# Mathematics

Mathematicians are critical thinkers who analyze, assess situations, and find solutions to problems. Direct applications of mathematics may be seen in many aspects of modern life, such as:

- cryptography
- mathematical biology
- mathematical genomics
- actuarial mathematics
- mathematical finance
- engineering
- operations research
- software design
- mathematical epidemiology

Knowledge of mathematics opens gateways to many different professions in fields such as commerce, economics, engineering, physics, chemistry, biology, law, medicine, computer science and mathematics. The applications of this knowledge tend to be quite concrete. For example, in economics the predictions of the stock markets are based on mathematical models, and individuals understanding these models and their limitations will have distinct advantages.

Aside from practical considerations, mathematics can be a highly satisfying intellectual pursuit. The field of mathematics is quite diverse, and it is a matter of personal taste which aspects you may find most appealing.

### Programs

- Mathematics (specialist, major and minor)
- Applied Mathematics (specialist)
- Mathematics and its Applications: Probability/Statistics (specialist)
- Mathematics and its Applications: Physical Science (specialist)
- Mathematics and its Applications: Teaching (specialist)
- Mathematics and Physics (specialist)
- Mathematics and Philosophy (specialist)
- Mathematical Applications in Economics and Finance (specialist)
- Economics and Mathematics - see economics
- Statistics and Math - see statistics

### Combined Degree Program (CDP)

The Combined Degree Program in Arts/Science and Education is designed to prepare the students with the required qualification for teaching in Ontario. Students earn an Honours Bachelor’s degree from the Faculty of Arts and Science (St. George) and an accredited professional Master of Teaching (MT) degree from the Ontario Institute for Studies in Education (OISE). Both degrees are completed over six years.

Program requirements include:

- Minor in Education and Society, Victoria College
- Major in Mathematics (first teaching subject)
- Minor in an area corresponding to the second teaching subject as determined by OISE

See the CDP calendar listing for additional information on the CDP, including admission, path to completion and contact information.

### First-Year Courses

- MAT 133Y1 - Calculus and Linear Algebra for Commerce
- MAT 135H1 - Calculus I (A)
- MAT 136H1 - Calculus I (B)
- MAT 137Y1 – Calculus
- MAT 138H1 – Introduction to Proofs Introduction to Proofs (It is strongly recommended that students who have not taken a proof-based course in their high school program complete MAT 138H1 in the summer before taking MAT 137Y1 or MAT157Y1. They can also take the courses concurrently in fall. After you have accepted the U of T offer, you may e-mail inquiries@math.utoronto.ca to request enrolment in the course)
- MAT 157Y1 - Analysis
- MAT 223H1 - Linear Algebra I
- MAT 224H1 – Linear Algebra II
- MAT 240H1 - Algebra I
- MAT 247H1 – Algebra II
- JMB 170Y1 - Biology, Models, and Mathematics

### Advice for First Year

Students who are interested in pursuing advanced mathematical studies should enroll in MAT138H1, MAT157Y1, MAT240H1 and MAT247H1. MAT138H1 is an introduction to proofs course that will allow students to develop mathematical skills that are crucial for success in the more advanced proof-based courses. MAT157Y1 is a theoretical course, emphasizing proofs and techniques as well as geometric and physical understanding. It is required for the Specialist in Mathematics, Applied Mathematics, Mathematics and Physics and the Mathematics and Philosophy specialist program of study. MAT240H1 and MAT247H1 are the introductory specialist courses in linear algebra.

Students should consider taking MAT137Y1 if they have a serious interest in mathematics but wish to avoid the theoretical challenges of MAT157Y1. MAT137Y1 is required by many of the physical or information science programs. It is also acceptable for four of our specialist programs: Mathematics and its Application (Physical Sciences), Mathematics and its Application (Probability/Statistics), Mathematics and its Application (Teaching) and Mathematics and its Application (Economics and Finance).

For students interested in the life sciences or commerce, the recommended courses are MAT133Y1 or MAT135H1 and MAT136H1. MAT135H1 & MAT136H1 are required by many of the life sciences programs and MAT133Y1 is designed for students interested primarily in commerce and economics. If a program requires mathematics courses beyond first year, students should not take MAT133Y1.

**Preparatory Course, MAT138H1 - Introduction to Proofs**

This course is an introduction to the reading and understanding of mathematical statements, analyzing definitions and properties, finding and writing precise arguments, and formulation of proofs. The course is designed as a preparation for MAT137Y1, MAT157Y1, MAT 237Y1, MAT257Y1, MAT240H1, MAT247H1 and other proof-oriented 200-level courses. Students may register and complete this half credit during the second semester in the summer term or in the fall of their first or second year.

**Preparatory Course, Preparing for University Mathematics Program (PUMP)**

PUMP is a non-credit course designed for students who have not taken the appropriate high school mathematics prerequisites for university calculus and linear algebra. It provides students with the necessary background knowledge required to succeed in first year mathematics courses. PUMP may also be taken by individuals who wish to close any existing gap between high school math and University level math courses or anyone who wish to review high school math before attempting University level math or other science courses. Students wishing to add the Psychology program may take PUMP in lieu of the high school math requirement.