Introduction

Mathematics teaches you to think, analytically and creatively. It is a foundation for advanced careers in a knowledge-based economy. Students who develop strong backgrounds in mathematics often have distinct advantages in other fields such as physics, computer science, economics, and finance.

The past century has been remarkable for discovery in mathematics. From space and number to stability and chaos, mathematical ideas evolve in the domain of pure thought. But the relationship between abstract thought and the real world is itself a source of mathematical inspiration. Problems in computer science, economics and physics have opened new fields of mathematical inquiry. And discoveries at the most abstract level lead to breakthroughs in applied areas, sometimes long afterwards.

The University of Toronto has the top mathematics department in Canada, and hosts the nearby Fields Institute (an international centre for research in mathematics). The Department offers students excellent opportunities to study the subject and glimpse current research frontiers. The Department offers three mathematical Specialist programs - Mathematics, Applied Mathematics, Mathematics and its Applications - as well as Major and Minor programs and several joint Specialist programs with other disciplines (for example, with Computer Science, Economics, Philosophy, Physics and Statistics).

The Specialist program in Mathematics is for students who want a deep knowledge of the subject. This program has been the main training-ground for Canadian mathematicians. A large proportion of our Mathematics Specialist graduates gain admission to the world’s best graduate schools.
The Specialist program in Applied Mathematics is for students interested in the fundamental ideas in areas of mathematics that are directed towards applications. The mathematics course requirements in the first two years are the same as in the Mathematics Specialist program; a strong student can take the courses needed to get a degree in both Specialist programs.

These programs are challenging, but small classes with excellent professors and highly-motivated students provide a stimulating and friendly learning environment.

The Specialist program in Mathematics and its Applications is recommended to students with strong interests in mathematics and with career goals in areas such as teaching, computer science, and the physical sciences. The program is flexible; there is a core of courses in mathematics and related disciplines, but you can choose among several areas of concentration. The mathematics courses required for the program are essentially the same as those required for a Major in Mathematics. (They are less intense than the courses required for the Specialist programs above.) In many cases it is possible to complete a Specialist program in Mathematics and its Applications with a given concentration along with a major in the other subject without taking many extra courses. You might even consider choosing your options to fulfill the requirements for a double Specialist degree, in both Mathematics and its Applications and in the other discipline.

The Specialist program in Mathematical Applications in Economics and Finance is recommended to students with career aspirations in any form of the financial sector. Furthermore, the program is an excellent preparation for an MBA and an MMF.

The Professional Experience Year program (“PEY”: see index) is available to eligible, full-time Specialist students after their second year of study. The PEY program is an optional 12-16 month work term providing industrial experience; its length often allows students to have the rewarding experience of initiating and completing a major project.

The Department operates a non-credit summer course, PUMP, limited to students admitted to the University. It is designed for students who require additional pre-university mathematics background. Details can be found at www.math.toronto.edu/cms/pump.

ssociate Chair for Undergraduate Studies: Bahen Building, 40 George Street, room 6236

Student Counselling: Bahen Building, room 6190

Mathematics Aid Centre: Sidney Smith Hall, room 1071

Departmental Office: Bahen Building, room 6290 (416-978-3323)

Mathematics Programs

Enrolment in the Mathematics programs requires completion of four courses; no minimum GPA is required.

Students with a good grade in MAT137Y1 (75%) or MAT135Y1 (85%) may apply to the Mathematics Undergraduate Office for permission to enter a Mathematics program requiring MAT157Y1.

Mathematics (Science program)

Consult Associate Chair for Undergraduate Studies, Department of Mathematics

Specialist program:

(12.0 full courses or their equivalent, including at least 1.5 full courses at the 400-level)

The Specialist Program in Mathematics is directed toward students who hope to pursue mathematical research as a career.

First Year:
MAT157Y1, MAT240H1, MAT247H1
Second Year:
MAT257Y1, MAT267H1
Third and Fourth Years:
1. MAT327H1, MAT347Y1, MAT354H1, MAT357H1
2. One of: APM351Y1; MAT457Y1/(MAT457H1, MAT458H1)
3. Three of: APM461H1; MAT309H1, MAT363H1, ANY 400-level APM/MAT
4. 2.5 APM/MAT including at least 1.5 at the 400 level (these may include options above not already chosen)
5. MAT477Y1

NOTE:
1. The Department recommends that PHY151H1 and PHY152H1 be taken in the First Year, and that CSC150H1 and STA257H1 be taken during the program. If you do not have a year course in programming from high school, the Department strongly recommends that you take CSC108H1 and then CSC148H1 instead of CSC150H1.
2. Students are required, as part of their degree, to take a course with a significant emphasis on ethics and social responsibility such as: PHL275H1/PHL265H1/PHL268H1/PHL271H1/PHL273H1 or similar courses in other departments.
3. Students planning to take specific fourth year courses should ensure that they have the necessary third year prerequisites.

Applied Mathematics (Science program)

Consult the Associate Chair for Undergraduate Studies, Department of Mathematics

Specialist program:

(13.5 full courses or their equivalent, including at least one full course at the 400-level)

The Specialist Program in Applied Mathematics is directed toward students who hope to pursue applied mathematical research as a career.

First Year:
MAT157Y1, MAT240H1, MAT247H1; (CSC108H1/CSC148H1)/CSC150H1
Second Year:
MAT257Y1, MAT267H1; MAT267H1; CSC260H1; (STA257H1, STA261H1)
Third and Fourth Years:
1. APM351Y1; MAT327H1, MAT347Y1, MAT354H1, MAT357H1,MAT363H1; STA347H1
2. At least 1.5 full courses chosen from: MAT332H1, MAT344H1, MAT454H1, MAT457Y1/(MAT457H1, MAT458H1), MAT464H1; STA302H1, STA457H1; CSC350H1, CSC351H1, CSC446H1, CSC456H1
3. Two courses from: APM421H1, APM426H1, APM436H1, APM441H1, APM446H1, APM461H1, APM462H1, APM466H1
4. MAT477Y1

NOTE:
1. The Department recommends that PHY151H1 and PHY152H1 be taken in the First Year, and STA257H1 be taken during the program. If you do not have a year course in programming from high school, the Department strongly recommends that you take (CSC108H1/CSC148H1) instead of CSC150H1.
2. Students are required, as part of their degree, to take a course with a significant emphasis on ethics and social responsibility such as: PHL275H1/PHL265H1/PHL268H1/PHL271H1/PHL273H1 or similar courses in other departments.
3. Students planning to take specific fourth year courses should ensure that they have the necessary third year prerequisites.

Mathematics and Physics(Science program)

Consult the Associate Chairs, Undergraduate Studies, Department of Mathematics and Department of Physics.

Specialist program:

(14-14.5 full courses or their equivalent, including at least one full course at the 400-level)

First Year:
MAT157Y1, MAT240H1, MAT247H1; PHY151H1, PHY152H1
Second Year:
MAT257Y1, MAT267H1; PHY224H1, PHY250H1, PHY252H1, PHY254H1, PHY256H1
Note: PHY252H1 and PHY324H1 may be taken in the 2nd or 3rd year.
Third Year:
1. APM351Y1; MAT334H1/MAT354H1, MAT357H1
2. One of: MAT327H1, MAT347Y1, MAT363H1
3. PHY324H1, PHY350H1, PHY354H1, PHY356H1
Fourth Year:
1. Two of: APM421H1, APM426H1, APM436H1; MAT446H1
2. Two of: PHY450H1, PHY452H1, PHY454H1, PHY456H1, PHY460H1
3. One of: MAT477Y1; PHY424H1, PHY478H1, PHY479Y1

NOTE:
1. Students who are intending to apply to graduate schools in mathematics would be well-advised to take MAT347Y1
2. Students are required, as part of their degree, to take a course with a significant emphasis on ethics and social responsibility such as: PHL275H1/PHL265H1/PHL268H1/PHL271H1/PHL273H1 or similar courses in other departments.
3. Students planning to take specific fourth year courses should ensure that they have the necessary third year prerequisites.

Mathematics and Its Applications (Science program)

Consult the Associate Chairs, Undergraduate Studies, Department of Mathematics and other Departments as required by the program concentration

Specialist program:

(11.5-12.5 full courses or their equivalent, including one full course at 400-level)

The program requirements are the core courses below, together with the courses in one of the following areas of concentration. If you get a specialist degree in Mathematics and its Applications, your transcript and degree will indicate also your area of concentration. Please be careful to check course prerequisites in choosing your program.

Core Courses:

First Year:
CSC108H1/CSC150H1; MAT137Y1/MAT157Y1, MAT223H1/MAT240H1
Note:
CSC150H1 is required for the Computer Science concentration. If you do not have a year course in programming from high school, the Department strongly recommends that you take CSC108H1 and CSC148H1 in place of CSC150H1.
Second Year:
MAT224H1/MAT247H1, MAT235Y1/MAT237Y1/MAT257Y1, MAT246H1(waived for students taking MAT157Y1), MAT244H1/MAT267H1;STA257H1
Note:
1. MAT237Y1/MAT257Y1 is a direct or indirect prerequisite for many courses in each of the areas of concentration except the Teaching Concentration. Students are advised to take MAT237Y1/MAT257Y1 unless they have planned their program and course selection carefully and are certain that they will not need it.
Higher Years:
MAT301H1, MAT334H1
NOTE:
1. Students are required, as part of their degree, to take a course with a significant emphasis on ethics and social responsibility such as: PHL275H1/PHL265H1/PHL268H1/PHL271H1/PHL273H1 or similar courses in other departments.
2. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.

Areas of Concentration

Teaching Concentration:

It may be to students’ advantage to keep in mind that OISE requires students to have a second teachable subject.
1. MAT329Y1, HPS/MAT390H1, HPS/MAT391H1
2. Two of:MAT332H1/MAT344H1, MAT335H1, MAT337H1, MAT363H1
3. Two of: MAT309H1, MAT315H1; STA302H1/STA347H1
4. MAT401H1/MAT402H1 and one half course at the 400-level from MAT475H1, APM, STA
Computer Science Concentration:
1. CSC148H1/CSC150H1, CSC165H1, CSC236H1/ CSC240H1, CSC209H1
2. CSC207H1, CSC236H1/CSC240H1, CSC209H1
3. MAT332H1/MAT344H1 and three of MAT309H1; CSC320H1, CSC350H1, CSC351H1, CSC373H1
4. Two of: APM461H1; CSC446H1, CSC456H1, CSC465H1, CSC487H1
NOTE:
1. In order to take the Computer Science concentration, you will be required to register also for a Computer Science Major. (The latter is a restricted enrolment program and has certain admission requirements and much higher fees; please see the Computer Science program description).

Physical Sciences Concentration:

1. PHY151H1, PHY152H1; AST221H1
2. Three of: AST222H1; PHY250H1, PHY252H1, PHY254H1, PHY256H1
3. APM346H1/APM351Y1
4. Three of: AST320H1, AST325H1; MAT337H1, MAT363H1; PHY350H1, PHY354H1, PHY356H1, PHY357H1, PHY358H1
5. Two of: APM421H1, APM426H1, APM441H1, APM446H1; PHY407H1, PHY408H1, PHY456H1

Probability/Statistics Concentration:

1. APM346H1/APM351Y1/APM462H1; MAT337H1; STA261H1, STA302H1, STA347H1, STA352Y1
2. One additional full credit at 300+level from APM/MAT/STA
3. Two of: STA437H1, STA438H1, STA442H1, STA447H1, STA457H1

Design-Your-Own Concentration:

Eleven half-courses of which at least six must be at the 300+ level including at least 2 at the 400 level. Choice of courses in program must be approved by the Department no later than the beginning of the third year or it will not be allowed. It is understood that the remaining 5 half-courses may be in the departments pertaining to the area of concentration.

Mathematical Applications in Economics and Finance (Science Program)

Consult the Associate Chair for Undergraduate Studies, Department of Mathematics

Specialist program:

(12-13 full courses or their equivalent including at least 1.5 full courses at the 400-level)

First Year:
ECO100Y1 (70% or more); MAT137Y1 (55%)/MAT157Y1 (55%), MAT223H1, MAT224H1
Second Year:
ECO206Y1; MAT237Y1, MAT244H1, MAT246H1 (waived for students takING157Y1); STA257H1, STA261H1
PHL295H1 (Business Ethics): This course may be taken in second, third, or fourth year.
Third Year:
1. APM346H1; ECO358H1; ECO359H1; MAT337H1; STA302H1/ECO327Y1/(ECO375H1, ECO376H1), STA347H1
2. One of: MAT332H1/MAT344H1, MAT334H1, MAT475H1
Fourth Year:
APM462H1, APM466H1; STA457H1
NOTE:
1. Students who do not include PHL295H1 (Business Ethics) as part of their degree are expected to take another Arts and Science course with a significant emphasis on ethics and social responsibility.
2. Students planning to take specific fourth year courses should ensure that they have the necessary third year prerequisites.

Mathematics and Philosophy (Science program)

Consult the Associate Chairs for Undergraduate Studies, Department of Mathematics and Department of Philosophy.

Specialist program:

(12 full courses or their equivalent including one full course at the 400-level)

First Year:
MAT157Y1, MAT240H1, MAT247H1; PHL245H1
Higher Years:
1. MAT257Y1, MAT327H1, MAT347Y1, MAT354H1/ MAT357H1
2. One full course from PHL200Y1/(PHL205H1, PHL206H1)/ PHL210Y1
3. PHL232H1, HPS250H1/ PHL246H5, PHL265H1/ PHL275H1
4. MAT309H1; PHL345H1
5. Two of: PHL331H1, PHL342H1, PHL351H1, PHL355H1/PHL356H1
6. Two of : MAT409H1; PHL404H1, PHL411H1, PHL451H1, PHL480H1, PHL481H1, PHL482H1
7. One additional full course credit in PHL or MAT courses to a total of 12 full courses.

NOTE:
1. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
2. If a course number ends in H5, the course is offered only at the University of Toronto Missisauga

Mathematics and Computer Science: see Computer Science

Mathematics and Economics: see Economics

Mathematics and Statistics: see Statistics

Mathematics (Science program)

Major program:

(7.5 full courses or their equivalent including at least 2.5 full courses at the 300+ level and at least .5 courses at the 400 level).

First Year:
MAT135Y1/MAT137Y1/MAT157Y1, MAT223H1/MAT240H1
Second Year:
MAT224H1/ MAT247H1, MAT235Y1/ MAT237Y1, MAT244H1, MAT246H1; PHL275H1, or PHL265H1/PHL268H1/PHL271/ PHL273H1
NOTE:
1. MAT224H1 may be taken in first year
2. PHL275H1, or PHL265H1/PHL268H1/PHL271H1/ PHL273H1 may be taken in any year.
Higher Years:
1. MAT301H1, MAT309H1/MAT315H1, MAT334H1
2. One half course at the 200 level from: ACT240H1; APM236H1; MAT309H1/MAT315H1/MAT335H1/ MAT337H1; STA247H1/STA250H1/STA257H1
3. One additional half course at the 300+level from: APM346H1, APM462H1; MAT309H1, MAT315H1, MAT332H1/MAT344H1, MAT335H1, MAT337H1, MAT475H1; HPS390H1, HPS391H1; PSL432H1
4. MAT401H1/MAT402H1
NOTE:
1. In the major program, higher level courses within the same topic are acceptable substitutions. With a judicious choice of courses, usually including introductory computer science, students can fulfil the requirements for a double major in mathematics and one of several other disciplines.
2. Students planning to take specific third and fourth year courses should ensure that they have the necessary first, second and third year prerequisites.

Minor program:

(4 full courses or their equivalent)

1. MAT135Y1/MAT137Y1
2. MAT223H1, MAT235Y1/MAT237Y1, MAT224H1/MAT244H1/APM236H1Note: MAT223H1 can be taken in first year
3. one 300+level full course or combination from: any APM; MAT; HPS390H1, HPS391H1; PSL432H1
NOTE:
1. In the minor program, higher level courses within the same topic are acceptable substitutions.
2. Students planning to take specific third and fourth year courses should ensure that they have the necessary first, second and third year prerequisites.