean plane geometry; plane tiling; polytopes in three and four dimensions; curved surfaces; Euler characteristic. This course is intended for a general audience, and is available to B.Math. students for credit only as a free elective.

Lectures three hours a week, tutorial one hour a week.

**MATH 2404 [0.5 credit]**

Ordinary Differential Equations I

Ordinary Differential Equations I

First-order equations, linear second- and higher-order equations, linear systems, stability of second-order systems.

Prerequisite(s): MATH 1002 and MATH 1102 (or MATH 1107 and MATH 2007).

Lectures three hours a week and one hour tutorial.

**MATH 2454 [0.5 credit]**

Ordinary Differential Equations (Honours)

Ordinary Differential Equations (Honours)

Existence and uniqueness theorems. First-order equations, linear second- and higher-order equations, linear systems, stability of second-order systems.

Prerequisite(s): MATH 1002 or MATH 2007 or MATH 1005 with a grade of C+ or higher, and MATH 1102 or MATH 2107 with a grade of C+ or higher.

Lectures three hours a week, tutorial one hour a week.

**MATH 2800 [0.5 credit]**

Discrete Mathematics and Algorithms

Discrete Mathematics and Algorithms

An introduction to discrete mathematics and algorithms in the context of the computational sciences. Basic number theory and counting methods, algorithms for strings, trees and sequences. Applications to DNA and protein sequencing problems. Analysis and complexity of algorithms.

Precludes additional credit for Only one of MATH 1805/COMP 1805 or MATH 2800/CMPS 2800 may count for credit in a B.Math. program.

Prerequisite(s): COMP 1006 and at least one of MATH 1007, MATH 1107, or STAT 2507.

Lectures three hours a week.

**MATH 2907 [0.5 credit]**

Directed Studies (Honours)

Directed Studies (Honours)

Available only to Honours students whose program requires a 0.5 credit not offered by the School of Mathematics and Statistics.

**MATH 3001 [0.5 credit]**

Real Analysis I (Honours)

Real Analysis I (Honours)

Metric spaces and their topologies, continuous maps, completeness, compactness, connectedness, introduction to Banach spaces.

Lectures three hours a week and one hour tutorial.

**MATH 3002 [0.5 credit]**

Real Analysis II (Honours)

Real Analysis II (Honours)

Function spaces, pointwise and uniform convergence, Weierstrass approximation theorem, Lebesgue measure and Lebesgue integral on the real line, Hilbert space, Fourier series.

Lectures three hours a week, tutorial one hour a week.

**MATH 3003 [0.5 credit]**

Advanced Differential Calculus (Honours)

Advanced Differential Calculus (Honours)

Review of multivariable differentiation and integration. Vector fields, differential forms and exterior algebra. Introduction to manifolds and tangent bundles. Stokes’ Theorem. Applications such as differential equations and the calculus of variations.

Lectures three hours a week, tutorial one hour a week.

**MATH 3007 [0.5 credit]**

Functions of a Complex Variable

Functions of a Complex Variable

Analytic functions, contour integration, residue calculus, conformal mapping. Intended for non-engineering students.

Prerequisite(s): one of MATH 2004, MATH 2008 or MATH 2009, or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 3008 [0.5 credit]**

Ordinary Differential Equations (Honours)

Ordinary Differential Equations (Honours)

Analytic ordinary differential equations: series solutions of ordinary differential equations about ordinary and regular singular points. Asymptotic solutions. Sturm-Liouville theory. Bessel and Legendre functions. Fourier series.

Prerequisite(s): i) MATH 2000 with a grade of C- or higher, or (MATH 3009 with a grade of B or higher, and permission of the instructor); and ii) MATH 2454 with a grade of C- or higher, or (MATH 2404 with a grade of B or higher, and permission of the instructor).

Lectures three hours a week and one hour tutorial.

**MATH 3009 [0.5 credit]**

Introductory Analysis

Introductory Analysis

The real number system, sequences and series, functions of a single real variable, derivatives, the definite integral, uniform convergence.

Prerequisite(s): one of MATH 2004, MATH 2008, MATH 2009, or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 3057 [0.5 credit]**

Functions of a Complex Variable (Honours)

Functions of a Complex Variable (Honours)

Analytic functions, contour integration, residue calculus, conformal mappings.

Prerequisite(s): MATH 2000 with a grade of C- or higher; or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 3101 [0.5 credit]**

Algebraic Structures with Computer Applications

Algebraic Structures with Computer Applications

Introduction to algebraic structures: groups, rings, fields, lattices, and Boolean algebras; with applications of interest to students in Computer Science. This course may not be used to meet the 3000-level course requirements in any General or Honours program in Mathematics and Statistics.

Prerequisite(s): i) MATH 2107 or MATH 1102; and ii) either COMP 1805/MATH 1805 or MATH 1800 (MATH 1800 may be taken concurrently, with permission of the School); or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 3106 [0.5 credit]**

Introduction to Group Theory (Honours)

Introduction to Group Theory (Honours)

Homomorphism theorems; groups acting on sets; permutation groups and groups of matrices; Sylow theory for finite groups; finitely generated abelian groups; generators and relations; applications.

Prerequisite(s): MATH 2100 with a grade of C- or higher; or (MATH 2108 or MATH 3101 with a grade of B or higher; and MATH 1800 with a grade of B or higher; and permission of the instructor); or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 3107 [0.5 credit]**

Linear Algebra III

Linear Algebra III

Similarity and unitary triangularization of matrices. Direct methods of solving a system of linear equations. Iterative techniques. Bounds for eigenvalues. Power method and deflation techniques of approximation. Emphasis is primarily on computational aspects.

Lectures three hours a week and one hour tutorial.

**MATH 3108 [0.5 credit]**

Abstract Algebra II

Abstract Algebra II

Groups and rings. Permutations. Finite symmetry groups. Polynomials, unique factorization domains. Quotient rings, ideals. Field extensions, finite fields. Polynomial equations. Geometric constructions - three famous problems: duplication of the cube, trisection of an arbitrary angle, quadrature of the circle.

Prerequisite(s): MATH 2108, or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 3158 [0.5 credit]**

Rings and Fields (Honours)

Rings and Fields (Honours)

Rings, integral domains, Euclidean and principal ideal domains, fields, polynomial rings over a field, algebraic extensions of fields, the fundamental theorem of Galois theory, finite fields, applications.

Prerequisite(s): MATH 2100 with a grade of C- or higher, or (MATH 2108 or MATH 3101 with a grade of B or higher and MATH 1800 with a grade of B or higher and permission of the instructor), or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 3206 [0.5 credit]**

Plane Projective Geometry

Plane Projective Geometry

Axioms of Desarguesian geometry, principle of duality; projectivities, perspectivities, and the fundamental theorem; collineations (homologies and elations); correlations (polarities and conics); algebraic model; projective curves; introduction to finite projective planes.

Prerequisite(s): MATH 2100 or MATH 2108 or MATH 3101.

Lectures three hours a week and one hour tutorial.

**MATH 3210 [0.5 credit]**

Euclidean and Non-Euclidean Geometry

Euclidean and Non-Euclidean Geometry

Euclidean isometry and similarity groups; geometry of circles; inversion; hyperbolic geometry: Poincare disk model of the hyperbolic plane.

Prerequisite(s): MATH 2100 or MATH 2108 or MATH 3101.

Lectures three hours a week, tutorial one hour a week.

**MATH 3306 [0.5 credit]**

Elements of Set Theory (Honours)

Elements of Set Theory (Honours)

Axioms of set theory. Development of the systems of natural numbers and the real numbers. Axiom of choice, Zorn's lemma, well-ordering. The Schröder-Bernstein theorem, cardinal numbers, ordinal numbers, transfinite induction, cardinal and ordinal arithmetics.

Lectures three hours a week and one hour tutorial.

**MATH 3355 [0.5 credit]**

Number Theory and Applications (Honours)

Number Theory and Applications (Honours)

Congruences, distribution of primes, arithmetic functions, primitive roots, quadratic residues, quadratic reciprocity law, continued fractions, Diophantine equations, and applications: public key cryptography, primality testing and factoring in relation to cryptography.

Prerequisite(s): MATH 2100 with a grade of C- or higher; or (MATH 2108 or MATH 3101 with a grade of B- or higher; and permission of the instructor); or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**MATH 3404 [0.5 credit]**

Ordinary Differential Equations II

Ordinary Differential Equations II

Series solutions of ordinary differential equations of second order about regular singular points; asymptotic solutions. Systems of ordinary differential equations of first order; matrix methods. Existence and uniqueness theorems. Nonlinear autonomous systems of order 2; qualitative theory. Numerical solutions of ordinary differential equations.

Prerequisite(s): MATH 2404, MATH 2008; and MATH 1102 or MATH 2107.

Lectures three hours a week and one hour tutorial.

**MATH 3705 [0.5 credit]**

Mathematical Methods I

Mathematical Methods I

Laplace transforms, series solutions of ordinary differential equations, the Frobenius method. Fourier series and Fourier transforms, solutions of partial differential equations of mathematical physics, boundary value problems, applications.

Prerequisite(s): i) MATH 1005 or MATH 2404, and ii) MATH 2004 or MATH 2008 or MATH 2009; or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 3800 [0.5 credit]**

Mathematical Modeling and Computational Methods

Mathematical Modeling and Computational Methods

Design and analysis of mathematical models for problems in science. Computational methods, including function evaluation, interpolation, solution of linear equations, root finding, integration, solution of differential equations, Fourier series and Monte Carlo methods.

Also listed as CMPS 3800.

Precludes additional credit for MATH 3806/COMP 3806.

Prerequisite(s): i) MATH 1107 or MATH 1104; ii) MATH 1005 or MATH 2007; and iii) knowledge of a computer language.

Lectures three hours a week, laboratory one hour a week.

**MATH 3801 [0.5 credit]**

Linear Programming

Linear Programming

Systems of linear inequalities, formulation of linear programming problems, geometric method, the simplex method, duality theory, complementary slackness, sensitivity analysis, branch-and-bound method and cutting plane method for integer linear programming, applications and extensions.

Prerequisite(s): MATH 1102 or MATH 2107, or permission of the School.

Lectures three hours a week and one hour tutorial.

**MATH 3802 [0.5 credit]**

Combinatorial Optimization

Combinatorial Optimization

Network flow problems, network simplex method, max-flow min-cut problem, integral polyhedra, minimum-weight spanning tree problem, maximum matching problem, maximum stable set problem, introduction to approximation algorithms.

Lectures three hours a week, tutorial one hour a week.

**MATH 3804 [0.5 credit]**

Design and Analysis of Algorithms I

Design and Analysis of Algorithms I

An introduction to the design and analysis of algorithms. Topics include: recurrence relations, sorting and searching, divide-and-conquer, dynamic programming, greedy algorithms, NP-completeness.

Prerequisite(s): i) one of COMP 2402 or SYSC 2100; and ii) one of COMP 2804 or MATH 3855 or MATH 3825 or COMP 3805.

Lectures three hours a week.

**MATH 3806 [0.5 credit]**

Numerical Analysis (Honours)

Numerical Analysis (Honours)

Elementary discussion of error, polynomial interpolation, quadrature, linear systems of equations and matrix inversion, non-linear equations, difference equations and ordinary differential equations. Implementation of numerical methods using a computer language.

Precludes additional credit for MATH 3800.

Prerequisite(s): i) MATH 2000 with a grade of C- or higher; and ii) MATH 1102 with a grade of C- or higher, or (MATH 1107 or MATH 1104 with a grade of B or higher and permission of the instructor).

Lectures three hours a week, laboratory one hour a week.

**MATH 3807 [0.5 credit]**

Mathematical Software (Honours)

Mathematical Software (Honours)

Implementation of numerical methods using numerical software packages. Development of scientific and/or operations research applications using application programming interfaces of numerical or optimization libraries. Functional programming for data analysis and machine learning. Experience working with Python, C++, or Java is essential.

Also listed as COMP 3807.

Prerequisite(s): A grade of C- or higher in MATH 3806 or COMP 3806.

Lectures three hours a week, laboratory one hour a week.

**MATH 3808 [0.5 credit]**

Mathematical Analyses of Games of Chance

Mathematical Analyses of Games of Chance

This course covers mathematics used in the modern casino gaming industry. The topics include probabilities, odds, house advantages, variance and risks, optimal strategies, random walks and gambler's ruin, and gaming revenue estimation. Examples are taken from various games such as Roulette, Blackjack, and Poker.

Lectures three hours a week, tutorial one hour a week.

**MATH 3809 [0.5 credit]**

Introduction to Number Theory and Cryptography

Introduction to Number Theory and Cryptography

Congruences, distribution of primes, general cryptographic systems, public key cryptographic systems and authentification using number theory, primality testing and factoring in relation to cryptography, continued fractions and Diophantine equations.

Lectures three hours a week and one hour tutorial.

**MATH 3819 [0.5 credit]**

Modern Computer Algebra

Modern Computer Algebra

Algorithms for multiplication, division, greatest common divisors and factorization over the integers, finite fields and polynomial rings. Basic tools include modular arithmetic, discrete Fourier transform, Chinese remainder theorem, Newton iteration, and Hensel techniques. Some properties of finite fields and applications to cryptography.

Prerequisite(s): MATH 2108 or MATH 3101 or MATH 2100, or permission of the School.

Lectures three hours a week, tutorial/laboratory one hour a week.

**MATH 3825 [0.5 credit]**

Discrete Structures and Applications

Discrete Structures and Applications

Enumeration: elementary methods, inclusion and exclusion, recurrence relations, generating functions and applications. Graph theory and algorithms: connectivity, planarity, Hamilton paths and Euler trails. Error-correcting codes.

Prerequisite(s): MATH 2108 or MATH 3101.

Lectures three hours a week, tutorial one hour a week.

**MATH 3855 [0.5 credit]**

Discrete Structures and Applications (Honours)

Discrete Structures and Applications (Honours)

Enumeration: inclusion and exclusion, recurrence relations, generating functions and applications. Graph theory: connectivity, planarity, Hamilton paths and Euler trails. Error-correcting codes. Designs and finite geometries. Symmetry and counting.

Precludes additional credit for MATH 3805 (no longer offered) and MATH 3825.

Prerequisite(s): MATH 2100 with a grade of C- or higher; or (MATH 2108 or MATH 3101) with a grade of B or higher.

Lectures three hours a week, tutorial one hour a week.

**MATH 3907 [0.5 credit]**

Directed Studies

Directed Studies

Available only to students whose program requires a 0.5 credit not offered by the School of Mathematics and Statistics.

**MATH 3999 [0.0 credit]**

Co-operative Work Term Report (Honours)

Co-operative Work Term Report (Honours)

On completion of each work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.

Prerequisite(s): registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.

**MATH 4002 [0.5 credit]**

Fourier Analysis (Honours)

Fourier Analysis (Honours)

Fourier series, Fourier integrals; introduction to harmonic analysis on locally compact abelian groups, Plancherel Theorem, Pontryagin duality; selected applications.

**MATH 4003 [0.5 credit]**

Functional Analysis (Honours)

Functional Analysis (Honours)

Banach spaces and bounded linear operators, Hahn-Banach extension and separation, dual spaces, bounded inverse theorems, uniform boundedness principle, applications. Compact operators.

Also offered at the graduate level, with different requirements, as MATH 5008, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4007 [0.5 credit]**

Measure and Integration Theory (Honours)

Measure and Integration Theory (Honours)

Lebesgue measure and integration on the real line; sigma algebras and measures; integration theory; Lp spaces; Fubini's theorem; decomposition theorems and Radon-Nikodym derivatives.

Also offered at the graduate level, with different requirements, as MATH 5007, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4102 [0.5 credit]**

Group Representations and Applications (Honours)

Group Representations and Applications (Honours)

An introduction to the group representations and character theory, with selected applications.

Also offered at the graduate level, with different requirements, as MATH 5102, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4105 [0.5 credit]**

Rings and Modules (Honours)

Rings and Modules (Honours)

Fundamental concepts in rings and modules, structure theorems, applications.

**MATH 4106 [0.5 credit]**

Group Theory (Honours)

Group Theory (Honours)

Fundamental principles as applied to abelian, nilpotent, solvable, free and finite groups; representations.

Also offered at the graduate level, with different requirements, as MATH 5106, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4107 [0.5 credit]**

Commutative Algebra (Honours)

Commutative Algebra (Honours)

Fields, including algebraic and transcendental extensions, Galois theory, valuation theory; Noetherian commutative rings, including Noether decomposition theorem and localization.

**MATH 4108 [0.5 credit]**

Homological Algebra and Category Theory (Honours)

Homological Algebra and Category Theory (Honours)

Axioms of set theory; categories, functors, natural transformations; free, projective, injective and flat modules; tensor products and homology functors, derived functors; dimension theory.

Also offered at the graduate level, with different requirements, as MATH 5108, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4109 [0.5 credit]**

Fields and Coding Theory (Honours)

Fields and Coding Theory (Honours)

Introduction to field theory, emphasizing the structure of finite fields, primitive elements and irreducible polynomials. The influence of computational problems will be considered. Theory and applications of error-correcting codes: algebraic codes, convolution codes, decoding algorithms, and analysis of code performance.

Lectures three hours a week.

**MATH 4205 [0.5 credit]**

Introduction to General Topology (Honours)

Introduction to General Topology (Honours)

Topological spaces, maps, subspaces, product and identification topologies, separation axioms, compactness, connectedness.

Also offered at the graduate level, with different requirements, as MATH 5205, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4206 [0.5 credit]**

Introduction to Algebraic Topology (Honours)

Introduction to Algebraic Topology (Honours)

An introduction to homotopy theory. Topics include the fundamental group, covering spaces and the classification of two-dimensional manifolds.

Also offered at the graduate level, with different requirements, as MATH 5206, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4207 [0.5 credit]**

Foundations of Geometry (Honours)

Foundations of Geometry (Honours)

A study of at least one modern axiom system of Euclidean and non-Euclidean geometry, embedding of hyperbolic and Euclidean geometries in the projective plane, groups of motions, models of non-Euclidean geometry.

Lectures three hours a week.

**MATH 4208 [0.5 credit]**

Introduction to Differentiable Manifolds (Honours)

Introduction to Differentiable Manifolds (Honours)

Introduction to differentiable manifolds; Riemannian manifolds; vector fields and parallel transport; geodesics; differential forms on a manifold; covariant derivative; Betti numbers.

**MATH 4305 [0.5 credit]**

Analytic Number Theory (Honours)

Analytic Number Theory (Honours)

Dirichlet series, characters, Zeta-functions, prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, binary quadratic forms.

Also offered at the graduate level, with different requirements, as MATH 5305, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4306 [0.5 credit]**

Algebraic Number Theory (Honours)

Algebraic Number Theory (Honours)

Algebraic number fields, bases, algebraic integers, integral bases, arithmetic in algebraic number fields, ideal theory, class number.

Also offered at the graduate level, with different requirements, as MATH 5306, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4600 [0.5 credit]**

Case Studies in Operations Research (Honours)

Case Studies in Operations Research (Honours)

Applications of the principles of Operations Research to practical problems in business, management, and science. Students present at least one case and analyze cases in the published literature. Cases may also be presented by visiting practitioners.

Precludes additional credit for Students in Honours Mathematics/Statistics programs may only take course as a free option.

Prerequisite(s): STAT 2509 (or STAT 2559) and MATH 3801; or permission of the School.

Seminars three hours a week.

**MATH 4700 [0.5 credit]**

Partial Differential Equations (Honours)

Partial Differential Equations (Honours)

First-order partial differential equations. Classification of second-order linear partial differential equations; the diffusion equation, wave equation and Laplace's equation; separation of variables; Fourier and Laplace transform methods for the solution of initial/boundary value problems; Green's functions.

Lectures three hours a week.

**MATH 4701 [0.5 credit]**

Topics in Differential Equations (Honours)

Topics in Differential Equations (Honours)

Topics in the theory and application of differential equations; for example, hyperbolic systems, fluid dynamics, nonlinear wave equations, optimal mass transport, control theory, calculus of variations.

Also offered at the graduate level, with different requirements, as MATH 5407, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4703 [0.5 credit]**

Dynamical Systems (Honours)

Dynamical Systems (Honours)

Basic concepts of dynamical systems. Vector formulation for systems. Theory of autonomous systems in one, two and higher dimensions. Limit sets, stability. Phase plane, qualitative interpretation, limit cycles and attractors. Parametric dependence, bifurcations and chaos. Applications.

**MATH 4708 [0.5 credit]**

Asymptotic Methods of Applied Mathematics (Honours)

Asymptotic Methods of Applied Mathematics (Honours)

Asymptotic series: properties, matching, application to differential equations. Asymptotic expansion of integrals: elementary methods, methods of Laplace, stationary phase and steepest descent, Watson’s lemma, Riemann-Lebesgue lemma. Perturbation methods: regular and singular perturbation for differential equations, multiple scale analysis, boundary layer theory, WKB theory.

Also offered at the graduate level, with different requirements, as MATH 5408, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4801 [0.5 credit]**

Topics in Combinatorics (Honours)

Topics in Combinatorics (Honours)

An in-depth study of one or more topics from: generating functions, Polya's theory of counting, block designs, coding theory, partially ordered sets and Ramsey theory.

**MATH 4802 [0.5 credit]**

Introduction to Mathematical Logic (Honours)

Introduction to Mathematical Logic (Honours)

Symbolic logic, propositional and predicate calculi, set theory and model theory, completeness.

**MATH 4803 [0.5 credit]**

Computable Functions (Honours)

Computable Functions (Honours)

Recursive functions and computability, algorithms, Church's thesis, Turing machines, computational logic, NP-completeness.

Prerequisite(s): MATH 2100 or MATH 3855 or permission of the School.

Lectures three hours a week.

**MATH 4805 [0.5 credit]**

Theory of Automata (Honours)

Theory of Automata (Honours)

Finite automata and regular expressions, properties of regular sets, context-free grammars, pushdown automata, deterministic context-free languages. Turing machines, the Chomsky hierarchy. Undecidability, intractable problems.

Prerequisite(s): MATH 3106 or MATH 3158 or MATH 3855 or permission of the School.

Also offered at the graduate level, with different requirements, as MATH 5605, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4806 [0.5 credit]**

Numerical Linear Algebra (Honours)

Numerical Linear Algebra (Honours)

Matrix computations, conditioning/stability, direct methods for linear systems, classical iterative methods: Jacobi, Gauss-Seidel; modern iterative methods, Arnoldi decomposition, GMRES and other Krylov subspace-based methods for sparse and structured matrices; numerical solution of eigenvalue problems, implementation using suitable programming language, application to differential equations/optimization problems.

Prerequisite(s): MATH 1102 or MATH 2107; MATH 2000 and MATH 3806; or permission of the School.

Lectures three hours a week.

**MATH 4807 [0.5 credit]**

Game Theory (Honours)

Game Theory (Honours)

One-player games, two-player zero-sum games, multi-player games, games in normal form, games in extensive form, utility theory, Nash equilibrium and Nash arbitration scheme, games in characteristic function form, cooperative solutions, dominations, stable sets, core, Shapley value, applications of game theory.

Also offered at the graduate level, with different requirements, as MATH 5607, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4808 [0.5 credit]**

Graph Theory and Algorithms (Honours)

Graph Theory and Algorithms (Honours)

Paths, circuits, Eulerian and Hamiltonian graphs, connectivity, colouring problems, matching, Ramsey theory, network flows.

Lectures three hours a week.

**MATH 4809 [0.5 credit]**

Mathematical Cryptography (Honours)

Mathematical Cryptography (Honours)

Topics covered include: a general survey of public key cryptography; classical applications of finite fields and number theory; relevant background in geometry and algebraic curves; computational issues concerning elliptic curves; elliptic curve cryptosystems; security issues.

**MATH 4811 [0.5 credit]**

Combinatorial Design Theory (Honours)

Combinatorial Design Theory (Honours)

Existence and construction of combinatorial designs: finite geometries, pairwise balanced designs, balanced incomplete block designs, Steiner triple systems, symmetric designs, PBD closure, latin squares, transversal designs, and applications to information theory.

**MATH 4816 [0.5 credit]**

Numerical Analysis for Differential Equations (Honours)

Numerical Analysis for Differential Equations (Honours)

Floating point arithmetic; numerical solution of ODEs; finite difference methods for PDEs; stability, accuracy and convergence: von Neumann analysis, CFL condition, Lax Theorem. Finite element methods: boundary value problems and elliptic PDEs. Spectral and pseudo-spectral methods.

Also offered at the graduate level, with different requirements, as MATH 5806, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4821 [0.5 credit]**

Quantum Computing (Honours)

Quantum Computing (Honours)

Space of quantum bits; entanglement. Observables in quantum mechanics. Density matrix and Schmidt decomposition. Quantum cryptography. Classical and quantum logic gates. Quantum Fourier transform. Shor's quantum algorithm for factorization of integers.

Also offered at the graduate level, with different requirements, as MATH 5821, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4822 [0.5 credit]**

Wavelets and Digital Signal Processing (Honours)

Wavelets and Digital Signal Processing (Honours)

Lossless compression methods. Discrete Fourier transform and Fourier-based compression methods. JPEG and MPEG. Wavelet analysis. Digital filters and discrete wavelet transform. Daubechies wavelets. Wavelet compression.

Also offered at the graduate level, with different requirements, as MATH 5822, for which additional credit is precluded.

Lectures three hours a week.

**MATH 4905 [0.5 credit]**

Honours Project (Honours)

Honours Project (Honours)

Consists of a written report on some approved topic or topics in the field of mathematics, together with a short lecture on the report.

Prerequisite(s): B.Math.(Honours) students only.

**MATH 4906 [0.5 credit]**

Directed Studies (Honours)

Directed Studies (Honours)

**MATH 4907 [0.5 credit]**

Directed Studies (Honours)

Directed Studies (Honours)

### Statistics (STAT) Courses

**STAT 2507 [0.5 credit]**

Introduction to Statistical Modeling I

Introduction to Statistical Modeling I

A data-driven introduction to statistics. Basic descriptive statistics, introduction to probability theory, random variables, discrete and continuous distributions, contingency tables, sampling distributions, distribution of sample mean, Central Limit Theorem, interval estimation and hypothesis testing. A statistical software package will be used.

Precludes additional credit for BIT 2000, BIT 2100 (no longer offered), BIT 2300 (no longer offered), ECON 2201 (no longer offered), ECON 2210, ENST 2006, GEOG 2006, STAT 2606, and STAT 3502. May not be counted for credit in any program if taken after successful completion of STAT 2559.

Prerequisite(s): an Ontario Grade 12 university-preparation Mathematics or equivalent, or permission of the School of Mathematics and Statistics.

Lectures three hours a week, laboratory one hour a week.

**STAT 2509 [0.5 credit]**

Introduction to Statistical Modeling II

Introduction to Statistical Modeling II

A data-driven approach to statistical modeling. Basics of experimental design, analysis of variance, simple linear regression and correlation, nonparametric procedures. A statistical software package will be used.

Precludes additional credit for STAT 2607, ECON 2202, ECON 2220.

Prerequisite(s): STAT 2507 or STAT 2606 or STAT 3502; or permission of the School.

Lectures three hours a week, laboratory one hour a week.

**STAT 2559 [0.5 credit]**

Basics of Statistical Modeling (Honours)

Basics of Statistical Modeling (Honours)

Estimation and hypothesis testing for one and two samples, analysis of categorical data, basics of experimental design, analysis of variance, simple linear regression and correlation. Nonparametric procedures. A statistical software package will be used.

Prerequisite(s): STAT 2655 or permission of the School.

Lectures three hours a week, tutorial/laboratory one hour a week.

**STAT 2605 [0.5 credit]**

Probability Models

Probability Models

Basic probability; discrete random variables with focus on binomial and Poisson random variables; continuous random variables, transformation theorem, simulating continuous random variables; exponential random variable, normal random variable, sums of random variables, central limit theorem. Elements of Markov chains, and introduction to Poisson processes.

Prerequisite(s): MATH 1007 or MATH 1004 or MATH 1002, and MATH 1104 or MATH 1107 (or MATH 1102). Restricted to students in Bachelor of Computer Science, Bachelor of Mathematics in Computer Mathematics, and Bachelor of Engineering in Communications Engineering.

Lectures three hours a week, tutorial one hour a week.

**STAT 2606 [0.5 credit]**

Business Statistics I

Business Statistics I

Introduction to statistical computing; probability concepts; descriptive statistics; estimation and testing of hypotheses. Emphasis on the development of an ability to interpret results of statistical analyses with applications from business. Restricted to students in the School of Business.

Precludes additional credit for BIT 2000, BIT 2100 (no longer offered), BIT 2300 (no longer offered), ECON 2201 (no longer offered), ECON 2210, ENST 2006, GEOG 2006, STAT 2507, and STAT 3502.

Prerequisite(s): An Ontario Grade 12 university-preparation Mathematics or equivalent, or permission the School of Mathematics and Statistics.

Lectures three hours a week and laboratory one hour a week.

**STAT 2607 [0.5 credit]**

Business Statistics II

Business Statistics II

Topics include: experimental design, multiple regression and correlation analysis, covariance analysis, and introductory time series. Use of computer packages. Restricted to students in the School of Business.

Precludes additional credit for STAT 2509, ECON 2202, ECON 2220.

Prerequisite(s): STAT 2606.

Lectures three hours a week and one hour laboratory.

**STAT 2655 [0.5 credit]**

Introduction to Probability with Applications (Honours)

Introduction to Probability with Applications (Honours)

Probability axioms, basic combinatorial analysis, conditional probability and independence, discrete and continuous random variables, joint and conditional distributions, expectation and moments, probability and moment generating functions, Chebyshev's inequality and weak law of large numbers, central limit theorem, sampling distributions, simulation and applications to descriptive statistics.

Prerequisite(s): MATH 1002 with a grade of C+ or higher or MATH 2007 or MATH 1005 with a grade of B+ or higher; and MATH 1102 with a grade of C+ or higher or MATH 2107 with a grade of B+ or higher; or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**STAT 2660 [0.5 credit]**

Mathematics for Finance (Honours)

Mathematics for Finance (Honours)

Interest rates, growth of money, discount functions, yield rates, time value of money, annuities, cash flows and portfolios, loans, mortgages, bonds, immunization, swaps, hedging and investment strategies, stocks and financial markets, arbitrage.

Lectures three hours a week, tutorial one hour a week.

**STAT 3502 [0.5 credit]**

Probability and Statistics

Probability and Statistics

Axioms of probability; conditional probability and independence; random variables; distributions: binomial, Poisson, hypergeometric, normal, gamma; central limit theorem; sampling distributions; point estimation: maximum likelihood, method of moments; confidence intervals; testing of hypotheses: one and two populations; engineering applications: acceptance sampling, control charts, reliability.

Precludes additional credit for BIT 2000, BIT 2100 (no longer offered), BIT 2300 (no longer offered), ECON 2201 (no longer offered), ECON 2210, STAT 2507, STAT 2605, and STAT 2606.

Prerequisite(s): MATH 2004 and enrolment in the Faculty of Engineering or B.Sc. programs of the Department of Physics [except Double Honours Mathematics and Physics].

Lectures three hours a week and one hour laboratory.

**STAT 3503 [0.5 credit]**

Regression Analysis

Regression Analysis

Review of simple and multiple regression with matrices, Gauss-Markov theorem, polynomial regression, indicator variables, residual analysis, weighted least squares, variable selection techniques, nonlinear regression, correlation analysis and autocorrelation. Computer packages are used for statistical analyses.

Precludes additional credit for STAT 3553.

Prerequisite(s): i) STAT 2509 or STAT 2607 or ECON 2202 or ECON 2220 or equivalent; and ii) MATH 1102 or MATH 1107 or MATH 1119 or equivalent; or permission of the School.

Lectures three hours a week and one hour laboratory.

**STAT 3504 [0.5 credit]**

Analysis of Variance and Experimental Design

Analysis of Variance and Experimental Design

Single and multifactor analysis of variance, orthogonal contrasts and multiple comparisons, analysis of covariance; nested, crossed and repeated measures designs; completely randomized, randomized block, Latin squares, factorial experiments, related topics. Computer packages are used for statistical analyses.

Precludes additional credit for STAT 4504.

Prerequisite(s): STAT 3503 or permission of the School.

Lectures three hours a week and one hour laboratory.

**STAT 3506 [0.5 credit]**

Stochastic Processes and Applications (Honours)

Stochastic Processes and Applications (Honours)

Conditional probability and conditional expectation; Stochastic modeling; discrete time Markov chains including classification of states, stationary and limiting distributions; exponential distribution and the Poisson processes; queueing models; applications to computer systems, operations research and social sciences.

Lectures three hours a week, tutorial one hour a week.

**STAT 3507 [0.5 credit]**

Sampling Methodology

Sampling Methodology

The sample survey as a vehicle for information collection in government, business, scientific and social agencies. Topics include: planning a survey, questionnaire design, simple random, stratified, systematic and cluster sampling designs, estimation methods, problem of non-response, related topics.

Prerequisite(s): one of: STAT 2507, STAT 2509, STAT 2606, STAT 2607, ECON 2201, ECON 2202, ECON 2210, ECON 2220, or equivalent; or permission of the School.

Lectures three hours a week and one hour laboratory.

**STAT 3508 [0.5 credit]**

Elements of Probability Theory

Elements of Probability Theory

Discrete and continuous distributions, moment-generating functions, marginal and conditional distributions, transformation theory, limiting distributions.

Prerequisite(s): i) MATH 2008 (or MATH 2004 or MATH 2009); and ii) one of STAT 2507, STAT 2606, ECON 2200, or ECON 2201 or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**STAT 3509 [0.5 credit]**

Mathematical Statistics

Mathematical Statistics

Point and interval estimation, sufficient statistics, hypothesis testing, chi-square tests with enumeration data.

Prerequisite(s): STAT 3508 or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**STAT 3553 [0.5 credit]**

Regression Modeling (Honours)

Regression Modeling (Honours)

Linear regression - theory, methods and application(s). Normal distribution theory. Hypothesis tests and confidence intervals. Model selection. Model diagnostics. Introduction to weighted least squares and generalized linear models.

Precludes additional credit for STAT 3503.

Prerequisite(s): i) STAT 2559 with a grade of C- or higher, or STAT 2509 with a grade of B or higher; and ii) a grade of C- or higher in MATH 1102 or MATH 1107 or MATH 1104; or permission of the School.

Lectures three hours a week, laboratory one hour a week.

**STAT 3558 [0.5 credit]**

Elements of Probability Theory (Honours)

Elements of Probability Theory (Honours)

Random variables and moment-generating functions, concepts of conditioning and correlation; laws of large numbers, central limit theorem; multivariate normal distribution; distributions of functions of random variables, sampling distributions, order statistics.

Prerequisite(s): i) STAT 2655 with a grade of C- or higher; and ii) MATH 2000 with a grade of C- or higher, or (a grade of C+ or higher in MATH 2008 or MATH 2004, and permission of the instructor); or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**STAT 3559 [0.5 credit]**

Mathematical Statistics (Honours)

Mathematical Statistics (Honours)

Empirical distribution functions, Monte Carlo methods, elements of decision theory, point estimation, interval estimation, tests of hypotheses, robustness, nonparametric methods.

Prerequisite(s): STAT 3558 with a grade of C- or higher; or (STAT 3508 with a grade of B or higher, and permission of the instructor); or permission of the School.

Lectures three hours a week, tutorial one hour a week.

**STAT 3660 [0.5 credit]**

Actuarial Mathematics I

Actuarial Mathematics I

Severity, frequency models, loss models, risk measures, value at risk, stochastic processes, Poisson process, characteristics of actuarial models, creating new univariate distributions, heavy-tailed distributions, mixed distributions, coverage modifications.

Lectures three hours a week, tutorial one hour a week.

**STAT 3661 [0.5 credit]**

Life Contingent Risk Modelling I

Life Contingent Risk Modelling I

Mixed distributions; conditional expectations; introduction to life insurance; traditional and modern insurance contracts; underwriting; premiums; pension plans and retirement benefits; survival models; reserves; present value random variable; force of mortality; life tables; insurance benefits; annuities; premium calculation.

Lectures three hours a week, tutorial one hour a week.

**STAT 3662 [0.5 credit]**

Life Contingent Risk Modelling II

Life Contingent Risk Modelling II

Policy values; multiple state models; formulae for probability; Markov multiple state models; pension mathematics; yield curves; interest rate risk; emerging costs for life insurance; equity linked insurance; deterministic and stochastic pricing; reserving, participating, and universal life insurance.

Lectures three hours a week, tutorial one hour a week.

**STAT 4500 [0.5 credit]**

Parametric Estimation (Honours)

Parametric Estimation (Honours)

Preliminaries on probability theory; exact and asymptotic sampling distributions; unbiasedness, consistency, efficiency, sufficiency and completeness; properties of maximum likelihood estimators; least squares estimation of location and scale parameters based on order statistics and sample quantiles; Best Asymptotically Normal (BAN) estimators.

Also offered at the graduate level, with different requirements, as STAT 5600, for which additional credit is precluded.

Lectures three hours a week.

**STAT 4501 [0.5 credit]**

Probability Theory (Honours)

Probability Theory (Honours)

Introduction to probability, characteristic functions, probability distributions, limit theorems.

**STAT 4502 [0.5 credit]**

Survey Sampling (Honours)

Survey Sampling (Honours)

Basic concepts in sampling from finite populations; simple random sampling; stratified sampling; choice of sampling unit; cluster and systematic sampling; introduction to multistage sampling; ratio estimation; sampling with unequal probabilities and with replacement; replicated sampling; related topics.

Lectures three hours a week.

**STAT 4503 [0.5 credit]**

Applied Multivariate Analysis (Honours)

Applied Multivariate Analysis (Honours)

Selected topics in regression and correlation non-linear models. Multivariate statistical methods, principal components, factor analysis, multivariate analysis of variance, discriminant analysis, canonical correlation, analysis of categorical data.

Also offered at the graduate level, with different requirements, as STAT 5509, for which additional credit is precluded.

Lectures three hours a week.

**STAT 4504 [0.5 credit]**

Statistical Design and Analysis of Experiments (Honours)

Statistical Design and Analysis of Experiments (Honours)

An extension of the designs discussed in STAT 2559 to include analysis of the completely randomized design, designs with more than one blocking variable, incomplete block designs, fractional factorial designs, multiple comparisons; and response surface methods.

Precludes additional credit for STAT 3504 and ECON 4706. PSYC 3000 is precluded for additional credit for students registered in a Mathematics program.

Prerequisite(s): STAT 3553 or STAT 3503; or permission of the School of Mathematics and Statistics.

Lectures three hours a week, laboratory one hour a week.

**STAT 4506 [0.5 credit]**

Nonparametric Statistics (Honours)

Nonparametric Statistics (Honours)

Order statistics; projections; U-statistics; L-estimators; rank, sign, and permutation test statistics; nonparametric tests of goodness-of-fit, homogeneity, symmetry, and independence; nonparametric density estimation; nonparametric regression analysis: kernel estimators, orthogonal series estimators, smoothing splines; high-dimensional inference and false discovery.

Also offered at the graduate level, with different requirements, as STAT 5516, for which additional credit is precluded.

Lectures three hours a week.

**STAT 4507 [0.5 credit]**

Statistical Inference (Honours)

Statistical Inference (Honours)

Sufficient statistics, simple and composite hypotheses, most powerful and similar region test, distribution-free tests, confidence intervals, goodness-of-fit and likelihood ratio tests, large sample theory, Bayesian and likelihood methods, sequential tests.

Also offered at the graduate level, with different requirements, as STAT 5501, for which additional credit is precluded.

Lectures three hours a week.

**STAT 4508 [0.5 credit]**

Stochastic Models (Honours)

Stochastic Models (Honours)

Review of discrete Markov chains and Poisson processes; continuous time Markov chains; pure jump Markov processes, and birth and death processes including the Q-matrix approach; the Kolmogorov equations; renewal theory; introduction to Brownian motion; queueing theory.

Also offered at the graduate level, with different requirements, as STAT 5701, for which additional credit is precluded.

Lectures three hours a week.

**STAT 4509 [0.5 credit]**

Advanced Mathematical Modeling (Honours)

Advanced Mathematical Modeling (Honours)

Real-life situations in the physical, social, and life sciences are often modeled using mathematical tools. This course will examine various models and techniques used in their analysis, e.g., matrix procedures in connection with population models. Students will use a computer package to obtain numerical results.

Also offered at the graduate level, with different requirements, as STAT 5601, for which additional credit is precluded.

Lectures three hours a week.

**STAT 4555 [0.5 credit]**

Monte Carlo Simulation (Honours)

Monte Carlo Simulation (Honours)

Basic ideas and algorithms of Monte Carlo; simulation of basic stochastic processes. Brownian motion and the Poisson process, applications to financial modelling, queueing theory. Output analysis; variance reduction. Markov chain Monte Carlo methods; Gibbs sampling, simulated annealing and Metropolis-Hastings samplers with applications.

Precludes additional credit for STAT 3555 (no longer offered).

Prerequisite(s): STAT 3558, or a grade of B or higher in STAT 3508, or permission of the School.

Lectures three hours a week, tutorial/laboratory one hour a week.

**STAT 4601 [0.5 credit]**

Data Mining I (Honours)

Data Mining I (Honours)

Data visualization; knowledge discovery in datasets; unsupervised learning: clustering algorithms; dimension reduction; supervised learning: pattern recognition, smoothing techniques, classification. Computer software will be used.

Prerequisite(s): STAT 3553 or STAT 3503 or MATH 3806, or permission of the School.

Lectures three hours a week, laboratory one hour a week.

**STAT 4603 [0.5 credit]**

Time Series and Forecasting (Honours)

Time Series and Forecasting (Honours)

Time series regression. Nonstationary and stationary time series models. Nonseasonal and seasonal time series models. ARIMA (Box-Jenkins) models. Smoothing methods. Parameter estimation, model identification, diagnostic checking. Forecasting techniques. A statistical software package will be used.

Prerequisite(s): STAT 3553 or STAT 3503, or permission of the School.

Lectures three hours a week, laboratory one hour a week.

**STAT 4604 [0.5 credit]**

Statistical Computing (Honours)

Statistical Computing (Honours)

Statistical computing techniques, pseudo-random number generation, tests for randomness, numerical algorithms in statistics; optimization techniques; environments for data analysis, efficient programming techniques; statistics with mainstream software.

Prerequisite(s): STAT 3553 or STAT 3503 or permission of the School.

Lectures three hours a week, laboratory one hour a week.

**STAT 4607 [0.5 credit]**

Bayesian Statistical Analysis (Honours)

Bayesian Statistical Analysis (Honours)

Probability basics for Bayesian statistics. Bayesian inference for simple exponential families. Markov Chain Monte Carlo for posterior inference. Empirical Bayes. Hierarchical Bayes. Bayesian inference for the multivariate normal model. Bayesian linear regression. More advanced topics may be included. Computer software will be used.

Prerequisite(s): STAT 3553 or permission of the School.

Lectures three hours a week, laboratory one hour a week.

**STAT 4660 [0.5 credit]**

Actuarial Mathematics II

Actuarial Mathematics II

Empirical models, complete data, grouped data, credibility theory, failure time, accuracy, kernel estimation, goodness of fit tests, Bayesian analysis, inference for loss models, frequentist estimation, model selection.

Lectures three hours a week, tutorial one hour a week.

**STAT 4661 [0.5 credit]**

Life Contingent Risk Modelling II

Life Contingent Risk Modelling II

Policy values; multiple state models; formulae for probability; Markov multiple state models; pension mathematics; yield curves; interest rate risk; emerging costs for life insurance; equity linked insurance; deterministic and stochastic pricing; reserving, participating, and universal life insurance.

**Summer session**: some of the courses listed in this Calendar are offered during the summer. Hours and scheduling for summer session courses will differ significantly from those reported in the fall/winter Calendar. To determine the scheduling and hours for summer session classes, consult the class schedule at central.carleton.ca

Not all courses listed are offered in a given year. For an up-to-date statement of course offerings for the current session and to determine the term of offering, consult the class schedule at central.carleton.ca

### Regulations

In addition to the program requirements described here and academic performance evaluation requirements listed below, students must satisfy the University regulations common to all undergraduate students (see the Academic Regulations section of this Calendar).

Students should consult with the School of Mathematics and Statistics when planning their program and selecting courses.

### Academic Performance Evaluation for Bachelor of Mathematics

The standard procedures for Academic Performance Evaluation are followed with the following additions:

*Good Standing* at any Academic Performance Evaluation requires that the CGPA over the following courses be at least 7.00 for Honours programs and at least 5.00 for General programs:

MATH 1007 [0.5] | Elementary Calculus I | |

or MATH 1004 [0.5] | Calculus for Engineering or Physics | |

MATH 1107 [0.5] | Linear Algebra I | |

or MATH 1104 [0.5] | Linear Algebra for Engineering or Science | |

MATH 2007 [0.5] | Elementary Calculus II | |

or MATH 1005 [0.5] | Differential Equations and Infinite Series for Engineering or Physics | |

MATH 2107 [0.5] | Linear Algebra II |

### B.Sc. Regulations

The regulations presented in this section apply to all Bachelor of Science programs. In addition to the requirements presented here, students must satisfy the University regulations common to all undergraduate students including the process of Academic Performance Evaluation (see the *Academic Regulations of the University* section of this Calendar).

#### Breadth Requirement for the B.Sc.

Students in Bachelor of Science Honours, Major, or General programs must present the following credits at graduation:

- 2.0 credits in Science Continuation courses not in the major discipline;
**students completing a double major are considered to have completed this requirement providing they have 2.0 credits in science continuation courses in each of the two majors** - 2.0 credits in courses outside of the faculties of Science and Engineering and Design (but may include NSCI 1000)

In most cases, the requirements for individual B.Sc. programs, as stated in this Calendar, contain these requirements, explicitly or implicitly.

Students admitted to B.Sc. programs by transfer from another institution must present at graduation (whether taken at Carleton or elsewhere):

- 2.0 credits in courses outside of the faculties of Science and Engineering and Design (but may include NSCI 1000) if, on transfer, the student received credit for fewer than 10.0 credits.
- 1.0 credit in courses outside of the faculties of Science and Engineering and Design (but may include NSCI 1000) if, on transfer, the student received credit for 10.0 or more credits.

#### Declared and Undeclared Students

Students who are registered in a program within the degree are called Declared students. Most students designate a program of study when they first apply for admission and so begin their studies as Declared students. Students may also choose to begin their studies within the B.Sc. degree without being registered in a program. These students are referred to as Undeclared students. The recommended course pattern for Undeclared students is provided in the Undeclared entry of the Programs section of this Calendar. Undeclared students normally must apply to enter a program before beginning their second year of study. The Science Student Success Centre (SSSC) provides Undeclared students guidance to the appropriate support services in making this decision.

#### Change of Program within the B.Sc. Degree

Students may transfer to a program within the B.Sc. degree if upon entry to the new program they would be in good academic standing.

Other applications for change of program will be considered on their merits; students may be accepted in the new program in *Good Standing* or on *Academic Warning*.

Applications to declare or change their program within the B.Sc. Degree must be made online through Carleton Central by completing a Change of Program Elements (COPE) application form within the published deadlines. Acceptance into a program or into a program element or option is subject to any enrolment, and/or specific program, program element or option requirements as published in the relevant Calendar entry.

#### Minors, Concentrations and Specializations

Students may add a minor, concentration or specialization by completing a Change of Program Elements (COPE) application form online through Carleton Central. Acceptance into a minor, concentration or specialization requires that the student be in *Good Standing* and is subject to any specific requirements of the intended Minor, Concentration or Specialization as published in the relevant Calendar entry.

#### Experimental Science Requirement

Students in B.Sc. Honours, Major, or General degree programs must present at graduation at least two full credits of experimental science chosen from two different departments or institutes from the list below:

Approved Experimental Science Courses | ||

Biochemistry | ||

BIOC 2200 [0.5] | Cellular Biochemistry | |

BIOC 4001 [0.5] | Methods in Biochemistry | |

BIOC 4201 [0.5] | Advanced Cell Culture and Tissue Engineering | |

Biology | ||

BIOL 1103 [0.5] | Foundations of Biology I | |

BIOL 1104 [0.5] | Foundations of Biology II | |

BIOL 2001 [0.5] | Animals: Form and Function | |

BIOL 2002 [0.5] | Plants: Form and Function | |

BIOL 2104 [0.5] | Introductory Genetics | |

BIOL 2200 [0.5] | Cellular Biochemistry | |

BIOL 2600 [0.5] | Ecology | |

Chemistry | ||

CHEM 1001 [0.5] | General Chemistry I | |

CHEM 1002 [0.5] | General Chemistry II | |

CHEM 1005 [0.5] | Elementary Chemistry I | |

CHEM 1006 [0.5] | Elementary Chemistry II | |

CHEM 2103 [0.5] | Physical Chemistry I | |

CHEM 2203 [0.5] | Organic Chemistry I | |

CHEM 2204 [0.5] | Organic Chemistry II | |

CHEM 2302 [0.5] | Analytical Chemistry I | |

CHEM 2303 [0.5] | Analytical Chemistry II | |

CHEM 2800 [0.5] | Foundations for Environmental Chemistry | |

Earth Sciences | ||

ERTH 1006 [0.5] | Exploring Planet Earth | |

ERTH 1009 [0.5] | The Earth System Through Time | |

ERTH 2102 [0.5] | Mineralogy to Petrology | |

ERTH 2404 [0.5] | Engineering Geoscience | |

ERTH 2802 [0.5] | Field Geology I | |

ERTH 3111 [0.5] | Vertebrate Evolution: Mammals, Reptiles, and Birds | |

ERTH 3112 [0.5] | Vertebrate Evolution: Fish and Amphibians | |

ERTH 3204 [0.5] | Mineral Deposits | |

ERTH 3205 [0.5] | Physical Hydrogeology | |

ERTH 3806 [0.5] | Structural Geology | |

Food Sciences | ||

FOOD 3001 [0.5] | Food Chemistry | |

FOOD 3002 [0.5] | Food Analysis | |

FOOD 3005 [0.5] | Food Microbiology | |

Geography | ||

GEOG 1010 [0.5] | Global Environmental Systems | |

GEOG 3108 [0.5] | Soil Properties | |

Neuroscience | ||

NEUR 3206 [0.5] | Sensory and Motor Neuroscience | |

NEUR 3207 [0.5] | Systems Neuroscience | |

NEUR 4600 [0.5] | Advanced Lab in Neuroanatomy | |

Physics | ||

PHYS 1001 [0.5] | Foundations of Physics I | |

PHYS 1002 [0.5] | Foundations of Physics II | |

PHYS 1003 [0.5] | Introductory Mechanics and Thermodynamics | |

PHYS 1004 [0.5] | Introductory Electromagnetism and Wave Motion | |

PHYS 1007 [0.5] | Elementary University Physics I | |

PHYS 1008 [0.5] | Elementary University Physics II | |

PHYS 2202 [0.5] | Wave Motion and Optics | |

PHYS 2604 [0.5] | Modern Physics I | |

PHYS 3007 [0.5] | Third Year Physics Laboratory: Selected Experiments and Seminars | |

PHYS 3606 [0.5] | Modern Physics II | |

PHYS 3608 [0.5] | Modern Applied Physics |

#### Course Categories for B.Sc. Programs

Science Geography Courses | ||

GEOG 1010 [0.5] | Global Environmental Systems | |

GEOG 2006 [0.5] | Introduction to Quantitative Research | |

GEOG 2013 [0.5] | Weather and Water | |

GEOG 2014 [0.5] | The Earth's Surface | |

GEOG 3003 [0.5] | Quantitative Geography | |

GEOG 3010 [0.5] | Field Methods in Physical Geography | |

GEOG 3102 [0.5] | Geomorphology | |

GEOG 3103 [0.5] | Watershed Hydrology | |

GEOG 3104 [0.5] | Principles of Biogeography | |

GEOG 3105 [0.5] | Climate and Atmospheric Change | |

GEOG 3106 [0.5] | Aquatic Science and Management | |

GEOG 3108 [0.5] | Soil Properties | |

GEOG 4000 [0.5] | Field Studies | |

GEOG 4005 [0.5] | Directed Studies in Geography | |

GEOG 4013 [0.5] | Cold Region Hydrology | |

GEOG 4017 [0.5] | Global Biogeochemical Cycles | |

GEOG 4101 [0.5] | Two Million Years of Environmental Change | |

GEOG 4103 [0.5] | Water Resources Engineering | |

GEOG 4104 [0.5] | Microclimatology | |

GEOG 4108 [0.5] | Permafrost |

Science Psychology Courses | ||

PSYC 2001 [0.5] | Introduction to Research Methods in Psychology | |

PSYC 2002 [0.5] | Introduction to Statistics in Psychology | |

PSYC 2700 [0.5] | Introduction to Cognitive Psychology | |

PSYC 3000 [1.0] | Design and Analysis in Psychological Research | |

PSYC 3506 [0.5] | Cognitive Development | |

PSYC 3700 [1.0] | Cognition (Honours Seminar) | |

PSYC 3702 [0.5] | Perception | |

PSYC 2307 [0.5] | Human Neuropsychology I | |

PSYC 3307 [0.5] | Human Neuropsychology II |

Science Continuation Courses | ||

A course at the 2000 level or above may be used as a Science Continuation credit in a B.Sc. program if it is not in the student's major discipline, and is chosen from the following: | ||

BIOC (Biochemistry) | ||

BIOL (Biology) | ||

CHEM (Chemistry) | ||

COMP (Computer Science) A maximum of two half-credits at the 1000-level in COMP, excluding COMP 1001 may be used as Science Continuation credits. | ||

Engineering. Students wishing to register in Engineering courses must obtain the permission of the Faculty of Engineering and Design. | ||

ENSC (Environmental Science) | ||

FOOD (Food Science and Nutrition) | ||

GEOM (Geomatics) | ||

HLTH (Health Sciences) | ||

MATH (Mathematics) | ||

NEUR (Neuroscience) | ||

PHYS (Physics), except PHYS 2903 | ||

Science Geography Courses (see list above) | ||

Science Psychology Courses (see list above) | ||

STAT (Statistics) | ||

TSES (Technology, Society, Environment) except TSES 2305. Biology General, Major, and Honours students may use these courses only as free electives. Integrated Science and Environmental Science students may include these courses in their programs but may not count them as part of the Science Sequence. |

Science Faculty Electives | ||

Science Faculty Electives are courses at the 1000-4000 level chosen from: | ||

BIOC (Biochemistry) | ||

COMP (Computer Science) except COMP 1001 | ||

Engineering | ||

FOOD (Food Science and Nutrition) | ||

GEOM (Geomatics) | ||

HLTH (Health Science) | ||

MATH (Mathematics) | ||

NEUR (Neuroscience) | ||

Science Geography (see list above) | ||

Science Psychology (see list above) | ||

STAT (Statistics) | ||

TSES (Technology, Society, Environment) Biology General, Major and Honours students may use these courses only as free electives. |

Advanced Science Faculty Electives | ||

Advanced Science Faculty Electives are courses at the 2000-4000 level chosen from the Science Faculty Electives list above. |

Approved Courses Outside the Faculties of Science and Engineering and Design (may include NSCI 1000) | ||

All courses offered by the Faculty of Arts and Social Sciences, the Faculty of Public Affairs, and the Sprott School of Business are approved as Arts or Social Sciences courses EXCEPT FOR: All Science Geography courses (see list above), all Geomatics (GEOM) courses, all Science Psychology courses (see list above). NSCI 1000 may be used as an Approved Course Outside the Faculties of Science and Engineering and Design. |

Free Electives | ||

Any course is allowable as a Free Elective providing it is not prohibited (see below). Students are expected to comply with prerequisite requirements and enrolment restrictions for all courses as published in this Calendar. | ||

Courses Allowable Only as Free Electives in any B.Sc. Program | ||

CHEM 1003 [0.5] | The Chemistry of Food, Health and Drugs | |

CHEM 1004 [0.5] | Drugs and the Human Body | |

CHEM 1007 [0.5] | Chemistry of Art and Artifacts | |

ERTH 1010 [0.5] | Our Dynamic Planet Earth | |

ERTH 1011 [0.5] | Evolution of the Earth | |

ERTH 2415 [0.5] | Natural Disasters | |

ISCI 1001 [0.5] | Introduction to the Environment | |

ISCI 2000 [0.5] | Natural Laws | |

ISCI 2002 [0.5] | Human Impacts on the Environment | |

MATH 0107 [0.5] | Algebra and Geometry | |

PHYS 1901 [0.5] | Planetary Astronomy | |

PHYS 1902 [0.5] | From our Star to the Cosmos | |

PHYS 1905 [0.5] | Physics Behind Everyday Life | |

PHYS 2903 [0.5] | Physics Towards the Future | |

Prohibited Courses | ||

The following courses are not acceptable for credit in any B.Sc. program: | ||

COMP 1001 [0.5] | Introduction to Computational Thinking for Arts and Social Science Students | |

MATH 0005 [0.5] | Precalculus: Functions and Graphs | |

MATH 0006 [0.5] | Precalculus: Trigonometric Functions and Complex Numbers | |

MATH 1009 [0.5] | Calculus: with Applications to Business | |

MATH 1119 [0.5] | Linear Algebra: with Applications to Business | |

MATH 1401 [0.5] | Elementary Mathematics for Economics I | |

MATH 1402 [0.5] | Elementary Mathematics for Economics II |

**Co-operative Education**

For more information about how to apply for the Co-op program and how the Co-op program works please visit the Co-op website.

All students participating in the Co-op program are governed by the Undergraduate Co-operative Education Policy.

### Undergraduate Co-operative Education Policy

**Admission Requirements**

Students can apply to co-op in one of two ways; directly from high school or after beginning a degree program at Carleton.

If a student is admitted to co-op from high school, their grades will be reviewed two terms to one year prior to their first work term to ensure they continue to meet the academic requirements after their 1st or 2nd year of study. The time at which evaluation takes place depends on the program of study. Students will automatically be notified via their Carleton email account if they are permitted to continue.

Students not admitted to Carleton University with the co-op option on their degree can apply for admission via the co-operative education program website. To view application deadlines, visit carleton.ca/co-op.

Admission to the co-op option is based on the completion of 5.0 or more credits at Carleton University, the CGPA requirement for the students' academic program as well as any course prerequisites. The articulated CGPA for each program is the normal standard for assessment. Please see the specific degree program sections for the unique admission and continuation requirements for each academic program.

**English Language Proficiency**

Students admitted to Carleton based on CAEL, IELTS or TOEFL assessments and who are required to take an ESL course must take and pass the Oral Proficiency in Communicative Settings (OPECS) Test. The test must be taken before being permitted to register in COOP 1000. Admission to the co-op program can be confirmed with a minimum score of 4+.

**Participation Requirements**

**COOP 1000**

Once a student has been given admission or continuation confirmation to the co-op option s/he must complete and pass COOP 1000 (a mandatory online 0.0 credit course). Students will have access to this course a minimum of two terms prior to their first work term and will be notified when to register.

**Communication with the Co-op Office**

Students must maintain contact with the co-op office during their job search and while on a work term. All email communication will be conducted via the students' Carleton email account.

**Employment**

Although every effort is made to ensure a sufficient number of job postings for all students enrolled in the co-op option of their degree program, no guarantee of employment can be made. Carleton's co-op program operates a competitive job search process and is dependent upon current market conditions. Academic performance, skills, motivation, maturity, attitude and potential will determine whether a student is offered a job. It is the student's responsibility to actively conduct a job search in addition to participation in the job search process operated by the co-op office. Once a student accepts a co-op job offer (verbally or written), his/her job search will end and access to co-op jobs will be removed for that term. Students that do not successfully obtain a co-op work term are expected to continue with their academic studies. The summer term is the exception to this rule. Students should also note that hiring priority is given to Canadian citizens for co-op positions in the Federal Government of Canada.

**Registering in Co-op Courses**

Students will be registered in a Co-op Work Term course while at work. The number of Co-op Work Term courses that a student is registered in is dependent upon the number of four-month work terms that a student accepts.

While on a co-op work term students may take a maximum of 0.5 credit throughout each four-month co-op work term. Courses must be scheduled outside of regular working hours.

Students must be registered as full-time before they begin their co-op job search (2.0 credits). All co-op work terms must be completed before the beginning of the final academic term. Students may not finish their degree on a co-op work term.

**Work Term Assessment and Evaluation**

To obtain a Satisfactory grade for the co-op work term students must have:

- A satisfactory work term evaluation by the co-op employer;
- A satisfactory grade on the work term report.

Students must submit a work term report at the completion of each four-month work term. Reports are due on the 16th of April, August, and December and students are notified of due dates through their Carleton email account.

Workplace performance will be assessed by the workplace supervisor. Should a student receive an unsatisfactory rating from their co-op employer, an investigation by the co-op program manager will be undertaken. An unsatisfactory employer evaluation does not preclude a student from achieving an overall satisfactory rating for the work term.

**Graduation with the Co-op Designation**

In order to graduate with the co-op designation, students must satisfy all requirements for their degree program in addition to the requirements according to each co-op program (i.e. successful completion of three or four work terms).

Note: Participation in the co-op option will add up to one additional year for a student to complete their degree program.

**Voluntary Withdrawal from the Co-op Option**

Students may withdraw from the co-op option of their degree program during a study term ONLY. Students at work may not withdraw from the work term or the co-op option until s/he has completed the requirements of the work term.

Students are eligible to continue in their regular academic program provided that they meet the academic standards required for continuation.

**Involuntary or Required Withdrawal from the Co-op Option**

Students may be required to withdraw from the co-op option of their degree program for one or any of the following reasons:

- Failure to achieve a grade of SAT in COOP 1000
- Failure to pay all co-op related fees
- Failure to actively participate in the job search process
- Failure to attend all interviews for positions to which the student has applied
- Declining more than one job offer during the job search process
- Continuing a job search after accepting a co-op position
- Dismissal from a work term by the co-op employer
- Leaving a work term without approval by the Co-op manager
- Receipt of an unsatisfactory work term evaluation
- Submission of an unsatisfactory work term report

**Standing and Appeals**

The Co-op and Career Services office administers the regulations and procedures that are applicable to all co-op program options. All instances of a student's failure during a work term or other issues directly related to their participation in the co-op option will be reported to the academic department.

Any decision made by the Co-op and Career Services office can be appealed via the normal appeal process within the University.

**International Students**

All International Students are required to possess a Co-op Work Permit issued by Immigration, Refugees and Citizenship Canada before they can begin working. It is illegal to work in Canada without the proper authorization. Students will be provided with a letter of support to accompany their application. Students must submit their application for their permit before being permitted to view and apply for jobs on the Co-op Services database. Confirmation of a position will not be approved until a student can confirm they have received their permit. Students are advised to discuss the application process and requirements with the International Student Services Office.

### Bachelor of Mathematics Honours, Combined B.Math./M.Sc.: Co-op Admission and Continuation Requirements

- Maintain full-time status in each study term (2.0 credits);
- Be eligible to work in Canada (for off-campus work)
- Have successfully completed COOP 1000 [0.0]

In addition to:

Students in any of these programs (excluding Biostatistics) must satisfy the following:

- Completion of 5.0 or more credits (at least 2.0 in Mathematics/Statistics) at Carleton in any Honours program (excluding Biostatistics), or the Combined B.Math./M.Sc. ("Fast Track") programs, offered by the School of Mathematics and Statistics
- A major CGPA of 8.00 or higher and an overall CGPA of 6.50 or higher

Students in the B.Math. (Combined Honours) Biostatistics program must satisfy the following:

- Full-time student in the B.Math. Biostatistics program;
- An overall CGPA of 8.00 or higher;
- Successfully completed all required first year courses before beginning the first work term
- Students must be eligible for third-year standing when they return for a study term after their first work term.

Students in these programs must successfully complete four (4) work terms to obtain the co-op designation.

**Co-op Work Term Course**: MATH 3999

**Work/Study Pattern:**

Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |||||
---|---|---|---|---|---|---|---|---|---|

Term | Pattern | Term | Pattern | Term | Pattern | Term | Pattern | Term | Pattern |

Fall | S | Fall | S | Fall | S | Fall | *W/S | Fall | S |

Winter | S | Winter | S | Winter | S | Winter | *W/S | Winter | S |

Summer | **O/W | Summer | *W | Summer | O/W | Summer | O/W |

**Legend S**: Study

**W**: Work

**O**: Optional

*****indicates recommended work study pattern

******student finds own employer for this work-term.

### Admissions Information

Admission Requirements are for the 2020-21 year only, and are based on the Ontario High School System. Holding the minimum admission requirements only establishes eligibility for consideration. The cut-off averages for admission may be considerably higher than the minimum. See also the **General Admission and Procedures **section of this Calendar. An overall average of at least 70% is normally required to be considered for admission. Some programs may also require specific course prerequisites and prerequisite averages and/or supplementary admission portfolios. Higher averages are required for admission to programs for which the demand for places by qualified applicants exceeds the number of places available. The overall average required for admission is determined each year on a program by program basis. Consult admissions.carleton.ca for further details.

Note: Courses listed as *recommended* are not mandatory for admission. Students who do not follow the recommendations will not be disadvantaged in the admission process.

### Degree

- Bachelor of Mathematics (B. Math.) (Honours)
- Bachelor of Mathematics (B.Math.) (General)

### Admission Requirements

### Honours Program

#### First Year

The Ontario Secondary School Diploma (OSSD) or equivalent including a minimum of six 4U or M courses. The six 4U or M courses must include two prerequisite courses (Advanced Functions and Calculus and Vectors).

The overall admission cut-off average and/or the prerequisite course average may be considerably higher than the stated minimum requirements for admission to the combined B.Math/M.Sc in Mathematics or Statistics.

#### Advanced Standing

Applications for admission beyond first year will be assessed on their individual merits. Applicants must normally be in Good Standing (see Undergraduate Calendar section 3.0 - Academic Regulations) for their year level. Advanced standing will be granted only for those subjects assessed as being appropriate for the program and the stream selected.

### General Program

#### First Year

The Ontario Secondary School Diploma (OSSD) or equivalent including a minimum of six 4U or M courses. The six 4U or M courses must include two prerequisite courses (Advanced Functions and Calculus and Vectors). Equivalent courses may be substituted between the old and new Ontario mathematics curriculum.

#### Advanced Standing

Applications for admission beyond first year will be assessed on their individual merits. Applicants must normally be in Good Standing (see Undergraduate Calendar section 3.0 - Academic Regulations) for their year level. Advanced standing will be granted only for those subjects assessed as being appropriate for the program and the stream selected.

#### Co-op Option

#### Direct Admission to the First Year of the Co-op Option

Applicants must:

- meet the required overall admission cut-off average and prerequisite course average. These averages may be higher than the stated minimum requirements;
- be registered as a full-time student in the Bachelor of Mathematics Honours program;
- be eligible to work in Canada (for off-campus work placements).

Meeting the above requirements only establishes eligibility for admission to the program. The prevailing job market (and thus the availability of co-op placement) may limit enrolment in the co-op option.

**Note: continuation requirements for students previously admitted to the co-op option and admission requirements for the co-op option after beginning the program are described in the Co-operative Education Regulations section of this Calendar.**

### Admissions Information

Admission Requirements are for the 2020-21 year only, and are based on the Ontario High School System. Holding the minimum admission requirements only establishes eligibility for consideration. The cut-off averages for admission may be considerably higher than the minimum. See also the **General Admission and Procedures **section of this Calendar. An overall average of at least 70% is normally required to be considered for admission. Some programs may also require specific course prerequisites and prerequisite averages and/or supplementary admission portfolios. Higher averages are required for admission to programs for which the demand for places by qualified applicants exceeds the number of places available. The overall average required for admission is determined each year on a program by program basis. Consult admissions.carleton.ca for further details.

Note: Courses listed as *recommended* are not mandatory for admission. Students who do not follow the recommendations will not be disadvantaged in the admission process.

### Degrees

- B.Sc. (Honours)
- B.Sc. (General)
- B.Sc. (Major)

### Admission Requirements

**Honours Program**

#### First Year

The Ontario Secondary School Diploma (OSSD) or equivalent including a minimum of six 4U or M courses. For most programs including Biochemistry, Bioinformatics, Biotechnology, Chemistry, Combined Honours in Biology and Physics, Chemistry and Physics, Computational Biochemistry, Food Science, Nanoscience, Neuroscience, Neuroscience and Mental Health, and Psychology, the six 4U or M courses must include Advanced Functions and two of Biology, Chemistry, Earth and Space Sciences or Physics. (Calculus and Vectors is strongly recommended).

**Specific Honours Admission Requirements**

For the Honours programs in Earth Sciences, Environmental Science, Geomatics, Interdisciplinary Science and Practice, and Physical Geography, Calculus and Vectors may be substituted for Advanced Functions.

For the Honours programs in Physics and Applied Physics and for double Honours in Mathematics and Physics, Calculus and Vectors is required in addition to Advanced Functions and one of 4U Physics Chemistry, Biology, or Earth and Space Sciences. For all programs in Physics, 4U Physics is strongly recommended.

For the Combined Honours program in Chemistry and Computer Science, 4U Chemistry and Calculus and Vectors are strongly recommended.

For Honours in Psychology, a 4U course in English is recommended.

For Honours in Environmental Science, a 4U course in Biology and Chemistry is recommended.

#### Advanced Standing

For entry to an Honours program after the completion of 5.0 included credits, a student must have a major CGPA of 5.50 or higher, an overall CGPA of 4.50 or higher and the recommendation of the Honours department or committee. A student beginning the final 10.0 credits towards an Honours degree must present a major CGPA of 6.00 or higher, an overall CGPA of 5.00 or higher and the recommendation of the Honours department or committee. A student beginning the final 5.0 credits towards an Honours degree must present a major CGPA of 6.50 or higher and an overall CGPA of 5.00 or higher, as calculated for graduation. Advanced standing will be granted for studies undertaken elsewhere when these are recognized as the equivalent of subjects offered at Carleton University.

**Major Program**

**General Program**

#### First Year

The Ontario Secondary School Diploma (OSSD) or equivalent including a minimum of six 4U or M courses. The six 4U or M courses must include Advanced Functions and two of Calculus and Vectors, Biology, Chemistry, Earth and Space Science or Physics (Calculus and Vectors is strongly recommended). For the B.Sc. Major in Physics. 4U Physics is strongly recommended. Equivalent courses may be substituted between the old and new Ontario mathematics curriculum.

#### Advanced Standing

For entry to a General or Major program after the completion of 5.0 included credits, a student must have a major and core CGPA of 3.50 or higher and an overall CGPA of 3.50 or higher. A student beginning the final 5.0 credits towards a General or Major degree must present a major and core CGPA of 4.00 or higher and an overall CGPA of 4.00 or higher, as calculated for graduation. Advanced standing will be granted for studies undertaken elsewhere when these are recognized as the equivalent of subjects offered at Carleton University.

#### Co-op Option

#### Direct Admission to the First Year of the Co-op Option

Applicants must:

- meet the required overall admission cut-off average and prerequisite course average. These averages may be higher than the stated minimum requirements;
- be registered as a full-time student in the Bachelor of Science Honours program;
- be eligible to work in Canada (for off-campus work placements).

Note that meeting the above requirements only establishes eligibility for admission to the program. The prevailing job market may limit enrolment in the co-op option.

Note: continuation requirements for students previously admitted to the co-op option and admission requirements for the co-op option after beginning the program are described in the Co-operative Education Regulations section of this Calendar.