Supervisor of Studies: R. Grinnell (416-287-5655) Email: raymond.grinnell@utoronto.ca

**Program Objectives**

This program provides the student with a sound foundation in the main areas of mathematics, and some exposure to computer programming and statistics. It comprises three streams: Comprehensive, Statistics, and Teaching, each serving a more specific goal.

The **Comprehensive Stream** provides a broad and deep knowledge of mathematics at the undergraduate level. It is the recommended program for students who plan to pursue graduate study in mathematics, but it is also suitable for other career paths.

The **Statistics Stream** provides greater exposure to statistics, and the areas of mathematics most closely associated with it. This stream prepares students for careers in industry, or for graduate study in certain mathematically-oriented subjects, including statistics and financial mathematics.

The **Teaching Stream** is intended for students with a serious interest in mathematics but whose career objectives lie in mathematics education at the elementary or secondary level.

**Enrolment Requirements**

Enrolment in the Specialist Program in Mathematics (all streams) is limited.

Students may apply to enter the program after completing 4.0 credits, and must have passed all of the A-level MAT and CSC courses required in the program ([CSCA08H3 or CSCA20H3], CSCA67H3/MATA67H3, MATA22H3, MATA31H3, and MATA37H3). Students are admitted on the basis of academic performance in program courses; for more information about the admission requirements, please visit the following CMS webpage.

**Program Requirements**

The Program requirements consist of a core 15 courses (7.5 credits), common to all streams, and additional requirements that depend on the stream, for a total of 26-27 courses (13.0-13.5 credits).

The structure of the programs allows for easy switching between streams until relatively late. Consequently, these programs should not be viewed as rigidly separated channels feeding students to different career paths, but as a flexible structure that provides guidance to students in their course selection based on their broad (but possibly fluid) interests.

**Core (7.5 credits)**

**1. Writing Requirement (0.5 credit)(*)**

*0.5 credits from the following:* ANTA01H3, ANTA02H3, (CLAA02H3), (CTLA19H3), CTLA01H3, ENGA10H3, ENGA11H3, ENGB06H3, ENGB07H3, ENGB08H3, ENGB09H3, ENGB17H3, ENGB19H3, ENGB50H3, (ENGB51H3), GGRA02H3, GGRA03H3, GGRB05H3, (GGRB06H3), (HISA01H3), (HLTA01H3), ACMA01H3, (HUMA01H3), (HUMA11H3), (HUMA17H3), (LGGA99H3), LINA01H3, PHLA10H3, WSTA01H3.

(*) It is recommended that this requirement be satisfied by the end of the second year.

**2. A-level courses (2.5 credits)**

[CSCA08H3 Introduction to Computer Science I or CSCA20H3 Introduction to Programming]

MATA22H3 Linear Algebra I for Mathematical Sciences

MATA31H3 Calculus I for Mathematical Sciences

MATA37H3 Calculus II for Mathematical Sciences

[MATA67H3 or CSCA67H3 Discrete Mathematics]

**3. B-level courses (3.5 credits)**

MATB24H3 Linear Algebra II

MATB41H3 Techniques of the Calculus of Several Variables I

MATB42H3 Techniques of the Calculus of Several Variables II

MATB43H3 Introduction to Analysis

MATB44H3 Differential Equations I

STAB52H3 Introduction to Probability (**)

STAB57H3 Introduction to Statistics (**)

(**) This course may be taken after the second year, except for the Statistics stream.

**4. C-level courses (1.0 credit)**

MATC01H3 Groups and Symmetry

MATC34H3 Complex Variables

**A. Comprehensive Stream**

This stream requires a total of 27 courses (13.5 credits) In addition to the core requirements 1-4 common to all streams, 12 other distinct courses must be chosen satisfying all of the following requirements:

**5. Additional courses in analysis and algebra (1.5 credits):**

1.5 credits from the following:

MATC37H3 Introduction to Real Analysis

MATC46H3 Differential Equations II

MATD01H3 Fields and Groups

MATD35H3 Introduction to Discrete Dynamical Systems

MATD46H3 Partial Differential Equations

*6. Courses in key areas of mathematics (1.0 credit):*

1.0 credit from the following:** **

MATC15H3 Introduction to Number Theory

MATC27H3 Introduction to Topology

MATC63H3 Differential Geometry

MATD02H3 Classical Plane Geometries and their Transformations

MATD34H3 Complex Variables II

*7. Mathematics of computation (1.0 credit):*

1.0 credit from the following:

CSCC37H3 Introduction to Numerical Algorithms for Computational Mathematics

CSCC63H3 Computability and Computational Complexity

CSCC73H3 Algorithm Design and Analysis

MATC09H3 Introduction to Mathematical Logic

MATC32H3 Graph Theory and Algorithms for its Applications

MATC44H3 Introduction to Combinatorics

MATD16H3 Coding Theory and Cryptography

MATD44H3 Topics in Combinatorics

*8. Electives (2.5 credits):*

2.5 credits from CSC/MAT/STA/PHY of which at least 1.5 must be at the C- or D-level MAT courses (excluding MATC90H3).

**B. Statistics Stream**

This stream requires a total of 26 courses (13.0 credits). In addition to the core requirements 1-4 common to all streams, 11 other distinct courses must be chosen, satisfying all of the following requirements (in choosing courses to satisfy requirements 7-9, students must select at least one D-level course).

*5. Algebra and Analysis (1.5 credits):*

MATB61H3 Linear Programming and Optimization

MATC46H3 Differential Equations II

MATD01H3 Fields and Groups

*6. Statistics (1.5 credits):*

STAC58H3 Statistical Inference

STAC62H3 Stochastic Processes

STAC67H3 Regression Analysis

*7. Discrete mathematics and geometry (0.5 credit):*

0.5 credit from the following:

MATC32H3 Graph Theory and Algorithms for its Applications

MATC44H3 Introduction to Combinatorics

MATD02H3 Classical Plane Geometries and their Transformations

MATD44H3 Topics in Combinatorics

MATD50H3 Mathematical Introduction to Game Theory

*8. Upper-level MAT electives (1.0 credit):*

1.0 credit from any C- or D-level MAT courses (*)

(*) For students wishing to pursue graduate studies in Mathematics or Statistics it is recommended that MATC37H3 be chosen as one of these two courses.

*9. Upper-level STA electives (1.0 credit):*

1.0 credit from the following:

(ACTB47H3) Introductory Life Contingencies

Any C- or D-level STA course, excluding STAC32H3, STAC53H3 and STAD29H3

**C. Teaching Stream**

This stream requires a total of 26 courses (13.0 credits). In addition to the core requirements 1-4 common to all streams, 11 other distinct courses must be chosen, satisfying all of the following requirements:

*5. Algebra, analysis, and geometry (1.5 credits):*

1.5 credits from the following:

MATC15H3 Introduction to Number Theory

MATD01H3 Fields and Groups

MATD02H3 Classical Plane Geometries and their Transformations

MATD35H3 Introduction to Discrete Dynamical Systems

MATD46H3 Partial Differential Equations

*6. Discrete mathematics (0.5 credit):*

0.5 credit from the following:

MATC32H3 Graph Theory and Algorithms for its Applications

MATC44H3 Introduction to Combinatorics

MATD44H3 Topics in Combinatorics

*7. MAT electives (1.5 credits):*

1.5 credits of any C- or D-level MAT courses

*8. MAT/STA/CSC electives (2.0 credits):*

2.0 credits of any C- or D-level MAT, STA, CSC courses, excluding STAC32H3, STAC53H3 and STAD29H3

It is recommended that students obtain a TA-ship within the Department of Computer and Mathematical Sciences.