2006-2007 Faculty of Arts and Science Calendar

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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 21) 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. Details can be found at www.math.utoronto.ca/pump

Associate Chair for Undergraduate Studies: Professor J.W. Lorimer, Sidney Smith Hall, 40 George Street, Room 6290 (416-978-5164)

Student Counselling: Bahen Building, Room 6290

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 (Science program)

Consult Professor J.W. Lorimer, Associate Chair, Department of Mathematics

Specialist program:

(13 full courses or their equivalent, including at least one 400-series course)

First Year:
MAT157Y1, MAT240H1, MAT247H1, CSC148H1/CSC150H1

Second Year:
MAT257Y1, MAT267H1; CSC260H1; STA257H1

Third and Fourth Years:
1. APM351Y1; MAT327H1, MAT354H1, MAT347Y1, MAT357H1, MAT363H1; STA347H1
2. At least 2 full courses chosen from: MAT344H1, MAT454H1, MAT457Y1, MAT464H1, MAT477H1; STA302H1, STA352Y1, STA438H1, STA457H1; CSC350H1, CSC351H1, CSC446H1, CSC456H1
3. Three courses from: APM421H1, APM426H1, APM461H1, APM462H1,APM466H1

NOTE: The Department recommends that PHY140Y1 be taken in First Year. If you do not have a year course in programming from high school, the Department strongly recommends that you take CSC107H1/CSC108H1 before attempting CSC148H1/CSC150H1.

Mathematics (Science program)

Consult Professor J.W. Lorimer, Associate Chair, Department of Mathematics

Specialist program:

(11.5 full courses or their equivalent, including at least one 400-series course)

First Year:
MAT157Y1, MAT240H1, MAT247H1

Second Year:
MAT257Y1, MAT267H1

Third and Fourth Years:
1. MAT327H1, MAT347Y1, MAT354H1, MAT357H1, MAT477H1
2. One of: APM351Y1, MAT457Y1
3. Three of: APM461H1, MAT309H1, MAT363H1 MAT415H1/MAT417H1, MAT454H1
4. At least 2.5 APM/MAT including at least 1.5 at the 400-level (these may include options above not already chosen)

NOTE: The Department recommends that PHY140Y1 be taken in First Year, that CSC148H1/CSC150H1/CSC260H1 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 CSC107H1/CSC108H1 before attempting CSC148H1/CSC150H1.

Major program:

(7 full courses or their equivalent)

First Year:
MAT135Y1/MAT136Y1/MAT137Y1,MAT223H1

Second Year:
MAT224H1/MAT247H1, MAT235Y1/MAT237Y1, MAT246H1/(CSC236H1/CSC240H1, PHL245H1), MAT244H1

NOTE:
MAT224H1 may be taken in first year

Higher Years:
1. MAT301H1, MAT334H1, PHL245H1
2. One half course or equivalent at the 200+level from: ACT, APM, MAT, STA
3. MAT401H1/MAT402H1; one half course at 300+level from: at least APM, MAT, HPS390H1, HPS391H1, PSL431H1, PSL432H1, 433H1; PHL346H1, PHL349H1

Minor program:

(4 full courses or their equivalent)

1. MAT135Y1/MAT136Y1/MAT137Y1, MAT235Y1/MAT237Y1, MAT223H1,MAT224H1/MAT244H1/APM236H1
2. One 300+-level full course or combination from: APM, MAT, including HPS390H1, HPS391H1, PSL 431H1, PSL432H1, 433H1

Note: in all programs, higher kevels courses within the same topic are acceptable substitutions.

Mathematics and Its Applications (Science program)

Specialist program:

(10.5 - 11.5 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:
CSC 107H1/CSC108H1, MAT135Y1/MAT136Y1/MAT137Y1/MAT157Y1 (MAT137Y1 strongly recommended), MAT223H1/MAT240H1

Second Year:
MAT224H1/MAT247H1, MAT235Y1/MAT237Y1/MAT257Y1 (MAT237Y1 strongly recommended), MAT246H1(waived for students taking MAT257Y1), MAT244H1/MAT267H1, STA257H1

Higher Years:
MAT301H1, MAT334H1

Areas of Concentration

Teaching Concentration:

1. MAT329Y1
2. Two of :MAT309H1, MAT315H1, MAT335H1, MAT337H1, MAT344H1, MAT363H1, MAT402H1
3. Two half courses at 300+ level from APM, STA

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. CSC207H1,CSC165H1, CSC258H1, CSC209H1;MAT344H1
2. Three of :APM461H1; CSC350H1, CSC351H1, CSC354H1, CSC363H1, 378H1, CSC438H1, CSC446H1, CSC456H1, CSC465H1, CSC487H1
3. Two CSC half courses at 300+level.

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.)

Physical Sciences Concentration:

1. PHY140Y1 (in first year); APM346H1/APM351Y1; AST221H1, AST222H1
2. Two of PHY251H1, PHY252H1, PHY255H1, PHY256H1
3. Two of APM421H1, APM436H1, APM441H1, APM446H1; AST320H1, AST325H1; MAT337H1; PHY307H1, PHY309H1, PHY315H1, PHY351H1, PHY352H1, PHY353H1, PHY355H1, PHY357H1, PHY358H1

Probability/Statistics Concentration:

1. CSC260H1/CSC207H1, CSC350H1; APM346H1/APM351Y1/APM462H1; MAT337H1; STA302H1, STA347H1, STA352Y1
2. Two of: STA422H1, STA437H1, STA438H1, STA442H1, STA447H1, STA457H1

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.

Mathematical Applications in Economics and Finance (Science Program)

Consult Professor J.W. Lorimer, Associate Chair, Department of Mathematics

Specialist program:

(11.5-12 full courses or their equivalent including one full course at the 400-level)

First Year:
ECO100Y1, MAT137Y1, MAT223H1, MAT224H1

Second Year:
ECO206Y1, MAT237Y1, 244H1, STA257H1, STA261H1

Higher Years:
APM346H1, APM462H1, APM466H1, ECO358H1, MAT337H1, STA302H1/ECO327Y1, STA347H1, STA457H1
Two of: ECO359H1, MAT315H1, MAT334H1

Mathematics and Computer Science: see Computer Science

Mathematics and Economics: see Economics

Mathematics and Philosophy (Science program)

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:
MAT157Y1, MAT240H1, MAT247H1; PHL245H1

Higher Years:
1. PHL245H1 (if not taken in First Year)
2. MAT257Y1, MAT327H1, MAT347Y1, MAT354H1/MAT357H1
3. PHL346H1/PHL349H1, MAT309H1/PHL344H1/PHL345H1
4. Four of: PHL246H1, PHL346H1, PHL347H1, PHL349H1, PHL480H1
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