APM236H1 - Applications of Linear Programming
Hours: 36L
Introduction to linear programming including a rapid review of linear algebra (row reduction, matrix inversion, linear independence), the simplex method with applications, the duality theorem, complementary slackness, the dual simplex method and the revised simplex method.
Prerequisite: MAT221H1/ MAT223H1/ MAT223H5/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5Breadth Requirements: The Physical and Mathematical Universes (5)
APM306Y1 - Mathematics and Law
Hours: 72L
This course examines the relationship between legal reasoning and mathematical logic; provides a mathematical perspective on the legal treatment of interest and actuarial present value; critiques ethical issues; analyzes how search engine techniques on massive databases transform legal research and considers the impact of statistical analysis and game theory on litigation strategies.
NOTE
This course counts as 0.5 credit in BR=3 and 0.5 credit in BR=5.
This course will only contribute 0.5 credit to the Math Minor program.
Prerequisite: MAT133Y1/ MAT135H1/ MAT135H5/ MAT136H1/ MAT136H5/ MAT137Y1/ MAT137Y5/ ( MAT137H5, MAT139H5)/ MAT157Y1/ MAT157Y5/ ( MAT157H5, MAT159H5), MAT221H1/ MAT223H1/ MAT240H1Breadth Requirements: The Physical and Mathematical Universes (5), Society and its Institutions (3)
APM346H1 - Partial Differential Equations
Hours: 36L
Sturm-Liouville problems, Green's functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transform, stationary phase method.
Prerequisite: MAT235Y1/ MAT235Y5/ ( MAT232H5, MAT236H5)/ ( MATB41H3, MATB42H3)/ MAT237Y1/ MAT237Y5/ MAT257Y1, ( MAT244H1/ MATB44H3/ MAT244H5/ MAT267H1)Exclusion: MAT351Y1Breadth Requirements: The Physical and Mathematical Universes (5)
APM348H1 - Mathematical Modelling
Previous Course Number: MAT482
Hours: 36L/22P
An overview of mathematical modelling. A variety of approaches for representing physical situations mathematically followed by analytical techniques and numerical simulations to gain insight. Questions from biology, economics, engineering, medicine, physics, physiology, and the social sciences formulated as problems in optimization, differential equations, and probability. Precise content varies with instructor.
Prerequisite: MAT244H1/ MAT267H1, MAT224H1/ MAT247H1, STA237H1/ STA247H1/ STA257H1/ MAT377H1Exclusion: MAT482H1 (Topics in Mathematics: Topics in Mathematical Modelling), offered in Winter 2019Breadth Requirements: The Physical and Mathematical Universes (5)
APM396H1 - Independent Reading in Applied Mathematics
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.
This course requires an application. Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA 3.5 for APM and MAT courses, permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.Breadth Requirements: The Physical and Mathematical Universes (5)
APM421H1 - Mathematical Foundations of Quantum Mechanics and Quantum Information Theory
Hours: 36L
Key concepts and mathematical structure of Quantum Mechanics, with applications to topics of current interest such as quantum information theory. The core part of the course covers the following topics: Schroedinger equation, quantum observables, spectrum and evolution, motion in electro-magnetic field, angular momentum and O(3) and SU(2) groups, spin and statistics, semi-classical asymptotics, perturbation theory. More advanced topics may include: adiabatic theory and geometrical phases, Hartree-Fock theory, Bose-Einstein condensation, the second quantization, density matrix and quantum statistics, open systems and Lindblad evolution, quantum entropy, quantum channels, quantum Shannon theorems.
Joint undergraduate/graduate course - APM421H1/MAT1723H
Prerequisite: ( MAT224H1/ MAT247H1, MAT337H1)/ MAT357H1Breadth Requirements: The Physical and Mathematical Universes (5)
APM426H1 - General Relativity
Hours: 36L
Einstein's theory of gravity. Special relativity and the geometry of Lorentz manifolds. Gravity as a manifestation of spacetime curvature. Einstein's equations. Cosmological implications: big bang and inflationary universe. Schwarzschild stars: bending of light and perihelion precession of Mercury. Topics from black hole dynamics and gravitational waves. The Penrose singularity theorem.
Joint undergraduate/graduate course - APM426H1/MAT1700H
Prerequisite: MAT363H1/ MAT367H1Breadth Requirements: The Physical and Mathematical Universes (5)
APM441H1 - Asymptotic and Perturbation Methods
Hours: 36L
Asymptotic series. Asymptotic methods for integrals: stationary phase and steepest descent. Regular perturbations for algebraic and differential equations. Singular perturbation methods for ordinary differential equations: W.K.B., strained co-ordinates, matched asymptotics, multiple scales. (Emphasizes techniques; problems drawn from physics and engineering)
Prerequisite: APM346H1/ MAT351Y1, MAT334H1/ MAT354H1Breadth Requirements: The Physical and Mathematical Universes (5)
APM446H1 - Applied Nonlinear Equations
Hours: 36L
Partial differential equations appearing in physics, material sciences, biology, geometry, and engineering. Nonlinear evolution equations. Existence and long-time behaviour of solutions. Existence of static, traveling wave, self-similar, topological and localized solutions. Stability. Formation of singularities and pattern formation. Fixed point theorems, spectral analysis, bifurcation theory. Equations considered in this course may include: Allen-Cahn equation (material science), Ginzburg-Landau equation (condensed matter physics), Cahn-Hilliard (material science, biology), nonlinear Schroedinger equation (quantum and plasma physics, water waves, etc). mean curvature flow (geometry, material sciences), Fisher-Kolmogorov-Petrovskii-Piskunov (combustion theory, biology), Keller-Segel equations (biology), and Chern-Simons equations (particle and condensed matter physics).
Joint undergraduate/graduate course - APM446H1/MAT1508H
Prerequisite: APM346H1/ MAT351Y1Breadth Requirements: The Physical and Mathematical Universes (5)
APM462H1 - Nonlinear Optimization
Hours: 36L
An introduction to first and second order conditions for finite and infinite dimensional optimization problems with mention of available software. Topics include Lagrange multipliers, Kuhn-Tucker conditions, convexity and calculus of variations. Basic numerical search methods and software packages which implement them will be discussed.
Prerequisite: ( MAT223H1, MAT224H1) / MAT247H1, MAT235Y1/ MAT237Y1/ MAT257Y1Recommended Preparation: MAT336H1/ MAT337H1Breadth Requirements: The Physical and Mathematical Universes (5)
APM466H1 - Mathematical Theory of Finance
Hours: 36L
Introduction to the basic mathematical techniques in pricing theory and risk management: Stochastic calculus, single-period finance, financial derivatives (tree-approximation and Black-Scholes model for equity derivatives, American derivatives, numerical methods, lattice models for interest-rate derivatives), value at risk, credit risk, portfolio theory.
Joint undergraduate/graduate course - APM466H1/MAT1856H
Prerequisite: APM346H1, STA347H1Corequisite: STA457H1Breadth Requirements: The Physical and Mathematical Universes (5)
APM496H1 - Independent Readings in Applied Mathematics
Independent study under the direction of a faculty member. Topic must be outside current undergraduate offerings. Similar workload to a course that has 36 lecture hours. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: minimum GPA 3.5 for APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisorBreadth Requirements: The Physical and Mathematical Universes (5)
MAT133Y1 - Calculus and Linear Algebra for Commerce
Hours: 72L
Mathematics of finance. Matrices and linear equations. Review of differential calculus; applications. Integration and fundamental theorem; applications. Introduction to partial differentiation; applications. Course material expects at minimum high school calculus has been completed prior to undertaking course. This course will be useful for students interested in learning applied calculus in relation to future studies in commerce and/or social science programs.
Prerequisite: High school level calculusExclusion: MAT133Y5/ ( MATA32H3, MATA33H3)Breadth Requirements: The Physical and Mathematical Universes (5)
MAT135H1 - Calculus I
Hours: 36L/12T
In this first introduction to Calculus, students will be introduced to the tools of differential calculus, the branch of calculus that is motivated by the problem of measuring how quantities change. Students will use these tools to solve other problems, including simplifying functions with straight lines, describing how different types of change are related, and computing maximum and minimum quantities. This course will focus on developing a deep understanding of why the tools of calculus make sense and how to apply them to the social, biological, and physical sciences. It will also emphasize translating between algebraic, graphical, numerical and verbal descriptions of each concept studied. This course will be useful for students interested in learning applied calculus in relation to future studies in economics, life science, and physical and mathematical science programs. The following concepts will be studied: Limits, asymptotes, continuity, derivatives, linear approximation of functions, the notion of a differential equation (DE) and a solution of a DE, slope fields, and Euler's method.
Prerequisite: High school level calculusExclusion: MAT135H5/ MAT136H5/ MATA30H3/ MATA31H3/ MATA36H3/ APS162H1/ APS163H1/ ESC194H1/ ESC195H1/ MAT186H1/ MAT187H1/ MAT196H1/ MAT197H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT136H1 - Calculus II
Hours: 36L/12T
This second part of the introductory Calculus sequence focuses on integral calculus beginning with the Fundamental Theorem of Calculus, the connection between two seemingly unrelated problems: measuring changing quantities and finding areas of curved shapes. Students will develop a deep understanding of the integral, and use it to: unpack equations involving derivatives; to make sense of infinite sums; to write complicated functions as 'infinite polynomials'; and to compute areas, volumes, and totals in applied problems. This course will further develop students' abilities to translate between algebraic, graphical, numerical, and verbal descriptions of mathematics in a variety of applied contexts. This course is a continuation of MAT135H1 and will be useful for students interested in learning applied calculus in relation to future studies in economics, life science, and physical and mathematical science programs. The following concepts will be studied: Integration, basic techniques of integration (substitution and by parts), improper integrals, using computer algebra systems (CAS) for integration, Taylor polynomials and Taylor series, ratio test for power series, radius of convergence of power series, first-order differential equations and systems of differential equations: modelling, separable DEs, and using CAS to study and find solutions.
Prerequisite: MAT135H1/ MAT135H5/ MATA30H3/ MATA31H3/ APS162H1/ ESC194H1/ MAT186H1/ MAT196H1Exclusion: MAT136H5/ MATA36H3/ APS163H1/ ESC195H1/ MAT187H1/ MAT197H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT137Y1 - Calculus with Proofs
Hours: 72L/24T
A conceptual approach for students interest in theoretical foundations of mathematics. Attention is given to computational aspects as well as problem-solving techniques. Limits and continuity, mean value theorem, elementary transcendental functions including trigonometric functions, inverse function theorem, differentiation, integration, fundamental theorem of calculus, Taylor's theorem, sequences and series, power series, and applications. This course will be useful for students interested in learning theoretical calculus and proofs in relation to future studies in computer science, economics, mathematics, physics, and statistics.
Prerequisite: High school level calculusExclusion: MAT137Y5/ ( MATA30H3/ MATA31H3, MATA37H3)Breadth Requirements: The Physical and Mathematical Universes (5)
MAT138H1 - Introduction to Proofs
Hours: 36L/12T
The goal of this course is for students to become comfortable with abstraction, rigour, logic, and proofs. They will practice reading and understanding mathematical statements, analyzing definitions and properties, formulating conjectures and generalizations, providing and writing reasonable and precise arguments, writing and critiquing proofs. The instructor may use specific mathematical content, which could vary from year to year, to practice these skills. Students who take MAT135H1 and MAT136H1 and wish to take MAT237Y1 are required to take MAT138H1 prior to undertaking MAT237Y1. Students who are taking MAT137Y1 or MAT157Y1 and/or MAT240H1 and are interested in more preparation with logical arguments are encouraged to take MAT138H1 concurrently.
Prerequisite: High school level calculusExclusion: MAT137Y1/ MAT137Y5/ ( MATA30H3/ MATA31H3, MATA37H3)/ MAT157Y1/ MAT157Y5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT157Y1 - Analysis I
Hours: 72L/48T
A theoretical course in calculus; emphasizing proofs and techniques. Elementary logic, limits and continuity, least upper bounds, intermediate and extreme value theorems. Derivatives, mean value and inverse function theorems. Integrals, fundamental theorem, elementary transcendental functions. Techniques of integration. Taylor's theorem; sequences and series; uniform convergence and power series. This course is required for the Mathematics Specialist, the Applied Mathematics Specialist, the Mathematics and Physics Specialist, and the Mathematics and Philosophy Specialist program and provides a strong theoretical mathematics background.
Prerequisite: High school level calculusExclusion: MAT157Y5Recommended Preparation: Preparing for University Math (PUMP) Level II. Students may also want to take MAT138H1 concurrently with MAT157Y1.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT193H1 - Women’s Mathematics
Hours: 36S
Mathematics has been shaped in significant ways by the work of outstanding female mathematicians such as Hypatia, Emmy Noether, Sofia Kovalevskaya, and Maryam Mirzakhani. Despite these successes, women still experience barriers to entering the field and participating at the highest levels. This course will blend an exploration of mathematics created by women with a study of the issue of women in mathematics. Students will have the opportunity to examine the complex factors that impact women’s participation in STEM, learn about the lives of female mathematicians, create their own mathematics, and sharpen their spatial cognition and logical thinking skills. Restricted to first-year students. Not eligible for CR/NCR option.
Prerequisite: High school level algebra.Exclusion: Not intended for students in a Mathematics Specialist or Major program.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT194H1 - Mathematical Personalities
Hours: 24L
An in-depth study of the life, times and work of several mathematicians who have been particularly influential. Examples may include but are not limited to: Coxeter, Euler, Germain, Grothendieck, Hilbert, Kovalevskaya, Kowalewski, Mirzhakhani, Newton, Noether, Ramanujan. Not intended for students in a Mathematics Specialist or Major program. Restricted to first-year students. Not eligible for CR/NCR option.
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT195H1 - Mathematics as an Interdisciplinary Pursuit
Hours: 24L
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. Not intended for students in a Mathematics Specialist or Major program. Restricted to first-year students. Not eligible for CR/NCR option.
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT197H1 - Mathematics as a Recreation, Mathematical Discovery and Creative Problem Solving
Hours: 24L
This course is an exploration into the creative process and use of imagination as they arise in the context of mathematical problem solving, puzzles, and recreational mathematics. The topics for the course may include a study of games, puzzles and problems that require a pre-Calculus background. One of the course’s main goals is to hone each participant’s creativity and mathematical problem-solving skills while guiding them towards the ‘Aha!’ experience which accompanies independent discovery. Not intended for students in Mathematics Specialist or Major programs. Restricted to first-year students. Not eligible for CR/NCR option.
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT198H1 - Cryptology: The Mathematics of Secrecy and Security
Hours: 24S
How do we send our own confidential information through secure channels, and how can we break codes to uncover the secret information of our adversaries? The mathematical field of cryptology is dedicated to answering such questions. In this course we will study breakthroughs in cryptology, from secret messages in the ancient world and the Enigma cipher in World War II, to modern cryptosystems that facilitate online commerce. Along the way, you will develop a sophisticated understanding of how numbers interact and develop the ability to communicate messages secretly and mathematics clearly. Restricted to first-year students. Not eligible for CR/NCR option.
Prerequisite: High school level algebra.Exclusion: Not intended for students in a Mathematics Specialist or Major program.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT199H1 - Aha! Mathematical Discovery and Creative Problem Solving
Hours: 36S
This course is an exploration into the creative process and use of imagination as they arise in the context of mathematical problem solving. The problems, which are all at a pre-calculus level, are chosen primarily by the criterion of aesthetic appeal, and emphasize reasoning rather than technique. Still, many of them are quite challenging, and substantial independent thinking will be required, the course is therefore appropriate for students from a variety of backgrounds and disciplines, including hard sciences. Its goal will be to hone each participant's creativity and mathematical problem-solving skills while guiding them towards the `Aha!' experience which accompanies independent discovery. Restricted to first-year students. Not eligible for CR/NCR option.
Prerequisite: High school level algebraBreadth Requirements: The Physical and Mathematical Universes (5)
MAT221H1 - Applied Linear Algebra
Hours: 36L/12T
An application-oriented approach to linear algebra, based on calculations in standard Euclidean space. Systems of linear equations, matrices, Gaussian elimination, subspaces, bases, orthogonal vectors and projections. Matrix inverses, kernel and range, rank-nullity theorem. Determinants, eigenvalues and eigenvectors, Cramer's rule, diagonalization. This course has strong emphasis on building computational skills in the area of algebra. Applications to curve fitting, economics, Markov chains and cryptography.
Prerequisite: High school level calculusExclusion: MAT223H1/ MAT223H5/ MATA22H3/ MATA23H3/ MAT224H1/ MAT224H5/ MATB24H3/ MAT240H1/ MAT240H5/ MAT185H1/ MAT188H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT223H1 - Linear Algebra I
Hours: 36L/12T
A first course on linear algebra in R^n emphasizing the interplay between algebraic and geometric perspectives. Topics include systems of equations, Gaussian elimination, representations of lines and planes, dot products, subspaces and translated subspaces, bases and change of basis, projections, the rank and nullity of a linear transformation, the rank/nullity/row space/column space of a matrix, matrix inverses, determinants, eigenvectors and eigenvalues, and matrix diagonalization. While not emphasizing proofs, this course does maintain a careful distinction between vectors and their representation in a basis as well as between matrices and linear transformations.
Prerequisite: High school level calculusExclusion: MAT223H5/ MATA22H3/ MATA23H3/ MAT224H1/ MAT224H5/ MATB24H3/ MAT240H1/ MAT240H5/ MAT247H1/ MAT247H5/ MAT185H1/ MAT188H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT224H1 - Linear Algebra II
Hours: 36L/12T
Fields, complex numbers, vector spaces over a field, linear transformations, matrix of a linear transformation, kernel, range, dimension theorem, isomorphisms, change of basis, eigenvalues, eigenvectors, diagonalizability, real and complex inner products, spectral theorem, adjoint/self-adjoint/normal linear operators, triangular form, nilpotent mappings, Jordan canonical form.
Prerequisite: MAT221H1(80%)/ MAT223H1/ MAT223H5/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT237Y1 - Multivariable Calculus with Proofs
Hours: 72L
Elementary topology in Euclidean space. Differential calculus of vector valued functions of a vector variable. Implicit and inverse function theorems, regular surfaces. Optimization, Lagrange multipliers, multivariable Taylor polynomials. Integral calculus with the Jordan measure. Fubini’s theorem, change of variables. Line and surface integrals. Vector calculus in two- and three-dimensions. Green’s theorem, Divergence theorem, Stokes’ theorem. Fourier series. This course is recommended for students interested in proof-based multivariable calculus with balanced emphasis between theory and applications.
Prerequisite: [ MAT133Y1/ ( MAT135H1, MAT136H1)/ ( MAT135H5, MAT136H5)/ ( MATA30H3/ MATA31H3, MATA36H3), MAT138H1/ MAT102H5/ MAT246H1]/ MAT137Y1/ MAT137Y5/ ( MAT137H5, MAT139H5)/ ( MATA30H3/ MATA31H3, MATA37H3)/ MAT157Y1/ MAT157Y5/ ( MAT157H5, MAT159H5), MAT223H1/ MATA22H3/ MATA23H3/ MAT240H1/ MAT240H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT240H1 - Algebra I
Hours: 36L/24T
A theoretical approach to: vector spaces over arbitrary fields, including C and Z_p. Subspaces, bases and dimension. Linear transformations, matrices, change of basis, similarity, determinants. Polynomials over a field (including unique factorization, resultants). Eigenvalues, eigenvectors, characteristic polynomial, diagonalization. Minimal polynomial, Cayley-Hamilton theorem.
Prerequisite: High school level calculusCorequisite: MAT157Y1Exclusion: MAT240H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT244H1 - Introduction to Ordinary Differential Equations
Hours: 36L
First order ordinary differential equations: Direction fields, integrating factors, separable equations, homogeneous equations, exact equations, autonomous equations, modeling. Existence and uniqueness theorem. Higher order equations: Constant coefficient equations, reduction of order, Wronskian, method of undetermined coefficients, variation of parameters. Solutions by series and integrals. First order linear systems, fundamental matrices. Non-linear equations, phase plane, stability. Applications in life and physical sciences and economics.
Prerequisite: ( MAT133Y1/ MAT135H1/ MAT135H5/ MATA35H3/ MATA30H3/ MATA31H3, MAT136H1/ MAT136H5/ MATA36H3/ MATA37H3)/ MAT135Y5/ MAT137Y1/ MAT137Y5/ ( MAT137H5, MAT139H5)/ MAT157Y1/ MAT157Y5/ ( MAT157H5, MAT159H5), MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5Corequisite: MAT235Y1/ MAT237Y1/ MAT257Y1Exclusion: MAT242H5/ MAT244H5/ MATB44H3/ MAT212H5/ MAT258Y5/ MAT292H1/ MAT267H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT245H1 - Mathematical Methods in Data Science
Hours: 36L/24P
An introduction to the mathematical methods behind scientific techniques developed for extracting information from large data sets. Elementary probability density functions, conditional expectation, inverse problems, regularization, dimension reduction, gradient methods, singular value decomposition and its applications, stability, diffusion maps. Examples from applications in data science and big data.
Prerequisite: MAT137Y1/ MAT157Y1, MAT223H1/ MAT240H1, MAT224H1/ MAT247H1Corequisite: MAT237Y1/ MAT257Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT247H1 - Algebra II
Hours: 36L
A theoretical approach to real and complex inner product spaces, isometries, orthogonal and unitary matrices and transformations. The adjoint. Hermitian and symmetric transformations. Spectral theorem for symmetric and normal transformations. Polar representation theorem. Primary decomposition theorem. Rational and Jordan canonical forms. Additional topics including dual spaces, quotient spaces, bilinear forms, quadratic surfaces, multilinear algebra.
Prerequisite: MAT240H1/ MAT240H5Corequisite: MAT157Y1Exclusion: MAT247H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT257Y1 - Analysis II
Hours: 72L/48T
Topology of R^n; compactness, functions and continuity, extreme value theorem. Derivatives; inverse and implicit function theorems, maxima and minima, Lagrange multipliers. Integration; Fubini's theorem, partitions of unity, change of variables. Differential forms. Manifolds in R^n; integration on manifolds; Stokes' theorem for differential forms and classical versions. Some topics may vary year-to-year.
Prerequisite: MAT157Y1/ ( MAT157H5, MAT159H5)/ MAT157Y5, MAT247H1/ MAT247H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT267H1 - Advanced Ordinary Differential Equations
Hours: 36L/12T
A theoretical course on Ordinary Differential Equations. First-order equations: separable equations, exact equations, integrating factors. Variational problems, Euler-Lagrange equations. Linear equations and first-order systems. Fundamental matrices, Wronskians. Non-linear equations. Existence and uniqueness theorems. Method of power series. Elementary qualitative theory; stability, phase plane, stationary points. Oscillation theorem, Sturm comparison. Applications in mechanics, physics, chemistry, biology and economics.
Prerequisite: MAT157Y1/ ( MAT157H5, MAT159H5)/ MAT157Y5, MAT247H1/ MAT247H5Corequisite: MAT257Y1Exclusion: MAT234H1/ MAT292H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT271H1 - Insights from Mathematics
Hours: 36L/6T
This breadth course is accessible to students with limited mathematical background. Various mathematical techniques will be illustrated with examples from humanities and social science disciplines. Some of the topics will incorporate user friendly computer explorations to give participants the feel of the subject without requiring skill at calculations.
Note: This course cannot be used to satisfy requirements of program in the math department.
Breadth Requirements: The Physical and Mathematical Universes (5)
MAT282H1 - Topics in Mathematics
Hours: 36L
A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/
Prerequisite: 1.0 MAT credit at the 100-level. Possible additional topic-specific prerequisites.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT295H1 - Independent Reading in Mathematics
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT296H1 - Independent Reading in Mathematics
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 36L course. Not eligible for CR/NCR option.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT297Y1 - Research Project in Mathematics
Independent research under the direction of a faculty member. Similar workload to a 72L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisorBreadth Requirements: The Physical and Mathematical Universes (5)
MAT301H1 - Groups and Symmetries
Hours: 36L
Congruences and fields. Permutations and permutation groups. Linear groups. Abstract groups, homomorphisms, subgroups. Symmetry groups of regular polygons and Platonic solids, wallpaper groups. Group actions, class formula. Cosets, Lagrange theorem. Normal subgroups, quotient groups. Classification of finitely generated abelian groups. Emphasis on examples and calculations.
Prerequisite: MAT257Y1/ ( MAT224H1/ MAT247H1, MAT235Y1/ MAT237Y1, MAT246H1/ MAT157Y1/ ( MAT157H5, MAT159H5)/ MAT157Y5/ CSC236H1/ CSC240H1)/ (MAT185H1, MAT194H1, MAT195H1)Exclusion: MAT347Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT327H1 - Introduction to Topology
Hours: 36L
Metric spaces, topological spaces and continuous mappings; separation, compactness, connectedness. Fundamental group and covering spaces. Brouwer fixed-point theorem. Students in the math specialist program wishing to take additional topology courses are advised to obtain permission to take MAT1300H, MAT1301H.
Prerequisite: MAT157Y1/ MAT157Y5/ ( MAT157H5, MAT159H5)/ [( MAT237Y1/ ( MATB41H3, MATB42H3/ MATB43H3)/ MAT237Y5), MAT246H1]Breadth Requirements: The Physical and Mathematical Universes (5)
MAT329Y1 - Concepts in Elementary Mathematics
Hours: 72L
This course is aimed at students intending to become elementary school teachers. Emphasis is placed on the formation and development of fundamental reasoning and learning skills required to understand and to teach mathematics at the elementary level. Topics may include: Problem Solving and Strategies, Sets and Elementary Logic, Numbers and Elements of Number Theory, Introductory Probability and Fundamentals of Geometry.
The course may include an optional practicum in school classrooms.
Prerequisite: 5.0 credits with a CGPA of at least 2.5, and MAT137Y1/ MAT137Y5/ ( MAT137H5, MAT139H5)/ MAT138H1/ ( MAT223H1/ MAT240H1)/ [ MAT246H1/ MAT157Y1/ MAT157Y5/ ( MAT157H5, MAT159H5)] Exclusion: MAT382H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT332H1 - Introduction to Graph Theory
Hours: 36L
This course will explore the following topics: Graphs, subgraphs, isomorphism, trees, connectivity, Euler and Hamiltonian properties, matchings, vertex and edge colourings, planarity, network flows and strongly regular graphs. Participants will be encouraged to use these topics and execute applications to such problems as timetabling, tournament scheduling, experimental design and finite geometries.
Prerequisite: MAT224H1/ MATB24H3/ MAT224H5/ MAT247H1/ MAT247H5Recommended Preparation: Students are encouraged to take MAT301H1 or MAT347Y1 concurrently or prior to undertaking this course.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT335H1 - Chaos, Fractals and Dynamics
Hours: 36L
An elementary introduction to a modern and fast-developing area of mathematics. One-dimensional dynamics: iterations of quadratic polynomials. Dynamics of linear mappings, attractors. Bifurcation, Henon map, Mandelbrot and Julia sets. History and applications.
Prerequisite: MAT137Y1/ ( MATA30H3, MATA31H3, MATA37H3)/ MAT137Y5/ ( MAT137H5, MAT139H5)/ MAT157Y1/ MAT157Y5/ ( MAT157H5, MAT159H5)/ MAT235Y1/ MAT235Y5/ ( MAT232H5, MAT236H5)/ ( MATB41H3, MATB42H3)/ MAT237Y1/ ( MATB41H3, MATB42H3, MATB43H3)/ MAT237Y5, MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT344H1 - Introduction to Combinatorics
Hours: 36L
Basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph theory with algorithms; applications (including network flows). Combinatorial structures including block designs and finite geometries.
Prerequisite: MAT223H1/ MATA23H3/ MAT223H5/ MAT240H1/ MAT240H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT347Y1 - Groups, Rings and Fields
Hours: 72L/24T
Groups, subgroups, quotient groups, Sylow theorems, Jordan-Hölder theorem, finitely generated abelian groups, solvable groups. Rings, ideals, Chinese remainder theorem; Euclidean domains and principal ideal domains: unique factorization. Noetherian rings, Hilbert basis theorem. Finitely generated modules. Field extensions, algebraic closure, straight-edge and compass constructions. Galois theory, including insolvability of the quintic.
Prerequisite: MAT257Y1/(85% in MAT247H1/ MAT247H5)Breadth Requirements: The Physical and Mathematical Universes (5)
MAT351Y1 - Partial Differential Equations
Hours: 72L
This is a first course in Partial Differential Equations, intended for Mathematics students with interests in analysis, mathematical physics, geometry, and optimization. The examples to be discussed include first-order equations, harmonic functions, the diffusion equation, the wave equation, Schrodinger's equation, and eigenvalue problems. In addition to the classical representation formulas for the solutions of these equations, there are techniques that apply more broadly: the notion of well-posedness, the method of characteristics, energy methods, maximum and comparison principles, fundamental solutions, Green's functions, Duhamel's principle, Fourier series, the min-max characterization of eigenvalues, Bessel functions, spherical harmonics, and distributions. Nonlinear phenomena such as shock waves and solitary waves are also introduced.
Prerequisite: MAT257Y1/ MAT237Y1 (85%), MAT267H1Exclusion: APM351Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT354H1 - Complex Analysis I
Hours: 36L
Complex numbers, the complex plane and Riemann sphere, Möbius transformations, elementary functions and their mapping properties, conformal mapping, holomorphic functions, Cauchy's theorem and integral formula. Taylor and Laurent series, maximum modulus principle, Schwarz' lemma, residue theorem and residue calculus.
Prerequisite: MAT257Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT357H1 - Foundations of Real Analysis
Hours: 36L
Function spaces; Arzela-Ascoli theorem, Weierstrass approximation theorem, Fourier series. Introduction to Banach and Hilbert spaces; contraction mapping principle, fundamental existence and uniqueness theorem for ordinary differential equations. Lebesgue integral; convergence theorems, comparison with Riemann integral, L^p spaces. Applications to probability.
Prerequisite: MAT257Y1Exclusion: MAT438H5Breadth Requirements: The Physical and Mathematical Universes (5)
MAT367H1 - Differential Geometry
Hours: 36L
Manifolds, partitions of unity, submersions and immersions, vector fields, vector bundles, tangent and cotangent bundles, foliations and Frobenius’ theorem, multilinear algebra, differential forms, Stokes’ theorem, Poincare-Hopf theorem.
Prerequisite: MAT257Y1/ [ MAT224H1/ MAT247H1, MAT237Y1, MAT246H1/ MAT157Y1/ MAT157Y5/ ( MAT157H5, MAT159H5)]Recommended Preparation: MAT257Y1, MAT240H1, MAT247H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT370H1 - Introduction to Mathematical Probability
Hours: 36L/12T
A rigorous introduction to the basic concepts of probability without measure theory. Random variables and their distributions, Independence, Limit theorems, Conditional Probability, Markov chains
Prerequisite: MAT224H1/ MAT224H5, MAT235Y1/ ( MAT232H5, MAT236H5)/ MAT237Y1/ MAT257Y1, MAT246H1Exclusion: MAT377H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT377H1 - Mathematical Probability Theory
Hours: 36L/12T
This course introduces students to various topics in mathematical probability theory. Topics include basic concepts (such as probability, random variables, expectations, conditional probability) from a mathematical point of view, examples of distributions and stochastic processes and their properties, convergence results (such as the law of large numbers, central limit theorem, random series, etc.), various inequalities, and examples of applications of probabilistic ideas beyond statistics (for example, in geometry and computer science).
Prerequisite: MAT247H1/ MAT247H5, MAT257Y1Exclusion: MAT370H1, STA347H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT382H1 - Topics in Mathematics
Hours: 36L
A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/
Prerequisite: 2.5 AMP/MAT credits at the 100/200-level. Possible additional topic-specific prerequisites.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT390H1 - History of Mathematics up to 1700
Hours: 24L/12T
A survey of ancient, medieval, and early modern mathematics with emphasis on historical issues.
Prerequisite: 1.0 APM/MAT credit at the 200-levelExclusion: HPS309H1/ HPS310Y1/ HPS390H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT391H1 - History of Mathematics after 1700
Hours: 24L/12T
A survey of the development of mathematics from 1700 to the present with emphasis on technical development.
Prerequisite: 1.0 APM/MAT credit at the 200 levelExclusion: HPS309H1/ HPS310H1/ HPS391H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT395H1 - Independent Reading in Mathematics
Independent reading under the direction of a faculty member. Topic must be outside current undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisorBreadth Requirements: The Physical and Mathematical Universes (5)
MAT396H1 - Independent Reading in Mathematics
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Similar workload to a 36L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT397Y1 - Research Project in Mathematics
Independent research under the direction of a faculty member. Workload similar to a 72L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT401H1 - Polynomial Equations and Fields
Hours: 36L
Commutative rings; quotient rings. Construction of the rationals. Polynomial algebra. Fields and Galois theory: Field extensions, adjunction of roots of a polynomial. Constructibility, trisection of angles, construction of regular polygons. Galois groups of polynomials, in particular cubics, quartics. Insolvability of quintics by radicals.
Prerequisite: MAT301H1Exclusion: MAT347Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT402H1 - Classical Geometries
Hours: 36L
Euclidean and non-Euclidean plane and space geometries. Real and complex projective space. Models of the hyperbolic plane. Connections with the geometry of surfaces.
Prerequisite: MAT301H1/ MAT347Y1, MAT235Y1/ MAT237Y1/ MAT257Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT403H1 - Classical Geometries II
Hours: 36L
This course is the second part of the "Classical Geometries" MAT402H1 course. It is mainly dedicated to detailed study of classical real projective geometry and projective geometry over other fields. It is also devoted to the study of spherical and elliptic geometry.
Prerequisite: MAT235Y1/ MAT237Y1/ MAT257Y1, MAT301H1/ MAT347Y1Recommended Preparation: MAT402H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT409H1 - Set Theory
Hours: 36L
Set theory and its relations with other branches of mathematics. ZFC axioms. Ordinal and cardinal numbers. Reflection principle. Constructible sets and the continuum hypothesis. Introduction to independence proofs. Topics from large cardinals, infinitary combinatorics and descriptive set theory.
Joint undergraduate/graduate course - MAT409H1/MAT1404H
Prerequisite: MAT357H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT415H1 - Algebraic Number Theory
Hours: 36L
A selection from the following: finite fields; global and local fields; valuation theory; ideals and divisors; differents and discriminants; ramification and inertia; class numbers and units; cyclotomic fields; Diophantine equations.
Prerequisite: MAT347Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT417H1 - Analytic Number Theory
Hours: 36L
A selection from the following: distribution of primes, especially in arithmetic progressions and short intervals; exponential sums; Hardy-Littlewood and dispersion methods; character sums and L-functions; the Riemann zeta-function; sieve methods, large and small; Diophantine approximation, modular forms.
Joint undergraduate/graduate course - MAT417H1/MAT1202H
Prerequisite: MAT334H1/ MAT354H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT425H1 - Differential Topology
Hours: 36L
Smooth manifolds, Sard's theorem and transversality. Morse theory. Immersion and embedding theorems. Intersection theory. Borsuk-Ulam theorem. Vector fields and Euler characteristic. Hopf degree theorem. Additional topics may vary.
Prerequisite: MAT257Y1, MAT327H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT436H1 - Introduction to Linear Operators
Hours: 36L
The course will survey the branch of mathematics developed (in its abstract form) primarily in the twentieth century and referred to variously as functional analysis, linear operators in Hilbert space, and operator algebras, among other names (for instance, more recently, to reflect the rapidly increasing scope of the subject, the phrase non-commutative geometry has been introduced). The intention will be to discuss a number of the topics in Pedersen's textbook Analysis Now. Students will be encouraged to lecture on some of the material, and also to work through some of the exercises in the textbook (or in the suggested reference books).
Joint undergraduate/graduate course - MAT436H1/MAT1011H
Prerequisite: 5.0 MAT credits, including MAT224H1/ MAT247H1 and MAT237Y1/ MAT257Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT437H1 - K-Theory and C* Algebras
Hours: 36L
The theory of operator algebras was begun by John von Neumann eighty years ago. In one of the most important innovations of this theory, von Neumann and Murray introduced a notion of equivalence of projections in a self-adjoint algebra (*-algebra) of Hilbert space operators that was compatible with addition of orthogonal projections (also in matrix algebras over the algebra), and so gave rise to an abelian semigroup, now referred to as the Murray-von Neumann semigroup.
Later, Grothendieck in geometry, Atiyah and Hirzebruch in topology, and Serre in the setting of arbitrary rings (pertinent for instance for number theory), considered similar constructions. The enveloping group of the semigroup considered in each of these settings is now referred to as the K-group (Grothendieck's terminology), or as the Grothendieck group.
Among the many indications of the depth of this construction was the discovery of Atiyah and Hirzebruch that Bott periodicity could be expressed in a simple way using the K-group. Also, Atiyah and Singer famously showed that K-theory was important in connection with the Fredholm index. Partly because of these developments, K-theory very soon became important again in the theory of operator algebras. (And in turn, operator algebras became increasingly important in other branches of mathematics.)
The purpose of this course is to give a general, elementary, introduction to the ideas of K-theory in the operator algebra context. (Very briefly, K-theory generalizes the notion of dimension of a vector space.)
The course will begin with a description of the method (K-theoretical in spirit) used by Murray and von Neumann to give a rough initial classification of von Neumann algebras (into types I, II, and III). It will centre around the relatively recent use of K-theory to study Bratteli's approximately finite-dimensional C*-algebras---both to classify them (a result that can be formulated and proved purely algebraically), and to prove that the class of these C*-algebras---what Bratteli called AF algebras---is closed under passing to extensions (a result that uses the Bott periodicity feature of K-theory).
Students will be encouraged to prepare oral or written reports on various subjects related to the course, including basic theory and applications.
Joint undergraduate/graduate course - MAT437H1/MAT1016H
Prerequisite: 5.0 MAT credits, including MAT224H1/ MAT247H1 and MAT237Y1/ MAT257Y1Recommended Preparation: Students are encouraged to execute basic research that answers the question, what is an abelian group?Breadth Requirements: The Physical and Mathematical Universes (5)
MAT445H1 - Representation Theory
Hours: 36L
A selection of topics from: Representation theory of finite groups, topological groups and compact groups. Group algebras. Character theory and orthogonality relations. Weyl's character formula for compact semisimple Lie groups. Induced representations. Structure theory and representations of semisimple Lie algebras. Determination of the complex Lie algebras.
Joint undergraduate/graduate - MAT445H1/MAT1196H
Prerequisite: MAT347Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT448H1 - Introduction to Commutative Algebra and Algebraic Geometry
Hours: 36L
Basic notions of algebraic geometry, with emphasis on commutative algebra or geometry according to the interests of the instructor. Algebraic topics: localization, integral dependence and Hilbert's Nullstellensatz, valuation theory, power series rings and completion, dimension theory. Geometric topics: affine and projective varieties, dimension and intersection theory, curves and surfaces, varieties over the complex numbers. This course will be offered in alternating years.
Joint undergraduate/graduate course - MAT448H1/MAT1155H
Prerequisite: MAT347Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT449H1 - Algebraic Curves
Hours: 36L
Projective geometry. Curves and Riemann surfaces. Algebraic methods. Intersection of curves; linear systems; Bezout's theorem. Cubics and elliptic curves. Riemann-Roch theorem. Newton polygon and Puiseux expansion; resolution of singularities. This course will be offered in alternating years.
Prerequisite: MAT347Y1, MAT354H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT454H1 - Complex Analysis II
Hours: 36L
Harmonic functions, Harnack's principle, Poisson's integral formula and Dirichlet's problem. Infinite products and the gamma function. Normal families and the Riemann mapping theorem. Analytic continuation, monodromy theorem and elementary Riemann surfaces. Elliptic functions, the modular function and the little Picard theorem.
Joint undergraduate/graduate course - MAT454H1/MAT1002H
Prerequisite: MAT354H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT457H1 - Advanced Real Analysis I
Hours: 36L
Lebesgue measure and integration; convergence theorems, Fubini's theorem, Lebesgue differentiation theorem, abstract measures, Caratheodory theorem, Radon-Nikodym theorem. Hilbert spaces, orthonormal bases, Riesz representation theorem, compact operators, L^p spaces, Hölder and Minkowski inequalities.
Joint undergraduate/graduate course - MAT457H1/MAT1000H
Prerequisite: MAT357H1Exclusion: MAT457Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT458H1 - Advanced Real Analysis II
Hours: 36L
Fourier series and transform, convergence results, Fourier inversion theorem, L^2 theory, estimates, convolutions. Banach spaces, duals, weak topology, weak compactness, Hahn-Banach theorem, open mapping theorem, uniform boundedness theorem.
Joint undergraduate/graduate course - MAT458H1/MAT1001H
Prerequisite: MAT457H1Exclusion: MAT457Y1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT461H1 - Hamiltonian Mechanics
Hours: 36L
This course focuses on key notions of classical mechanics: Newton equations, variational principles, Lagrangian formulation and Euler-Lagrange equations, the motion in a central force, the motion of a rigid body, small oscillations, Hamiltonian formulation, canonical transformations, Hamilton-Jacobi theory, action-angle variables, and integrable systems.
Prerequisite: MAT244H1/ MAT267H1, MAT337H1/ MAT367H1, APM346H1/ MAT351Y1Recommended Preparation: MAT267H1, MAT367H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT464H1 - Riemannian Geometry
Hours: 36L
Riemannian metrics. Levi-Civita connection. Geodesics. Exponential map. Second fundamental form. Complete manifolds and Hopf-Rinow theorem. Curvature tensors. Ricci curvature and scalar curvature. Spaces of constant curvature.
Joint undergraduate/graduate course - MAT464H1/MAT1342H
Prerequisite: MAT367H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT475H1 - Problem Solving Seminar
This course addresses the question: How do you attack a problem the likes of which you have never seen before? Students will apply Polya's principles of mathematical problem solving, draw upon their previous mathematical knowledge, and explore the creative side of mathematics in solving a variety of interesting problems and explaining those solutions to others.
Prerequisite: MAT224H1/ MAT247H1, MAT235Y1/ MAT237Y1/ MAT257Y1, and at least 1.0 credit at the 300+ level in APM/MATBreadth Requirements: The Physical and Mathematical Universes (5)
MAT477H1 - Seminar in Mathematics
Seminar in an advanced topic. Content will generally vary from semester to semester. Student presentations are required.
Prerequisite: MAT347Y1, MAT354H1, MAT357H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT478H1 - Seminar in Mathematics
Seminar in an advanced topic. Content will generally vary from semester to semester. Student presentations are required.
Prerequisite: MAT347Y1, MAT354H1, MAT357H1Breadth Requirements: The Physical and Mathematical Universes (5)
MAT482H1 - Topics in Mathematics
Hours: 36L
A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/.
Joint undergraduate/graduate course - MAT482H1/MAT1901H
Prerequisite: 6.0 APM/MAT credits at the 100, 200 and 300-level. Possible additional topic-specific prerequisites.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT483H1 - Topics in Mathematics
Hours: 36L
A course in mathematics on a topic outside the current undergraduate offerings. For information on the specific topic to be studied and possible additional prerequisites, go to http://www.math.toronto.edu/cms/current-students-ug/.
Prerequisite: 6.0 APM/MAT credits at the 100, 200 and 300-level. Possible additional topic-specific prerequisites.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT495H1 - Independent Reading in Mathematics
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 36L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisorBreadth Requirements: The Physical and Mathematical Universes (5)
MAT496H1 - Independent Reading in Mathematics
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 36L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.Breadth Requirements: The Physical and Mathematical Universes (5)
MAT497Y1 - Research Project in Mathematics
Independent research under the direction of a faculty member. Not eligible for CR/NCR option. Similar workload to a 72L course.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisorBreadth Requirements: The Physical and Mathematical Universes (5)
MAT499Y1 - Readings in Mathematics
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings. Workload equivalent to a 72L course. Not eligible for CR/NCR option.
Completed applications for this course are due to the Math Undergraduate Program Office no later than the third day of the term that the reading course will start.
Prerequisite: Minimum GPA of 3.5 in APM and MAT courses. Permission of the Associate Chair for Undergraduate Studies and of the prospective supervisor.Breadth Requirements: The Physical and Mathematical Universes (5)