Mathematics


Faculty List

Professor and Chair of the Department 
R. Jerrard, MSc, PhD, FRSC

Professor and Associate Chair (Research) 
D. Panchenko, BS, MS, PhD

Professor and Associate Chair (Graduate)
H. Kim, B Sc, MSc, PhD

Professor and Associate Chair (Undergraduate) 
S. Yoshinobu, BA, MA, PhD

University Professors
J. Friedlander, MA, PhD, FRSC (UTSC) 
I.M. Sigal, BA, PhD, FRSC

Professors
D. Bar-Natan, BSc, PhD
E. Bierstone, MA, PhD, FRSC 
I. Binder, BSc, MSc, PhD (UTM) 
A. Braverman, BSc, PhD 
J. Bremer, BSc, BSc, P D (UTSC)
G. Elliott, BSc, PhD, FRSC 
M. Goldstein, BSc, PhD (UTSC) 
M. Gualtieri, BSc, PhD 
F. Herzig, BA, PhD 
V. Ivrii, MA, PhD, Dr Math, FRSC 
L. Jeffrey, AB, PhD, FRSC (UTSC) 
J. Kamnitzer, BSc, PhD 
V. Kapovitch, BSc, PhD 
Y. Karshon, BSc, PhD (UTM) 
K. Khanin, MSc, PhD (UTM) 
B. Khesin, MSc, PhD 
A. Khovanskii, MSc, PhD 
H. Kim, BSc, PhD 
S. Kudla, BA, MA, PhD, FRSC
R. McCann, BSc, PhD, FRSC
E. Meinrenken, BSc, PhD, FRSC 
K. Murty, BSc, PhD, FRSC 
A. Nabutovsky, MSc, PhD 
A. Nachman, BSc, PhD 
D. Panchenko, BSc, MSc, PhD 
M. Pugh, BSc, PhD
J. Quastel, MSc, PhD, FRSC
K. Rafi, BSc, PhD

J. Repka, BSc, PhD (U)
R. Rotman BA, PhD
L. Seco, BA, PhD (UTM) 
C. Sulem, MSc, Dr D’Etat, FRSC 
S. Todorcevic, BSc, PhD, FRSC
J. Tsimerman, BSc, PhD 
I. Uriarte-Tuero, BSc, MSc, MPhil, PhD
B. Virag, BA, PhD (UTSC) 
M. Yampolsky, BSc, PhD (UTM) 

Associate Professors
S. Aretakis, MA, PhD (UTSC)
J. de Simoi, BSc, MSc, PhD (UTM)
R. Haslhofer, BSc, MSc, PhD (UTSC)
S. Kopparty, BSc, MSc, PhD
F. Pusateri, MS, PhD
B. Rossman, BA, MA, PhD
S. Saraf, BSc, MSc, PhD
A. Shankar (UTM), BSc, PhD
G. Tiozzo, BA, MA, PhD (UTSC)
K. Zhang (UTM), BSc, PhD

Associate Professor, Teaching Stream 
B. Galvao-Sousa, BSc, MSc, PhD 

Assistant Professors 
D. Dauvergne, PhD (UTM)
J. Desjardins, BSc, MSc, MSc, PhD (UTM, CLTA)
M. Groechenig, BSc, DPhil (UTM)
A. Kupers, BSc, BSc, MSc, PhD (UTSC)
B. Landon, BSc, MSc, PhD
J. Lefebvre, BSc, PhD
Y. Liokumovich, BSc, MSc, PhD (UTM)
D. Litt, BA, PhD
S. Olano, BSc, MSc, PhD (CLTA)
W. Pan, BS, PhD
V. Papyan, PhD
K. Serkh, PhD
Y. Shlapentokh-Rothman, PhD (UTM)
A. Stinchombe, BMath, PhD
S. Unger, PhD (UTM)
I. Varma, BSc, MSc, PhD
W. Yu, PhD (UTSC)

Assistant Professors, Teaching Stream 
C. Blois, BSc, MSc, PhD 
X. Cui, BSc, MSc, PhD (CLTA)
S. Homayouni, BSc, PhD 
N. Jung, BA, MSc, PhD 
C. Karimian Pour, PhD
J. Kawach, BSc, MSc, PhD
J. Korman, PhD
S. Mayes-Tang, Bc, MS, PhD
F. Parsch, BSc, MSc, PhD
L. Shorser, BSc, MSc, PhD 
J. Siefken, HBS, MS, PhD
S. Uppal, BSc, MSc
A. Zaman, BSc, MSc, PhD

Lecturers 
E.A.P. LeBlanc, MA, PhD 
J. Tate, BSc, BEd

Professors Emeriti 
M.A. Akcoglu, MSc, PhD, FRSC
J.G. Arthur, MA, PhD, FRSC, FRS
E.J. Barbeau, MA PhD (U) 
J. Bland, MSc, PhD 
T. Bloom, MA, PhD, FRSC 
M. D. Choi, MA, P D, FRSC 
H.C. Davis, MA, PhD (N) 
E.W. Ellers, Dr Rer Nat 
I.R. Graham, BSc, PhD (UTM) 
S. Halperin, MSc, PhD, FRSC 
V. Jurdjevic, MS, PhD 
J.W. Lorimer, MSc, PhD (U) 
E. Mendelsohn, MSc, PhD (UTSC)
P. Milman, Dipl Maths, P D, FRSC
K. Murasugi, MA, DSc, FRSC 
F. Murnaghan, MSc, PhD 
P. Rosenthal, MA, PhD, LLB
P. Selick, BSc, MA, PhD (UTSC) 
D.K. Sen, MSc, Dr s Sc 
F. D. Tall, AB, PhD (UTM)
W.A.R. Weiss, MSc, PhD (UTM) 

Associate Professors Emeriti
N.A. Derzko, BSc, PhD 
J. Scherk, DPhil (UTSC) 
S.M. Tanny, BSc, PhD (UTM) 

Associate Professors Emeriti, Teaching Stream
D. Burbulla, BSc, BEd, MA 
A. Igelfeld, MSc
A. Lam, MSc 

Senior Lecturers Emeriti
P. Kergin, PhD
F. Recio, MSc, PhD

Introduction

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, Mathematics & 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 asip@utoronto.ca.

 

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 https://www.mathematics.utoronto.ca/undergraduate/prospective-students/preparing-university-math-program-pump.

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.mathematics.utoronto.ca/undergraduate/prospective-students/PUMP-courses 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 1styear@math.toronto.edu.

 

Contact Information

First Year Inquiries: 1styear@math.toronto.edu
Program Inquiries: math.undergrad@utoronto.ca

Bahen Centre, Room 6291

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

Website: https://www.mathematics.utoronto.ca/undergraduate

 

Mathematics Programs

Mathematics Specialist (Science Program) - ASSPE1165

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

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory analysis and algebra in their first year of study ( MAT157Y1, MAT240H1, MAT247H1).

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematics Specialist in the Summer after Year 2.

Completion Requirements:

12.5 credits, including at least 3.0 credits at the 400-level

Mathematics Fundamentals

1. Analysis: MAT157Y1, MAT257Y1
2. Algebra: MAT240H1, MAT247H1
3. Advanced Ordinary Differential Equations: MAT267H1

Ethical and Social Responsibility

4. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Higher Studies in Mathematics

5. Topology: MAT327H1
6. Groups, Rings and Fields: MAT347Y1
7. Partial Differential Equations: MAT351Y1
8. Complex and Real Analysis: MAT354H1, MAT357H1
9. Geometry: MAT363H1/​ MAT367H1
10. Advanced Topics: 4.0 credits of further APM/MAT 300+ level courses including at least 2.5 credits of APM/MAT courses at the 400-level

Research Seminar in Mathematics

11. MAT477H1

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credits.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math Website.
  • To enrich your studies in mathematics, students in the Mathematics Specialists are encouraged to take PHY151H1 and PHY152H1 in the first year of study, as well as CSC148H1 and STA257H1 before graduation. If a student has not taken a year-long high school programming course, students are advised to take CSC108H1 prior to CSC148H1.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS286H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate

Applied Mathematics Specialist (Science Program) - ASSPE2053

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

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory analysis, algebra, and computer programming in their first year of study ( MAT157Y1, MAT240H1, MAT247H1, CSC108H1, CSC148H1).

Completion Requirements:

13.0-13.5 credits, including at least 1.5 credits at the 400-level

Applied Mathematics Fundamentals

1. Analysis: MAT157Y1, MAT257Y1
2. Algebra: MAT240H1, MAT247H1
3. Advanced Ordinary Differential Equations: MAT267H1
4. Computer Programming: CSC108H1, CSC148H1
5. Probability and Statistics: STA257H1, STA261H1, STA347H1

Ethical and Social Responsibility

6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Higher Studies in Mathematics

7. Topology: MAT327H1
8. Groups, Rings and Fields: MAT347Y1
9. Partial Differential Equations: MAT351Y1
10. Complex and Real Analysis: MAT354H1, MAT357H1
11. Geometry: MAT363H1/​ MAT367H1
12. Advanced Applied Mathematics: 1.0 credit from APM421H1/​ APM426H1/​ APM441H1/​ APM446H1/​ APM461H1/​ APM462H1/​ APM466H1
13. Related Topics: 1.5 credits from: MAT332H1/​ MAT344H1/​ MAT454H1/​ MAT457H1/​ MAT458H1/​ MAT464H1/​ STA302H1/​ STA457H1/​ CSC336H1/​ CSC436H1/​ CSC446H1/​ CSC456H1

Research Seminar in Mathematics

14. MAT477H1

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • CSC108H1 is waived for students who complete CSC148H1 first. If a student has not taken a year-long course in programming in secondary school, it is strongly recommended that students take CSC108H1 first.
  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credit.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math website.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS268H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate

Mathematics and Physics Specialist (Science Program) - ASSPE0397

The Specialist in Mathematics and Physics is directed toward students who want a strong background in both Mathematics and Physics, with the goal of applying sophisticated Mathematical techniques to the study of Physics, especially theoretical Physics.

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory analysis, algebra, and physics in their first year of study ( MAT157Y1, MAT240H1, MAT247H1, PHY151H1, PHY152H1).

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematics and Physics Specialist in the Summer after Year 2.

Completion Requirements:

14.5 credits, including at least 1.0 credit at the 400-level

Mathematics and Physics Fundamentals

1. Analysis: MAT157Y1, MAT257Y1
2. Algebra: MAT240H1, MAT247H1
3. Advanced Ordinary Differential Equations: MAT267H1
4. Foundations of Physics: PHY151H1, PHY152H1

Ethical and Social Responsibility

5. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Further Studies in Physics

6. Practical Physics: PHY224H1, PHY324H1
7. Electricity and Magnetism: PHY250H1, PHY350H1
8. Thermal Physics: PHY252H1
9. Classical Mechanics: PHY254H1, PHY354H1
10. Quantum Physics: PHY256H1, PHY356H1
11. Topics: 1.0 credit further from PHY450H1/​ PHY452H1/​ PHY454H1/​ PHY456H1/​ PHY460H1

Further Studies in Mathematics

12. Partial Differential Equations: MAT351Y1
13. Advanced Math related to the study of Physics: 1.0 credit from MAT334H1/​ MAT354H1/​ MAT357H1
14. Algebra, Topology, and Differential Geometry: 0.5 credit from MAT327H1/​ MAT347Y1/​ MAT363H1/​ MAT367H1
15. Mathematical Techniques for Physics: 1.0 credit from APM421H1/​ APM426H1/​ APM446H1/​ APM441H1

Research and Exploration in Mathematics and Physics

16. 0.5 credit from MAT477H1/​ PHY424H1/​ PHY478H1/​ PHY479Y1

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • CSC108H1 is waived for students who complete CSC148H1 first. If a student has not taken a year-long course in programming in secondary school, it is strongly recommended that students take CSC108H1 first.
  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credit.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math website.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS268H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate

Mathematics and Philosophy Specialist (Science Program) - ASSPE1361

The Specialist in Mathematics and Philosophy is directed toward students who are fascinated by the confluence of Mathematical and Philosophical precision.

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory analysis and algebra required for the program ( MAT157Y1, MAT240H1, MAT247H1) as well as PHL100Y1/​ PHL101Y1, which is recommended preparation for the program, in their first year of study.

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematics and Philosophy Specialist in the Summer after Year 2.


Completion Requirements:

12.0 credits including at least 1.0 credit at the 400-level

Mathematics and Philosophy Fundamentals

1. Analysis: MAT157Y1, MAT257Y1
2. Algebra: MAT240H1, MAT247H1
3. Philosophy related to science: 0.5 credit from PHL232H1/​ PHL233H1/​ PHL255H1

Further Studies in Philosophy

4. History of Philosophy: 1.0 credit from PHL200Y1/​ PHL205H1/​ PHL206H1/​ PHL210Y1
5. Logic: 1.0 credit from MAT309H1/​​ PHL348H1, PHL345H1
6. Politics and Ethics: PHL265H1/​​ PHL275H1
7. Topics: 2.0 credits further from PHL325H1/​ PHL331H1/​ PHL332H1/​ PHL346H1/​​ PHL354H1/​ PHL347H1/​ PHL349H1/​ PHL355H1/​ PHL451H1/​ PHL480H1

Further Studies in Mathematics

8. Topology: MAT327H1
9. Groups, Rings and Fields: MAT347Y1
10. Complex or Real Analysis: MAT354H1/​ MAT357H1
11. Topics: 2.0 credits further of PHL/APM/MAT courses at the 300+ level

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math website.

Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700

The Specialist in Mathematical Applications in Economics and Finance is directed toward students who need a strong Mathematics grounding for use in the study of Economics and Finance. It is an excellent preparation for an MBA.

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory calculus, algebra, and economics in their first year of study ( MAT157Y1/​ MAT137Y1, MAT223H1, MAT224H1, ECO101H1, ECO102H1).

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematical Applications in Economics and Finance Specialist in the Summer after Year 2.

Completion Requirements:

12.0-12.5 credits

Fundamentals for Mathematical Applications in Economics and Finance

1. Calculus, Analysis, and Proofs: 2.0 – 2.5 credits from MAT157Y1/​ ( MAT137Y1, MAT246H1), MAT237Y1
2. Linear Algebra: MAT223H1, MAT224H1
3. Ordinary Differential Equations: MAT244H1/​ MAT267H1
4. Principles in Economics: ECO101H1, ECO102H1
5. Probability and Statistics: STA257H1, STA261H1, STA347H1

Ethical and Social Responsibility

6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Further Studies in Economics and Finance

7. Microeconomics: ECO206Y1
8. Financial Economics: ECO358H1, ECO359H1
9. Analyzing Data relevant to Finance: STA302H1/​ ECO375H1
10. Mathematical Theory of Finance: APM466H1

Further Studies in Mathematics

11. Partial Differential Equations: APM346H1
12. Real Analysis: MAT337H1
13. Special Interest Topics: 0.5 credit further from MAT332H1/​ MAT344H1/​ MAT475H1
14. Time Series Analysis: STA457H1
15. Nonlinear Optimization: APM462H1

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credit.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math website.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS268H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate

Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758

The Specialist in Mathematics & Its Applications (Physical Science) is directed toward students who enjoy Mathematics and who wish to use it to pursue studies in another Physical Science discipline. It can provide an entrée into the vast and rapidly growing array of subjects that rely on Mathematical techniques.

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory calculus/analysis, algebra, physics, and computer programing in their first year of study ( MAT157Y1/​ MAT137Y1, MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1, PHY151H1, PHY152H1, CSC108H1, CSC148H1).

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematics & Its Applications Specialist (Physical Science) in the Summer after Year 2.

Completion Requirements:

12.5-13.0 credits

Fundamentals for Mathematical Applications in the Physical Sciences

1. Calculus, Analysis and Proofs: 2.0 – 2.5 credits from MAT157Y1/​ ( MAT137Y1, MAT246H1), MAT235Y1/​ MAT237Y1/​ MAT257Y1
2. Algebra: 1.0 credit from MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1
3. Ordinary Differential Equations: MAT244H1/​ MAT267H1
4. Computer Programing: CSC108H1, CSC148H1
5. Probability and Statistics: STA257H1
6. Foundations of Physics: PHY151H1, PHY152H1
7. Foundations of Astronomy and Astrophysics: AST221H1

Ethical and Social Responsibility

8. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Further Studies in the Physical Sciences:

9. Topics in Physics: 1.5 credits from AST222H1/​ PHY250H1/​ PHY252H1/​ PHY254H1/​ PHY256H1
10. Additional Topics: 1.5 credits from AST320H1/​ AST325H1/​ MAT337H1/​ MAT363H1/​ MAT367H1/​ PHY350H1/​ PHY354H1/​ PHY356H1/​ PHY357H1/​ PHY358H1

Further Studies in Mathematics

11. Groups and Symmetries: MAT301H1
12. Complex Variables: MAT334H1
13. Partial Differential Equations: 0.5 credit from APM346H1/​ MAT351Y1
14. Advanced Topics: 1.0 credit from APM421H1/​ APM426H1/​ APM441H1/​ APM446H1/​ PHY407H1/​ PHY408H1/​ PHY456H1

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • CSC108H1 is waived for students who complete CSC148H1 first. If a student has not taken a year-long course in programming in secondary school, it is strongly recommended that students take CSC108H1 first.
  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credit.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math website.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS268H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate


Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890

The Specialist in Mathematics & Its Applications (Probability/Statistics) is directed toward students whose interests include both Mathematics and its applications in Probability and Statistics. These skills are in high demand in a world in which the uses of AI are expanding by leaps and bounds.

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory calculus/analysis, algebra, and computer programming in their first year of study ( MAT157Y1/​ MAT137Y1, MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1, CSC108H1, CSC148H1).

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematics & Its Applications Specialist (Probability/Statistics) in the Summer after Year 2.

Completion Requirements:

11.5-12.5 credits

Fundamentals for Mathematical Applications in Probability and Statistics

1. Calculus, Analysis and Proofs: 2.0 – 2.5 credits from MAT157Y1/​ ( MAT137Y1, MAT246H1), MAT237Y1/​ MAT257Y1
2. Algebra: 1.0 credit from MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1
3. Ordinary Differential Equations: MAT244H1/​ MAT267H1
4. Computer Programming: CSC108H1, CSC148H1
5. Probability and Statistics: STA257H1, STA261H1, STA347H1

Ethical and Social Responsibility

6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Further Studies in Probability and Statistics

7. Data Analysis: STA302H1
8. Related Structures: 1.0 credit from STA452H1/​ STA453H1/​ MAT332H1/​ MAT344H1/​ APM348H1/​ MAT377H1/​ APM461H1/​ any 300+level course from STA
9. Advanced Statistics: 1.0 credit from STA437H1/​ STA442H1/​ STA447H1/​ STA457H1

Further Studies in Mathematics

10. Groups and Symmetries: MAT301H1
11. Complex Variables: MAT334H1
12. Real Analysis: MAT337H1
13. Partial Differential Equations or Optimization: 0.5 credit from APM346H1/​ MAT351Y1/​ APM462H1
14. Advanced Topics: Additional 1.0 credit at the 300+ level from APM/MAT/STA courses

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • CSC108H1 is waived for students who complete CSC148H1 first. If a student has not taken a year-long course in programming in secondary school, it is strongly recommended that students take CSC108H1 first.
  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credit.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math website.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS268H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate

Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580

The Specialist Mathematics & Its Applications Specialist (Teaching) is directed toward students who are interested in teaching at the elementary or secondary level and who wish to bring a strong Mathematics background to bear in the classroom.

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory analysis, algebra, and programming in their first year of study ( MAT157Y1/​ MAT137Y1, MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1, CSC108H1).

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematics & Its Applications Specialist (Teaching) in the Summer after Year 2.

Completion Requirements:

10.5-11.0 credits, including at least 1.0 credit at the 400-level

Fundamentals for Mathematical Applications related to Teaching

1. Calculus, Analysis and Proofs: 2.0 – 2.5 credits from MAT157Y1/​ ( MAT137Y1, MAT246H1), MAT235Y1/​ MAT237Y1/​ MAT257Y1
2. Algebra: 1.0 credit from MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1
3. Ordinary Differential Equations: MAT244H1/​ MAT267H1
4. Computer Programing: CSC108H1
5. Probability and Statistics: STA257H1

Ethical and Social Responsibility

6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Further Studies in Mathematics related to Teaching

7. Concepts in Elementary Mathematics: MAT329Y1
8. History of Mathematics: 1.0 credit from HPS390H1/​​ MAT390H1, HPS391H1/​​ MAT391H1
9. Intriguing Topics: 1.0 credit from MAT309H1/​ MAT315H1/​ STA302H1/​​ STA347H1

Further Studies in Mathematics:

10. Groups & Symmetries: MAT301H1
11. Complex Variables: MAT334H1
12. Advanced Topics: 1.0 credit further from MAT332H1/​ MAT335H1/​ MAT337H1/​ MAT344H1/​ MAT363H1/​ MAT367H1
13. Further Topics: 1.0 credit of any APM/MAT 400-level courses, MAT401H1/​ MAT402H1 recommended

Notes:

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.
  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.
  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credit.
  • Students in their last year of study with a cGPA of 3.5 or higher may be permitted to take up to 1.5 credits of Math graduate courses. These courses may count toward specialist program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for graduate courses as an undergraduate student, find more information on the A&S Math website.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS268H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate

Mathematics Major (Science Program) - ASMAJ1165

The Major in Mathematics is directed toward students who are interested in combining a solid knowledge of Mathematics with studies in other disciplines. While typically less in-depth than the Specialist Programs, it still covers a broad swath of the subject.

Students in this program have the option to complete the Arts & Science Internship Program (ASIP) stream.

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory calculus/analysis and algebra in their first year of study [( MAT135H1, MAT136H1)/ MAT137Y1/​ MAT157Y1)], MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1

Arts & Science Internship Program

Students in this program have the option to request enrolment in the Arts & Science Internship Program (ASIP) stream. Students can apply for the ASIP stream after Year 1 (Year 2 entry) or after Year 2 (Year 3 entry, starting Fall 2024). Full details about ASIP, including student eligibility, selection and enrolment, are available in the ASIP section of the Arts & Science Academic Calendar. Please note that the majority of students enter ASIP in Fall term of Year 2. Space is more limited for Year 3 entry and students applying for Year 3 entry must have been admitted to the Mathematics Major in the Summer after Year 2.

Completion Requirements:

7.5 credits, including 2.5 credits at the 300+ level with a minimum of 0.5 credit at the 400 level

Mathematics Fundamentals

1. 2.5 credits from ( MAT135H1, MAT136H1, MAT246H1)/ ( MAT137Y1, MAT246H1)/ ( MAT157Y1, 0.5 credit from APM/MAT200+ courses), MAT235Y1/​​ MAT237Y1/​​ MAT257Y1

2. Algebra: 1.0 credit from MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1

3. Ordinary Differential Equations: MAT244H1/​ MAT267H1

Ethical and Social Responsibility

4. 0.5 credit with a significant emphasis on ethics and social responsibility (list below)

Higher Studies in Mathematics

5. Groups and Symmetries: MAT301H1

6. Mathematical Logic or Number Theory: MAT309H1/​ MAT315H1

7. Complex Variables: MAT334H1

8. Further Topics: 1.5 credits including 1.0 credit at the 300+ level including 0.5 credit at the 400-level: ACT240H1/​​ ACT230H1/​​ APM236H1/​ APM346H1/​ any APM400-level course/ HPS390H1/​ HPS391H1/​ MAT309H1/​​ MAT315H1/​​ MAT332H1/​ MAT335H1/​​ MAT337H1/​ MAT344H1/​ MAT363H1/​ MAT390H1/​ MAT391H1/​ any MAT400-level course/ PSL432H1/​ STA247H1/​​ STA257H1

Notes:

  • Only 0.5 credit of HPS390H1/​ MAT390H1/​ HPS391H1/​ MAT391H1 may count toward the major completion requirement of "further topics."

  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.

  • Students may use CR/NCR on the course they use toward the ethics and social responsibility credit.

  • 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.

Courses accepted towards this program’s ethics requirement:
CSC300H1/​ CSE240H1/​ CSE270H1/​ EEB215H1/​ ENV200H1/​ ESS205H1/​ any ETH200+/ FOR201H1/​ HIS268H1/​ HPS200H1/​ HPS202H1/​ INS200H1/​ JPH441H1/​ PHL265H1/​ PHL271H1/​ PHL273H1/​ PHL275H1/​ PHL281H1/​ PHL295H1/​ SDS256H1/​ another suitable course with permission from the Associate Chair, Undergraduate

Mathematics Minor (Science Program) - ASMIN1165

Enrolment Requirements:

This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.

Students are encouraged to take their introductory calculus/analysis and algebra in their first year of study [( MAT135H1, MAT136H1)/ MAT137Y1/​ MAT157Y1)], MAT223H1/​ MAT240H1, MAT224H1/​ MAT247H1

Completion Requirements:

4.0 credits, including 1.0 at the 300+ level

  1. Calculus: 2.0 credits from ( MAT135H1, MAT136H1)/ MAT137Y1/​ MAT157Y1, MAT235Y1/​ MAT237Y1/​ MAT257Y1

  2. Algebra: MAT221H1(80%+)/ MAT223H1/​ MAT240H1

  3. Further Fundamentals in Mathematics: MAT224H1/​ MAT244H1/​ MAT246H1/​ APM236H1/​ MAT247H1

  4. Advanced Topics: 1.0 credit at the 300+ level from APM/MAT courses

Notes:

  • Only 0.5 credit of APM306Y1 may count toward the Minor program

  • A minimum of 80% is required for MAT221H1 so that it may be used as a pre-requisite for higher level courses that accept MAT221H1 as a pre-requisite option.

  • PSL432H1, HPS390H1, HPS391H1 may count toward the "Advanced Topics" requirement.

  • Each course can count toward only one requirement, even if listed as options to multiple requisites of the program.

  • Not all courses listed have priority enrolment for students enrolled in this program. Students are responsible for checking priority of courses and meeting course prerequisites for courses they wish to take.

Combined Degree Program (CDP) offered with Victoria College and Ontario Institute for Studies in Education (OISE)

  • Combined Degree Program in HBA/HBSc and Master of Teaching (MT)

Students enrolled in the Minor in Education and Society and Major in Mathematics may apply for this Combined Degree Program. For details about application and program requirements, see the Combined Degree Programs section.

 

Joint Programs

  • Economics and Mathematics, see Economics
  • Statistics and Mathematics, see Statistical Sciences
  • Combined Degree Program: STG, Honours Bachelor of Science, Major in Mathematics / Master of Teaching

Mathematics Courses

MAT133Y1 - Calculus and Linear Algebra for Commerce

Hours: 72L

Mathematics of finance. Matrices and linear equations. Review of differential calculus; applications. Integration and fundamental theorem; applications. Introduction to partial differentiation; applications. Course material expects at minimum high school calculus has been completed prior to undertaking course. This course will be useful for students interested in learning applied calculus in relation to future studies in commerce and/or social science programs.

Prerequisite: High school level calculus
Exclusion: MAT133Y5/ ( MATA32H3, MATA33H3)
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT135H1 - Calculus I

Hours: 36L/12T

In this first introduction to Calculus, students will be introduced to the tools of differential calculus, the branch of calculus that is motivated by the problem of measuring how quantities change. Students will use these tools to solve other problems, including simplifying functions with straight lines, describing how different types of change are related, and computing maximum and minimum quantities. This course will focus on developing a deep understanding of why the tools of calculus make sense and how to apply them to the social, biological, and physical sciences. It will also emphasize translating between algebraic, graphical, numerical and verbal descriptions of each concept studied. This course will be useful for students interested in learning applied calculus in relation to future studies in economics, life science, and physical and mathematical science programs. The following concepts will be studied: Limits, asymptotes, continuity, derivatives, linear approximation of functions, the notion of a differential equation (DE) and a solution of a DE, slope fields, and Euler's method.

Prerequisite: High school level calculus
Exclusion: MAT135H5/ MAT136H5/ MAT135Y5/ MATA30H3/ MATA31H3/ MATA36H3/ APS162H1/ APS163H1/ ESC194H1/ ESC195H1/ MAT186H1/ MAT187H1/ MAT196H1/ MAT197H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT136H1 - Calculus II

Hours: 36L/12T

This second part of the introductory Calculus sequence focuses on integral calculus beginning with the Fundamental Theorem of Calculus, the connection between two seemingly unrelated problems: measuring changing quantities and finding areas of curved shapes. Students will develop a deep understanding of the integral, and use it to: unpack equations involving derivatives; to make sense of infinite sums; to write complicated functions as 'infinite polynomials'; and to compute areas, volumes, and totals in applied problems. This course will further develop students' abilities to translate between algebraic, graphical, numerical, and verbal descriptions of mathematics in a variety of applied contexts. This course is a continuation of MAT135H1 and will be useful for students interested in learning applied calculus in relation to future studies in economics, life science, and physical and mathematical science programs. The following concepts will be studied: Integration, basic techniques of integration (substitution and by parts), improper integrals, using computer algebra systems (CAS) for integration, Taylor polynomials and Taylor series, ratio test for power series, radius of convergence of power series, first-order differential equations and systems of differential equations: modelling, separable DEs, and using CAS to study and find solutions.

Prerequisite: MAT135H1/ MAT135H5/ MATA30H3/ MATA31H3/ APS162H1/ ESC194H1/ MAT186H1/ MAT196H1
Exclusion: MAT136H5/ MAT135Y5/ MATA36H3/ APS163H1/ ESC195H1/ MAT187H1/ MAT197H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT137Y1 - Calculus with Proofs

Hours: 72L/24T

A conceptual approach for students interest in theoretical foundations of mathematics. Attention is given to computational aspects as well as problem-solving techniques. Limits and continuity, mean value theorem, elementary transcendental functions including trigonometric functions, inverse function theorem, differentiation, integration, fundamental theorem of calculus, Taylor's theorem, sequences and series, power series, and applications. This course will be useful for students interested in learning theoretical calculus and proofs in relation to future studies in computer science, economics, mathematics, physics, and statistics.

Prerequisite: High school level calculus
Exclusion: MAT137Y5/ ( MATA30H3/ MATA31H3, MATA37H3)
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT138H1 - Introduction to Proofs

Hours: 36L/12T

The goal of this course is for students to become comfortable with abstraction, rigour, logic, and proofs. They will practice reading and understanding mathematical statements, analyzing definitions and properties, formulating conjectures and generalizations, providing and writing reasonable and precise arguments, writing and critiquing proofs. The instructor may use specific mathematical content, which could vary from year to year, to practice these skills. Students who take MAT135H1 and MAT136H1 and wish to take MAT237Y1 are required to take MAT138H1 prior to undertaking MAT237Y1. Students who are taking MAT137Y1 or MAT157Y1 and/or MAT240H1 and are interested in more preparation with logical arguments are encouraged to take MAT138H1 concurrently.

Prerequisite: High school level calculus
Exclusion: MAT137Y1/ MAT137Y5/ ( MATA30H3/ MATA31H3, MATA37H3)/ MAT157Y1/ MAT157Y5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT157Y1 - Analysis I

Hours: 72L/48T

A theoretical course in calculus; emphasizing proofs and techniques. Elementary logic, limits and continuity, least upper bounds, intermediate and extreme value theorems. Derivatives, mean value and inverse function theorems. Integrals, fundamental theorem, elementary transcendental functions. Techniques of integration. Taylor's theorem; sequences and series; uniform convergence and power series. This course is required for the Mathematics Specialist, the Applied Mathematics Specialist, the Mathematics and Physics Specialist, and the Mathematics and Philosophy Specialist program and provides a strong theoretical mathematics background.

Prerequisite: High school level calculus
Exclusion: MAT157Y5
Recommended Preparation: Preparing for University Math (PUMP) Level II. Students may also want to take MAT138H1 concurrently with MAT157Y1.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT193H1 - Women’s Mathematics

Hours: 36S

Mathematics has been shaped in significant ways by the work of outstanding female mathematicians such as Hypatia, Emmy Noether, Sofia Kovalevskaya, and Maryam Mirzakhani. Despite these successes, women still experience barriers to entering the field and participating at the highest levels. This course will blend an exploration of mathematics created by women with a study of the issue of women in mathematics. Students will have the opportunity to examine the complex factors that impact women’s participation in STEM, learn about the lives of female mathematicians, create their own mathematics, and sharpen their spatial cognition and logical thinking skills. Restricted to first-year students. Not eligible for CR/NCR option.

Prerequisite: High school level algebra.
Exclusion: Not intended for students in a Mathematics Specialist or Major program.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT198H1 - Cryptology: The Mathematics of Secrecy and Security

Hours: 24S

How do we send our own confidential information through secure channels, and how can we break codes to uncover the secret information of our adversaries? The mathematical field of cryptology is dedicated to answering such questions. In this course we will study breakthroughs in cryptology, from secret messages in the ancient world and the Enigma cipher in World War II, to modern cryptosystems that facilitate online commerce. Along the way, you will develop a sophisticated understanding of how numbers interact and develop the ability to communicate messages secretly and mathematics clearly. Restricted to first-year students. Not eligible for CR/NCR option.

Prerequisite: High school level algebra.
Exclusion: Not intended for students in a Mathematics Specialist or Major program.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT199H1 - Aha! Mathematical Discovery and Creative Problem Solving

Hours: 36S

This course is an exploration into the creative process and use of imagination as they arise in the context of mathematical problem solving. The problems, which are all at a pre-calculus level, are chosen primarily by the criterion of aesthetic appeal, and emphasize reasoning rather than technique. Still, many of them are quite challenging, and substantial independent thinking will be required, the course is therefore appropriate for students from a variety of backgrounds and disciplines, including hard sciences. Its goal will be to hone each participant's creativity and mathematical problem-solving skills while guiding them towards the `Aha!' experience which accompanies independent discovery. Restricted to first-year students. Not eligible for CR/NCR option.

Prerequisite: High school level algebra
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

JUM202H1 - Mathematics as an Interdisciplinary Pursuit

Hours: 24L/12T

A study of the interaction of mathematics with other fields of inquiry: how mathematics influences, and is influenced by, the evolution of science and culture. Art, music, and literature, as well as the more traditionally related areas of the natural and social sciences may be considered. (Offered every three years)

JUM202H1 is particularly suited as a Science Distribution Requirement course for Humanities and Social Science students.

Exclusion: JUM102H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

JUM203H1 - Mathematics as a Recreation

Hours: 24L/12T

A study of games, puzzles and problems focusing on the deeper principles they illustrate. Concentration is on problems arising out of number theory and geometry, with emphasis on the process of mathematical reasoning. Technical requirements are kept to a minimum. A foundation is provided for a continuing lay interest in mathematics. (Offered every three years)

JUM203H1 is particularly suited as a Science Distribution Requirement course for Humanities and Social Science students.

Exclusion: JUM103H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

JUM205H1 - Mathematical Personalities

Hours: 24L/12T

An in-depth study of the life, times and work of several mathematicians who have been particularly influential. Examples may include Newton, Euler, Gauss, Kowalewski, Hilbert, Hardy, Ramanujan, Gödel, Erdös, Coxeter, Grothendieck. (Offered every three years)

JUM205H1 is particularly suited as a Science Distribution Requirement course for Humanities and Social Science students.

Exclusion: JUM105H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT221H1 - Applied Linear Algebra

Hours: 36L/12T

An application-oriented approach to linear algebra, based on calculations in standard Euclidean space. Systems of linear equations, matrices, Gaussian elimination, subspaces, bases, orthogonal vectors and projections. Matrix inverses, kernel and range, rank-nullity theorem. Determinants, eigenvalues and eigenvectors, Cramer's rule, diagonalization. This course has strong emphasis on building computational skills in the area of algebra. Applications to curve fitting, economics, Markov chains and cryptography.

Prerequisite: High school level calculus
Exclusion: MAT223H1/ MAT223H5/ MATA22H3/ MATA23H3/ MAT224H1/ MAT224H5/ MATB24H3/ MAT240H1/ MAT240H5/ MAT185H1/ MAT188H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT223H1 - Linear Algebra I

Hours: 36L/12T

A first course on linear algebra in R^n emphasizing the interplay between algebraic and geometric perspectives. Topics include systems of equations, Gaussian elimination, representations of lines and planes, dot products, subspaces and translated subspaces, bases and change of basis, projections, the rank and nullity of a linear transformation, the rank/nullity/row space/column space of a matrix, matrix inverses, determinants, eigenvectors and eigenvalues, and matrix diagonalization. While not emphasizing proofs, this course does maintain a careful distinction between vectors and their representation in a basis as well as between matrices and linear transformations.

Prerequisite: High school level calculus
Exclusion: MAT223H5/ MATA22H3/ MATA23H3/ MAT224H1/ MAT224H5/ MATB24H3/ MAT240H1/ MAT240H5/ MAT247H1/ MAT247H5/ MAT185H1/ MAT188H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT224H1 - Linear Algebra II

Hours: 36L/12T

Fields, complex numbers, vector spaces over a field, linear transformations, matrix of a linear transformation, kernel, range, dimension theorem, isomorphisms, change of basis, eigenvalues, eigenvectors, diagonalizability, real and complex inner products, spectral theorem, adjoint/self-adjoint/normal linear operators, triangular form, nilpotent mappings, Jordan canonical form.

Prerequisite: MAT221H1(80%)/ MAT223H1/ MAT223H5/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT235Y1 - Multivariable Calculus

Hours: 72L

Parametric equations and polar coordinates. Vectors, vector functions and space curves. Differential and integral calculus of functions of several variables. Line integrals and surface integrals and classic vector calculus theorems. Examples from life sciences and physical science applications.

Prerequisite: MAT133Y1/ MAT133Y5/ ( MATA32H3, MATA33H3)/ ( MAT135H1, MAT136H1)/ ( MAT135H5, MAT136H5)/ MAT134Y5/ MAT135Y5/ ( MATA30H3/ MATA31H3, MATA36H3/ MATA37H3)/ MAT137Y1/ MAT137Y5/ MAT157Y1/ MAT157Y5

Exclusion: MAT235Y5/ ( MAT232H5/ MAT233H5, MAT236H5/ MAT368H5)/ ( MATB41H3, MATB42H3)/ MAT237Y1/ MAT291H1/ MAT294H1

Recommended Preparation: MAT223H1/ MAT223H5/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM236H1 - Applications of Linear Programming

Hours: 36L

Introduction to linear programming including a rapid review of linear algebra (row reduction, matrix inversion, linear independence), the simplex method with applications, the duality theorem, complementary slackness, the dual simplex method and the revised simplex method.

Prerequisite: MAT221H1/ MAT223H1/ MAT223H5/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT237Y1 - Multivariable Calculus with Proofs

Hours: 72L

Elementary topology in Euclidean space. Differential calculus of vector valued functions of a vector variable. Implicit and inverse function theorems, regular surfaces. Optimization, Lagrange multipliers, multivariable Taylor polynomials. Integral calculus with the Jordan measure. Fubini’s theorem, change of variables. Line and surface integrals. Vector calculus in two- and three-dimensions. Green’s theorem, Divergence theorem, Stokes’ theorem. Fourier series. This course is recommended for students interested in proof-based multivariable calculus with balanced emphasis between theory and applications.

Prerequisite: [ MAT133Y1/ ( MAT135H1, MAT136H1)/ ( MAT135H5, MAT136H5)/ MAT134Y5/ MAT135Y5/ ( MATA30H3/ MATA31H3, MATA36H3), MAT138H1/ MAT102H5/ MAT246H1]/ MAT137Y1/ MAT137Y5/ ( MATA30H3/ MATA31H3, MATA37H3)/ MAT157Y1/ MAT157Y5, MAT223H1/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT240H1 - Algebra I

Hours: 36L/24T

A theoretical approach to: vector spaces over arbitrary fields, including C and Z_p. Subspaces, bases and dimension. Linear transformations, matrices, change of basis, similarity, determinants. Polynomials over a field (including unique factorization, resultants). Eigenvalues, eigenvectors, characteristic polynomial, diagonalization. Minimal polynomial, Cayley-Hamilton theorem.

Prerequisite: High school level calculus
Corequisite: MAT157Y1
Exclusion: MAT240H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT244H1 - Introduction to Ordinary Differential Equations

Hours: 36L

First order ordinary differential equations: Direction fields, integrating factors, separable equations, homogeneous equations, exact equations, autonomous equations, modeling. Existence and uniqueness theorem. Higher order equations: Constant coefficient equations, reduction of order, Wronskian, method of undetermined coefficients, variation of parameters. Solutions by series and integrals. First order linear systems, fundamental matrices. Non-linear equations, phase plane, stability. Applications in life and physical sciences and economics.

Prerequisite: ( MAT133Y1/ MAT135H1/ MAT135H5/ MATA35H3/ MATA30H3/ MATA31H3, MAT136H1/ MAT136H5/ MATA36H3/ MATA37H3)/ MAT135Y5/ MAT137Y1/ MAT137Y5/ MAT157Y1/ MAT157Y5, MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5
Corequisite: MAT235Y1/ MAT237Y1/ MAT257Y1
Exclusion: MAT267H1/ MAT242H5/ MAT244H5/ MATB44H3/ MAT212H5/ MAT258Y5/ MAT292H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT245H1 - Mathematical Methods in Data Science

Hours: 36L/24P

An introduction to the mathematical methods behind scientific techniques developed for extracting information from large data sets. Elementary probability density functions, conditional expectation, inverse problems, regularization, dimension reduction, gradient methods, singular value decomposition and its applications, stability, diffusion maps. Examples from applications in data science and big data.

Prerequisite: MAT137Y1/ MAT157Y1, MAT223H1/ MAT240H1, MAT224H1/ MAT247H1
Corequisite: MAT237Y1/ MAT257Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT246H1 - Concepts in Abstract Mathematics

Hours: 36L/12T

Designed to introduce students to mathematical proofs and abstract mathematical concepts. Topics may include modular arithmetic, sizes of infinite sets, and a proof that some angles cannot be trisected with straightedge and compass.

Prerequisite: MAT133Y1/ MAT133Y5/ ( MATA32H3, MATA33H3)/ ( MAT135H1, MAT136H1)/ ( MAT135H5, MAT136H5)/ MAT134Y5/ MAT135Y5/ ( MATA30H3/ MATA31H3, MATA36H3/ MATA37H3)/ MAT137Y1/ MAT137Y5, MAT223H1/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5
Exclusion: MAT157Y1/ MAT157Y5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT247H1 - Algebra II

Hours: 36L

A theoretical approach to real and complex inner product spaces, isometries, orthogonal and unitary matrices and transformations. The adjoint. Hermitian and symmetric transformations. Spectral theorem for symmetric and normal transformations. Polar representation theorem. Primary decomposition theorem. Rational and Jordan canonical forms. Additional topics including dual spaces, quotient spaces, bilinear forms, quadratic surfaces, multilinear algebra.

Prerequisite: MAT240H1/ MAT240H5
Corequisite: MAT157Y1
Exclusion: MAT247H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT257Y1 - Analysis II

Hours: 72L/48T

Topology of R^n; compactness, functions and continuity, extreme value theorem. Derivatives; inverse and implicit function theorems, maxima and minima, Lagrange multipliers. Integration; Fubini's theorem, partitions of unity, change of variables. Differential forms. Manifolds in R^n; integration on manifolds; Stokes' theorem for differential forms and classical versions. Some topics may vary year-to-year.

Prerequisite: MAT157Y1/ MAT157Y5, MAT247H1/ MAT247H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT267H1 - Advanced Ordinary Differential Equations

Hours: 36L/12T

A theoretical course on Ordinary Differential Equations. First-order equations: separable equations, exact equations, integrating factors. Variational problems, Euler-Lagrange equations. Linear equations and first-order systems. Fundamental matrices, Wronskians. Non-linear equations. Existence and uniqueness theorems. Method of power series. Elementary qualitative theory; stability, phase plane, stationary points. Oscillation theorem, Sturm comparison. Applications in mechanics, physics, chemistry, biology and economics.

Prerequisite: MAT157Y1/ MAT157Y5, MAT247H1/ MAT247H5
Corequisite: MAT257Y1
Exclusion: MAT234H1/ MAT292H1

Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT271H1 - Insights from Mathematics

Hours: 36L/6T

This breadth course is accessible to students with limited mathematical background. Various mathematical techniques will be illustrated with examples from humanities and social science disciplines. Some of the topics will incorporate user friendly computer explorations to give participants the feel of the subject without requiring skill at calculations.

Note: This course cannot be used to satisfy requirements of program in the math department.

Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT282H1 - Topics in Mathematics

Hours: 36L

A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/

Prerequisite: 1.0 MAT credit at the 100-level. Possible additional topic-specific prerequisites.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT295H1 - Independent Reading in Mathematics

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT296H1 - Independent Reading in Mathematics

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 36L course. Not eligible for CR/NCR option.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT297Y1 - Research Project in Mathematics

Independent research under the direction of a faculty member. Similar workload to a 72L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT299Y1 - Research Opportunity Program

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities…. Not eligible for CR/NCR option.

Distribution Requirements: Science

MAT301H1 - Groups and Symmetries

Hours: 36L

Congruences and fields. Permutations and permutation groups. Linear groups. Abstract groups, homomorphisms, subgroups. Symmetry groups of regular polygons and Platonic solids, wallpaper groups. Group actions, class formula. Cosets, Lagrange theorem. Normal subgroups, quotient groups. Classification of finitely generated abelian groups. Emphasis on examples and calculations.

Prerequisite: MAT257Y1/ ( MAT224H1/ MAT247H1, MAT235Y1/ MAT237Y1, MAT246H1/ MAT157Y1/ CSC236H1/ CSC240H1)/ (MAT185H1, MAT194H1, MAT195H1)
Exclusion: MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM306Y1 - Mathematics and Law

Hours: 72L

This course examines the relationship between legal reasoning and mathematical logic; provides a mathematical perspective on the legal treatment of interest and actuarial present value; critiques ethical issues; analyzes how search engine techniques on massive databases transform legal research and considers the impact of statistical analysis and game theory on litigation strategies.

NOTE

This course counts as 0.5 credit in BR=3 and 0.5 credit in BR=5.

This course will only contribute 0.5 credit to the Math Minor program.

Prerequisite: MAT133Y1/ MAT135H1/ MAT135H5/ MAT136H1/ MAT136H5/ MAT137Y1/ MAT157Y1, MAT221H1/ MAT223H1/ MAT240H1
Exclusion: JUM206Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5), Society and its Institutions (3)

MAT309H1 - Introduction to Mathematical Logic

Hours: 36L

Predicate calculus. Relationship between truth and provability; Gödel's completeness theorem. First order arithmetic as an example of a first-order system. Gödel's incompleteness theorem; outline of its proof. Introduction to recursive functions.

Prerequisite: MAT257Y1/ [ MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5, MAT235Y1/ MAT235Y5/ ( MAT232H5, MAT236H5)/ ( MATB41H3, MATB42H3/ MATB43H3)/ MAT237Y1/ MAT237Y5, MAT246H1/ MAT157Y1/ CSC236H1/ CSC240H1]
Exclusion: CSC438H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT315H1 - Introduction to Number Theory

Hours: 36L

Elementary topics in number theory: arithmetic functions; polynomials over the residue classes modulo m, characters on the residue classes modulo m; quadratic reciprocity law, representation of numbers as sums of squares.

Prerequisite: ( MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5, MAT235Y1/ MAT235Y5/( MAT232H5, MAT236H5)/( MATB41H3, MATB42H3)/ MAT237Y1/( MATB41H3, MATB42H3, MATB43H3)/ MAT237Y5, MAT246H1/ CSC236H1/ CSC240H1)/ MAT157Y1/ MAT157Y5/ MAT247H1/ MAT247H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT327H1 - Introduction to Topology

Hours: 36L

Metric spaces, topological spaces and continuous mappings; separation, compactness, connectedness. Fundamental group and covering spaces. Brouwer fixed-point theorem. Students in the math specialist program wishing to take additional topology courses are advised to obtain permission to take MAT1300H, MAT1301H.

Prerequisite: MAT157Y1/ MAT157Y5/ [( MAT237Y1/( MATB41H3, MATB42H3/ MATB43H3)/ MAT237Y5), MAT246H1]
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT329Y1 - Concepts in Elementary Mathematics

Hours: 72L

This course is aimed at students intending to become elementary school teachers. Emphasis is placed on the formation and development of fundamental reasoning and learning skills required to understand and to teach mathematics at the elementary level. Topics may include: Problem Solving and Strategies, Sets and Elementary Logic, Numbers and Elements of Number Theory, Introductory Probability and Fundamentals of Geometry.

The course may include an optional practicum in school classrooms.

Prerequisite: 5.0 credits with a CGPA of at least 2.5, and MAT137Y1/ MAT138H1/ ( MAT223H1/ MAT240H1)/ ( MAT246H1/ MAT157Y1
Exclusion: MAT382H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT332H1 - Introduction to Graph Theory

Hours: 36L

This course will explore the following topics: Graphs, subgraphs, isomorphism, trees, connectivity, Euler and Hamiltonian properties, matchings, vertex and edge colourings, planarity, network flows and strongly regular graphs. Participants will be encouraged to use these topics and execute applications to such problems as timetabling, tournament scheduling, experimental design and finite geometries.

Prerequisite: MAT224H1/ MATB24H3/ MAT224H5/ MAT247H1/ MAT247H5
Recommended Preparation: Students are encouraged to take MAT301H1 or MAT347Y1 concurrently or prior to undertaking this course.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT334H1 - Complex Variables

Hours: 36L

Theory of functions of one complex variable, analytic and meromorphic functions. Cauchy's theorem, residue calculus, conformal mappings, introduction to analytic continuation and harmonic functions.

Prerequisite: MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5, MAT235Y1/ MAT235Y5/( MAT232H5, MAT236H5)/( MATB41H3, MATB42H3)/ MAT237Y1/( MATB41H3, MATB42H3, MATB43H3)/ MAT237Y5/ MAT257Y1
Exclusion: MAT354H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT335H1 - Chaos, Fractals and Dynamics

Hours: 36L

An elementary introduction to a modern and fast-developing area of mathematics. One-dimensional dynamics: iterations of quadratic polynomials. Dynamics of linear mappings, attractors. Bifurcation, Henon map, Mandelbrot and Julia sets. History and applications.

Prerequisite: MAT137Y1/( MATA30H3, MATA31H3, MATA37H3)/ MAT137Y5/ MAT157Y1/ MAT157Y5/ MAT235Y1/ MAT235Y5/( MAT232H5, MAT236H5)/( MATB41H3, MATB42H3)/ MAT237Y1/( MATB41H3, MATB42H3, MATB43H3)/ MAT237Y5, MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT336H1 - Elements of Analysis

Hours: 36L/12T

This course provides the foundations of analysis and rigorous calculus for students who will take subsequent courses where these mathematical concepts are central of applications, but who have only taken courses with limited proofs. Topics include topology of Rn, implicit and inverse function theorems and rigorous integration theory.

Prerequisite: MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5, MAT235Y1/ MAT235Y5/ ( MAT232H5, MAT236H5)/ ( MATB41H3, MATB42H3)/ MAT237Y1/ ( MATB41H3, MATB42H3, MATB43H3)/ MAT237Y5/ (MAT185H1, MAT195H1/ ESC195H1)
Exclusion: MAT257Y1/ MAT337H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT337H1 - Introduction to Real Analysis

Hours: 36L

Construction of Real Numbers. Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings; existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension.

Prerequisite: MAT257Y1/ [ MAT224H1/ MATA24H3/ MAT224H5/ MAT247H1/ MAT247H5, MAT235Y1/ MAT235Y5/ ( MAT232H5, MAT236H5)/ ( MATB41H3, MATB42H3/ MATB43H3)/ MAT237Y1/ MAT237Y5, MAT246H1/ MAT157Y1]
Exclusion: MAT357H1/ MAT378H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT344H1 - Introduction to Combinatorics

Hours: 36L

Basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph theory with algorithms; applications (including network flows). Combinatorial structures including block designs and finite geometries.

Prerequisite: MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM346H1 - Partial Differential Equations

Hours: 36L

Sturm-Liouville problems, Green's functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transform, stationary phase method.

Prerequisite: MAT235Y1/ MAT235Y5/ ( MAT232H5, MAT236H5)/ ( MATB41H3, MATB42H3)/ MAT237Y1/ MAT237Y5/ MAT257Y1, ( MAT244H1/ MATB44H3/ MAT244H5/ MAT267H1)
Exclusion: MAT351Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT347Y1 - Groups, Rings and Fields

Hours: 72L/24T

Groups, subgroups, quotient groups, Sylow theorems, Jordan-Hölder theorem, finitely generated abelian groups, solvable groups. Rings, ideals, Chinese remainder theorem; Euclidean domains and principal ideal domains: unique factorization. Noetherian rings, Hilbert basis theorem. Finitely generated modules. Field extensions, algebraic closure, straight-edge and compass constructions. Galois theory, including insolvability of the quintic.

Prerequisite: MAT257Y1/(85% in MAT247H1/ MAT247H5)
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM348H1 - Mathematical Modelling

Previous Course Number: MAT482

Hours: 36L/22P

An overview of mathematical modelling. A variety of approaches for representing physical situations mathematically followed by analytical techniques and numerical simulations to gain insight. Questions from biology, economics, engineering, medicine, physics, physiology, and the social sciences formulated as problems in optimization, differential equations, and probability. Precise content varies with instructor.

Prerequisite: MAT244H1/ MAT267H1, MAT224H1/ MAT247H1, STA237H1/ STA247H1/ STA257H1/ MAT377H1
Exclusion: MAT482H1 (Topics in Mathematics: Topics in Mathematical Modelling), offered in Winter 2019
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT351Y1 - Partial Differential Equations

Hours: 72L

This is a first course in Partial Differential Equations, intended for Mathematics students with interests in analysis, mathematical physics, geometry, and optimization. The examples to be discussed include first-order equations, harmonic functions, the diffusion equation, the wave equation, Schrodinger's equation, and eigenvalue problems. In addition to the classical representation formulas for the solutions of these equations, there are techniques that apply more broadly: the notion of well-posedness, the method of characteristics, energy methods, maximum and comparison principles, fundamental solutions, Green's functions, Duhamel's principle, Fourier series, the min-max characterization of eigenvalues, Bessel functions, spherical harmonics, and distributions. Nonlinear phenomena such as shock waves and solitary waves are also introduced.

Prerequisite: MAT257Y1/ MAT237Y1 (85%), MAT267H1
Exclusion: APM351Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT354H1 - Complex Analysis I

Hours: 36L

Complex numbers, the complex plane and Riemann sphere, Möbius transformations, elementary functions and their mapping properties, conformal mapping, holomorphic functions, Cauchy's theorem and integral formula. Taylor and Laurent series, maximum modulus principle, Schwarz' lemma, residue theorem and residue calculus.

Prerequisite: MAT257Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT357H1 - Foundations of Real Analysis

Hours: 36L

Function spaces; Arzela-Ascoli theorem, Weierstrass approximation theorem, Fourier series. Introduction to Banach and Hilbert spaces; contraction mapping principle, fundamental existence and uniqueness theorem for ordinary differential equations. Lebesgue integral; convergence theorems, comparison with Riemann integral, L^p spaces. Applications to probability.

Prerequisite: MAT257Y1
Exclusion: MAT438H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT363H1 - Geometry of Curves and Surfaces

Hours: 36L

Curves and surfaces in 3-spaces. Frenet formulas. Curvature and geodesics. Gauss map. Minimal surfaces. Gauss-Bonnet theorem for surfaces. Surfaces of constant curvature.

Prerequisite: MAT224H1/ MATB24H3/ MAT224H5/ MAT247H1/ MAT247H5, MAT237Y1/ ( MATB41H3, MATB42H3, MATB43H3)/ MAT237Y5/ MAT257Y1 ( MAT257Y1 can be taken concurrently). For FASE students, MAT185H1, MAT194H1, MAT195H1, AER210H1.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT367H1 - Differential Geometry

Hours: 36L

Manifolds, partitions of unity, submersions and immersions, vector fields, vector bundles, tangent and cotangent bundles, foliations and Frobenius’ theorem, multilinear algebra, differential forms, Stokes’ theorem, Poincare-Hopf theorem.

Prerequisite: MAT257Y1/ ( MAT224H1/ MAT247H1, MAT237Y1, MAT246H1/ MAT157Y1)
Recommended Preparation: MAT257Y1, MAT240H1, MAT247H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT377H1 - Mathematical Probability

Hours: 36L/12T

This course introduces students to various topics in mathematical probability theory. Topics include basic concepts (such as probability, random variables, expectations, conditional probability) from a mathematical point of view, examples of distributions and stochastic processes and their properties, convergence results (such as the law of large numbers, central limit theorem, random series, etc.), various inequalities, and examples of applications of probabilistic ideas beyond statistics (for example, in geometry and computer science).

Prerequisite: MAT247H1/ MAT247H5, MAT257Y1
Exclusion: STA347H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT382H1 - Topics in Mathematics

Hours: 36L

A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/

Prerequisite: 2.5 AMP/MAT credits at the 100/200-level. Possible additional topic-specific prerequisites.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT390H1 - History of Mathematics up to 1700

Hours: 36L

A survey of ancient, medieval, and early modern mathematics with emphasis on historical issues. (Offered in alternate years)

Prerequisite: 1.0 APM/MAT credit at the 200-level
Exclusion: HPS309H1/ HPS310Y1/ HPS390H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT391H1 - History of Mathematics after 1700

Hours: 24L/12T

A survey of the development of mathematics from 1700 to the present with emphasis on technical development. (Offered in alternate years)

Prerequisite: 1.0 APM/MAT credit at the 200 level
Exclusion: HPS309H1/ HPS310H1/ HPS391H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT395H1 - Independent Reading in Mathematics

Independent reading under the direction of a faculty member. Topic must be outside current undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT396H1 - Independent Reading in Mathematics

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM396H1 - Independent Reading in Applied Mathematics

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.

This course requires an application. Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA 3.5 for APM and MAT courses, permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT397Y1 - Research Project in Mathematics

Independent research under the direction of a faculty member. Workload similar to a 72L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT398H0 - Research Excursions

An instructor-supervised group project in an off-campus setting. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities…. Not eligible for CR/NCR option.

Distribution Requirements: Science

MAT398Y0 - Research Excursions

An instructor-supervised group project in an off-campus setting. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities…. Not eligible for CR/NCR option.

Distribution Requirements: Science

MAT399Y1 - Research Opportunity Program

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities…. Not eligible for CR/NCR option.

MAT401H1 - Polynomial Equations and Fields

Hours: 36L

Commutative rings; quotient rings. Construction of the rationals. Polynomial algebra. Fields and Galois theory: Field extensions, adjunction of roots of a polynomial. Constructibility, trisection of angles, construction of regular polygons. Galois groups of polynomials, in particular cubics, quartics. Insolvability of quintics by radicals.

Prerequisite: MAT301H1
Exclusion: MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT402H1 - Classical Geometries

Hours: 36L

Euclidean and non-Euclidean plane and space geometries. Real and complex projective space. Models of the hyperbolic plane. Connections with the geometry of surfaces.

Prerequisite: MAT301H1/ MAT347Y1, MAT235Y1/ MAT237Y1/ MAT257Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT403H1 - Classical Geometries II

Hours: 36L

This course is the second part of the "Classical Geometries" MAT402H1 course. It is mainly dedicated to detailed study of classical real projective geometry and projective geometry over other fields. It is also devoted to the study of spherical and elliptic geometry.

Prerequisite: MAT235Y1/ MAT237Y1/ MAT257Y1, MAT301H1/ MAT347Y1
Recommended Preparation: MAT402H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT409H1 - Set Theory

Hours: 36L

Set theory and its relations with other branches of mathematics. ZFC axioms. Ordinal and cardinal numbers. Reflection principle. Constructible sets and the continuum hypothesis. Introduction to independence proofs. Topics from large cardinals, infinitary combinatorics and descriptive set theory.

Joint undergraduate/graduate course - MAT409H1/MAT1404H

Prerequisite: MAT357H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT415H1 - Algebraic Number Theory

Hours: 36L

A selection from the following: finite fields; global and local fields; valuation theory; ideals and divisors; differents and discriminants; ramification and inertia; class numbers and units; cyclotomic fields; Diophantine equations.

Prerequisite: MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT417H1 - Analytic Number Theory

Hours: 36L

A selection from the following: distribution of primes, especially in arithmetic progressions and short intervals; exponential sums; Hardy-Littlewood and dispersion methods; character sums and L-functions; the Riemann zeta-function; sieve methods, large and small; Diophantine approximation, modular forms.

Joint undergraduate/graduate course - MAT417H1/MAT1202H

Prerequisite: MAT334H1/ MAT354H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM421H1 - Mathematical Foundations of Quantum Mechanics and Quantum Information Theory

Hours: 36L

Key concepts and mathematical structure of Quantum Mechanics, with applications to topics of current interest such as quantum information theory. The core part of the course covers the following topics: Schroedinger equation, quantum observables, spectrum and evolution, motion in electro-magnetic field, angular momentum and O(3) and SU(2) groups, spin and statistics, semi-classical asymptotics, perturbation theory. More advanced topics may include: adiabatic theory and geometrical phases, Hartree-Fock theory, Bose-Einstein condensation, the second quantization, density matrix and quantum statistics, open systems and Lindblad evolution, quantum entropy, quantum channels, quantum Shannon theorems.

Joint undergraduate/graduate course - APM421H1/MAT1723H

Prerequisite: ( MAT224H1/ MAT247H1, MAT337H1)/ MAT357H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT425H1 - Differential Topology

Hours: 36L

Smooth manifolds, Sard's theorem and transversality. Morse theory. Immersion and embedding theorems. Intersection theory. Borsuk-Ulam theorem. Vector fields and Euler characteristic. Hopf degree theorem. Additional topics may vary.

Prerequisite: MAT257Y1, MAT327H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM426H1 - General Relativity

Hours: 36L

Einstein's theory of gravity. Special relativity and the geometry of Lorentz manifolds. Gravity as a manifestation of spacetime curvature. Einstein's equations. Cosmological implications: big bang and inflationary universe. Schwarzschild stars: bending of light and perihelion precession of Mercury. Topics from black hole dynamics and gravitational waves. The Penrose singularity theorem.

Joint undergraduate/graduate course - APM426H1/MAT1700H

Prerequisite: MAT363H1/ MAT367H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT436H1 - Introduction to Linear Operators

Hours: 36L

The course will survey the branch of mathematics developed (in its abstract form) primarily in the twentieth century and referred to variously as functional analysis, linear operators in Hilbert space, and operator algebras, among other names (for instance, more recently, to reflect the rapidly increasing scope of the subject, the phrase non-commutative geometry has been introduced). The intention will be to discuss a number of the topics in Pedersen's textbook Analysis Now. Students will be encouraged to lecture on some of the material, and also to work through some of the exercises in the textbook (or in the suggested reference books).

Joint undergraduate/graduate course - MAT436H1/MAT1011H

Prerequisite: 5.0 MAT credits, including MAT224H1/ MAT247H1 and MAT237Y1/ MAT257Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT437H1 - K-Theory and C* Algebras

Hours: 36L

The theory of operator algebras was begun by John von Neumann eighty years ago. In one of the most important innovations of this theory, von Neumann and Murray introduced a notion of equivalence of projections in a self-adjoint algebra (*-algebra) of Hilbert space operators that was compatible with addition of orthogonal projections (also in matrix algebras over the algebra), and so gave rise to an abelian semigroup, now referred to as the Murray-von Neumann semigroup.

Later, Grothendieck in geometry, Atiyah and Hirzebruch in topology, and Serre in the setting of arbitrary rings (pertinent for instance for number theory), considered similar constructions. The enveloping group of the semigroup considered in each of these settings is now referred to as the K-group (Grothendieck's terminology), or as the Grothendieck group.

Among the many indications of the depth of this construction was the discovery of Atiyah and Hirzebruch that Bott periodicity could be expressed in a simple way using the K-group. Also, Atiyah and Singer famously showed that K-theory was important in connection with the Fredholm index. Partly because of these developments, K-theory very soon became important again in the theory of operator algebras. (And in turn, operator algebras became increasingly important in other branches of mathematics.)

The purpose of this course is to give a general, elementary, introduction to the ideas of K-theory in the operator algebra context. (Very briefly, K-theory generalizes the notion of dimension of a vector space.)

The course will begin with a description of the method (K-theoretical in spirit) used by Murray and von Neumann to give a rough initial classification of von Neumann algebras (into types I, II, and III). It will centre around the relatively recent use of K-theory to study Bratteli's approximately finite-dimensional C*-algebras---both to classify them (a result that can be formulated and proved purely algebraically), and to prove that the class of these C*-algebras---what Bratteli called AF algebras---is closed under passing to extensions (a result that uses the Bott periodicity feature of K-theory).

Students will be encouraged to prepare oral or written reports on various subjects related to the course, including basic theory and applications.

Joint undergraduate/graduate course - MAT437H1/MAT1016H

Prerequisite: 5.0 MAT credits, including MAT224H1/ MAT247H1 and MAT237Y1/ MAT257Y1
Recommended Preparation: Students are encouraged to execute basic research that answers the question, what is an abelian group?
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM441H1 - Asymptotic and Perturbation Methods

Hours: 36L

Asymptotic series. Asymptotic methods for integrals: stationary phase and steepest descent. Regular perturbations for algebraic and differential equations. Singular perturbation methods for ordinary differential equations: W.K.B., strained co-ordinates, matched asymptotics, multiple scales. (Emphasizes techniques; problems drawn from physics and engineering)

Prerequisite: APM346H1/ MAT351Y1, MAT334H1/ MAT354H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT445H1 - Representation Theory

Hours: 36L

A selection of topics from: Representation theory of finite groups, topological groups and compact groups. Group algebras. Character theory and orthogonality relations. Weyl's character formula for compact semisimple Lie groups. Induced representations. Structure theory and representations of semisimple Lie algebras. Determination of the complex Lie algebras.

Joint undergraduate/graduate - MAT445H1/MAT1196H

Prerequisite: MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM446H1 - Applied Nonlinear Equations

Hours: 36L

Partial differential equations appearing in physics, material sciences, biology, geometry, and engineering. Nonlinear evolution equations. Existence and long-time behaviour of solutions. Existence of static, traveling wave, self-similar, topological and localized solutions. Stability. Formation of singularities and pattern formation. Fixed point theorems, spectral analysis, bifurcation theory. Equations considered in this course may include: Allen-Cahn equation (material science), Ginzburg-Landau equation (condensed matter physics), Cahn-Hilliard (material science, biology), nonlinear Schroedinger equation (quantum and plasma physics, water waves, etc). mean curvature flow (geometry, material sciences), Fisher-Kolmogorov-Petrovskii-Piskunov (combustion theory, biology), Keller-Segel equations (biology), and Chern-Simons equations (particle and condensed matter physics).

Joint undergraduate/graduate course - APM446H1/MAT1508H

Prerequisite: APM346H1/ MAT351Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT448H1 - Introduction to Commutative Algebra and Algebraic Geometry

Hours: 36L

Basic notions of algebraic geometry, with emphasis on commutative algebra or geometry according to the interests of the instructor. Algebraic topics: localization, integral dependence and Hilbert's Nullstellensatz, valuation theory, power series rings and completion, dimension theory. Geometric topics: affine and projective varieties, dimension and intersection theory, curves and surfaces, varieties over the complex numbers. This course will be offered in alternating years.

Joint undergraduate/graduate course - MAT448H1/MAT1155H

Prerequisite: MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT449H1 - Algebraic Curves

Hours: 36L

Projective geometry. Curves and Riemann surfaces. Algebraic methods. Intersection of curves; linear systems; Bezout's theorem. Cubics and elliptic curves. Riemann-Roch theorem. Newton polygon and Puiseux expansion; resolution of singularities. This course will be offered in alternating years.

Prerequisite: MAT347Y1, MAT354H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT454H1 - Complex Analysis II

Hours: 36L

Harmonic functions, Harnack's principle, Poisson's integral formula and Dirichlet's problem. Infinite products and the gamma function. Normal families and the Riemann mapping theorem. Analytic continuation, monodromy theorem and elementary Riemann surfaces. Elliptic functions, the modular function and the little Picard theorem.

Joint undergraduate/graduate course - MAT454H1/MAT1002H

Prerequisite: MAT354H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT457H1 - Advanced Real Analysis I

Hours: 36L

Lebesgue measure and integration; convergence theorems, Fubini's theorem, Lebesgue differentiation theorem, abstract measures, Caratheodory theorem, Radon-Nikodym theorem. Hilbert spaces, orthonormal bases, Riesz representation theorem, compact operators, L^p spaces, Hölder and Minkowski inequalities.

Joint undergraduate/graduate course - MAT457H1/MAT1000H

Prerequisite: MAT357H1
Exclusion: MAT457Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT458H1 - Advanced Real Analysis II

Hours: 36L

Fourier series and transform, convergence results, Fourier inversion theorem, L^2 theory, estimates, convolutions. Banach spaces, duals, weak topology, weak compactness, Hahn-Banach theorem, open mapping theorem, uniform boundedness theorem.

Joint undergraduate/graduate course - MAT458H1/MAT1001H

Prerequisite: MAT457H1
Exclusion: MAT457Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM461H1 - Combinatorial Methods

Hours: 36L

A selection of topics from such areas as graph theory, combinatorial algorithms, enumeration, construction of combinatorial identities.

Joint undergraduate/graduate course - APM461H1/MAT1302H

Prerequisite: MAT224H1/ MAT247H1, MAT137Y1/ MAT157Y1, MAT301H1/ MAT347Y1
Recommended Preparation: MAT344H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT461H1 - Hamiltonian Mechanics

Hours: 36L

This course focuses on key notions of classical mechanics: Newton equations, variational principles, Lagrangian formulation and Euler-Lagrange equations, the motion in a central force, the motion of a rigid body, small oscillations, Hamiltonian formulation, canonical transformations, Hamilton-Jacobi theory, action-angle variables, and integrable systems.

Prerequisite: MAT244H1/ MAT267H1, MAT337H1/ MAT367H1, APM346H1/ MAT351Y1
Recommended Preparation: MAT267H1, MAT367H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM462H1 - Nonlinear Optimization

Hours: 36L

An introduction to first and second order conditions for finite and infinite dimensional optimization problems with mention of available software. Topics include Lagrange multipliers, Kuhn-Tucker conditions, convexity and calculus of variations. Basic numerical search methods and software packages which implement them will be discussed.

Prerequisite: ( MAT223H1, MAT224H1) / MAT247H1, MAT235Y1/ MAT237Y1/ MAT257Y1
Recommended Preparation: MAT336H1/ MAT337H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT464H1 - Riemannian Geometry

Hours: 36L

Riemannian metrics. Levi-Civita connection. Geodesics. Exponential map. Second fundamental form. Complete manifolds and Hopf-Rinow theorem. Curvature tensors. Ricci curvature and scalar curvature. Spaces of constant curvature.

Joint undergraduate/graduate course - MAT464H1/MAT1342H

Prerequisite: MAT367H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM466H1 - Mathematical Theory of Finance

Hours: 36L

Introduction to the basic mathematical techniques in pricing theory and risk management: Stochastic calculus, single-period finance, financial derivatives (tree-approximation and Black-Scholes model for equity derivatives, American derivatives, numerical methods, lattice models for interest-rate derivatives), value at risk, credit risk, portfolio theory.

Joint undergraduate/graduate course - APM466H1/MAT1856H

Prerequisite: APM346H1, STA347H1
Corequisite: STA457H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT475H1 - Problem Solving Seminar

This course addresses the question: How do you attack a problem the likes of which you have never seen before? Students will apply Polya's principles of mathematical problem solving, draw upon their previous mathematical knowledge, and explore the creative side of mathematics in solving a variety of interesting problems and explaining those solutions to others.

Prerequisite: MAT224H1/ MAT247H1, MAT235Y1/ MAT237Y1/ MAT257Y1, and at least 1.0 credit at the 300+ level in APM/MAT
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT477H1 - Seminar in Mathematics

Seminar in an advanced topic. Content will generally vary from semester to semester. Student presentations are required.

Prerequisite: MAT347Y1, MAT354H1, MAT357H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT478H1 - Seminar in Mathematics

Seminar in an advanced topic. Content will generally vary from semester to semester. Student presentations are required.

Prerequisite: MAT347Y1, MAT354H1, MAT357H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT482H1 - Topics in Mathematics

Hours: 36L

A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/.

Joint undergraduate/graduate course - MAT482H1/MAT1901H

Prerequisite: 6.0 APM/MAT credits at the 100, 200 and 300-level. Possible additional topic-specific prerequisites.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT483H1 - Topics in Mathematics

Hours: 36L

A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/.

Prerequisite: 6.0 APM/MAT credits at the 100, 200 and 300-level. Possible additional topic-specific prerequisites.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT495H1 - Independent Reading in Mathematics

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 36L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

APM496H1 - Independent Readings in Applied Mathematics

Independent study under the direction of a faculty member. Topic must be outside current undergraduate offerings. Similar workload to a course that has 36 lecture hours. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: minimum GPA 3.5 for APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT496H1 - Independent Reading in Mathematics

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 36L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT497Y1 - Research Project in Mathematics

Independent research under the direction of a faculty member. Not eligible for CR/NCR option. Similar workload to a 72L course.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

MAT499Y1 - Readings in Mathematics

Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 72L course. Not eligible for CR/NCR option.

Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.

Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)

Printer-friendly Version