Physical and Mathematical Sciences

University of Toronto · St. George

4 years
Duration (years)
4 years (standard HBA/HBSc honours degree)
Toronto University College registrar: honours four-year degree
Paid internship in eligible study options
Work experience
The Mathematics Major is an example of a later option eligible for the Arts & Science Internship Program. Admission to ASIP is separate. It includes 12–20 months of paid, full-time work and professional development. ASIP students usually finish in five years.
U of T Arts & Science Calendar, internship eligibility and duration
~Mid to high 80s
Entering average
Published approximate guidance: Mid to high 80s. 2027/28. Ontario high-school entry in 2027/28, exact St. George route TPG. Later major selection and other applicant categories are separate.
Toronto – St. George university-supplied OUInfo: Mathematical & Physical Sciences, Ontario entry 2027/28

Deadlines

November 2026

Mon	Tue	Wed	Thu	Fri	Sat	Sun
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18		20	21	22
23	24	25	26	27	28	29
30

Next deadlineThursday, November 19, 2026

OUAC. Ontario high schools report midterm/final 4U/M grades
2027 entry
School deadline, not a student task. Universities receive these grades by November 26. Verbatim: "Deadline for the OUAC to receive all midterm or final grades available for 4U/M courses from Ontario high schools. Schools may report in-progress grades for full-year courses as soon as they are available." Universities receive these by the target date of November 26, 2026. This is a deadline on the high school, not on the student, but it governs which grades a university sees in the first round.
Official deadline

Other deadline details

No single OUAC deadline, deadlines are set by each university and sometimes by programOUAC Undergraduate application, applicants who are not Ontario high school students (Group B)2026 entry

No single OUAC deadline, deadlines are set by each university and sometimes by program
No single OUAC deadline
University, program, transcript, portfolio, interview, and audition dates still apply

Full source wording

Verbatim: "There is no specific Undergraduate application deadline if you are a Group B applicant. Deadlines vary at each university and sometimes depend on the program. Visit the university websites or contact the universities directly for their deadlines. If you are interested in a program but the deadline has passed, you may contact the university's admission office for help. Be aware of university-specific deadlines for submitting transcripts and portfolios, if required, and for arranging interviews and auditions. You must ensure the OUAC has enough time to process your choices before the universities' program deadlines." OUAC defines Group B as anyone who does not meet the Group A criteria, e.g. not currently taking an Ontario high school course, a Canadian outside Ontario, an international applicant, a postsecondary transfer student, or a mature applicant.

SourceChecked Aug 14, 2026

Requirements

Admission requirements

High-school prerequisites

ENG4U / EAE4UEnglish
MCV4UCalculus & Vectors

Application steps

Entry terms · Fall

September 2027 full-time undergraduate entry to St. George Physical and Mathematical Sciences.

Step 1Check the admission requirements
- Check the published entry route for your applicant category.
University of Toronto current St. George exact-programme Ontario admission tableUniversity of Toronto current St. George exact-programme Ontario admission table
Step 2Apply through OUAC
- Create your application and select this program.
OUACOUAC
Step 3Secondary and postsecondary academic records
- Disclose all attempted secondary and postsecondary studies. Current full-time Ontario high school grades must arrive through OUAC; do not upload unsolicited Ontario transcripts. Applicants who completed Grade 11 elsewhere must also provide those results. Your portal lists the documents needed for your background.
U of T required application documentsU of T required application documents
Step 4Translations for documents outside English or French
- If your academic documents are in another language, submit notarized translations with the original records.
U of T document translationsU of T document translations
Step 5Apply through OUAC to the exact entry programme/admission category; provide required applicant academic records.
- Complete this item using the university’s applicant instructions.
University of Toronto current St. George exact-programme Ontario admission tableUniversity of Toronto current St. George exact-programme Ontario admission table
Step 6Select St. George Physical and Mathematical Sciences (TPG) through OUAC. U of T allows one application to St. George Arts & Science per cycle.
- Complete this item using the university’s applicant instructions.
University of Toronto current St. George exact-programme Ontario admission tableUniversity of Toronto current St. George exact-programme Ontario admission table

Applicant pathways

St. George programme Ontario admission

Ontario high-school applicants to this St. George programme only; other campuses do not share this table

Ontario Secondary School Diploma (OSSD) with six subjects at the 4U/M level, including English
The co-op component of Grade 12 courses will not be used for admission purposes
English: ENG4U / EAE4U
Calculus & Vectors: MCV4U

General full-IB credential route

Full IB Diploma applicants; campus/faculty subject and supplemental rules remain separate

Present the full IB Diploma, including English at HL or SL. Other programme prerequisites must be at senior/Grade 12 equivalent level. Individual IB courses can support admission only with another recognized secondary-school diploma.

Canadian high school outside Ontario

Canadian secondary-school curriculum, outside Ontario

British Columbia and Yukon · Six Grade 12 academic courses including English Studies 12 or English First Peoples 12. Calculus equivalent: Calculus 12 or AP Calculus AB/BC.
Alberta and Nunavut · Five 30/31 academic subjects including English Language Arts 30-1. Calculus equivalent: Math 31 or AP Calculus AB/BC.
Manitoba · Five Grade 12 academic subjects. Include English 40S, three other 40S subjects and a fifth 40S or 40G subject. Calculus equivalent: Calculus 42U, AP Calculus AB/BC or both Intro Calculus 45S and Advanced Mathematics 45S.
New Brunswick · Six college-preparatory 120, 121 or 122 subjects including English 120, 121 or 122, or Anglais 22411 in the francophone system. Calculus equivalent: Calculus 120, AP Calculus AB/BC or Mathématiques 30421.
Newfoundland and Labrador · Ten academic credits at the 3000 level, including English 3201. Calculus equivalent: Math 3208 or AP Calculus AB/BC.
Northwest Territories · Six Grade 12 academic courses, including English Studies 12 or English Indigenous Peoples 12. Calculus equivalent: Calculus 12 or AP Calculus AB/BC.
Nova Scotia · Five Grade 12 academic or advanced subjects, including English 12 or English 12 African Heritage. Calculus equivalent: Calculus 12 or AP Calculus AB/BC.
Prince Edward Island · Five Grade 12 academic subjects at the 611 or 621 level, including English 621. Calculus equivalent: Math 611B or AP Calculus AB/BC.
Quebec · Six academic subjects for the Grade 12 route. A DES alone is insufficient. For CEGEP, U of T reviews the R score, at least 12 academic courses excluding course 109, and two terms of English or Anglais. Calculus equivalent: MCV4U or AP Calculus AB/BC for Grade 12, or Calculus 1 for CEGEP.
Saskatchewan · Five academic Grade 12 subjects at the 30 level, including English Language Arts 30. Calculus equivalent: Calculus 30 or AP Calculus AB/BC.

U.S.-patterned high school

U.S.-patterned secondary-school curriculum

Complete an accredited high-school diploma with senior-year English or an accepted AP or IB English course. SAT or ACT results are optional.
Present an accepted calculus course, AP Calculus, or one semester of college calculus. Pre-calculus does not meet this requirement.

British-patterned high school

British-patterned secondary-school curriculum

Normally present five different academic IGCSE, GCSE or Ordinary Level subjects and three different academic A Levels. English at IGCSE, GCSE, Ordinary, AS or A Level is required.
Present Mathematics at AS or A Level to meet the calculus prerequisite.

French Baccalaureate

French Baccalauréat général applicants

Complete the Baccalauréat général and take Anglais in terminale.
Present Spécialité Mathématiques in both première and terminale.

Prerequisites for specific study options

Ontario high-school applicants considering these subject options

SCH4U is also listed for Chemical Physics, Chemistry, Earth and Environmental Systems, Geology, Geoscience, and Synthetic and Catalytic Chemistry.
SPH4U is also listed for Astronomy and Physics, Mathematics and Its Applications: Physical Science, Mathematics and Physics, Physics, and Physics and Philosophy.
Geophysics and Planetary Science also list SCH4U and SPH4U. Materials Science also lists SBI4U, SCH4U and SPH4U.

International Baccalaureate calculus equivalent

Full International Baccalaureate Diploma applicants

Present Mathematics Analysis and Approaches at SL or HL, or Mathematics Applications and Interpretation at HL.

Degree requirements

Credits and degree requirements

The HBA/HBSc requires 20.0 credits, including at least 10.0 offered by Arts and Science.
Complete one specialist, two majors, or one major and two minors; the two-program combinations must contain at least 12.0 different credits.
Earn at least 13.0 credits at the 200 level or above, including at least 6.0 at the 300 level or above.
Count at most 15.0 credits with the same course prefix toward the 20.0-credit degree total. A specialist includes at least 1.0 credit at the 400 level.
Choose only one program type in a given subject when the specialist, major or minor share the same four-digit program code.

References

Grades and academic standing

Minimum cumulative GPA: 1.85.

References

Required courses and electives

For breadth, earn 1.0 credit in each of four categories, or 1.0 in each of three and 0.5 in each of the other two.

References

Program facts

Entering average~Mid to high 80s

Ontario high-school entry in 2027/28, exact St. George route TPG. Later major selection and other applicant categories are separate.

InternshipPaid internship in eligible study options

The Mathematics Major is an example of a later option eligible for the Arts & Science Internship Program. Admission to ASIP is separate. It includes 12–20 months of paid, full-time work and professional development. ASIP students usually finish in five years.

Check work experience options

Majors & specializations

Physical and Mathematical Sciences is a first-year admission category. After 4.0 credits, students can enrol in open programs or apply to limited-enrolment programs. The course lists show the named study example.

Mathematics

BSc

Enter through Mathematical and Physical Sciences (TPG), then declare the major after completing 4.0 credits. Requires calculus, algebra and differential equations.

Published requirements

Courses

Separate study choices within this entry program. Each course block belongs to its named choice; it is not required of every student in the degree. After 4.0 credits, choose subject programs such as Actuarial Science, Astronomy and Astrophysics, Chemistry, Mathematics, Physics and Statistics. Limited-enrolment programs require a separate application.

Mathematics200 listed

Current programme requirements and the related departmental course menu, including alternatives. Each major or specialist has separate completion requirements; the menu is not a list of courses everyone must take. Mathematics Specialist (Science Program) - ASSPE1165: 12.5 credits, including at least 3.0 credits at the 400-level Mathematics Specialist (Science Program) - ASSPE1165: 4. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Mathematics Specialist (Science Program) - ASSPE1165: 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 Mathematics Specialist (Science Program) - ASSPE1165: 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. Mathematics Specialist (Science Program) - ASSPE1165: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematics Specialist (Science Program) - ASSPE1165: Students may use CR/NCR on the course they use toward the ethics and social responsibility credits. Mathematics Specialist (Science Program) - ASSPE1165: Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Mathematics Specialist (Science Program) - ASSPE1165: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematics Specialist (Science Program) - ASSPE1165: 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 , or CSC110Y1 . Mathematics Specialist (Science Program) - ASSPE1165: 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: 13.0-13.5 credits, including at least 1.5 credits at the 400-level Applied Mathematics Specialist (Science Program) - ASSPE2053: 6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Applied Mathematics Specialist (Science Program) - ASSPE2053: 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 Applied Mathematics Specialist (Science Program) - ASSPE2053: 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. Applied Mathematics Specialist (Science Program) - ASSPE2053: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Applied Mathematics Specialist (Science Program) - ASSPE2053: 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. Applied Mathematics Specialist (Science Program) - ASSPE2053: Students may use CR/NCR on the course they use toward the ethics and social responsibility credit. Applied Mathematics Specialist (Science Program) - ASSPE2053: Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Applied Mathematics Specialist (Science Program) - ASSPE2053: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Applied Mathematics Specialist (Science Program) - ASSPE2053: 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: 14.5 credits, including at least 1.0 credit at the 400-level Mathematics and Physics Specialist (Science Program) - ASSPE0397: 5. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Mathematics and Physics Specialist (Science Program) - ASSPE0397: 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 Mathematics and Physics Specialist (Science Program) - ASSPE0397: 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 Mathematics and Physics Specialist (Science Program) - ASSPE0397: 16. 0.5 credit from MAT477H1 / PHY424H1 / PHY478H1 / PHY479Y1 Mathematics and Physics Specialist (Science Program) - ASSPE0397: 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. Mathematics and Physics Specialist (Science Program) - ASSPE0397: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematics and Physics Specialist (Science Program) - ASSPE0397: 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. Mathematics and Physics Specialist (Science Program) - ASSPE0397: Students may use CR/NCR on the course they use toward the ethics and social responsibility credit. Mathematics and Physics Specialist (Science Program) - ASSPE0397: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematics and Physics Specialist (Science Program) - ASSPE0397: ⁠Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Mathematics and Physics Specialist (Science Program) - ASSPE0397: 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: 12.0 credits including at least 1.0 credit at the 400-level Mathematics and Philosophy Specialist (Science Program) - ASSPE1361: 1. Analysis: ( MAT158H1 , MAT159H1 )/ MAT157Y1 , MAT257Y1 2. Algebra: MAT240H1 , MAT247H1 3. Philosophy related to science: 0.5 credit from PHL232H1 / PHL233H1 / PHL255H1 Mathematics and Philosophy Specialist (Science Program) - ASSPE1361: 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 Mathematics and Philosophy Specialist (Science Program) - ASSPE1361: 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 Mathematics and Philosophy Specialist (Science Program) - ASSPE1361: 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. Mathematics and Philosophy Specialist (Science Program) - ASSPE1361: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematics and Philosophy Specialist (Science Program) - ASSPE1361: Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Mathematics and Philosophy Specialist (Science Program) - ASSPE1361: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: 12.0-12.5 credits Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: 1. Calculus, Analysis, and Proofs: 2.0 – 2.5 credits from ( MAT158H1 , MAT159H1 )/ MAT157Y1 / [( MAT148H1 , MAT149H1 )/ MAT137Y1 , MAT246H1 ], MAT237Y1 2. Linear Algebra: MAT223H1 , MAT224H1 3. Ordinary Differential Equations: MAT244H1 / MAT267H1 4. Principles in Economics: ECO101H1 , ECO102H1 5. Probability and Statistics: STA237H1 / STA257H1 , STA238H1 / STA261H1 , STA347H1 / MAT370H1 Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: 6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: 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 Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: 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. Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: Students may use CR/NCR on the course they use toward the ethics and social responsibility credit. Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: Students may be permitted to take Math graduate courses. A 0.5 credit of 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: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematical Applications in Economics and Finance Specialist (Science Program) - ASSPE1700: 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: 12.5-13.0 credits Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: 1. Calculus, Analysis and Proofs: 2.0 – 2.5 credits from [( MAT158H1 , MAT159H1 )/ MAT157Y1 ]/ [( MAT148H1 , MAT149H1 )/ MAT137Y1 , MAT246H1 ], ( MAT235H1 , MAT236H1 )/ [( MAT235H1 , MAT236H1 ), MAT235Y1 ]/ MAT237Y1 / MAT257Y1 2. Algebra: 1.0 credit from MAT223H1 / MAT240H1 , MAT224H1 / MAT247H1 3. Ordinary Differential Equations: MAT244H1 / MAT267H1 4. Computer Programming: CSC108H1 , CSC148H1 / CSC110Y1 5. Probability and Statistics: STA237H1 / STA257H1 6. Foundations of Physics: PHY151H1 , PHY152H1 7. Foundations of Astronomy and Astrophysics: AST221H1 Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: 8. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: 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 Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: 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 Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: 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. Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: 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. Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: Students may use CR/NCR on the course they use toward the ethics and social responsibility credit. Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematics & Its Applications Specialist (Physical Science) (Science Program) - ASSPE1758: 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: 11.5-12.5 credits Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: 1. Calculus, Analysis and Proofs: 2.0 – 2.5 credits from ( MAT158H1 , MAT159H1 )/ MAT157Y1 / [( MAT148H1 , MAT149H1 )/ 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 / CSC110Y1 5. Probability and Statistics: STA237H1 / STA257H1 , STA238H1 / STA261H1 , STA347H1 / MAT377H1 / MAT370H1 Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: 6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: 7. Data Analysis: STA302H1 8. Related Structures: 1.0 credit from STA355H1 / MAT332H1 / MAT344H1 / APM348H1 / APM461H1 9. Advanced Statistics: 1.0 credit from STA452H1 / STA453H1 / STA437H1 / STA442H1 / STA447H1 / STA465H1 / STA410H1 Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: 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 courses Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: 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. Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: 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. Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: Students may use CR/NCR on the course they use toward the ethics and social responsibility credit. Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematics & Its Applications Specialist (Probability/Statistics) (Science Program) - ASSPE1890: 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: 10.5-11.0 credits, including at least 1.0 credit at the 400-level Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: 1. Calculus, Analysis and Proofs: 2.0 – 2.5 credits from [( MAT158H1 , MAT159H1 )/ MAT157Y1 ]/ [( MAT148H1 , MAT149H1 )/ MAT137Y1 , MAT246H1 ], ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT237Y1 / MAT257Y1 2. Algebra: 1.0 credit from MAT223H1 / MAT240H1 , MAT224H1 / MAT247H1 3. Ordinary Differential Equations: MAT244H1 / MAT267H1 4. Computer Programming: CSC108H1 / CSC110Y1 5. Probability and Statistics: STA237H1 / STA257H1 Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: 6. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: 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 / MAT370H1 Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: 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 Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: 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. Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: Students may use CR/NCR on the course they use toward the ethics and social responsibility credit. Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematics & Its Applications Specialist (Teaching) (Science Program) - ASSPE1580: 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: 7.5 credits, including 2.5 credits at the 300+ level with a minimum of 0.5 credit at the 400 level Mathematics Major (Science Program) - ASMAJ1165: 1. 2.5 credits from ( MAT130H1 / MAT135H1 , MAT136H1 , MAT246H1 )/ [( MAT148H1 , MAT149H1 )/ MAT137Y1 , MAT246H1 ]/ [( MAT158H1 , MAT159H1 )/ MAT157Y1 , 0.5 credit from APM/MAT 200+ courses], ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT237Y1 / MAT257Y1 Mathematics Major (Science Program) - ASMAJ1165: 2. Algebra: 1.0 credit from MAT223H1 / MAT240H1 , MAT224H1 / MAT247H1 Mathematics Major (Science Program) - ASMAJ1165: 4. 0.5 credit with a significant emphasis on ethics and social responsibility (list below) Mathematics Major (Science Program) - ASMAJ1165: 5. Algebra, Number Theory, Graph Theory, Combinatorics: 0.5 credit from MAT301H1 / MAT315H1 / MAT332H1 / MAT344H1 Mathematics Major (Science Program) - ASMAJ1165: 6. Analysis: 0.5 credit from MAT334H1 / MAT337H1 / MAT336H1 Mathematics Major (Science Program) - ASMAJ1165: 7. Further Topics: 2.0 APM/MAT credits at the 300+ level including 0.5 credit at the 400-level: ACT230H1 / ACT240H1 / STA247H1 / STA257H1 / APM236H1 / APM346H1 / any APM400-level course/ HPS390H1 / HPS391H1 / MAT309H1 / MAT315H1 / MAT332H1 / MAT335H1 / MAT337H1 / MAT344H1 / MAT363H1 / MAT390H1 / MAT391H1 / any MAT 400-level course/ PSL432H1 Mathematics Major (Science Program) - ASMAJ1165: Requirement 7: students can take any combination of 300+ and 400+ level APM or MAT courses that adds up to 2.0 credits, with the condition that at least a 0.5 credit is at the 400+ level. Recommended courses for majors are: APM346H1 / APM348H1 / any APM400-level course/ HPS390H1 / HPS391H1 / MAT301H1 / MAT309H1 / MAT315H1 / MAT332H1 / MAT334H1 / MAT335H1 / MAT337H1 / MAT344H1 / MAT363H1 / MAT370H1 / MAT390H1 / MAT391H1 / MAT401H1 / APM462H1 / MAT402H1 / MAT403H1 / MAT475H1 / PSL432H1 Mathematics Major (Science Program) - ASMAJ1165: Only 0.5 credit of HPS390H1 / MAT390H1 / HPS391H1 / MAT391H1 / APM306Y1 / MAT329Y1 may count toward the major completion requirement of "further topics" except for students enrolled in the Education and Society Minor, who may apply 1.0 credit of MAT329Y1 toward their Minor program. Mathematics Major (Science Program) - ASMAJ1165: Each course can count toward only one requirement, even if listed as options to multiple requisites of the program. Mathematics Major (Science Program) - ASMAJ1165: 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. Mathematics Major (Science Program) - ASMAJ1165: Students may use CR/NCR on the course they use toward the ethics and social responsibility credit. Mathematics Major (Science Program) - ASMAJ1165: Students may be permitted to take Math graduate courses. A 0.5 credit of 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. Mathematics Major (Science Program) - ASMAJ1165: Students may be permitted to take an independent reading course. A 0.5 credit of these courses may count towards program requirements, where relevant (e.g., as courses “at the 400-level”). To review eligibility criteria and apply for independent reading courses as an undergraduate student, find more information on the A&S Math website. Mathematics Major (Science Program) - ASMAJ1165: 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. Mathematics Major (Science Program) - ASMAJ1165: 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 Eligible Mathematics majors and specialists can apply to ASIP. Paid full-time work: 12–20 months for Year 2 entry or 12–16 months for Year 3 entry; normal degree completion with ASIP is 5 years. Entry is limited and requires a supplementary application.

MAT130H1Calculus I for Life Sciences0.5 credits
Apply differential calculus, modelling and approximation to life-science problems.
Prerequisite: High school level calculus Alternative calculus route; check your intended major or specialist.
MAT133Y1Calculus and Linear Algebra for Commerce1 credits
Apply finance mathematics, matrices, calculus and partial differentiation to commerce and social sciences.
Prerequisite: High school level calculus
MAT135H1Calculus I0.5 credits
Develop differential-calculus tools and applications in science and economics.
Prerequisite: High school level calculus Alternative calculus route; check your intended major or specialist.
MAT136H1Calculus II0.5 credits
Study integration, series and differential-equation applications.
Prerequisite: MAT130H1 / MAT135H1 / MAT135H5 / MATA30H3 / MATA31H3 / APS162H1 / ESC194H1 / MAT186H1 / MAT196H1 Alternative calculus route; check your intended major or specialist.
MAT138H1Introduction to Proofs0.5 credits
Practise abstraction, logic, mathematical statements and proof writing.
Prerequisite: High school level calculus
MAT148H1Calculus I with Proofs0.5 credits
Study differential calculus with logic, proofs and theoretical foundations.
Prerequisite: High school level calculus Alternative calculus route; check your intended major or specialist.
MAT149H1Calculus II with Proofs0.5 credits
Study integral calculus, sequences and series through a proof-based approach.
Prerequisite: MAT148H1 / MAT135H1 (70% or higher)/ MAT130H1 (70% or higher)/ MAT158H1 Alternative calculus route; check your intended major or specialist.
MAT158H1Analysis 1A0.5 credits
Develop rigorous calculus using proofs, limits, derivatives and integrals.
Prerequisite: High school calculus Alternative calculus route; check your intended major or specialist.
MAT159H1Analysis 1B0.5 credits
Continue theoretical calculus through integration, Taylor’s theorem and convergence.
Prerequisite: MAT158H1 / MAT148H1 (70% or higher grade)/ MAT157H5 Alternative calculus route; check your intended major or specialist.
MAT192H1Mathematics and Art0.5 credits
Explore connections between mathematical ideas and artistic media.
Prerequisite: High school algebra
MAT193H1Women’s Mathematics0.5 credits
Explore mathematics created by women and barriers to women’s participation in mathematics.
Prerequisite: High school level algebra.
MAT194H1Mathematical Personalities0.5 credits
Study the lives and work of influential mathematicians.
MAT195H1Mathematics as an Interdisciplinary Pursuit0.5 credits
Explore mathematics’ relationships with science, culture and other fields.
MAT197H1Mathematics as a Recreation, Mathematical Discovery and Creative Problem Solving0.5 credits
Develop creative problem-solving through games, puzzles and recreational mathematics.
MAT198H1Cryptology: The Mathematics of Secrecy and Security0.5 credits
Explore cryptology, historical ciphers and modern secure communication.
Prerequisite: High school level algebra.
MAT199H1Aha! Mathematical Discovery and Creative Problem Solving0.5 credits
Solve challenging pre-calculus problems using reasoning and creative thinking.
Prerequisite: High school level algebra
MAT221H1Applied Linear Algebra0.5 credits
Develop computational linear-algebra skills using matrices, vectors and eigenvalues.
Prerequisite: High school level calculus
MAT223H1Linear Algebra I0.5 credits
Study linear systems, vectors, matrices and eigenvalues geometrically and algebraically.
Prerequisite: High school level calculus Linear-algebra alternative; specialist and major requirements differ.
MAT224H1Linear Algebra II0.5 credits
Study vector spaces, linear operators, inner products and canonical forms.
Prerequisite: MAT221H1 (80%)/ MAT223H1 / MAT223H5 / MATA22H3 / MATA23H3 / MAT240H1 / MAT240H5 Linear-algebra alternative; specialist and major requirements differ.
MAT235H1Vector Calculus I0.5 credits
Study multivariable differential calculus with life- and physical-science applications.
Prerequisite: MAT133Y1 / MAT133Y5 / ( MATA32H3 , MATA33H3 )/ ( MAT130H1 / MAT135H1 , MAT136H1 )/ ( MAT135H5 , MAT136H5 )/ ( MATA30H3 / MATA31H3 , MATA36H3 / MATA37H3 )/ ( MAT148H1 , MAT149H1 )/ MAT137Y1 / MAT137Y5 / ( MAT137H5 , MAT139H5 )/ ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 )
APM236H1Applications of Linear Programming0.5 credits
Study linear programming, simplex methods, duality and applications.
Prerequisite: MAT221H1 / MAT223H1 / MAT223H5 / MATA22H3 / MATA23H3 / MAT240H1 / MAT240H5
MAT236H1Vector Calculus II0.5 credits
Study multivariable integration, line and surface integrals and vector-calculus theorems.
Prerequisite: MAT133Y1 / MAT133Y5 / ( MATA32H3 , MATA33H3 )/ ( MAT135H1 , MAT136H1 )/ ( MAT130H1 / MAT135H5 , MAT136H5 )/ ( MATA30H3 / MATA31H3 , MATA36H3 / MATA37H3 )/ ( MAT148H1 , MAT149H1 )/ MAT137Y1 / MAT137Y5 / ( MAT137H5 , MAT139H5 )/ ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 ), MAT235H1
MAT237Y1Multivariable Calculus with Proofs1 credits
Study rigorous multivariable calculus, topology, optimization and vector integration.
Prerequisite: [ MAT133Y1 / ( MAT130H1 / MAT135H1 , MAT136H1 )/ ( MAT135H5 , MAT136H5 )/ ( MATA30H3 / MATA31H3 , MATA36H3 ), MAT138H1 / MAT102H5 / MAT246H1 ]/ ( MAT148H1 , MAT149H1 )/ MAT137Y1 / MAT137Y5 / ( MAT137H5 , MAT139H5 )/ ( MATA30H3 / MATA31H3 , MATA37H3 )/ ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 ), MAT223H1 / MATA22H3 / MATA23H3 / MAT240H1 / MAT240H5
MAT240H1Algebra I0.5 credits
Study theoretical linear algebra over general fields, including polynomials and eigenvalues.
Prerequisite: High school level calculus Linear-algebra alternative; specialist and major requirements differ.
MAT244H1Introduction to Ordinary Differential Equations0.5 credits
Model physical situations with ordinary differential equations and analyse their solutions.
Prerequisite: ( MAT133Y1 / MAT130H1 / MAT135H1 / MAT135H5 / MATA35H3 / MATA30H3 / MATA31H3 , MAT136H1 / MAT136H5 / MATA36H3 / MATA37H3 )/ MAT135Y5 / ( MAT148H1 , MAT149H1 )/ MAT137Y1 / MAT137Y5 / ( MAT137H5 , MAT139H5 )/ ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 ), MAT223H1 / MATA23H3 / MAT223H5 / MAT240H1 / MAT240H5
MAT245H1Mathematical Methods in Data Science0.5 credits
Explore mathematical methods for extracting information from large datasets.
Prerequisite: ( MAT148H1 , MAT149H1 )/ MAT137Y1 / ( MAT158H1 , MAT159H1 )/ MAT157Y1 , MAT223H1 / MAT240H1 , MAT224H1 / MAT247H1
MAT246H1Concepts in Abstract Mathematics0.5 credits
Develop mathematical proofs and abstract reasoning through selected topics.
Prerequisite: MAT133Y1 / MAT133Y5 / ( MATA32H3 , MATA33H3 )/ ( MAT130H1 / MAT135H1 , MAT136H1 )/ ( MAT135H5 , MAT136H5 )/ ( MATA30H3 / MATA31H3 , MATA36H3 / MATA37H3 )/ ( MAT148H1 , MAT149H1 ) / MAT137Y1 / MAT137Y5 / ( MAT137H5 , MAT139H5 ), MAT223H1 / MATA22H3 / MATA23H3 / MAT240H1 / MAT240H5
MAT247H1Algebra II0.5 credits
Study inner-product spaces, spectral theory and canonical forms.
Prerequisite: MAT240H1 / MAT240H5 Linear-algebra alternative; specialist and major requirements differ.
MAT257Y1Analysis II1 credits
Study topology, multivariable calculus, differential forms and integration on manifolds.
Prerequisite: ( MAT158H1 , MAT159H1 )/ MAT157Y1 / ( MAT157H5 , MAT159H5 )/ MAT157Y5 , MAT247H1 / MAT247H5
MAT267H1Advanced Ordinary Differential Equations0.5 credits
Study ordinary differential equations theoretically, including existence, uniqueness and stability.
Prerequisite: ( MAT158H1 , MAT159H1 )/ MAT157Y1 / ( MAT157H5 , MAT159H5 )/ MAT157Y5 , MAT247H1 / MAT247H5
MAT271H1Insights from Mathematics0.5 credits
Explore mathematical methods through humanities and social-science examples.
MAT282H1Topics in Mathematics0.5 credits
Explore a mathematics topic outside the regular undergraduate menu; content varies by offering.
Prerequisite: 1.0 MAT credit at the 100-level. Possible additional topic-specific prerequisites.
MAT295H1Independent Reading in Mathematics0.5 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
MAT296H1Independent Reading in Mathematics0.5 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
MAT297Y1Research Project in Mathematics1 credits
Undertake faculty-supervised independent research.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
MAT299H1Research Opportunity Program0.5 credits
Participate in a supervised faculty research project for course credit.
MAT299Y1Research Opportunity Program1 credits
Participate in a supervised faculty research project for course credit.
MAT301H1Groups and Symmetries0.5 credits
Study groups, symmetry, congruences and fields through examples and calculations.
Prerequisite: MAT257Y1 / ( MAT224H1 / MAT247H1 ,( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT237Y1 , MAT246H1 / ( MAT158H1 , MAT159H1 )/ MAT157Y1 / ( MAT157H5 , MAT159H5 )/ MAT157Y5 / CSC236H1 / CSC240H1 )/ ( MAT185H1 , MAT194H1 , MAT195H1 )
APM306Y1Mathematics and Law1 credits
Examine connections between mathematics, legal reasoning, ethics and litigation strategies.
Prerequisite: MAT221H1 / MAT223H1 / MAT240H1 , 0.5 credit from MAT133Y1 / MAT130H1 / MAT135H1 / MAT135H5 / MAT136H1 / MAT136H5 / MAT148H1 / MAT149H1 / MAT137Y1 / MAT137H5 / MAT139H5 / MAT137Y5 / MAT158H1 / MAT159H1 / MAT157Y1 / MAT157Y5
MAT309H1Introduction to Mathematical Logic0.5 credits
Study logic, truth, provability and Gödel’s completeness and incompleteness theorems.
Prerequisite: MAT257Y1 / [ MAT223H1 / MATA23H3 / MAT223H5 / MAT240H1 / MAT240H5 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT235Y5 / ( MAT232H5 , MAT236H5 )/ ( MATB41H3 , MATB42H3 / MATB43H3 )/ MAT237Y1 / MAT237Y5 , MAT246H1 / (MAT1581, MAT159H1 )/ MAT157Y1 / ( MAT157H5 , MAT159H5 )/ MAT157Y5 / CSC236H1 / CSC240H1 ]
MAT315H1Introduction to Number Theory0.5 credits
Study elementary number theory, including modular arithmetic and quadratic reciprocity.
Prerequisite: ( MAT223H1 / MATA23H3 / MAT223H5 / MAT240H1 / MAT240H5 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT235Y5 / ( MAT232H5 , MAT236H5 )/ ( MATB41H3 , MATB42H3 )/ MAT237Y1 / ( MATB41H3 , MATB42H3 , MATB43H3 )/ MAT237Y5 , MAT246H1 / CSC236H1 / CSC240H1 )/ ( MAT158H1 , MAT159H1 ) / MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 )/ MAT247H1 / MAT247H5
MAT327H1Introduction to Topology0.5 credits
Study topology, continuous mappings, compactness and fundamental groups.
Prerequisite: ( MAT158H1 , MAT159H1 ) / MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 )/ [( MAT237Y1 / ( MATB41H3 , MATB42H3 / MATB43H3 )/ MAT237Y5 ), MAT246H1 ]
MAT329Y1Concepts in Elementary Mathematics1 credits
Develop mathematical reasoning and teaching approaches for elementary education.
Prerequisite: 5.0 credits with a CGPA of at least 2.5, and ( MAT148H1 , MAT149H1 )/ MAT137Y1 / MAT137Y5 / ( MAT137H5 , MAT139H5 )/ MAT138H1 / ( MAT223H1 / MAT240H1 )/ [ MAT246H1 / ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 )]
MAT332H1Introduction to Graph Theory0.5 credits
Study graph theory and applications to scheduling, networks and finite geometries.
Prerequisite: MAT224H1 / MATB24H3 / MAT224H5 / MAT247H1 / MAT247H5
MAT334H1Complex Variables0.5 credits
Study complex functions, residues, conformal mappings and analytic continuation.
Prerequisite: MAT223H1 / MATA23H3 / MAT223H5 / MAT240H1 / MAT240H5 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT235Y5 / ( MAT232H5 , MAT236H5 )/ ( MATB41H3 , MATB42H3 )/ MAT237Y1 / ( MATB41H3 , MATB42H3 , MATB43H3 )/ MAT237Y5 / MAT257Y1
MAT335H1Chaos, Fractals and Dynamics0.5 credits
Explore dynamical systems, bifurcations and fractals.
Prerequisite: ( MAT148H1 , MAT149H1 )/ MAT137Y1 / ( MATA30H3 , MATA31H3 , MATA37H3 )/ MAT137Y5 / ( MAT137H5 , MAT139H5 )/ ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 )/ ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT235Y5 / ( MAT232H5 , MAT236H5 )/ ( MATB41H3 , MATB42H3 )/ MAT237Y1 / ( MATB41H3 , MATB42H3 , MATB43H3 )/ MAT237Y5 , MAT223H1 / MATA23H3 / MAT223H5 / MAT240H1 / MAT240H5
MAT336H1Elements of Analysis0.5 credits
Develop rigorous foundations for analysis and multivariable calculus.
Prerequisite: MAT223H1 / MATA23H3 / MAT223H5 / MAT240H1 / MAT240H5 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT235Y5 / ( MAT232H5 , MAT236H5 )/ ( MATB41H3 , MATB42H3 )/ MAT237Y1 / ( MATB41H3 , MATB42H3 , MATB43H3 )/ MAT237Y5 / ( MAT185H1 , MAT195H1 / ESC195H1 )
MAT337H1Introduction to Real Analysis0.5 credits
Study real analysis, convergence, function spaces and differential-equation foundations.
Prerequisite: MAT257Y1 / [ MAT224H1 / MATA24H3 / MAT224H5 / MAT247H1 / MAT247H5 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT235Y5 / ( MAT232H5 , MAT236H5 )/ ( MATB41H3 , MATB42H3 / MATB43H3 )/ MAT237Y1 / MAT237Y5 , MAT246H1 / ( MAT158H1 , MAT159H1 )/ MAT157Y1 ]
MAT344H1Introduction to Combinatorics0.5 credits
Study counting, generating functions, graph algorithms and combinatorial structures.
Prerequisite: MAT223H1 / MATA23H3 / MAT223H5 / MAT240H1 / MAT240H5
APM346H1Partial Differential Equations0.5 credits
Study mathematical methods for differential equations, integral equations and transforms.
Prerequisite: ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT235Y5 / ( MAT232H5 , MAT236H5 )/ ( MATB41H3 , MATB42H3 )/ MAT237Y1 / MAT237Y5 / MAT257Y1 , ( MAT244H1 / MATB44H3 / MAT244H5 / MAT267H1 )
MAT347Y1Groups, Rings and Fields1 credits
Study groups, rings, modules, field extensions and Galois theory.
Prerequisite: MAT257Y1 /(85% in MAT247H1 / MAT247H5 )
APM348H1Mathematical Modelling0.5 credits
Model problems across science and society using optimization, differential equations and probability.
Prerequisite: MAT244H1 / MAT267H1 , MAT224H1 / MAT247H1 , STA237H1 / STA247H1 / STA257H1 / MAT370H1 / MAT377H1
MAT351Y1Partial Differential Equations1 credits
Study partial differential equations, solution techniques and nonlinear phenomena.
Prerequisite: MAT257Y1 / MAT237Y1 (85%), MAT267H1
MAT354H1Complex Analysis I0.5 credits
Study complex analysis, holomorphic functions, series and residue calculus.
Prerequisite: MAT257Y1 / ( MAT237Y1 (85%), MAT327H1 )
MAT357H1Foundations of Real Analysis0.5 credits
Study function spaces, functional analysis and Lebesgue integration.
Prerequisite: MAT257Y1 / ( MAT237Y1 (85%), MAT327H1 )
MAT363H1Geometry of Curves and Surfaces0.5 credits
Study curves, surfaces, curvature and geodesics in three-dimensional spaces.
Prerequisite: MAT224H1 / MATB24H3 / MAT224H5 / MAT247H1 / MAT247H5 , MAT237Y1 / ( MATB41H3 , MATB42H3 , MATB43H3 )/ MAT237Y5 / MAT257Y1 ( MAT257Y1 can be taken concurrently). For FASE students, MAT185H1 , MAT194H1 , MAT195H1 , AER210H1 .
MAT367H1Differential Geometry0.5 credits
Study manifolds, vector bundles, differential forms and geometric theorems.
Prerequisite: MAT257Y1 / [ MAT224H1 / MAT247H1 , MAT237Y1 , MAT246H1 / ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 )]
MAT370H1Introduction to Mathematical Probability0.5 credits
Study probability, independence, limit theorems and Markov chains without measure theory.
Prerequisite: MAT224H1 / MAT224H5 ,( MAT235H1 , MAT236H1 )/ MAT235Y1 / ( MAT232H5 , MAT236H5 )/ MAT237Y1 / MAT257Y1 , MAT246H1
MAT377H1Mathematical Probability Theory0.5 credits
Explore mathematical probability, stochastic processes and applications beyond statistics.
Prerequisite: MAT247H1 / MAT247H5 and MAT257Y1 / ( MAT237Y1 (85%), MAT327H1 )
MAT382H1Topics in Mathematics0.5 credits
Explore a mathematics topic outside the regular undergraduate menu; content varies by offering.
Prerequisite: 2.5 AMP/MAT credits at the 100/200-level. Possible additional topic-specific prerequisites.
MAT390H1History of Mathematics up to 17000.5 credits
Survey ancient, medieval and early modern mathematics historically.
Prerequisite: 1.0 APM/MAT credit at the 200-level
MAT391H1History of Mathematics after 17000.5 credits
Study technical developments in mathematics from 1700 onwards.
Prerequisite: 1.0 APM/MAT credit at the 200 level
MAT395H1Independent Reading in Mathematics0.5 credits
Complete faculty-supervised reading on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
APM396H1Independent Reading in Applied Mathematics0.5 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA 3.5 for APM and MAT courses, permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
MAT396H1Independent Reading in Mathematics0.5 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
MAT397Y1Research Project in Mathematics1 credits
Undertake faculty-supervised independent research.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
MAT399H1Research Opportunity Program0.5 credits
Participate in a supervised faculty research project for course credit.
MAT399Y1Research Opportunity Program1 credits
Participate in a supervised faculty research project for course credit.
MAT401H1Polynomial Equations and Fields0.5 credits
Study rings, fields and Galois theory, including polynomial equations and geometric constructions.
Prerequisite: MAT301H1
MAT402H1Classical Geometries0.5 credits
Study Euclidean, non-Euclidean and projective geometries.
Prerequisite: MAT224H1 / MAT247H1 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT237Y1 / MAT257Y1
MAT403H1Classical Geometries II0.5 credits
Continue classical geometry through projective, spherical and elliptic geometry.
Prerequisite: ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT237Y1 / MAT257Y1 , MAT301H1 / MAT347Y1
MAT409H1Set Theory0.5 credits
Study set-theory axioms, ordinals, cardinals and independence proofs.
Prerequisite: MAT357H1
MAT415H1Algebraic Number Theory0.5 credits
Explore selected topics in algebraic number theory, such as number fields and Diophantine equations.
Prerequisite: MAT347Y1
MAT417H1Analytic Number Theory0.5 credits
Explore selected topics in analytic number theory, including primes and L-functions.
Prerequisite: MAT334H1 / MAT354H1
APM421H1Mathematical Foundations of Quantum Mechanics and Quantum Information Theory0.5 credits
Study quantum mechanics mathematically, including observables, evolution and angular momentum.
Prerequisite: ( MAT224H1 / MAT247H1 , MAT337H1 )/ MAT357H1
MAT425H1Differential Topology0.5 credits
Study smooth manifolds, transversality, Morse theory and intersection theory.
Prerequisite: MAT257Y1 , MAT327H1
APM426H1General Relativity0.5 credits
Study general relativity, spacetime curvature, cosmology and black holes.
Prerequisite: MAT363H1 / MAT367H1
MAT436H1Introduction to Linear Operators0.5 credits
Explore functional analysis and operator algebras on Hilbert spaces.
Prerequisite: 5.0 MAT credits, including MAT224H1 / MAT247H1 and MAT237Y1 / MAT257Y1
MAT437H1K-Theory and C* Algebras0.5 credits
Study operator algebras, equivalence of projections and associated algebraic structures.
Prerequisite: 5.0 MAT credits, including MAT224H1 / MAT247H1 and MAT237Y1 / MAT257Y1
APM441H1Asymptotic and Perturbation Methods0.5 credits
Apply asymptotic and perturbation methods to physics and engineering problems.
Prerequisite: APM346H1 / MAT351Y1 , MAT334H1 / MAT354H1
MAT445H1Representation Theory0.5 credits
Explore selected topics in group and Lie-algebra representation theory.
Prerequisite: MAT347Y1
APM446H1Applied Nonlinear Equations0.5 credits
Study nonlinear partial differential equations, solution behaviour and stability.
Prerequisite: APM346H1 / MAT351Y1
MAT448H1Introduction to Commutative Algebra and Algebraic Geometry0.5 credits
Explore algebraic geometry through commutative algebra and geometric topics.
Prerequisite: MAT347Y1
MAT449H1Algebraic Curves0.5 credits
Study projective curves, Riemann surfaces and algebraic geometry.
Prerequisite: MAT347Y1 , MAT354H1
MAT454H1Complex Analysis II0.5 credits
Study advanced complex analysis, analytic continuation and Riemann surfaces.
Prerequisite: MAT354H1
MAT457H1Advanced Real Analysis I0.5 credits
Study measure theory, Lebesgue integration, Hilbert spaces and operators.
Prerequisite: MAT357H1
MAT458H1Advanced Real Analysis II0.5 credits
Study Fourier analysis, Banach spaces and foundational functional-analysis theorems.
Prerequisite: MAT457H1
APM461H1Combinatorial Methods0.5 credits
Explore selected combinatorics topics, including graphs, algorithms and enumeration.
Prerequisite: MAT224H1 / MAT247H1 , MAT137Y1 / MAT137Y5 / ( MAT137H5 , MAT139H5 )/ ( MAT158H1 , MAT159H1 )/ MAT157Y1 / MAT157Y5 / ( MAT157H5 , MAT159H5 ), MAT301H1 / MAT347Y1
MAT461H1Hamiltonian Mechanics0.5 credits
Study classical mechanics through variational, Lagrangian and Hamiltonian methods.
Prerequisite: MAT244H1 / MAT267H1 , MAT337H1 / MAT367H1 , APM346H1 / MAT351Y1
APM462H1Nonlinear Optimization0.5 credits
Study finite- and infinite-dimensional optimization and numerical search methods.
Prerequisite: ( MAT223H1 , MAT224H1 )/ MAT247H1 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT237Y1 / MAT257Y1
MAT464H1Riemannian Geometry0.5 credits
Study Riemannian geometry, geodesics and curvature.
Prerequisite: MAT367H1
APM466H1Mathematical Theory of Finance0.5 credits
Apply stochastic calculus to financial derivatives, risk management and portfolios.
Prerequisite: APM346H1 , STA347H1
MAT475H1Problem Solving Seminar0.5 credits
Practise strategies for unfamiliar mathematical problems and explain their solutions.
Prerequisite: MAT224H1 / MAT247H1 , ( MAT235H1 , MAT236H1 )/ MAT235Y1 / MAT237Y1 / MAT257Y1 , and at least 1.0 credit at the 300+ level in APM/MAT
MAT477H1Seminar in Mathematics0.5 credits
Explore an advanced mathematics topic through a seminar and student presentations.
Prerequisite: MAT347Y1 , MAT354H1 , MAT357H1
MAT478H1Seminar in Mathematics0.5 credits
Explore an advanced mathematics topic through a seminar and student presentations.
Prerequisite: MAT347Y1 , MAT354H1 , MAT357H1
MAT482H1Topics in Mathematics0.5 credits
Explore a mathematics topic outside the regular undergraduate menu; content varies by offering.
Prerequisite: 6.0 APM/MAT credits at the 100, 200 and 300-level. Possible additional topic-specific prerequisites.
MAT483H1Topics in Mathematics0.5 credits
Explore a mathematics topic outside the regular undergraduate menu; content varies by offering.
Prerequisite: 6.0 APM/MAT credits at the 100, 200 and 300-level. Possible additional topic-specific prerequisites.
MAT495H1Independent Reading in Mathematics0.5 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
MAT496H1Independent Reading in Mathematics0.5 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
APM496H1Independent Readings in Applied Mathematics0.5 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: minimum GPA 3.5 for APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
MAT497Y1Research Project in Mathematics1 credits
Undertake faculty-supervised independent research.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor
MAT499Y1Readings in Mathematics1 credits
Complete faculty-supervised study on a topic outside the current undergraduate menu.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.
PHY151H1Foundations of Physics I0.5 credits
Develop physics foundations in mechanics, energy, momentum and special relativity.
PHY152H1Foundations of Physics II0.5 credits
Study fields, rotation, oscillations, waves, electricity and magnetism.
CSC148H1Introduction to Computer Science0.5 credits
Study data structures, object-oriented programming, recursion and program efficiency.
STA257H1Probability and Statistics I0.5 credits
Study probability rigorously, including random variables, distributions and limit theorems.
CSC108H1Introduction to Computer Programming0.5 credits
Learn introductory programming, algorithms, testing and problem-solving without prior experience.
CSC110Y1Foundations of Computer Science I1 credits
Learn Python programming alongside mathematical reasoning, proofs and algorithm analysis.
CSC300H1Computers and Society0.5 credits
Examine computing ethics, privacy, AI, social inequality and environmental impacts.
CSE240H1Introduction to Critical Equity and Solidarity Studies0.5 credits
Examine systemic inequality, oppression and grassroots resistance through an intersectional approach.
CSE270H1Community Dis/Engagement and Solidarity0.5 credits
Explore community engagement and solidarity from anti-colonial perspectives.
EEB215H1Conservation Biology0.5 credits
Explore conservation biology, threats to biodiversity and ecosystem protection.
ENV200H1Assessing Global Change: Science and the Environment0.5 credits
Study global environmental concerns through scientific approaches to climate and biodiversity.
ESS205H1Confronting Global Change0.5 credits
Examine human impacts on climate, pollution, resources and planetary habitability.
FOR201H1Conservation of Tropical and Subtropical Forests0.5 credits
Study tropical-forest conservation and sustainable management through ecological and social perspectives.
HPS200H1Science and Values0.5 credits
Explore interactions among science, social values, religion and public policy.
HPS202H1Technology in the Modern World0.5 credits
Examine technology and society since 1800 through race, class and gender perspectives.
INS200H1Introduction to Indigenous Truth and Resilience0.5 credits
Explore Indigenous experiences, resilience and knowledge through interdisciplinary and experiential learning.
JPH441H1Physical Science in Contemporary Society0.5 credits
Examine ethical and philosophical questions about scientific work, evidence and publication.
PHL265H1Introduction to Political Philosophy0.5 credits
Explore political philosophy, justice, liberty and approaches to good government.
PHL271H1Law and Morality0.5 credits
Examine ethical questions at the intersection of law and morality.
PHL273H1Environmental Ethics0.5 credits
Explore environmental ethics, future generations and responsibilities towards nature.
PHL275H1Introduction to Ethics0.5 credits
Explore moral values, rights, duties, virtues and ethical theories.
PHL281H1Bioethics0.5 credits
Examine ethical and legal questions in medicine, biomedical research and health policy.
PHL295H1Business Ethics0.5 credits
Examine ethical responsibilities and philosophical questions in business.
SDS256H1Methods in Queer and Trans Studies0.5 credits
Explore research methods for sexuality and gender diversity in the humanities and social sciences.
STA237H1Probability, Statistics and Data Analysis I0.5 credits
Study probability, distributions and sampling through mathematics and computer simulations.
STA238H1Probability, Statistics and Data Analysis II0.5 credits
Study statistical inference and the linear model using computation and simulation.
STA261H1Probability and Statistics II0.5 credits
Study statistical-inference theory, estimation, testing and computing.
STA347H1Probability0.5 credits
Study probability, convergence and introductory stochastic processes without measure theory.
STA302H1Methods of Data Analysis I0.5 credits
Analyse data using regression, inference, diagnostics and model selection.
STA457H1Time Series Analysis0.5 credits
Study time-series models, forecasting, filtering and spectral methods.
CSC336H1Numerical Methods0.5 credits
Study numerical methods for linear algebra, nonlinear equations and approximation.
CSC436H1Numerical Algorithms0.5 credits
Analyse numerical algorithms for eigenvalues, approximation, integration and differential equations.
CSC446H1Computational Methods for Partial Differential Equations0.5 credits
Study finite-difference and finite-element methods for partial differential equations.
CSC456H1High-Performance Scientific Computing0.5 credits
Implement and evaluate scientific-computing algorithms on parallel computers.
HIS268H1Law and History0.5 credits
Explore law through different historical approaches and legal traditions.
PHY224H1Practical Physics I0.5 credits
Develop experimental and computational physics skills, including uncertainty analysis.
PHY324H1Practical Physics II0.5 credits
Extend practical physics skills through experimental, computational and independent-project modules.
PHY250H1Electricity and Magnetism0.5 credits
Study electric and magnetic fields and foundational electromagnetic laws.
PHY350H1Electromagnetic Theory0.5 credits
Extend electromagnetic theory to matter, boundary problems, conservation laws and waves.
PHY252H1Thermal Physics0.5 credits
Study thermodynamics through quantum statistics and microscopic descriptions of systems.
PHY254H1Classical Mechanics0.5 credits
Analyse linear, nonlinear and chaotic classical-mechanical systems.
PHY354H1Advanced Classical Mechanics0.5 credits
Study advanced mechanics through symmetry, conservation and Hamiltonian methods.
PHY256H1Introduction to Quantum Physics0.5 credits
Explore quantum-physics foundations, uncertainty, scattering and tunnelling.
PHY356H1Quantum Mechanics I0.5 credits
Study wave mechanics, operators, angular momentum, atoms and spin.
PHY450H1Relativistic Electrodynamics0.5 credits
Study relativistic electrodynamics, moving charges and electromagnetic radiation.
PHY452H1Statistical Mechanics0.5 credits
Study classical and quantum statistical mechanics and their thermodynamic foundations.
PHY454H1Continuum Mechanics0.5 credits
Study continuous matter, fluid mechanics, instability and turbulence.
PHY456H1Quantum Mechanics II0.5 credits
Study advanced quantum dynamics, approximation methods and scattering.
PHY460H1Nonlinear Physics0.5 credits
Analyse nonlinear systems, chaos, bifurcations and fractals.
PHY424H1Advanced Physics Laboratory0.5 credits
Conduct advanced experiments connected with current physics research.
PHY478H1Undergraduate Research Project0.5 credits
Undertake an individual experimental or theoretical project with a faculty supervisor.
PHY479Y1Undergraduate Research Project1 credits
Undertake an individual experimental or theoretical project with a faculty supervisor.
PHL232H1Knowledge and Reality0.5 credits
Explore metaphysics, knowledge and related questions in philosophy of science.
PHL233H1Philosophy for Scientists0.5 credits
Explore philosophical questions relevant to mathematics and science.
PHL255H1Philosophy of Science0.5 credits
Study contemporary philosophy of science, evidence and scientific authority.
PHL200Y1Ancient Philosophy1 credits
Study central texts in ancient philosophy, including Plato and Aristotle.
PHL205H1Early Medieval Philosophy0.5 credits
Explore reason, faith, God and universals in early medieval philosophy.
PHL206H1Later Medieval Philosophy0.5 credits
Explore reason, faith and the universe in later medieval philosophy.
PHL210Y117th-and 18th-Century Philosophy1 credits
Study major seventeenth- and eighteenth-century philosophers.
PHL348H1Logic and Computation0.5 credits
Study incompleteness theorems, computation and their philosophical implications.
PHL345H1Intermediate Logic0.5 credits
Study first-order logic, metalogic and foundational results such as completeness.
PHL325H1Early Analytic Philosophy0.5 credits
Examine early analytic philosophy through Frege, Russell and Wittgenstein.
PHL331H1Metaphysics0.5 credits
Explore metaphysical questions about reality, existence, possibility and causality.
PHL332H1Epistemology0.5 credits
Study knowledge, belief, justification and skepticism.
PHL354H1Philosophy of Mathematics0.5 credits
Explore foundational philosophical views of mathematics and logic.
PHL347H1Modal Logic and Philosophical Applications of Logic0.5 credits
Study modal logic, necessity, possibility and philosophical applications.
PHL349H1Set Theory0.5 credits
Explore set theory and its philosophical role in mathematics and logic.
PHL355H1Philosophy of Natural Science0.5 credits
Examine scientific explanation, methods, realism and instrumentalism.
PHL451H1Seminar in Philosophy of Language0.5 credits
Investigate an advanced philosophy-of-language topic in a seminar.
PHL480H1Advanced Topics in Logic0.5 credits
The live course description repeats the title; detailed topics are not published there.
ECO101H1Principles of Microeconomics0.5 credits
Use economic analysis to study prices, markets, decisions and public policy.
ECO102H1Principles of Macroeconomics0.5 credits
Study trade, money, banking and macroeconomic policy.
ECO206Y1Microeconomic Theory1 credits
Study microeconomic theory through a rigorous mathematical approach.
ECO358H1Financial Economics I0.5 credits
Study financial markets, asset pricing, market efficiency and interest-rate structure.
ECO359H1Financial Economics II: Corporate Finance0.5 credits
Explore information, contracts and financial constraints in corporate finance.
ECO375H1Applied Econometrics I0.5 credits
Apply regression and econometric software to economic questions and causality problems.
AST221H1Stars and Planets0.5 credits
Study stars and planets, their formation and evolution, and astronomical instruments.
AST222H1Galaxies and Cosmology0.5 credits
Study stellar systems, galaxies and the Universe’s structure and evolution.
AST320H1Introduction to Astrophysics0.5 credits
Study the formation and evolution of structures across astronomical scales.
AST325H1Introduction to Practical Astronomy0.5 credits
Collect and analyse astronomical data using observations, instruments and modelling.
PHY357H1Nuclear and Particle Physics0.5 credits
Study nuclei, particles, fundamental interactions and conservation laws.
PHY358H1Quantum Materials: from Atoms to Crystals0.5 credits
Explore how quantum mechanics determines the properties of atoms, molecules and crystals.
PHY407H1Computational Physics0.5 credits
Use Python and numerical methods to solve and visualize physics problems.
PHY408H1Time Series Analysis0.5 credits
Analyse digital time series using filtering, Fourier methods and correlation.
STA355H1Theory of Statistical Practice0.5 credits
Study statistical models, likelihood-based inference and Bayesian inference.
STA452H1Mathematical Statistics I0.5 credits
Study advanced statistical theory, distributions, linear models and inference.
STA453H1Mathematical Statistics II0.5 credits
Continue advanced statistical theory through estimation, testing and Bayesian or frequentist inference.
STA437H1Methods for Multivariate Data0.5 credits
Analyse multivariate data using reduction, estimation, regression and classification methods.
STA442H1Methods of Applied Statistics0.5 credits
Apply advanced statistical models and diagnostics through case studies.
STA447H1Stochastic Processes0.5 credits
Study stochastic processes, martingales and applications of stochastic modelling.
STA465H1Spatial Data Analysis0.5 credits
Analyse and visualize spatial and spatiotemporal data.
STA410H1Statistical Computation0.5 credits
Use statistical programming, simulation and algorithms for estimation and inference.
HPS390H1The Story of Number: Mathematics from the Babylonians to the Scientific Revolution0.5 credits
Survey ancient, medieval and early modern mathematics historically.
HPS391H1Rebels Who Count: The History of Mathematics from 1700 to the Present0.5 credits
Study technical developments in mathematics from 1700 onwards.
ACT230H1Mathematics of Finance for Non-Actuaries0.5 credits
Study interest, present values, annuities, loans and bonds for non-actuarial audiences.
ACT240H1Mathematics of Investment & Credit0.5 credits
Apply financial mathematics to investments, credit and repayment schedules.
STA247H1Probability with Computer Applications0.5 credits
Study probability through mathematics and computer simulations for computer-science applications.
PSL432H1Theoretical Physiology0.5 credits
Use mathematical modelling to analyse neurophysiological systems.

Mathematics

Introductory calculus routes7 listed

Choose the calculus sequence required by your intended programme. The Mathematics Specialist encourages MAT158/MAT159, or the retained MAT157 alternative, in first year.

MAT130H1Calculus I for Life Sciences0.5 credits
Apply differential calculus, modelling and approximation to life-science problems.
Prerequisite: High school level calculus Alternative calculus route; check your intended major or specialist.
MAT135H1Calculus I0.5 credits
Develop differential-calculus tools and applications in science and economics.
Prerequisite: High school level calculus Alternative calculus route; check your intended major or specialist.
MAT136H1Calculus II0.5 credits
Study integration, series and differential-equation applications.
Prerequisite: MAT130H1 / MAT135H1 / MAT135H5 / MATA30H3 / MATA31H3 / APS162H1 / ESC194H1 / MAT186H1 / MAT196H1 Alternative calculus route; check your intended major or specialist.
MAT148H1Calculus I with Proofs0.5 credits
Study differential calculus with logic, proofs and theoretical foundations.
Prerequisite: High school level calculus Alternative calculus route; check your intended major or specialist.
MAT149H1Calculus II with Proofs0.5 credits
Study integral calculus, sequences and series through a proof-based approach.
Prerequisite: MAT148H1 / MAT135H1 (70% or higher)/ MAT130H1 (70% or higher)/ MAT158H1 Alternative calculus route; check your intended major or specialist.
MAT158H1Analysis 1A0.5 credits
Develop rigorous calculus using proofs, limits, derivatives and integrals.
Prerequisite: High school calculus Alternative calculus route; check your intended major or specialist.
MAT159H1Analysis 1B0.5 credits
Continue theoretical calculus through integration, Taylor’s theorem and convergence.
Prerequisite: MAT158H1 / MAT148H1 (70% or higher grade)/ MAT157H5 Alternative calculus route; check your intended major or specialist.

Introductory algebra choices4 listed

MAT223/240 and MAT224/247 are alternatives in programme rules. The Mathematics Specialist encourages MAT240 and MAT247 in first year.

MAT223H1Linear Algebra I0.5 credits
Study linear systems, vectors, matrices and eigenvalues geometrically and algebraically.
Prerequisite: High school level calculus Linear-algebra alternative; specialist and major requirements differ.
MAT224H1Linear Algebra II0.5 credits
Study vector spaces, linear operators, inner products and canonical forms.
Prerequisite: MAT221H1 (80%)/ MAT223H1 / MAT223H5 / MATA22H3 / MATA23H3 / MAT240H1 / MAT240H5 Linear-algebra alternative; specialist and major requirements differ.
MAT240H1Algebra I0.5 credits
Study theoretical linear algebra over general fields, including polynomials and eigenvalues.
Prerequisite: High school level calculus Linear-algebra alternative; specialist and major requirements differ.
MAT247H1Algebra II0.5 credits
Study inner-product spaces, spectral theory and canonical forms.
Prerequisite: MAT240H1 / MAT240H5 Linear-algebra alternative; specialist and major requirements differ.

Elective choices

Available electives depend on the chosen specialist, major and minor combination and the outstanding breadth requirements.
The breadth categories cover culture, thought and behaviour, society, living systems, and physical and mathematical sciences.

Study locations