2002/2003 Calendar
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MAT Courses

| Course Winter Timetable |


SCI199Y1
First Year Seminar 52T

Undergraduate seminar that focuses on specific ideas, questions, phenomena or controversies, taught by a regular Faculty member
deeply engaged in the discipline. Open only to newly admitted first year students. It may serve as a breadth requirement course; see
page 44.


JUM102H1
Mathematics as an Interdisciplinary Pursuit 26L, 13T

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, are considered. (Offered every three years)
JUM102H is particularly suited as a Science Distribution Requirement course for Humanities and Social Science students.


JUM103H1
Mathematics as a Recreation 26L, 13T

A study of games, puzzles and problems focusing on the deeper principles they illustrate. Concentration is on problems arising out of
number theory and geometry, with emphasis on the process of mathematical reasoning. Technical requirements are kept to a
minimum. A foundation is provided for a continuing lay interest in mathematics. (Offered every three years)
JUM103H is particularly suited as a Science Distribution Requirement course for Humanities and Social Science students.


JUM105H1
Mathematical Personalities 26L, 13T

An in-depth study of the life, times and work of several mathematicians who have been particularly influential. Examples may include
Newton, Euler, Gauss, Kowalewski, Hilbert, Hardy, Ramanujan, Gödel, Erdös, Coxeter, Grothendieck. (Offered every three years)
JUM105H is particularly suited as a Science Distribution Requirement course for Humanities and Social Science students.


MAT123H,124H: see below MAT 133Y
MAT125H,126H: see below MAT 135Y


MAT133Y1
Calculus and Linear Algebra for Commerce 78L, 24T

Mathematics of finance. Matrices and linear equations. Review of differential calculus; applications. Integration and fundamental
theorem; applications. Introduction to partial differentiation; applications.
NOTE: please note prerequisites listed below. Students without the proper prerequisites for MAT133Y1 may be deregistered from this
course.
Exclusion: MAT123H1, 124H1, 125H1, 126H1, 135Y1, 136Y1, 137Y1, 157Y1
Prerequisite: Calc + A&G/FM


MAT133Y counts as a Social Science course


MAT123H1
Calculus and Linear Algebra for Commerce (A) 39L

First term of MAT133Y1. Students in academic difficulty in MAT133Y1 who have written two midterm examinations with a mark of at least 20% in the second may withdraw from MAT133Y1 and enrol in MAT123H1 in the Spring Term. These students are informed of this option by the beginning of the Spring Term. Classes begin in the second week of the Spring Term; late enrolment is not permitted. Students not enrolled in MAT133Y1 in the Fall Term are not allowed to enrol in MAT123H1. MAT123H1 together with MAT124H1 is equivalent for program and prerequisite purposes to MAT133Y1.
Exclusion: MAT125H1, 126H1, 133Y1, 135Y1, 136Y1, 137Y1, 157Y1
NOTE: students who enrol in MAT133Y1 after completing MAT123H1 but not MAT124H1 do not receive degree credit for MAT133Y1; it is counted ONLY as an “Extra Course.”
Prerequisite: Enrolment in MAT133Y1, and withdrawal from MAT133Y1 after two midterms, with a mark of at least 20% in the sec-ond midterm.
MAT123H is a Social Science course


MAT124H1
Calculus and Linear Algebra for Commerce (B) 39L, 13T

Second Term content of MAT133Y1; the final examination includes topics covered in MAT123H1. Offered in the Summer Session
only; students not enrolled in MAT123H1 in the preceding Spring Term will NOT be allowed to enrol in MAT124H1. MAT123H1
together with MAT124H1 is equivalent for program and prerequisite purposes to MAT133Y1.
Exclusion: MAT125H1, 126H1, 133Y1, 135Y1, 136Y1, 137Y1, 157Y1
Prerequisite: MAT123H1 successfully completed in the preceding Spring Term
MAT124H is a Social Science course


MAT135Y1
Calculus I 78L, 24T

Review of differential calculus; applications. Integration and fundamental theorem; applications. Series. Introduction to differential
equations.
Exclusion: MAT123H1, 124H1, 125H1, 126H1, 133Y1, 136Y1, 137Y1, 157Y1
Prerequisite: Calc


MAT125H1
Calculus I (A) 39L

First term of MAT135Y1. Students in academic difficulty in MAT135Y1 who have written two midterm examinations with a mark of at
least 20% in the second may withdraw from MAT135Y1 and enrol in MAT125H1 in the Spring Term. These students are informed of
this option by the beginning of the Spring Term. Classes begin in the second week of the Spring Term; late enrolment is not permitted.
Students not enrolled in MAT135Y1 in the Fall Term will not be allowed to enrol in MAT125H1. MAT125H1 together with MAT126H1
is equivalent for program and prerequisite purposes to MAT135Y1.
Exclusion: MAT123H1, 124H1, 133Y1, 135Y1, 136Y1, 137Y1, 157Y1
NOTE: students who enrol in MAT135Y1 after completing MAT125H1 but not MAT126H1 do not receive degree credit for MAT135Y1; it is counted ONLY as an “Extra Course.”
Prerequisite: Enrolment in MAT135Y1, and withdrawal from MAT135Y1 after two midterms, with a mark of at least 20% in the sec-ond midterm.


MAT126H1
Calculus I (B) 39L, 13T

Second Term content of MAT135Y1; the final examination includes topics covered in MAT125H1. Offered in the Summer Session
only; students not enrolled in MAT125H1 in the preceding Spring Term will NOT be allowed to enrol in MAT126H1. MAT125H1
together with MAT126H1 is equivalent for program and prerequisite purposes to MAT135Y1.
Exclusion: MAT123H1, 124H1, 133Y1, 135Y1, 136Y1, 137Y1
Prerequisite: MAT125H1 successfully completed in the preceding Spring Term


MAT136Y1
Calculus and its Foundations 104L, 48T

Limited to out-of-province students interested in the biological, physical, or computer sciences, whose high school mathematics
preparation is strong but does not include calculus. Develops the concepts of calculus at least at the level of MAT135Y1. May include
background material on functions, analytic geometry, and trigonometry, as well as on calculus. Note that this course counts as full-
course credit, although it involves double the number of lecture and tutorial hours as MAT 135Y1.
Exclusion: MAT123H1, 124H1, 125H1, 126H1, 133Y1, 135Y1, 137Y1, 157Y1, OAC Calc, AP Calc
Prerequisite: Solid background in high school mathematics, including senior years


MAT137Y1
Calculus! 78L, 26T

A conceptual approach for students with a serious interest in mathematics. Geometric and physical intuition are emphasized but some
attention is also given to the theoretical foundations of calculus. Material covers the basic concepts of calculus: limits and continuity,
the mean value and inverse function theorems, the integral, the fundamental theorem, elementary transcendental functions, Taylor’s
theorem, sequence and series, uniform convergence and power series.
Exclusions: MAT123H1, 124H1, 125H1, 126H1, 133Y1, 135Y1, 136Y1, 157Y1
Prerequisite: Calc + A&G


MAT157Y1
Analysis I 78L, 52T

A theoretical course in calculus; emphasizing proofs and techniques, as well as geometric and physical understanding. Limits and
continuity; least upper bounds, intermediate and extreme value theorems. Derivatives, mean value and inverse function theorems.
Integrals; fundamental theorem; elementary transcendental functions. Taylor’s theorem; sequences and series; uniform convergence
and power series.
Exclusion: MAT137Y1
Prerequisite: Calc + A&G


JMB170Y1
Biology, Models, and Mathematics 52L, 26T

Applications of mathematics to biological problems in physiology, biomechanics, genetics, evolution, growth, population dynamics,
cell biology, ecology and behaviour.
Prerequisite: OAC Biology
Co-requisite: BIO150Y1


MAT223H1
Linear Algebra I 39L, 13T

Matrices, linear systems, elementary matrices and the inverse of a matrix. Vector spaces over R, subspaces, basis and dimension. Real
inner product spaces, geometry in Rn, lines and hyperplanes. Linear transformation, kernel, range. The determinant, Cramer’s rule,
the adjoint matrix. Eigenvalues, eigenvectors, similarity, diagonalization. Projections, Gram-Schmidt process, orthogonal
transformations and orthogonal diagonalization, quadratic forms, conics.
Exclusion: MAT240H1
Prerequisite: Calc + A&G


MAT224H1
Linear Algebra II 39L, 13T

Fields. Vector spaces over a field. Linear transformations. Diagonalizability, direct sums. Invariant subspaces, Cayley-Hamilton
theorem. Complex inner product, orthogonality, the adjoint of a linear operator, the projection matrix and the method of least squares.
Normal, self-adjoint and unitary operators. Spectral theorem. Conditioning and Rayleigh quotient. Jordan canonical form.
Exclusion: MAT247H1
Prerequisite: MAT223H1/240H1


MAT235Y1
Calculus II 78L

Differential and integral calculus of functions of several variables. Line and surface integrals, the divergence theorem, Stokes’
theorem. Sequences and series, including an introduction to Fourier series. Some partial differential equations of Physics.
Exclusion: MAT237Y1, 257Y1
Prerequisite: MAT135Y1/136Y1/137Y1/157Y1


MAT237Y1
Multivariable Calculus 78L

Sequences and series. Uniform convergence. Convergence of integrals. Elements of topology in R2 and R3. Differential and integral
calculus of vector valued functions of a vector variable, with emphasis on vectors in two and three dimensional euclidean space.
Extremal problems, Lagrange multipliers, line and surface integrals, vector analysis, Stokes’ theorem, Fourier series, calculus of
variations.
Exclusion: MAT235Y1, 257Y1
Prerequisite: MAT135Y1(80%)/136Y1/137Y1/157Y1


MAT240H1
Algebra I 39L, 26T

A theoretical approach to: vector spaces over arbitrary fields including C,Zp. 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.
Exclusion: MAT223H1
Prerequisite: Calc + A&G
Co-requisite: MAT157Y1


MAT244H1
Introduction to Ordinary Differential Equations 39L

Ordinary differential equations of the first and second order, existence and uniqueness; solutions by series and integrals; linear
systems of first order; non-linear equations; difference equations.
Exclusion: MAT267H1
Prerequisite: MAT135Y1/136Y1/137Y1/157Y1, 223H1/240H1
Co-requisite: MAT235Y1/237Y1


MAT246Y1
Concepts in Abstract Mathematics 78L

Designed to introduce students to mathematical proofs and abstract mathematical concepts. Topics may include modular arithmetic,
prime numbers, sizes of infinite sets, a proof that some angles cannot be trisected with straightedge and compass, an introduction to
group theory, or an introduction to topology.
Prerequisite: MAT133Y1/135Y1/136Y1/137Y1


MAT247H1
Algebra II 39L, 13T

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. Examples of symmetry groups and linear groups,
stochastic matrices, matrix functions.
Exclusion: MAT224H1
Prerequisite: MAT240H1, 157Y1


MAT257Y1
Analysis II 78L, 26T

Topology of Rn; compactness, functions and continuity, extreme value theorem. Derivatives; inverse and implicit function
theorems, maxima and minima, Lagrange multipliers. Integrals; Fubini’s theorem, partitions of unity, change of variables.
Differential forms. Manifolds in Rn; integration on manifolds; Stokes’ theorem for differential forms and classical versions.
Exclusion: MAT237Y1
Prerequisite: MAT157Y1, 240H1
Co-requisite: MAT247H1


MAT267H1
Advanced Ordinary Differential Equations I 39L, 13T

First-order equations. Linear equations and first-order systems. Non-linear first-order systems. Existence and uniqueness theorems
for the Cauchy problem. Method of power series. Elementary qualitative theory; stability, phase plane, stationary points. Examples
of applications in mechanics, physics, chemistry, biology and economics.
Exclusion: MAT244H1
Prerequisite: MAT157Y1, 247H1
Co-requisite: MAT257Y1


MAT299Y1
Research Opportunity Program


MAT301H1
Groups and Symmetries 39L

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’s
theorem. Normal subgroups, quotient groups. Classification of finitely generated abelian groups. Emphasis on examples and
calculations.
Exclusion: MAT347Y1
Prerequisite: MAT224H1, 246Y1/(CSC238H1, PHL245H1)/MAT257Y1


MAT302H1
Polynomial Equations and Fields 39L

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. Solvable groups, simple groups. Insolvability of quintics by radicals.
Exclusion: MAT347Y1
Prerequisite: MAT301H1


MAT309H
Introduction to Mathematical Logic 39L

Predicate calculus. Relationship between truth and provability; Gödel’s completeness theorem. First order arithmetic as an example
of a first-order system. Gödel’s incompleteness theorem; outline of its proof. Introduction to recursive functions.
Exclusion: CSC438H1
Prerequisite: MAT223H1/240H1, 235Y1/237Y1, 246Y1/(CSC238H1, PHL245H1)/MAT257Y1


MAT315H1
Introduction to Number Theory 39L

Elementary topics in number theory: arithmetic functions; polynomials over the residue classes modulo m, characters on the residue
classes modulo m; quadratic reciprocity law, representation of numbers as sums of squares.
Prerequisite: MAT(235Y1/237Y1, 223H1/240H1)/257Y1


MAT327H1
Introduction to Topology 39L

Metric spaces, topological spaces and continuous mappings; separation, compactness, connectedness. Topology of function spaces.
Fundamental group and covering spaces. Cell complexes, topological and smooth manifolds, Brouwer fixed-point theorem.
Prerequisite: MAT257Y1/237H1 and permission of the instructor


MAT329Y1
Concepts in Elementary Mathematics 78L

The formation of mathematical concepts and techniques, and their application to the everyday world. Nature of mathematics and
mathematical understanding. Role of observation, conjecture, analysis, structure, critical thinking and logical argument. Numeration,
arithmetic, geometry, counting techniques, recursion, algorithms.
This course is specifically addressed to students intending to become elementary school teachers and is strongly recommended by the
Faculty of Education. Previous experience working with children is useful. The course is taught jointly by the Department of
Mathematics and the Faculty of Education. The course content is considered in the context of elementary school teaching. In
particular, the course may include a practicum in school classrooms. The course has an enrolment limit of 40, and students are
required to ballot.
Prerequisite: Any 7 full courses with a CGPA of at least 3.0


MAT334H1
Complex Variables 39L

Theory of functions of one complex variable, analytic and meromorphic functions. Cauchy’s theorem, residue calculus, conformal
mappings, introduction to analytic continuation and harmonic functions.
Exclusion: MAT354H1
Prerequisite: MAT235Y1/237Y1/257Y1


MAT335H1
Chaos, Fractals and Dynamics 39L

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: MAT137Y1/200-level calculus


MAT337H1
Introduction to Real Analysis 39L

Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange
of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings;
existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension.
Exclusion: MAT357H1
Prerequisite: MAT223H1/240H1, (237Y1, 246Y1)/257Y1


MAT344H1
Introduction to Combinatorics 39L

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: MAT223H1/240H1


MAT347Y1
Groups, Rings and Fields 78L, 26T

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: MAT247H1, 257Y1


MAT354H1
Complex Analysis I 39L, 13T

Complex numbers, the complex plane and Riemann sphere, Mobius 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’s lemma, residue theorem and residue calculus.
Prerequisite: MAT247H1, 257Y1


MAT357H1
Real Analysis I 39L, 13T

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, Lp spaces. Applications to probability.
Exclusion: MAT337H1
Prerequisite: MAT247H1, 257Y1, (327H1 or permission of instructor)


MAT363H1
Introduction to Differential Geometry 39L

Geometry of curves and surfaces in 3-spaces. Curvature and geodesics. Minimal surfaces. Gauss-Bonnet theorem for surfaces.
Surfaces of constant curvature.
Prerequisite: MAT224H1/247H1, 237Y1/257Y1


MAT365H1
Classical Geometries 39L

Euclidean and non-Euclidean plane and space geometries. Real and complex projective space. Models of the hyperbolic plane.
Connections with the geometry of surfaces.
Co-requisite: MAT301H1/347Y1


MAT390H1
History of Mathematics up to 1700 39L

A survey of ancient, medieval, and early modern mathematics with emphasis on historical issues. (Offered in alternate years)
Exclusion: HPS309H1, 310Y1, 390H1
Prerequisite: at least one full MAT 200-level course


MAT391H1
History of Mathematics after 1700 26L, 13T

A survey of the development of mathematics from 1700 to the present with emphasis on technical development. (Offered in alternate
years)
Exclusion: HPS309H1, 310H1, 391H1
Prerequisite: At least one full 200-level MAT course


MAT393Y1/394Y1
Independent Work in Mathematics

TBA
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings.
Prerequisite: Minimum GPA of 3.5 in math courses. Permission of the Associate Chair for Undergraduate Studies and prospective
supervisor


MAT395H1/396H1/397H1
Independent Work in Mathematics

TBA
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings.
Prerequisite: Minimum GPA of 3.5 in math courses. Permission of the Associate Chair for Undergraduate Studies and prospective
supervisor


MAT398H0/399Y0
Independent Experiential Study Project


MAT409H1
Set Theory 39L

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.
Prerequisite: MAT257Y1/337H1, 309H1/CSC 438H1


MAT415H1
Topics in Algebraic Number Theory 39L

A selection from the following: finite fields; global and local fields; valuation theory; ideals and divisors; differents and
discriminants; ramification and inertia; class numbers and units; cyclotomic fields; diophantine equations.
Prerequisite: MAT347Y1 or permission of instructor


MAT417H1
Topics in Analytic Number Theory 39L

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.
Prerequisite: MAT334H1/354H1 or permission of instructor


MAT425H1
Differential Topology 39L

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, 327H1


MAT427H1
Algebraic Topology 39L

Introduction to homology theory: singular and simplicial homology; homotopy invariance, long exact sequence, excision, Mayer-
Vietoris sequence; applications. Homology of CW complexes; Euler characteristic; examples. Singular cohomology; products;
cohomology ring. Topological manifolds; orientation; Poincare duality.
Prerequisite: MAT327H1, 347Y1


MAT443H1
Computer Algebra 39L

Introduction to algebraic algorithms used in computer science and computational mathematics. Topics may include: generating
sequences of random numbers, fast arithmetic, Euclidean algorithm, factorization of integers and polynomials, primality tests,
computation of Galois groups, Gröbner bases. Symbolic maniputlators such as Maple and Mathematica are used.
Prerequisite: MAT347Y1


MAT445H1
Representation Theory 39L

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.
Prerequisite: MAT347Y1


MAT448H1
Introduction to Commutative Algebra and Algebraic Geometry 39L

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.
Prerequisite: MAT347Y1


MAT449H1
Algebraic Curves 39L

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.
Prerequisite: MAT347Y1, 354H1


MAT454H1
Complex Analysis II 39L

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.
Prerequisite: MAT354H1


MAT457Y1
Real Analysis II 78L

Measure theory and Lebesgue integration; convergence theorems. Riesz representation theorem, Fubini’s theorem, complex
measures. Banach spaces; Lp spaces, density of continuous functions. Hilbert spaces; weak and strong topologies; self-adjoint,
compact and projection operators. Hahn-Banach theorem, open mapping and closed graph theorems. Inequalities. Schwartz space;
introduction to distributions; Fourier transforms on Rn (Schwartz space and L2). Spectral theorem for bounded normal operators.
Prerequisite: MAT357H1


MAT464H1
Differential Geometry 39L

Riemannian metrics and connections. Geodesics. Exponential map. Complete manifolds. Hopf-Rinow theorem. Riemannian
curvature. Ricci and scarlar curvature. Tensors. Spaces of constant curvature. Isometric immersions. Second fundamental form.
Topics from: Cut and conjugate loci. Variation energy. Cartan-Hadamard theorem. Vector bundles.
Prerequisite: MAT363H1


MAT468H1
Ordinary Differential Equations II 39L

Sturm-Liouville problem and oscillation theorems for second-order linear equations. Qualitative theory; integral invariants, limit
cycles. Dynamical systems; invariant measures; bifurcations, chaos. Elements of the calculus of variations. Hamiltonian systems.
Analytic theory; singular points and series solution. Laplace transform.
Prerequisite: MAT267H1, 354H1, 357H1


MAT477H1
Seminar in Mathematics


MAT495H1/496H1/497H1/498Y1/499Y1
Readings in Mathematics

TBA
Independent study under the direction of a faculty member. Topic must be outside undergraduate offerings.
Prerequisite: Minimum GPA of 3.5 in math courses. Permission of the Associate Chair for Undergraduate Studies and prospective
supervisor
• MEDIAEVAL STUDIES — See SMC: St. Michael’s College
• MICROBIOLOGY — See MPL: Life Sciences
• Middle east & islamic studies — See nmc: near & middle eastern civilizations


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Copyright © 2002, University of Toronto

Calendar Home ~ C ale ndar Contents~ Contact Us ~ Arts and Science Home
Copyright © 2002, University of Toronto