Applied Mathematics

Mathematics is the study of shape, quantity, pattern and structure. It serves as a tool for our scientific understanding of the world. Knowledge of mathematics opens gateways to many different professions such as economics, finance, computing, engineering, and the natural sciences. Aside from practical considerations, mathematics can be a highly satisfying intellectual pursuit, with career opportunities in teaching and research.

The department counts many of Canada's leading research mathematicians among its faculty. Our mathematics programs are flexible, allowing students to select courses based on specialization and interest. Contents range from calculus and linear algebra in the non-specialist programs to more advanced topics such as real and complex analysis, ordinary and partial differential equations, differential geometry, topology, commutative algebra, graph theory, mathematical logic, number theory, and functional analysis.

The department offers eight specialist programs in addition to the major and minor programs.

In the Mathematics, Applied Mathematics, Mathematics and Physics, and Mathematics and Philosophy specialist programs, students acquire an in-depth knowledge and expertise in mathematical reasoning and the language of mathematics, with its emphasis on rigor and precision. These programs are designed for students wishing to pursue graduate studies; most of the graduates of these programs continue on to graduate school with some of them gaining admission to the world's best graduate schools.

The Mathematical Applications in Economics and Finance specialist program is designed to prepare students for direct entry into the world of finance. It can also serve as a gateway to an MBA or a Master of Finance degree, possibly followed by an eventual doctorate.

The Mathematics and its Applications specialist programs offer three areas of concentration: teaching, physical science, and probability/statistics. These specialist programs are designed as `enhanced double majors.' The required courses for these concentrations are almost identical for the first two years, but they diverge in the upper years. Students in these programs can also continue on to graduate studies.

The Major and Minor programs are intended for students who want to combine mathematical skills with work in other subjects. These programs require less coursework than the specialist programs, but still require the completion of some upper year mathematics courses. 

Students interested in becoming K-12 teachers should consider applying to the combined degree program --- a six-year program that leads to an Honours Bachelor of Science (HBSc) from the University of Toronto and a Master of Teaching (MT) from the Ontario Institute for Studies in Education (OISE).  The HBSc part of this program involves completing a Math Major, a Minor in Education and Society (offered by Victoria College) and a Minor in an area that would lead to a second "teachable" subject.  Please see the Victoria College website for more information.

Arts & Science Internship Program

As of Fall 2021, the new Arts & Science Internship Program (ASIP) stream is available to students who are entering Year 2 or Year 3 of study and enrolled in the Mathematics Specialist, Applied Mathematics Specialist, Mathematics & Physics Specialist, Mathem1atics & Philosophy Specialist, Mathematical Applications in Economics & Finance Specialist, Mathematics & its Applications Specialist, and Mathematics Major.

Enrolment is limited and requires a supplemental application. Students enrolled in the ASIP stream will be required to complete mandatory Professional Development programming plus a minimum of 12 and maximum of 20 months (Year-2 entry) or a minimum of 12 and maximum of 16 months (Year-3 entry) of paid, full-time work experience. The time to degree completion for students enrolled in ASIP will normally be 5 years. There is an additional cost to participate in the ASIP stream.

Students will typically be admitted to the ASIP stream for the Fall term of Year 2 of study, however, in exceptional circumstances students, including transfer students, who enrolled in an eligible program in the Summer after Year 2 can be admitted to the ASIP stream for the Fall of Year 3. Acceptance into an ASIP stream in Year 3 is dependent on space and requires approval of the student's academic unit and the Faculty of Arts & Science Experiential Learning & Outreach Support (ELOS) Office. Please refer to the ASIP eligibility page for further details.

Further details about ASIP, including eligibility requirements and application procedures, can be found here. Students may also visit the ASIP webpage or contact the ELOS office at [email protected].

Introductory Courses

The Department of Mathematics offers introductory courses for incoming students to foster the development of mathematics skills.

PUMP Level 1 and PUMP Level 2 (Preparing for University Mathematics Program)

Both programs are non-credit courses that equip students with the necessary background knowledge required to succeed in first year mathematics courses. The content for the courses may be viewed at http://www.math.toronto.edu/cms/undergraduate-program/current-students-ug/pump-courses-2/.

PUMP Level 1 provides a quick math review during the months of July and August, for students who would like to take six weeks prior to the start of the first semester to practice pre-calculus math skills. During other terms, it is scheduled as a longer course, for students who have not taken the appropriate high school mathematics prerequisites for university calculus and linear algebra. This course is recommended for any student who wish to close any existing gap between high school math and University level math courses or anyone who wishes to review high school math before attempting University level math or other science courses.

PUMP Level 2 is an Introduction to Proofs course. The curriculum provides background knowledge that is a preparation for MAT137Y1, MAT157Y1, MAT240H1, MAT247H1, MAT237Y1, and other proof-oriented advanced courses. The course covers the reading and comprehension of mathematical statements, analyzing definitions and properties, formulation of arguments, and strategies for proofs. This course is recommended for any student who wish to add to their knowledge by joining the group of students who will commence their preparation for the more challenging concepts in the advance analytical programs, during the months of July and August.

Visit https://www.math.toronto.edu/cms/undergraduate-program/potential-students-ug/ for up-to-date information on the availability of PUMP Level 1 and PUMP Level 2.

If you have questions about the content of these courses, e-mail [email protected].

Contact Information

First Year Inquiries: [email protected]
Program Inquiries: [email protected]

Bahen Centre, Room 6291

Departmental Office: Bahen Centre, Room 6290 (416-978-3323)

Websites: https://www.math.toronto.edu/cms/potential-students-ug/

https://www.math.toronto.edu/cms/current-students-ug/

Use the University of Toronto International Application if you:

• currently reside outside of Canada, AND 
• are not currently studying, and have not previously studied in Canada, AND
• are not applying to any other Ontario university

Prospective international applicants who wish to apply to other Ontario universities in addition to the University of Toronto should use the OUAC 105 Application (see below).

If you have already applied with the OUAC 105 Application, you do not need to apply to the University of Toronto with the International Application. (If you submit both applications, your second application will be cancelled with no possibility of a refund.)

Note that you will need to pay a non-refundable fee of $180.

University of Toronto has contracted with the Ontario Universities’ Application Centre (OUAC) to provide application processing services. When you begin the application process, you will be transferred to the OUAC website where you will complete and submit your application. You will be required to create an OUAC Account (if you do not already have one). You may have only one OUAC Account. Direct any application process questions to the OUAC.