2001-2002 Calendar: Mathematics

MAT Mathematics

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, the physical sciences and finance. 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.) If you are interested in mathematics and are contemplating a double Major in Mathematics and in another discipline (let us take Computer Science, as an example), you should consider the advantages of fulfilling the requirements for a Specialist degree in Mathematics and its Applications with a computer science concentration. In this way, you can also get a Major in Computer Science; the difference in course requirements with a double major is that, among the courses you can choose for a Computer Science Major, you will be required to take some of a more mathematical nature. You might even consider choosing your options to fulfil the requirements for a double Specialist degree, in both Mathematics and its Applications and in the other discipline.

The Professional Experience Year program ("PEY": see also Page 22) is available to eligible, full-time Specialist students after their second year of study. The PEY program is an optional 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.

Associate Chair for Undergraduate Studies:

Professor E. Bierstone, Sidney Smith Hall, 100 St. George Street, Room 4072 (416-978-5164)

Student Counselling:

Sidney Smith Hall, Room 4072

Mathematics Aid Centres:

Sidney Smith Hall, Room 1071; University College, Room UC48

Departmental Office:

Sidney Smith Hall, Room 4072 (416-978-3323)

MATHEMATICS PROGRAMS

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

APPLIED MATHEMATICS (Hon.B.Sc.)
Consult Professor E. Bierstone, Associate Chair, Department of Mathematics

Specialist program:
(12 full courses or their equivalent, including at least one 400-series course)

First Year:
MAT 157Y, 240H

First or Second Year:
CSC 260H
Second Year
: MAT 247H, 257Y, 267H; STA 257H

Third and Fourth Years:

1. APM 351Y; MAT 327H, 354H, 357H, 363H
2. At least 2.5 courses chosen from 400-level APM courses and MAT 301H/347Y, 468H; STA 347H
3. At least 2 courses, including at least one full course equivalent at the 400-level chosen from options above not already selected and
CSC 350H, 351H, 446H, 456H; MAT 344H, 454H, 457Y, 464H, 477H; STA 348H, 352Y, 457H
NOTE: The Department recommends that students acquire a reading knowledge of French.

MATHEMATICS (B.Sc.)
Consult Professor E. Bierstone, Associate Chair, Department of Mathematics

Specialist program (Hon.B.Sc.):
(11.5 full courses or their equivalent, including at least one 400-series course)

First Year:
MAT 157Y, 240H

Second Year:
MAT 247H, 257Y, 267H

Third and Fourth Years:

1. MAT 327H, 347Y, 354H, 357H, 477H
2. One of: APM 351Y, MAT 457Y
3. Three of: APM 461H, MAT 309H, 363H, 365H, 415H/417H, 454H
4. At least 2.5 APM/MAT courses including at least 1.5 at the 400-level (these may include options above not already chosen)
NOTE: The Department recommends that PHY 140Y be taken in First Year, that CSC 148H/260H and STA 257H be taken during the program, and that students acquire a reading knowledge of French.

Major program (B.Sc.):
(7.5 full courses or their equivalent)

First Year:
MAT 135Y/136Y/137Y

Second Year:
MAT 223H/240H, 224H/247H, 235Y/237Y, 246Y/(CSC 238H, PHL 245H), MAT 244H
NOTE: MAT 223H, 224H, 240H may be taken in first year

Higher Years:

1. MAT 301H/302H, 334H
2. One full course combination or equivalent at the 200+level in ACT, APM, CSC, MAT or STA
3. One full course combination or equivalent at the 300-level from Humanities/Social Sciences/Sciences

Minor program (B.Sc.):
(4 full courses or their equivalent)
1. 3 full courses in MAT/APM, or 2.5 full courses in MAT/APM plus.5 from ACT/CSC/STA
2. One 300-level course in MAT/APM or combination
NOTE: MAT 329Y may not be counted towards the requirements of this program

MATHEMATICS AND ITS APPLICATIONS (Hon.B.Sc.)
Consult Professor E. Bierstone, Associate Chair, Department of Mathematics

Specialist program:
(10.5 - 11.5 full courses or their equivalent including one full course at the 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:
CSC 148H/260H; MAT 135Y/136Y/137Y/157Y (MAT 137Y strongly recommended), 223H/240H

Second Year:
MAT 224H/247H, 235Y/237Y/257Y (MAT 237Y strongly recommended),
MAT 246Y/(CSC 238H, PHL 245H) (waived for students taking MAT 257Y), MAT 244H/267H

Second or Third Years:
STA 257H

Third Year:
MAT 301H/302H, 334H

AREAS OF CONCENTRATION:
Teaching Concentration:
1. MAT 301H, 302H, 315H, 329Y, 344H
2. Three of APM 261H, 346H; MAT 309H, 335H, 337H, 363H, 365H
3. Two 300/400-level APM or STA half-courses
This program addresses an increasing need for highly qualified mathematics teachers. Students planning to apply for admission to a B.Ed. program are encouraged also to get practical teaching experience at a level of their interests. Students successfully completing the Teaching Concentration and having practical experience will be highly competitive for admission to initial teaching programs at OISE/UT.
Computer Science Concentration:
1. CSC 209H/228H/260H, 258H, 270H; MAT 344H
2. Three of APM 461H; CSC 350H, 351H, 354H, 364H, 378H, 438H, 446H, 456H, 465H, 478H, 487H
3. Two 300/400-level CSC half-courses
NOTE: 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; please see the Computer Science program description.)
Finance Concentration:
APM 346H, 466H; CSC 350H, 351H, 446H; MAT 337H; STA 347H, 457H
NOTE: The stated prerequisites for STA 457H, though recommended, can be waived for students in the Finance concentration.
Physical Sciences Concentration:
1. PHY 140Y (in first year); APM 346H/351Y; AST 221H, 222H
2. Two of PHY 251H, 252H, 255H, 256H
3. Two of APM 421H, 436H, 441H, 446H; AST 320H, 325H; MAT 337H; PHY 307H, 309H, 315H, 351H, 352H, 353H, 355H, 357H, 358H
Probability/Statistics Concentration:
1. CSC 350H; APM 346H/351Y/361H; MAT 337H; STA 302H, 347H, 352Y
2. Two of STA 422H, 437H, 438H, 442H, 447H, 457H
Design-Your-Own Concentration:
Nine half-courses of which at least six must be at the 300+level, to be approved by the Department no later than the beginning of your third year.

MATHEMATICS AND COMPUTER SCIENCE - See COMPUTER SCIENCE

MATHEMATICS AND ECONOMICS - See ECONOMICS

MATHEMATICS AND PHILOSOPHY (Hon.B.Sc.)
Consult the Undergraduate Coordinators of the Departments of Mathematics and Philosophy.

Specialist program:
(13 full courses or their equivalent including one full course at the 400-level)

First Year:
MAT 157Y, 240H; PHL245H

Higher Years:

1. PHL245H (if not taken in First Year)
2. MAT 247H, 257Y, 327H, 347Y, 354H/357H
3. CSC 364H, 438H/MAT 309H/PHL 344H
4. Four of: PHL 246H, 346H, 347H, 349H, 480H
5. One course in epistemology and/or philosophy of science
6. 3.5 additional PHL courses, preferably including two in the history of philosophy and one in ethics or social/political philosophy

MATHEMATICS AND PHYSICS (Hon.B.Sc.)
Consult Professor E. Bierstone, Associate Chair, Department of Mathematics, and the Associate Chair, Department of Physics.

Specialist program:
(13.5 full courses or their equivalent, including at least one 400-series course)

First Year:
MAT 157Y, 240H; PHY 140Y

Second Year:
MAT 247H, 257Y, 267H; PHY 225H, 251H, 252H, 255H, 256H

Third Year:
APM 351Y, MAT 327H, 354H, 357H, 363H; PHY 351H, 352H, 355H

Fourth Year:
APM 421H, 426H; PHY 457H; APM 446H/PHY 459H/460H

MATHEMATICS AND STATISTICS - See STATISTICS