Mathematics

Program Requirements and Path to Completion:

• Year 1 to 4: HBA/ HBSc degree requirements:
  • students must complete all of the HBA/ HBSc program and degree requirements;
  • students are expected to carry a full course load of 5.0 credits over the three academic sessions (Fall, Winter, Summer) of each year;
  • in Year 3, qualified students may apply to the MT and the CDP and may be offered conditional admission to the MT;
  • by the end of Year 3 students must complete at least 3.0 credits required for the first teaching subject, and at least 1.5 credits for the second teaching subject (or 3.0 credits if the second teaching subject is French as a Second Language or Science);
  • in Year 4, students who receive a conditional offer of admission to the CDP must complete any two of the graduate elective half courses recommended by OISE for CDP students; these courses (1.0 credit) are counted towards the completion of both the HBA/ HBSc degree and the MT program and degree; CDP students are graded as graduate students in these courses and are required to meet graduate expectations;
  • by the end of Year 4, students must complete all HBA/ HBSc program requirements and degree requirements, including at least 6.0 credits required for the first teaching subject, and  at least 3.0 credits for the second teaching subject (or 6.0 credits if the second teaching subject is French as a Second Language or Science).
• Year 5 and 6: Remaining MT program and degree requirements:
  • students must complete 11.0 credits as identified by OISE.

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.

Program Requirements
Students must complete the program requirements as described in the Specialist Program in Mathematics.

Co-op Work Term Requirements
Students must satisfactorily complete three Co-op work terms, each of four-months duration. To be eligible for their first work term, students must be enrolled in the Specialist (Co-op) Program in Mathematics and have completed at least 10.0 credits.
In addition to their academic program requirements, Co-op students complete up to five Co-op specific courses. These courses are designed to prepare students for their job search and work term experience, and to maximize the benefits of their Co-op work terms. They cover a variety of topics intended to assist students in developing the skills and tools required to secure work terms that are appropriate to their program of study, and to perform professionally in the workplace. These courses must be completed in sequence, and are taken in addition to a full course load. They are recorded on transcripts as credit/no credit (CR/NCR) and are considered to be additive credit to the 20.0 required degree credits. No additional course fee is assessed as registration is included in the Co-op Program fee.

Co-op Preparation Course Requirements:

1. COPB50H3/​(COPD01H3) – Foundations for Success in Arts & Science Co-op
- Students entering Co-op from outside of UTSC (high school or other postsecondary) will complete this course in Fall or Winter of their first year at UTSC. Enrolment in each section is based on admission category: Typically, students in Computer Science, Mathematics and Statistics enroll in the Fall semester while all other Arts & Science Co-op admission categories enroll in the Winter semester however this may vary year to year.
- Current UTSC students entering Co-op in April/May will complete this course in the Summer semester.
- Current UTSC students entering Co-op in July/August will complete this course in the Fall semester.

2. COPB51H3/​(COPD03H3) – Preparing to Compete for your Co-op Work Term
- This course will be completed eight months in advance of the first scheduled work term.

3. COPB52H3/​(COPD11H3) – Managing your Work Term Search & Transition to Work
- This course will be completed four months in advance of the first work scheduled work term.

4. COPC98H3/​(COPD12H3) – Integrating Your Work Term Experience Part I
- This course will be completed four months in advance of the second scheduled work term.

5. COPC99H3/​(COPD13H3) – Integrating Your Work Term Experience Part II
- This course will be completed four months in advance of the third scheduled work term (for programs that require the completion of 3 work terms and/or four months in advance of any additional work terms that have been approved by the Arts and Science Co-op Office.

Students must be available for work terms in each of the Fall, Winter and Summer semesters and must complete at least one of their required work terms in either a Fall or Winter semester. This, in turn, requires that students take courses during at least one Summer semester.

For information on fees, status in Co-op programs, and certification of completion of Co-op programs, see Section 6B.5 or the Arts and Science Co-op section in the UTSC Calendar.

Program Requirements
This stream requires a total of 8.5 credits, chosen so as to satisfy all of the following requirements:

1. Foundational courses - 5.5 credits from the following:
[MATA67H3 or CSCA67H3 Discrete Mathematics]
MATA22H3 Linear Algebra I for Mathematical Sciences
MATA31H3 Calculus I for Mathematical Sciences
MATA37H3 Calculus II for Mathematical Sciences
CSCA08H3 Introduction to Computer Science I
MATB24H3 Linear Algebra II
MATB41H3 Techniques of the Calculus of Several Variables I
MATB42H3 Techniques of the Calculus of Several Variables II
MATB44H3 Differential Equations I
STAB52H3 Introduction to Probability
[MATC01H3 Groups and Symmetry OR MATC15H3 Introduction to Number Theory]

2. Further analysis courses - 1.0 credit from the following:
MATB43H3 Introduction to Analysis
MATC27H3 Introduction to Topology
MATC34H3 Complex Variables

MATC46H3 Differential Equations II

MATD35H3 Introduction to Discrete Dynamical Systems

MATD46H3 Partial Differential Equations
MATD67H3 - Differentiable Manifolds

3. Further algebra, geometry, and discrete mathematics courses - 1.0 credit from the following:
MATC01H3 Groups and Symmetry
MATC09H3 Introduction to Mathematical Logic
MATC15H3 Introduction to Number Theory
MATC32H3 Graph Theory and Algorithms for its Applications
MATC44H3 Introduction to Combinatorics
MATC63H3 Differential Geometry
MATD01H3 Fields and Groups
MATD02H3 Classical Plane Geometries and their Transformations

MATD44H3 Topics in Combinatorics

4. Elective courses - 1.0 credit from the following:
MATB61H3 Linear Programming and Optimization
STAB57H3 Introduction to Statistics

MATD50H3 Mathematical Introduction to Game Theory

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

Recommended Writing Course
Students are urged to take a course from the following list of courses by the end of their second year.
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, PHLA11H3, WSTA01H3.

Program Requirements
Students must complete the program requirements as described in the Major Program in Mathematics.

Co-op Work Term Requirements
Students must satisfactorily complete three Co-op work terms, each of four-months duration. To be eligible for their first work term, students must be enrolled in the Major (Co-op) Program in Mathematics and have completed at least 7.0 credits.

In addition to their academic program requirements, Co-op students complete up to five Co-op specific courses. These courses are designed to prepare students for their job search and work term experience, and to maximize the benefits of their Co-op work terms. They cover a variety of topics intended to assist students in developing the skills and tools required to secure work terms that are appropriate to their program of study, and to perform professionally in the workplace. These courses must be completed in sequence, and are taken in addition to a full course load. They are recorded on transcripts as credit/no credit (CR/NCR) and are considered to be additive credit to the 20.0 required degree credits. No additional course fee is assessed as registration is included in the Co-op Program fee.

Co-op Preparation Course Requirements:

1. COPB50H3/​(COPD01H3) – Foundations for Success in Arts & Science Co-op
- Students entering Co-op from outside of UTSC (high school or other postsecondary) will complete this course in Fall or Winter of their first year at UTSC. Enrolment in each section is based on admission category: Typically, students in Computer Science, Mathematics and Statistics enroll in the Fall semester while all other Arts & Science Co-op admission categories enroll in the Winter semester however this may vary year to year.
- Current UTSC students entering Co-op in April/May will complete this course in the Summer semester.
- Current UTSC students entering Co-op in July/August will complete this course in the Fall semester.

2. COPB51H3/​(COPD03H3) – Preparing to Compete for your Co-op Work Term
- This course will be completed eight months in advance of the first scheduled work term.

3. COPB52H3/​(COPD11H3) – Managing your Work Term Search & Transition to Work
- This course will be completed four months in advance of the first work scheduled work term.

4. COPC98H3/​(COPD12H3) – Integrating Your Work Term Experience Part I
- This course will be completed four months in advance of the second scheduled work term.

5. COPC99H3/​(COPD13H3) – Integrating Your Work Term Experience Part II
- This course will be completed four months in advance of the third scheduled work term (for programs that require the completion of 3 work terms and/or four months in advance of any additional work terms that have been approved by the Arts and Science Co-op Office.

Students must be available for work terms in each of the Fall, Winter and Summer semesters and must complete at least one of their required work terms in either a Fall or Winter semester. This, in turn, requires that students take courses during at least one Summer semester.

For information on fees, status in Co-op programs, and certification of completion of Co-op programs, see Section 6B.5 or the Arts and Science Co-op section in the UTSC Calendar.