You are here
Mathematics
Faculty List
Professor and Chair of the Department
J. Quastel, MSc, Ph D, FRSC
Professor and Associate Chair (Research)
S. Alexakis, BA, Ph D
Professor and Associate Chair (Graduate)
K. Rafi, B Sc, Ph D
Professor and Associate Chair (Undergraduate)
J. Repka, B Sc, Ph D (U)
University Professors
J.G. Arthur, MA, Ph D, FRSC, FRS
J. Friedlander, MA, Ph D, FRSC (UTSC)
I.M. Sigal, BA, Ph D, FRSC
Professors
D. Bar-Natan, B Sc, Ph D
E. Bierstone, MA, Ph D, FRSC
I. Binder, B Sc, M Sc, Ph D (UTM)
J. Bland, M Sc, Ph D
A. Braverman, B Sc, Ph D
A. Burchard, B Sc, Ph D
G. Elliott, B Sc, Ph D, FRSC
M. Goldstein, B Sc, Ph D (UTSC)
M. Gualtieri, B Sc, Ph D
V. Ivrii, MA, Ph D, Dr Math, FRSC
L. Jeffrey, AB, Ph D, FRSC (UTSC)
R. Jerrard, M Sc, Ph D (U), FRSC
J. Kamnitzer, B Sc, Ph D
V. Kapovitch, B Sc, Ph D
Y. Karshon, B Sc, Ph D (UTM)
K. Khanin, M Sc, Ph D (UTM)
B. Khesin, M Sc, Ph D
A. Khovanskii, M Sc, Ph D
H. Kim, B Sc, Ph D
S. Kudla, B A, MA, Ph D, FRSC
M. Marcolli, M Sc, Ph D
R. McCann, BSc, Ph D, FRSC
E. Meinrenken, B Sc, Ph D, FRSC
P. Milman, Dipl Maths, Ph D, FRSC
F. Murnaghan, M Sc, Ph D
K. Murty, B Sc, Ph D, FRSC
A. Nabutovsky, M Sc, Ph D
A. Nachman, B Sc, Ph D
D. Panchenko, B Sc, M Sc, Ph D
M. Pugh, BSc, Ph D
R. Rotman BA, Ph D
L. Seco, BA, Ph D (UTM)
C. Sulem, M Sc, Dr D’Etat, FRSC
S. Todorcevic, B Sc, Ph D, FRSC
B. Virag, BA, Ph D (UTSC)
W.A.R. Weiss, M Sc, Ph D (UTM)
M. Yampolsky, B Sc, Ph D (UTM)
Associate Professors
F. Herzig, BA, Ph D
J. Scherk, D Phil (UTSC)
J. Tsimerman, Ph D
Associate Professors, Teaching Stream
D. Burbulla, B Sc, B Ed, MA
Assistant Professors
S. Aretakis, MA, Ph D (UTSC)
C. Blois, B Sc, M Sc, Ph D
J. de Simoi, M Sc, Ph D (UTM)
V. Dimitrov, AB, M Sc, Ph D (Coxeter, CLTA)
M. Groechenig, B Sc, D Phil (UTM)
R. Haslhofer, B Sc, M Sc, Ph D (UTSC)
J. Lefebvre, B Sc, Ph D
Y. Liokumovich, B Sc, M Sc, Ph D (UTM)
F. Pusateri, BS, MS, Ph D
B. Rossman, BA, MA, Ph D
K. Serkh, Ph D
A. Shankar, B Sc, Ph D (UTM)
A. Stinchombe, BMath, Ph D
G. Tiozzo, MA, Ph D (UTSC)
I. Varma, Ph D
W. Yu, Ph D (UTSC)
H. Yuen, BA, Ph D
A. Zaman, B Sc, M Sc, Ph D
K. Zhang, B Sc, Ph D (UTM)
Assistant Professors, Teaching Stream
B. Galvao-Souza, Ph D
A. Gracia-Saz, Ph D
N. Hoell BA, MA, M Phil, Ph D - CLTA
S. Mayes-Tang, Bc, MS, Ph D
F. Parsch, B Sc, M Sc, Ph D
B. Rossman, BA, MA, Ph D
J. Siefken, HBS, MS, Ph D
Lecturers
S. Homayouni, B Sc, Ph D
N. Jung, BA, MSc, Ph D
E.A.P. LeBlanc, MA, Ph D
J. Tate, B Sc, B Ed
S. Uppal, M Sc
Professors Emeriti
M.A. Akcoglu, M Sc, Ph D, FRSC
E.J. Barbeau, MA Ph D (U)
T. Bloom, MA, Ph D, FRSC
M. D. Choi, MA, Ph D, FRSC
H.C. Davis, MA, Ph D (N)
E.W. Ellers, Dr Rer Nat
I.R. Graham, B Sc, Ph D (UTM)
S. Halperin, M Sc, Ph D, FRSC
V. Jurdjevic, MS, PhD
J.W. Lorimer, M Sc, Ph D (U)
E. Mendelsohn, M Sc, Ph D (UTSC)
K. Murasugi, MA, D Sc, FRSC
P. Rosenthal, MA, Ph D, LLB
P. Selick, B Sc, MA, Ph D (UTSC)
D.K. Sen, M Sc, Dr s Sc
F. D. Tall, AB, Ph D (UTM)
Associate Professors Emeriti
N.A. Derzko, B Sc, Ph D
S.M. Tanny, B Sc, Ph D (UTM)
Associate Professors Emeriti, Teaching Stream
A. Igelfeld, M Sc
A. Lam, M Sc
Senior Lecturers Emeriti
P. Kergin, Ph D
F. Recio, MSc, Ph D
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.
The Professional Experience Year Co-op Program is available to eligible full-time Specialist and Major students after their second or third year of study. The PEY Co-op program is an optional 12-16-month work term providing industrial experience. It gives students an opportunity to apply their skills in the context of a paid internship.
The Department of Mathematics offers introductory courses for incoming students to foster the development of mathematics skills.
PUMP Level 1 and PUMP Level 2 (Preparing for University Mathematics Program)
Both programs are non-credit courses that equip students with the necessary background knowledge required to succeed in first year mathematics courses. The content for the courses may be viewed at http://www.math.toronto.edu/cms/undergraduate-program/current-students-ug/pump-courses-2/.
PUMP Level 1 provides a quick math review during the months of July and August, for students who would like to take six weeks prior to the start of the first semester to practice pre-calculus math skills. During other terms, it is scheduled as a longer course, for students who have not taken the appropriate high school mathematics prerequisites for university calculus and linear algebra. This course is recommended for any student who wish to close any existing gap between high school math and University level math courses or anyone who wishes to review high school math before attempting University level math or other science courses.
PUMP Level 2 is an Introduction to Proofs course. The curriculum provides background knowledge that is a preparation for MAT137Y1, MAT157Y1, MAT240H1, MAT247H1, MAT237Y1, and other proof-oriented advanced courses. The course covers the reading and comprehension of mathematical statements, analyzing definitions and properties, formulation of arguments, and strategies for proofs. This course is recommended for any student who wish to add to their knowledge by joining the group of students who will commence their preparation for the more challenging concepts in the advance analytical programs, during the months of July and August.
Visit https://www.math.toronto.edu/cms/undergraduate-program/potential-students-ug/ for up-to-date information on the availability of PUMP Level 1 and PUMP Level 2.
If you have questions about the content of these courses, e-mail 1styear@math.toronto.edu.
Course Change Dates
Some of the more advanced first- and second-year courses have "change dates" during the first few weeks of the academic year. The "change date" occurs after the general "add date" for courses and before the "drop date" for courses. For example, a student enrolled in MAT157Y1 can change their enrolment to MAT137Y1 or MAT135H1 at any time on or before the change date. For deadlines and further details, see https://www.math.toronto.edu/cms/undergraduate-program/current-students-ug/change-dates/.
Contact Information
Associate Chair for Undergraduate Studies
Enquiries and student counseling: Bahen Centre, Room 6291
Departmental Office: Bahen Centre, Room 6290 (416-978-3323)
Websites: https://www.math.toronto.edu/cms/potential-students-ug/
Mathematics Programs
Mathematics Specialist (Science Program) - ASSPE1165
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(12.5 FCE, including at least 3.0 FCE at the 400-level)
The Specialist Program in Mathematics is directed toward students who hope to pursue mathematical research as a career.
First Year:
MAT157Y1, MAT240H1, MAT247H1
Second Year:
MAT257Y1, MAT267H1
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
NOTE: Students may use the CR/NCR option with this H course and have it count toward the Mathematics Specialist program. Students in the VIC program may also use VIC172Y1.
2. MAT327H1
Third and Fourth Years:
1. MAT347Y1, MAT354H1, MAT357H1, MAT363H1/ MAT367H1 ( MAT363H1 can be taken in the second year, if desired)
2. 2.0 FCE of: MAT309H1, MAT351Y1, ANY 400-level APM/MAT
3. 3.0 FCE of APM/MAT at the 300+ level, including at least 2.0 FCE at the 400 level (these may include options above not already chosen)
4. MAT477H1
NOTE:
1. The Department recommends that PHY151H1 and PHY152H1 be taken in the First Year, and that CSC148H1 and STA257H1 be taken during the program. If you do not have a year-long course in programming from high school, the Department strongly recommends that you take CSC108H1 prior to CSC148H1.
2. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
3. Students with a CGPA of 3.5 and above may apply to have graduate level math courses count towards their 400-level course requirements.
Applied Mathematics Specialist (Science Program) - ASSPE2053
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(13.0-13.5 FCE, including at least 1.5 FCE at the 400-level)
The Specialist Program in Applied Mathematics is directed toward students who hope to pursue applied mathematical research as a career.
First Year:
MAT157Y1, MAT240H1, MAT247H1, ( CSC108H1, CSC148H1)/ CSC150H1
Second Year:
MAT257Y1, MAT267H1, STA257H1, STA261H1
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
NOTE: Students may use the CR/NCR option with this H course and have it count toward the program. Students in the VIC program may also use VIC172Y1.
Third and Fourth Years:
1. MAT351Y1, MAT327H1, MAT347Y1, MAT354H1, MAT357H1, MAT363H1/ MAT367H1 ( MAT363H1 can be taken in the second year, if desired), STA347H1
2. At least 1.5 FCE chosen from: MAT332H1, MAT344H1, MAT454H1, MAT457H1, MAT458H1, MAT464H1, STA302H1, STA457H1, CSC336H1, CSC436H1, CSC446H1, CSC456H1
3. 1.0 FCE from: APM421H1, APM426H1, APM441H1, APM446H1, APM461H1, APM462H1, APM466H1
4. MAT477H1
NOTE:
1. The Department recommends that PHY151H1 and PHY152H1 be taken in the First Year, and that CSC148H1 and STA257H1 be taken during the program. If you do not have a year-long course in programming from high school, the Department strongly recommends that you take CSC108H1 prior to CSC148H1.
2. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
3. Students with a CGPA of 3.5 and above may apply to have graduate level math courses count towards their 400-level course requirements.
Mathematics and Physics Specialist (Science Program) - ASSPE0397
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(14.5-15.5 FCE, including at least 1.0 FCE at the 400-level)
First Year:
MAT157Y1, MAT240H1, MAT247H1, PHY151H1, PHY152H1
Second Year:
MAT257Y1, MAT267H1, PHY224H1, PHY250H1, PHY252H1, PHY254H1, PHY256H1
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
NOTE: Students may use the CR/NCR option with this H course and have it count toward the program. Students in the VIC program may also use VIC172Y1.
2. Note: PHY252H1 and PHY324H1 may be taken in the 2nd or 3rd year.
Third Year:
1. MAT351Y1, MAT334H1/ MAT354H1, MAT357H1
2. One of: MAT327H1, MAT347Y1, MAT363H1/ MAT367H1 ( MAT363H1 can be taken in the second year, if desired)
3. PHY324H1, PHY350H1, PHY354H1, PHY356H1
Fourth Year:
1. Two of: APM421H1, APM426H1, APM446H1, APM441H1
2. Two of: PHY450H1, PHY452H1, PHY454H1, PHY456H1, PHY460H1
3. One of: MAT477H1, PHY424H1, PHY478H1, PHY479Y1
NOTE:
1. Students who are intending to apply to graduate schools in mathematics would be well-advised to take MAT347Y1.
2. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
3. Students with a CGPA of 3.5 and above may apply to have graduate level math courses count towards their 400-level course requirements.
Mathematics and Philosophy Specialist (Science Program) - ASSPE1361
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
Consult the Undergraduate Coordinators of the Departments of Mathematics and Philosophy.
(12.0 FCE including at least 1.0 FCE at the 400-level)
First Year:
MAT157Y1, MAT240H1, MAT247H1; PHL232H1 or PHL233H1
Higher Years:
1. MAT257Y1, MAT327H1, MAT347Y1, MAT354H1/ MAT357H1
2. PHL345H1, MAT309H1/ PHL348H1
3. Four of: PHL325H1, PHL331H1, PHL332H1, PHL346H1/PHL354H1, PHL347H1, PHL349H1, PHL355H1, PHL451H1, PHL480H1
4. 1.0 FCE from PHL200Y1/ PHL205H1/ PHL206H1/ PHL210Y1
5. PHL265H1/ PHL275H1
6. 2.0 FCE of PHL/APM/MAT at the 300+ level, to a total of 12.0 FCE.
NOTE: Students with a CGPA of 3.5 and above may apply to have graduate level math courses count towards their 400-level course requirements.
Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(12-12.5 FCE, including at least 1.5 FCE at the 400-level)
First Year:
ECO100Y/( ECO101H1, ECO102H1); MAT137Y1/ MAT157Y1, MAT223H1, MAT224H1
(Please check the requirements for ECO206Y1 to ensure that you pass these first year courses with grades that allow registration in ECO206Y1)
Second Year:
ECO206Y1; MAT237Y1, MAT244H1, MAT246H1 (waived for students taking MAT157Y1); STA257H1, STA261H1
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
Note: Students may use the CR/NCR option with this H course and have it count toward the program. Students in the VIC program may also use VIC172Y1.
Third Year:
1. APM346H1; ECO358H1; ECO359H1; MAT337H1; STA302H1/ ECO375H1; STA347H1
2. One of: MAT332H1, MAT344H1, MAT334H1, MAT475H1
Fourth Year:
NOTE:
1. Students planning to take specific fourth year courses should ensure that they have the necessary third year prerequisites.
2. Please note that STA457H1 lists STA302H1 as one of the prerequisites so you are encouraged to plan ahead.
Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(13.5-14.5 FCE, including at least 1.0 FCE at the 400 level)
Core Courses:
First Year:
( CSC108H1, CSC148H1)/ CSC150H1, MAT137Y1/ MAT157Y1, MAT223H1/ MAT240H1,
MAT224H1/ MAT247H1 (recommended, can also be taken in 2nd year)
Second Year:
MAT235Y1/ MAT237Y1/ MAT257Y1, MAT246H1 (waived for students taking MAT157Y1), MAT244H1/ MAT267H1, STA257H1
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
Note: Students may use the CR/NCR option with this H course and have it count toward the program. Students in the VIC program may also use VIC172Y1.
Higher Years:
NOTE:
1. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
Physical Sciences Concentration:
2. PHY151H1, PHY152H1, AST221H1
3. Three of: AST222H1, PHY250H1, PHY252H1, PHY254H1, PHY256H1
4. APM346H1/ MAT351Y1
5. Three of: AST320H1, AST325H1, MAT337H1, MAT363H1/ MAT367H1, PHY350H1, PHY354H1, PHY356H1, PHY357H1, PHY358H1
6. Two of: APM421H1, APM426H1, APM441H1, APM446H1, PHY407H1, PHY408H1, PHY456H1
Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(11.5-13.0 FCE, including at least 1.0 FCE at the 400 level)
Core Courses:
First Year:
( CSC108H1, CSC148H1)/ CSC150H1; MAT137Y1/ MAT157Y1, MAT223H1/ MAT240H1, MAT224H1/ MAT247H1
Second Year:
MAT235Y1/ MAT237Y1/ MAT257Y1, MAT246H1 (waived for students taking MAT157Y1), MAT244H1/ MAT267H1; STA257H1
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
Note: Students may use the CR/NCR option with this H course and have it count toward the program. Students in the VIC program may also use VIC172Y1.
Higher Years:
MAT301H1, MAT334H1
NOTE:
1. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
Probability/Statistics Concentration:
1. APM346H1/ MAT351Y1/ APM462H1; MAT337H1; STA261H1, STA302H1, STA347H1, STA352Y1/( STA452H1, STA453H1)
2. Additional 1.0 FCE at the 300+level from APM/MAT/STA
3. Two of: STA437H1, STA442H1, STA447H1, STA457H1
Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(11.5-12.0 FCE, including at least 1.0 FCE at the 400 level)
Core Courses:
First Year:
CSC108H1; MAT137Y1/ MAT157Y1, MAT223H1/ MAT240H1, MAT224H1/ MAT247H1 (recommended, can also be taken in 2nd year)
Second Year:
MAT235Y1/ MAT237Y1/ MAT257Y1, MAT246H1 (waived for students taking MAT157Y1), MAT244H1/ MAT267H1; STA257H1
NOTE:
1. MAT237Y1/ MAT257Y1 is a direct or indirect prerequisite for many courses in each of the areas of concentration except the Teaching Concentration. Students are advised to take MAT237Y1/ MAT257Y1 unless they have planned their program and course selection carefully and are certain that they will not need it.
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
Note: Students may use the CR/NCR option with this H course and have it count toward the program. Students in the VIC program may also use VIC172Y1.
Higher Years:
MAT301H1, MAT334H1
NOTE:
1. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
Teaching Concentration:
For course selection, note that OISE requires students to have a second teachable subject.
1. MAT329Y1, HPS390H1/ MAT390H1, HPS391H1/ MAT391H1
2. Two of: MAT332H1/ MAT344H1, MAT335H1, MAT337H1, MAT363H1/ MAT367H1
3. Two of: MAT309H1, MAT315H1; STA302H1/ STA347H1
4. MAT401H1/ MAT402H1 and 0.5 FCE at the 400-level from MAT, APM, STA
Mathematics Major (Science Program) - ASMAJ1165
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(7.5 full courses or their equivalent. These must include at least 2.5 full course equivalent (FCE) at the 300+ level. Of those 2.5 FCE,at least 0.5 FCE must be at the 400 level).
First Year:
( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1, MAT223H1/ MAT240H1, MAT224H1/ MAT247H1
Second Year:
MAT235Y1/ MAT237Y1/ MAT257Y1, MAT244H1, MAT246H1
NOTE:
1. MAT224H1 may be taken in first year
Second and Higher Years:
1. 0.5 FCE with a significant emphasis on ethics and social responsibility: ANT100Y1/ ANT253H1/ CSC300H1/ EEB215H1/ ENV200H1/ ENV333H1/ ESS205H1/ ETH201H1/ ETH210H1/ ETH220H1/ FOR200H1/ HMB203H1/ HPS200H1/ HPS250H1/ HPS301H1/ HST209H1/ IMC200H1/ JPH441H1/ PHL240H1/ PHL244H1/ PHL265H1/ PHL271H1/ PHL273H1/ PHL275H1/ PHL281H1/ PHL295H1 or another H course approved by the Department.
Note: Students may use the CR/NCR option with this H course and have it count toward the program. Students in the VIC program may use VIC172Y1.
Higher Years:
1. MAT301H1, MAT309H1/ MAT315H1, MAT334H1
2. Additional 0.5 FCE at the 200+ level from: ACT240H1/ ACT230H1 APM236H1, MAT309H1/ MAT315H1/ MAT335H1/ MAT337H1, STA247H1/ STA257H1
3. Additional 0.5 FCE at the 300+level from: APM346H1, APM462H1, MAT309H1, MAT315H1, MAT332H1/ MAT344H1, MAT335H1, MAT337H1, MAT363H1, MAT475H1, HPS390H1, HPS391H1, PSL432H1
4. MAT401H1/ MAT402H1 or any other MAT/APM 400-level course
NOTES:
1. Students using MAT157Y1 towards the first year program requirements must replace the exclusion course MAT246H1 with a different H level MAT/APM course at the 200+ level.
2. In the major program, higher level courses within the same topic are acceptable substitutions. With a judicious choice of courses, usually including introductory computer science, students can fulfill the requirements for a double major in mathematics and one of several other disciplines.
3. Students planning to take specific fourth year courses should ensure that they have the necessary second and third year prerequisites.
4. 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 (H B Sc) from the University of Toronto and a Master of Teaching (M T) 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.
Mathematics Minor (Science Program) - ASMIN1165
This is an open enrolment program. A student who has completed 4.0 credits may enrol in the program.
(4.0 FCE)
1. ( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1
2. MAT221H1(80%+)/ MAT223H1/ MAT240H1, MAT235Y1/ MAT237Y1/ MAT257Y1, MAT224H1/ MAT244H1/ MAT246H1/ APM236H1/ MAT247H1
Note: MAT221H1/ MAT223H1 should be taken in first year
3. Additional 1.0 FCE at the 300+ level from APM/MAT/ HPS390H1/ HPS391H1/ PSL432H1 [note that APM306Y1 will be counted as 0.5 FCE towards this requirement.].
NOTE:
1. In the minor program, higher level courses within the same topic are acceptable substitutions.
2. Students planning to take specific third and fourth year courses should ensure that they have the necessary first, second and third year prerequisites.
3. APM306Y1 will be counted for 0.5 credits of Society and its Institutions (BR3) and 0.5 credits of The Physical and Mathematical Universes (BR5).
Joint Programs
- Economics and Mathematics, see Economics
- Statistics and Mathematics, see Statistics
- Combined Degree Program: STG, Honours Bachelor of Science, Major in Mathematics / Master of Teaching
Combined Degree Program (CDP) in Science and Education: Mathematics (Major), Honours Bachelor of Science/Master of Teaching
The Combined Degree Program in Arts/Science and Education is designed for students interested in studying the intersections of teaching subjects and Education, coupled with professional teacher preparation. Students earn an Honours Bachelor’s degree from the Faculty of Arts and Science (St. George) and an accredited professional Master of Teaching (MT) degree from the Ontario Institute for Studies in Education (OISE). They will be recommended to the Ontario College of Teachers for an Ontario Teacher’s Certificate of Qualifications as elementary or secondary school teachers. The CDP permits the completion of both degrees in six years with 1.0 FCE that may be counted towards both the undergraduate and graduate degrees.
Program requirements:
1. Minor in Education and Society, Victoria College
2. Major in Mathematics (first teaching subject)
3. Minor in an area corresponding to the second teaching subject as determined by OISE (see http://pepper.oise.utoronto.ca/~jhewitt/mtresources/intermediate_senior_teaching_subject_prerequisites_2016-17.pdf)
See here for additional information on the CDP, including admission, path to completion and contact information.
Mathematics Courses
MAT133Y1 - Calculus and Linear Algebra for Commerce
Mathematics of finance. Matrices and linear equations. Review of differential calculus; applications. Integration and fundamental theorem; applications. Introduction to partial differentiation; applications.
NOTE: please note Prerequisites listed below. Students without the proper prerequisites for MAT133Y1 may be deregistered from this course.
Note that MAT133Y is not a valid prerequisite for a number of more advanced quantitative courses. Students who are considering a quantitative non-Commerce PoSt, such as a math minor or a stats minor, may want to consider MAT135H and MAT136H, MAT137Y, or MAT157Y instead of MAT133Y. Specifically, a student who took MAT133Y may need to subsequently take MAT135H and MAT136H as "extra" or take MAT137Y or MAT157Y in order to proceed in non-Commerce PoSts.
Exclusion: MAT135H1, MAT136H1, MAT137Y1, MAT157Y1, MATA30H3, MATA31H3, MATA32H3, MATA33H3, MATA35H3, MATA36H3, MATA37H3, MAT133Y5, MAT134Y5, MAT135Y5, MAT137Y5, MAT138Y5, MAT186H, MAT187H, MAT196H & MAT197H, ESC194H, ESC195H
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT135H1 - Calculus I
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.
Exclusion: MAT133Y1, MAT136H1, MAT137Y1, MAT157Y1, MATA30H3, MATA31H3, MATA32H3, MATA33H3, MATA35H3, MATA36H3, MATA37H3, MAT133Y5, MAT134Y5, MAT135Y5, MAT137Y5, MAT138Y5, MAT186H, MAT187H, MAT196H, MAT197H, ESC194H, ESC195H,
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT136H1 - Calculus II
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.
Exclusion: MAT133Y1, MAT137Y1, MAT157Y1, MATA32H3, MATA33H3, MATA36H3, MATA37H3, MAT133Y5, MAT134Y5, MAT135Y5, MAT137Y5, MAT138Y5, MAT186H, MAT187H, MAT196H, MAT197H, ESC194H, ESC195H.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT137Y1 - Calculus with Proofs
A conceptual approach for students with a serious interest in mathematics. Attention is given to computational aspects as well as theoretical foundations and problem solving techniques. Review of Trigonometry. Limits and continuity, mean value theorem, inverse function theorem, differentiation, integration, fundamental theorem of calculus, elementary transcendental functions, Taylor's theorem, sequence and series, power series. Applications.
Exclusion: MAT135H1, MAT136H1, MAT157Y1, MATA35H3, MATA36H3, MATA37H3, MAT135Y5, MAT137Y5, MAT138Y5, MAT187H, MAT196H, MAT197H, ESC194H, ESC195H.
Recommended Preparation: Students will receive credit for both MAT137Y1 and MAT138H1 if MAT138H1 is taken before or along with MAT137Y1.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT138H1 - Introduction to Proofs
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. The course is aimed at students interested in the creative character of mathematics, particularly those planning to take any of our proof-oriented courses, and is an excellent preparation for MAT137Y1, MAT157Y1, or MAT240H1.
Note: students may take this course concurrently with MAT157Y1 or MAT137Y1, or prior to registering in MAT157Y1 or MAT137Y1. This course can also be used by students who have already taken MAT136H1 and wish to bridge the gap to MAT237Y1.
Exclusion: MAT157Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT157Y1 - Analysis I
A theoretical course in calculus; emphasizing proofs and techniques, as well as geometric and physical understanding. Trigonometric identities. 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.
Exclusion: MAT137Y1, MATA37H3, MAT137Y5, MAT157Y5, MAT197H1, ESC195H1.
Recommended Preparation: Students should consider taking the Preparing for University Math Level II in order to prepare in advance for MAT157Y1. Students may also take MAT138H1 concurrently with MAT157Y1. Students will receive credit for both MAT157Y1 and MAT138H1 if MAT138H1 is taken before or along with MAT157Y1.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
JMB170Y1 - Biology, Models, and Mathematics
Applications of mathematics to biological problems in physiology, genetics, evolution, growth, population dynamics, cell biology, ecology, and behaviour. Mathematical topics include: power functions and regression; exponential and logistic functions; binomial theorem and probability; calculus, including derivatives, max/min, integration, areas, integration by parts, substitution; differential equations, including linear constant coefficient systems; dynamic programming; Markov processes; and chaos. This course is intended for students in Life Sciences.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT193H1 - Mathematics through Literature & Poetry
Mathematics intersects with literature and poetry in a multitude of ways. In this seminar, students will study literary works that include mathematicians, are about mathematicians, and contain mathematical forms. These works will be a springboard for mathematical investigations that build a deeper understanding of and appreciation for mathematics. This course is appropriate for students with all mathematical backgrounds who are not taking another math course. Restricted to first-year students. Not eligible for CR/NCR option.
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
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.
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
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
JUM202H1 - Mathematics as an Interdisciplinary Pursuit
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
JUM203H1 - Mathematics as a Recreation
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
JUM205H1 - Mathematical Personalities
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT221H1 - Applied Linear Algebra
An application-oriented approach to linear algebra, based on calculations in standard Euclidean space. Systems of linear equations, matrices, Gauss-Jordan 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.
Exclusion: MAT223H1, MATA23H3, MAT223H5, MAT224H1, MAT240H1, MAT240H5, MAT247H1, MAT247H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT223H1 - Linear Algebra I
Systems of linear equations, matrix algebra, real vector spaces, subspaces, span, linear dependence and independence, bases, rank, inner products, orthogonality, orthogonal complements, Gram-Schmidt, linear transformations, determinants, Cramer's rule, eigenvalues, eigenvectors, eigenspaces, diagonalization.
Exclusion: MATA22H3, MATA23H3, MAT223H5, MAT224H1, MAT240H1, MAT240H5, MAT247H1, MAT247H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT224H1 - Linear Algebra II
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.
Exclusion: MAT247H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT235Y1 - Calculus II
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.
Exclusion: MAT237Y1, MAT257Y1, MATB41H3, MATB42H3, MAT232H5, MAT233H5, MAT236H5, MAT368H5, MAT291H & MAT294H
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM236H1 - Applications of Linear Programming
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT237Y1 - Multivariable Calculus
Sequences and series. Uniform convergence. Convergence of integrals. Elements of topology in R^2 and R^3. Differential and integral calculus of vector valued functions of a vector variable, with emphasis on vectors in two and three dimensional euclidean space. Extremal problems, Lagrange multipliers, line and surface integrals, vector analysis, Stokes' theorem, Fourier series, calculus of variations.
Exclusion: MAT235Y1, MAT257Y1, MATB41H3, MATB42H3, MATB43H3 & MAT368H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT240H1 - Algebra I
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.
Corequisite: MAT157Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT244H1 - Introduction to Ordinary Differential Equations
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.
Corequisite: MAT235Y1/MAT237Y1/MAT257Y1
Exclusion: MAT267H1, MAT212H5, MAT258Y5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT245H1 - Mathematical Methods in Data Science
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.
Corequisite: MAT237Y1/MAT257Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT246H1 - Concepts in Abstract Mathematics
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.
Exclusion: MAT157Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT247H1 - Algebra II
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.
Corequisite: MAT157Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT257Y1 - Analysis II
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT267H1 - Advanced Ordinary Differential Equations
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.
Corequisite: MAT257Y1
Exclusion: APM288H1, MAT244H1, MATB44H3, MAT242H5, MAT252H5, MAT234H1, MAT292H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT271H1 - Insights from Mathematics
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.
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT282H1 - Topics in Mathematics
A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional preqrequisites, go to http://www.math.toronto.edu/cms/current-students-ug/
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.
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.
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.
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.
MAT301H1 - Groups and Symmetries
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.
Exclusion: MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM306Y1 - Mathematics and Law
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 FCE in BR3 and 0.5 FCE in BR5.
This course will only contribute 0.5FCE to the Math Minor program.
Exclusion: JUM206Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5); Society and its Institutions (3)
MAT309H1 - Introduction to Mathematical Logic
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.
Exclusion: CSC438H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT315H1 - Introduction to Number Theory
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT327H1 - Introduction to Topology
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT329Y1 - Concepts in Elementary Mathematics
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.
Exclusion: MAT382H5
Recommended Preparation: Participation in the practicum requires the presentation of an Ontario Police Report that declares suitability to work with minors and other special groups.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT332H1 - Introduction to Graph Theory
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.
Corequisite: Recommended Corequisite: MAT301H1/MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT334H1 - Complex Variables
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.
Exclusion: MAT354H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT335H1 - Chaos, Fractals and Dynamics
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT336H1 - Elements of Analysis
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.
Exclusion: MAT257Y1, MAT337H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT337H1 - Introduction to Real Analysis
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.
Exclusion: MAT357H1 & MAT378H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT344H1 - Introduction to Combinatorics
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM346H1 - Partial Differential Equations
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.
Exclusion: MAT351Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT347Y1 - Groups, Rings and Fields
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM348H1 - Mathematical Modelling
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.
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
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.
Exclusion: APM351Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT354H1 - Complex Analysis I
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT357H1 - Foundations of Real Analysis
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.
Exclusion: MAT438H5
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT363H1 - Geometry of Curves and Surfaces
Curves and surfaces in 3-spaces. Frenet formulas. Curvature and geodesics. Gauss map. Minimal surfaces. Gauss-Bonnet theorem for surfaces. Surfaces of constant curvature.
Exclusion: MAT367H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT367H1 - Differential Geometry
Manifolds, partitions of unity, submersions and immersions, vector fields, vector bundles, tangent and cotangent bundles, foliations and Frobenius’ theorem, multillinear algebra, differential forms, Stokes’ theorem, Poincare-Hopf theorem
Recommended Preparation: Multivariable calculus (MAT257Y1), Linear algebra (MAT240H1, MAT247H1)
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT377H1 - Mathematical Probability
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).
Exclusion: STA347H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT382H1 - Topics in Mathematics
A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional preqrequisites, go to http://www.math.toronto.edu/cms/current-students-ug/
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT390H1 - History of Mathematics up to 1700
A survey of ancient, medieval, and early modern mathematics with emphasis on historical issues. (Offered in alternate years)
Exclusion: HPS309H1, HPS310Y1, HPS390H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT391H1 - History of Mathematics after 1700
A survey of the development of mathematics from 1700 to the present with emphasis on technical development. (Offered in alternate years)
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.
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.
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.
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.
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.
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.
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
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.
Exclusion: MAT347Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT402H1 - Classical Geometries
Euclidean and non-euclidean plane and space geometries. Real and complex projective space. Models of the hyperbolic plane. Connections with the geometry of surfaces.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT409H1 - Set Theory
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT415H1 - Algebraic Number Theory
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT417H1 - Analytic Number Theory
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM421H1 - Mathematical Foundations of Quantum Mechanics
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT425H1 - Differential Topology
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM426H1 - General Relativity
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT436H1 - Introduction to Linear Operators
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT437H1 - K-Theory and C* Algebras
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
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
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)
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT445H1 - Representation Theory
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM446H1 - Applied Nonlinear Equations
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-Simmons equations (particle and condensed matter physics).
Joint undergraduate/graduate course - APM446H1/MAT1508H
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT448H1 - Introduction to Commutative Algebra and Algebraic Geometry
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT449H1 - Algebraic Curves
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT454H1 - Complex Analysis II
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT457H1 - Advanced Real Analysis I
Lebesque 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
Exclusion: MAT457Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT458H1 - Advanced Real Analysis II
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
Exclusion: MAT457Y1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM461H1 - Combinatorial Methods
A selection of topics from such areas as graph theory, combinatorial algorithms, enumeration, construction of combinatorial identities.
Joint undergraduate/graduate course - APM461H1/MAT1302H
Recommended Preparation: MAT344H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM462H1 - Nonlinear Optimization
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 variations. Basic numerical search methods and software packages which implement them will be discussed.
Recommended Preparation: MAT336H1/MAT337H1
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT464H1 - Riemannian Geometry
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
APM466H1 - Mathematical Theory of Finance
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
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT477H1 - Seminar in Mathematics
MAT478H1 - Seminar in Mathematics
MAT482H1 - Topics in Mathematics
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
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT483H1 - Topics in Mathematics
A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional preqrequisites, go to http://www.math.toronto.edu/cms/current-students-ug/
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.
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.
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.
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.
Distribution Requirements: Science
Breadth Requirements: The Physical and Mathematical Universes (5)