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Derivation of the classical partial differential equations of applied mathematics, solutions using separation of variables. Fourier expansions and their applications to boundary value problems. Introduction to Fourier Transforms. Emphasis on building an appropriate mathematical model from a physical problem, solving the mathematical problem, and carefully interpreting the mathematical results in the context of the original physical problem. Prerequisites: MATH 201 and 209. Notes: (1) Open only to students in Engineering, Specialization Physics, and Specialization Geophysics. (2) Credit can be obtained in at most one of MATH 300 and 337. (3) Course cannot be taken for credit if credit has been obtained in ECE 341.

Derivation of the classical partial differential equations of applied mathematics, solutions using separation of variables. Fourier expansions and their applications to boundary value problems. Introduction to Fourier Transforms. Emphasis on building an appropriate mathematical model from a physical problem, solving the mathematical problem, and carefully interpreting the mathematical results in the context of the original physical problem. Prerequisites: MATH 201 and 209. Notes: (1) Open only to students in Engineering, Specialization Physics, and Specialization Geophysics. (2) Credit can be obtained in at most one of MATH 300 and 337. (3) Course cannot be taken for credit if credit has been obtained in ECE 341.

Derivation of the classical partial differential equations of applied mathematics, solutions using separation of variables. Fourier expansions and their applications to boundary value problems. Introduction to Fourier Transforms. Emphasis on building an appropriate mathematical model from a physical problem, solving the mathematical problem, and carefully interpreting the mathematical results in the context of the original physical problem. Prerequisites: MATH 201 and 209. Notes: (1) Open only to students in Engineering, Specialization Physics, and Specialization Geophysics. (2) Credit can be obtained in at most one of MATH 300 and 337. (3) Course cannot be taken for credit if credit has been obtained in ECE 341.

Complex numbers, analytic functions, Cauchy-Riemann equation, Cauchy Theorem, power series and Laurent expansions, residues, inverse Laplace transform. Complex inner product spaces, orthogonal expansions, Gram-Schmidt orthogonalization completeness, Fourier expansions applied to signals, Parseval's relation and Bessel's inequality. Prerequisite: MATH 209. Notes: (1) Restricted to Engineering students. (2) This course may not be taken for credit if credit has already been obtained in MATH 311 or 411.

Complex numbers, analytic functions, Cauchy-Riemann equation, Cauchy Theorem, power series and Laurent expansions, residues, inverse Laplace transform. Complex inner product spaces, orthogonal expansions, Gram-Schmidt orthogonalization completeness, Fourier expansions applied to signals, Parseval's relation and Bessel's inequality. Prerequisite: MATH 209. Notes: (1) Restricted to Engineering students. (2) This course may not be taken for credit if credit has already been obtained in MATH 311 or 411.

Complex numbers, analytic functions, Cauchy-Riemann equation, Cauchy Theorem, power series and Laurent expansions, residues, inverse Laplace transform. Complex inner product spaces, orthogonal expansions, Gram-Schmidt orthogonalization completeness, Fourier expansions applied to signals, Parseval's relation and Bessel's inequality. Prerequisite: MATH 209. Notes: (1) Restricted to Engineering students. (2) This course may not be taken for credit if credit has already been obtained in MATH 311 or 411.

Complex numbers. Complex series. Functions of a complex variable. Cauchy's theorem and contour integration. Residue Theorem and its applications. Corequisite: MATH 215 or MATH 315 or MATH 317 or MA PH 351. Note: This course may not be taken for credit if credit has already been obtained in MATH 309 or 411.

Construction of real numbers, Heine-Borel and related theorems, differentiation and Riemann integral of functions, topological concepts in metric spaces, sequences, continuous maps, contraction maps, and applications. Prerequisite: MATH 209 or 215 or equivalent. Note: This course may not be taken for credit if credit has already been obtained in MATH 217.

Vector calculus. Line and surface integrals. The divergence, Green's, and Stokes' theorems. Differential forms. Prerequisite: One of MATH 102, 125 or 127, and either MATH 214 or MATH 217. Notes: Credit can be obtained in at most one of MATH 215 and MATH 315. This course may not be taken for credit if credit has already been obtained in MATH 209 or 317.

Implicit function theorem. Proof of the Change of Variables Theorem. Line integrals. Theorems of Green, Gauss and Stokes in their classical form. Differential forms and Stokes' Theorem in their context. Sequences and series of functions. Uniform convergence. Prerequisite: MATH 217.

Graphs, paths and cycles, trees, planarity and duality, coloring problems, digraphs, matching problems, matroid theory. Prerequisite: One of MATH 102, 125 or 127, and any 200-level MATH course. (MATH 216 or MATH 228 recommended.)

Divisibility, prime numbers, congruences, quadratic residues, quadratic reciprocity, arithmetic functions and diophantine equations; sums of squares. Prerequisites: MATH 227 or 228.

Hermitian and unitary matrices, spectral theorem. Jordan canonical form. Cayley-Hamilton Theorem. Bilinear forms, positive-definiteness, Sylvester's Law of inertia, geometric lattices. Numerical methods. Application to discrete system evolution, matrix exponentials and differential equations. Prerequisite: MATH 225. Note: This course may not be taken for credit if credit has already been obtained in MATH 227.

Rings, fields, polynomials, algebras. Homomorphisms, ideals, quotients. Ring extensions, field extensions, construction of finite fields. Integral domains: Euclidean, principal ideal, unique factorization. Chain conditions. Introduction to modules. Modules over a principal ideal domain, finitely generated abelian groups, matrix canonical forms. Prerequisite MATH 227, or both MATH 225 and 228.

Basic group theory: Groups, subgroups, normal subgroups, homomorphisms, quotient groups, coset decomposition, Example: Permutation group and general linear group; basic (commutative) ring theory: Rings, subrings, homomorphisms, ideals, quotient rings, modules over rings, submodules and quotient modules, fraction field; further group theory: Groups operating on a set, Sylow theorems. Prerequisite : One of MATH 226 or MATH 227. Note: Credit can be obtained in at most one of MATH 326 and MATH 327.

Groups, subgroups, homomorphisms. Symmetry groups. Matrix groups. Permutations, symmetric group, Cayley's Theorem. Group actions. Cosets and Lagrange's Theorem. Normal subgroups, quotient groups, isomorphism theorems. Direct and semidirect products. Finite Abelian groups. Prerequisite: MATH 227 or 228. This course may not be taken for credit if credit has already been obtained in MATH 229.

Factorial rings and principal ideal domains; Noetherian rings and modules, Hilbert basis theorem; field extensions, separable and normal extensions; finite Galois theory; solvable groups and equations, construction by ruler and compass, solution by radicals. Prerequisite : MATH 327. Note: Credit can be obtained in a most one of MATH 328 and 329.

First order equations, linear equations of higher order. Power series solution. Laplace transform methods. Introduction to special functions. Introduction to linear systems. Prerequisites: One of MATH 102, 125 or 127, and one of MATH 209, 214 or 217. Note: Credit can be obtained in at most one of MATH 201, MATH 334, MATH 336, or MA PH 251.

First order differential equations. Linear systems of differential equations and linear differential equations of higher order. Stability and qualitative theory of 2-dimensional linear and non-linear systems. Laplace transform methods. Existences and uniqueness theorems. Prerequisites: MATH 225 or 227, and either MATH 209, 217, 314 or both 214 and 216. Note: Credit can be obtained in at most one of MATH 201, MATH 334, MATH 336, and MA PH 251.

Boundary value problems of classical Math Physics, orthogonal expansions, classical special functions. Advanced transform techniques. Prerequisites: One of MATH 209, 215, 217, 315 or MA PH 351, and one of MATH 201, MATH 334, MATH 336, or MA PH 251. Notes: (1) Credit can be obtained in at most one of MATH 300 or 337. (2) Course cannot be taken for credit if credit has been obtained in ECE 341.

Combinatorial geometry and topology, convex sets, sets with constant width, Helly-type problems, extremal problems. Prerequisite: One of MATH 102, 125, 127, 222 or 241.

Projective geometry, Poncelet-Steiner constructions, inverse geometry, Mohr-Mascheroni constructions, Principle of Duality, conic sections. Prerequisite: MATH 241.

Frenet-Seret theory of curves in the plane and in 3-space, examples; local theory of surfaces in 3-space: first and second fundamental forms, Gauss map and Gauss curvature, geodesics and parallel transport, theorema egregium, mean curvature and minimal surfaces. Prerequisites: One of MATH 102, 125 or 127 and one of MATH 209, 215, 217, 315 or MA PH 351.

Simple Market Model: one-step binomial model, basic notions and assumptions. Risk-Free Assets: simple interest, zero-coupon bonds, money market account. Risky Assets: dynamic of stock prices, binomial tree model, trinomial tree model. Discrete time market model: stock and money market model, extended models. Portfolio management: risk, two securities, capital asset pricing model. Prerequisite: MATH 253 and one of STAT 265 or MATH 281, or consent of the Department.

Forward and futures contracts: forward and futures prices, hedging with futures. Options: put-call parity, bounds on option prices, time value of options. Option pricing: European and American options in the binomial tree model, Black-Scholes formula. Financial engineering: hedging option positions, hedging business risk. Variable interest rates: maturity-independent yields, general term structure. Stochastic interest rates: arbitrage pricing of bonds, interest rate derivative securities. Prerequisite: MATH 356 or consent of the Department.

Model development, computation, and analysis for problems in the life sciences. Models include differential equations, difference equations and stochastic formulations. Model evaluation and prediction. Applications are chosen from epidemiology, ecology, population biology, physiology and medicine. Prerequisites: One of MATH 102, 125 or 127, and one of MATH 209, 214 or 217. Note: No previous computing experience is needed.

This course is designed to develop the students' problem-solving abilities along heuristic lines and to illustrate the processes of Applied Mathematics. Students will be encouraged to recognize and formulate problems in mathematical terms, solve the resulting mathematical problems and interpret the solution in real world terms. Typical problems considered include nonlinear programming, optimization problems, diffusion models. Prerequisites: One of MATH 102, 125 or 127, and one of MATH 209, 214 or 217.

Introduction to optimization. Problem formulation. Linear programming. The simplex method and its variants (revised Simplex method, dual simplex method). Extreme points of polyhedral sets. Theory of linear inequalities (Farkas Lemma). Complementary slackness and duality. Post-optimality analysis. Interior point methods. Applications (elementary games, transportation problems, networks, etc.). Prerequisites: One of MATH 102, 125 or 127, and one of MATH 209, 214 or 217.

Approximation of functions by Taylor series, Newton's formulae, Lagrange and Hermite interpolation. Splines. Orthogonal polynomials and least-squares approximation of functions. Direct and iterative methods for solving linear systems. Methods for solving non-linear equations and systems of non-linear equations. Introduction to computer programming. Prerequisites: One of MATH 102, 125 or 127, and one of MATH 209, 214 or 217. Notes: (1) Credit can be obtained in at most one of MATH 280, 381 or CMPUT 340. (2) Extra classes may be held for students lacking a background in one of the major programming languages such as Fortran, C, C++ or Matlab.

Principles of Monte Carlo methods. Essentials of stochastics. Introduction to financial derivatives pricing. Generating random variables. Simulating stochastic differential equations. Application to financial derivatives pricing and interest rate models. Variance reduction techniques. Prerequisite: STAT 471, or E E 387 and consent of the Department.

Complex number system. Analytic functions. Cauchy's Integral theorem and formula. Applications including the maximum modulus principle, Taylor expansion and Laurent expansion. Harmonic functions. The residue theorem with applications; calculus of residues, argument principle, and Rouche's theorem. Basics of analytic continuation. Additional topics at the instructor's discretion such as: Normal families, The Riemann mapping Theorem, Picard's Theorem. Prerequisite: MATH 314 or 317. Notes: (1) This course is primarily for Honors students in Mathematics or Physics. (2) Offered in alternate years. It may be offered in intervening years if demand is sufficient.

Valuations and their extensions, ramifications; integral dependence, algebraic number fields, ideals and divisors, class number. Prerequisite: MATH 326 or equivalent.

Differentiation of maps in Rn, implicit function and mapping theorems, sequences of functions, Riemann-Stielties integration, additional topics at the discretion of the instructor. Prerequisite: MATH 314. Note: This course may not be taken for credit if credit has already been obtained in MATH 317.

Review of probability tools for discrete financial analysis; Conditional probabilities/expectations. Filtrations, adapted and predictable processes. Martingales, submartingales and supermartingales in discrete-time. Doob decomposition for supermartingales. Predictable representation. Discrete- time financial modes: Arbitrage, complete and incomplete markets. Self-financing property, value and gain processes. Valuation of contingent claims. Binomial model: Model specifications, Perfect hedging. Utility functions and consumption/ investment problems. European and American options in discrete time. Futures and forward contracts in discrete time. Transition to the continuous-time framework. Corequisite: STAT 471 or consent of the Department.

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisite: MATH 317 or 414.

Classical Banach spaces. Hahn-Banach, open mapping and closed graphs theorems. Hilbert spaces, orthonormal bases. Elements of spectral theory, spectra of compact operators, spectral theorem for compact self-adjoint operators. Prerequisite: MATH 417. Corequisite: MATH 447.

Permutations and combinations, Binomial Theorem, Principle of Inclusion-Exclusion, recurrence relations, generating functions, orthogonal Latin squares, balanced incomplete block designs, Steiner triple systems, perfect difference sets, Boolean algebra and Finite State Machines. Prerequisites: Either MATH 326 or one of MATH 111 or 228 and a 300-level MATH course (MATH 322 recommended).

Elements of group theory, cosets, Lagrange's theorem, binary group codes, polynomials, finite field theory, error correcting codes. Prerequisites: either (1) MATH 227 or (2) MATH 228 and a 300-level MATH course.

Field extensions. Groups of automorphisms of fields. Galois theory. Finite fields and applications. Solvable groups, the insolvability of the quintic equation. Ruler and compass construction. Prerequisites: MATH 326 (or MATH 228 by consent of the Department) and MATH 328. Note: This course cannot be taken for credit if credit has already been obtained in MATH 427 or 329.

Introduction to commutative algebra, algebraic geometry, and homological algebra. Additional topics at the discretion of the instructor. Prerequisite: MATH 326 or consent of Department.

Group actions, Sylow Theory, solvable and nilpotent groups, Galois Theory. Prerequisite: MATH 328 or consent of the Department.

Elementary existence and uniqueness theorems. Systems of equations, stability, perturbation theory. Introduction to numerical methods. Introduction to phase plane analysis. Prerequisite: One of MATH 201, MATH 334, MATH 336, or MA PH 251

Partial differential equations as physical models. Introduction to basic generalized functions. Theory of linear and quasi-linear first-order equations: general solution, initial value problem, generalized solutions and propagation of singularities, characteristic surfaces, shock formation. Theory of fully nonlinear first order equations: complete solution and the initial value problem. Hamilton-Jacobi equation and its applications. Second order linear equations in n dimensions: classification, canonical form, characteristic surfaces and shock formation, initial and boundary value problem. Prerequisite: MATH 300 or MATH 337.

General point-set topology. Compactness, Tychonoff's tbeorem, connectedness. Metric spaces, completeness, Baire's theorem. Urysohn's lemma. Topological manifolds. Homotopy theory, fundamental group, covering spaces. Prerequisite : MATH 216 or 217. Corequisites: MATH 328 or MA PH 464. Offered in alternate years. It may be offered in intervening years if demand is sufficient.

Riemannian geometry of n-space, metric tensors, various curvature concepts and their relationships, covariant differentiation, geodesics, parallel transport. Additional topics at the discretion of the instructor. Prerequisite: MATH 348, or MATH 217 and one of MATH 225 or 227. Note: Offered in alternate years. It may be offered in intervening years if demand is sufficient.

Birth-death processes; continuous-time Markov chains; functional central limit theorem; Brownian motion; weak solutions to stochastic differential equations; weak uniqueness; filtrations; discrete and continuous martingales; martingales problems; strong Markov property; Kolmogorov forward and backward equations; stationary distributions; null and positive recurrence; transience; particle filtering. Prerequisite: STAT 281 or STAT 371. Note: Credit cannot be obtained in MATH 471 if credit has already been in STAT 471.

This course will cover advanced algebraic topics not taught in regular courses in the curriculum or will provide a more in-depth continuation of an existing course. Prerequisite: at least one of MATH 326, MATH 327, MATH 328, MATH 329, or equivalent. Note: Upon approval by the Department of Mathematical and Statistical Sciences, this course may be taken for credit multiple times.

This course is designed to give credit to mature and able students for reading in areas not covered by courses, under the supervision of a staff member. A student, or group of students, wishing to use this course should find a staff member willing to supervise the proposed reading program. A detailed description of the material to be covered should be submitted to the Chair of the Department Honors Committee. (This should include a description of testing methods to be used.) The program will require the approval of both the Honors Committee, and the Chair of the Department. The students' mastery of the material of the course will be tested by a written or oral examination. This course may be taken in Fall or Winter and may be taken any number of times, subject always to the approval mentioned above. Prerequisite: Any 300-level MATH course.

This topics course is designed for new course offerings that may be offered in a given term. Prerequisites: One of MATH 209, 214, or 217 and one of MATH 225 or 227. Additional prerequisites may be required. Note: Credit for this course may be obtained more than once.

This course provides students in Specialization and Honors programs an opportunity to pursue research in mathematics under the direction of a member of the Department. Course requirements include at least one oral presentation and a written final report. Students interested in taking this course should contact the course coordinator two months in advance. Credit for this course may be obtained more than once. Prerequisites: a 300-level MATH course and consent of the course coordinator.

Discrete-time stochastic analysis: Stochastic basis, filtration, stochastic sequences. Absolute continuity of probability measures and conditional expectations. Martingale-like and predictable stochastic sequences. Doob's decomposition. Stopping times and related properties. Uniformly integrable stochastic sequences. Transition from discrete-time to continuous-time stochastic analysis. Introduction to stochastic integration with respect to Brownian motion. Prerequisites: STAT 471 or consent of the Department.

A review and some extensions of single variable complex analysis. Complex linearity and holomorphicity in several variables, Hartog's theorem, Weierstrass preparation theorem, Riemann extension theorem, Weierstrass division theorem, analytic Nullstellensatz, implicit and inverse function theorems, complex manifolds and analytic subvarieties, meromorphic maps. Prerequisite: MATH 411.

Principles of Monte Carlo methods. Essentials of stochastics. Introduction to financial derivatives pricing. Generating random variables. Simulating stochastic differential equations. Application to financial derivatives pricing and interest rate models. Variance reduction techniques. Prerequisite: STAT 471 or FIN 654 or ECON 598 or consent of the Department. Note: This course may not be taken for credit if credit has already been obtained in MATH 408.

Basic data analysis with R, SAS, and Python. Program development with Jupyter notebooks. Cloud computing, collaborative software development, docker containers, kubernets. Internet security, privacy and ethics. Technologies will be updated as new developments arise. Prerequisites: No programming skills are needed.

Continuous semimartingales and quadratic variation. Stochastic integrals for continuous semimartingales. Ito's formula. Change of probability measure (Girsanov transformation). Martingale representation theorem for Brownian filtrations. Stochastic differential equations, diffusions. Introduction to discontinuous semimartingales with emphasis on Poisson processes. Prerequisites: MATH 505 or consent of the Department.

Valuations and their extensions, ramifications; integral dependence, algebraic number fields, ideals and divisors, class number. Prerequisite: MATH 326 or equivalent.

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisites: Math 317.

Review of probability tools for discrete financial analysis; Conditional probabilities/expectations. Filtrations, adapted and predictable processes. Martingales, submartingales and supermartingales in discrete-time. Doob decomposition for supermartingales. Predictable representation. Discrete-time financial modes: Arbitrage, complete and incomplete markets. Self-financing property, value and gain processes. Valuation of contingent claims. Binomial model: Model specifications, Perfect hedging. Utility functions and consumption/investment problems. European and American options in discrete time. Futures and forward contracts in discrete time. Transition to the continuous-time framework. Prerequisite: STAT 471 or consent of the Department. Note: This course may not be taken for credit if credit has already been obtained in MATH 415.

Classical Banach spaces. Hahn-Banach, open mapping and closed graphs theorems. Hilbert spaces, orthonormal bases. Elements of spectral theory, spectra of compact operators, spectral theorem for compact self-adjoint operators. Prerequisite: MATH 417. Corequisite: MATH 447.

Locally convex spaces, weak topologies and duality in Banach spaces, weak compactness in Banach spaces, structure of classical Banach spaces, local structures, infinite-dimensional geometry of Banach spaces and applications. Prerequisite: MATH 516. Corequisite: MATH 447 or consent of Department.

Banach algebras and spectral theory, compact and Fredholm operators, the spectral theorem for bounded normal operators, operator algebras, representations of C+-algebras, elementary von Neumann algebra theory, and other topics. Prerequisite: MATH 516. Corequisite: MATH 447 or consent of Department.

Financial markets in continuous-time: Arbitrage, completeness, self-financing strategies. Black Scholes model. Option pricing and hedging: European, American and exotic options. Consumption-investment problem: Utility maximization, optimal portfolio and optimal consumption. Prerequisite: MATH 515. Corequisite: MATH 510 or consent of the Department.

Finite dimensional manifolds/submanifolds; tangent bundle, differential, inverse, and implicit function theorems, partitions of unity; imbeddings, immersions, submersions; vector fields and associated flows; Lie derivative, Lie bracket; tensor analysis, differential forms, orientation, integration, Stokes' theorem; basics of smooth bundle theory, Riemannian metrics; notion of a Lie group with basic examples, smooth Lie group actions, principal bundles. Prerequisite: MATH 446 or 448.

Existence theorems, uniqueness theorems; linear systems (basic theory); stability (basic theory); nonlinear systems (local theory); nonlinear systems (global theory); bifurcations. Prerequisite: MATH 334 or 336, or equivalent.

Asymptotics; boundary value problems; Poincare-Bendixson theory. Additional material will be chosen from among the following topics at the option of the instructor: separation; dichotomies; comparison and oscillation theory; bifurcation theory; nonautonomous systems; dynamical systems; functional differential equations; contingent equations; differential equations in Banach spaces. Prerequisite: MATH 524 or equivalent.

Notions; Elliptic PDE's; Parabolic PDE's; Hyperbolic PDE's; Nonlinear Integrable PDE's. Prerequisite: MATH 436 or equivalent; corequisite: MATH 516.

Particular background from point set topology (pasting and quotienting constructions); homotopy relation between maps and spaces; fundamental group; Seifert VanKampen theorem; covering spaces. Additional topics at the discretion of the instructor. Prerequisites: MATH 227, 317 and 447 or consent of Department.

Direct and iterative methods for solving linear systems, iterative methods for nonlinear systems, polynomial and spline interpolations, least square approximation, numerical differentiation and integration, initial value problems for ODE's (one-step, multistep methods, stiff ODE's). Prerequisite: 400-level MATH course. Students are required to have knowledge of advanced Calculus and introductory knowledge in Analysis and Linear Algebra and some computer programming. Note 1: Restricted to graduate students only. Note 2: May not be taken for credit if credit has already been obtained in MATH 381, 481 or 486 or equivalent.

Finite difference and finite element methods for boundary-value problems of elliptic equations. Numerical algorithms for large systems of linear algebraic equations: direct, classical relaxation, multigrid and preconditioned conjugate gradient methods. Algorithms for vector/parallel computers and the domain decomposition method. Prerequisites: MATH 337, 436 or equivalent and some computer programming.

Asymptotic analysis of integrals: Laplace, stationary phase, and steepest descent methods. Regular and singular perturbations: trained coordinates, multiple scales, asymptotic matching, renormalization techniques, WKB theory, Hamiltonian perturbation theory, center manifolds and stability. Singularities in differential equations. Applications to algebraic, ordinary and partial differential equations. Prerequisite: MATH 438 or equivalent.

Linear part:structure of function spaces, Sobolev spaces, embeddings, topologies, linear operators, adjoint and inverse operators, spectra, distributions, semigroup theory, integral equations, well-posedness and the notion of a solution. Nonlinear part: inequalities, Frechet and Gateaux derivatives, fixed point theorems. Applications from mechanics, reaction-diffusion equations, the Navier-Stokes equations, nonlinear Schrödinger equation. Prerequisite: MATH 438 or equivalent.

Review, theory and extension of Fourier series for square integrable functions; orthonormal systems, Bessel's inequality, completeness, Parseval's identity, Riesz-Fischer Theorem. Extension to Fourier series for functions in other Lebesgue classes; Fejer means, conjugate series, Dirichlet, Fejer and Poisson kernels. Norm convergence; remarks on pointwise convergence. Fourier transforms and series in several dimensions; inverse transform, Plancherel formula, Poisson Formula, maximal functions, Riesz-Thorin Theorem and applications. Elementary distribution theory; D, D', S, S' and some elementary results, Fourier transforms of tempered distributions. Examination of some earlier results with tempered distributions instead of functions and getting familiar with basic concepts. Prerequisite: MATH 418.

Review of basic measure and integration theory. Signed and complex measures. Hahn and Jordan decompositions. The Radon-Nikodym theorem. Lebesgue decomposition. The Lebesgue-Stieltjes integral. Measure theory over locally compact Hausdorff spaces, in particular, the Riesz representation theorem and Haar measures. Hausdorff measure. Introduction to martingales. Prerequisite: One of MATH 417 or MATH 514, and MATH 447 or equivalent.

Fundamentals including continuum hypothesis surface tension, classical thermodynamics, and transport phenomena. Introduction to Cartesian tensors. Kinematics of flow including Lagrangian and Eulerian descriptions, streamline, path line, streak line, vorticity and circulation. Derivation of the conservation laws for mass, momentum, and energy and a detailed description of the Boussinesq approximation. Conservation laws in a rotating frame. Vortex lines and tubes, role of viscosity in vortices, Kelvin's circulation theorem, the vorticity equation in nonrotating and rotating frames. Irrotational flow including its relevance, velocity potential, sources and sinks, and flow past various shapes. Gravity waves in deep and shallow water with and without surface tension in both the linear and nonlinear contexts. Dynamic similarity and Buckingham's Pi Theorem. Prerequisites: One of MATH 311, 411 and MATH 436 or consent of Instructor.

Mathematical modeling in the biological and medical sciences. Students will learn how to apply mathematical methods and theory to a variety of different biological problems. Topics will be taken from: (i) continuous and discrete dynamical systems describing interacting and structured populations, resource management, biological control, reaction kinetics, biological oscillators and switches, the dynamics of infectious diseases and genetics and (ii) models of spatial processes in biology including random walks, pattern formation in morphogenesis and ecology, applications of traveling waves to population dynamics, epidemiology, chemical reactions, and models for neural patterns. Prerequisites: MATH 524 and a 400 or 500 level course on Partial Differential Equations or consent of Instructor.

Developing mathematical models to solve real-world problems, model analysis, fitting model to data, model validation and selection, and interpretation of model outcomes. Types of models include difference equation models, differential equation models, network models, and stochastic models. Prerequisites: Linear algebra and differential equations or consent of the instructor.

Development of mathematical models for the transmission dynamics of infectious diseases, incorporation of important epidemiological factors including disease latency, recovery, relapse and reinfection, isolation and quarantine, vaccination and immunity. Stability and bifurcation analysis of mathematical models. Estimation of model parameters from public health data, and numerical simulations of models. Prediction of the time course of epidemics and long-term patterns of endemic diseases. Prerequisites: MATH 334 or MATH 336, or with instructor's consent.

Group actions, Sylow Theory, solvable and nilpotent groups, Galois Theory. Additional topics at the discretion of the instructor. Prerequisite: MATH 328 or consent of the Department.

Introduction to commutative algebra, algebraic geometry, and homological algebra. Additional topics at the discretion of the instructor. Prerequisite: MATH 326 or consent of the Department.

This course will cover advanced algebraic topics not taught in regular courses in the curriculum or will provide a more in-depth continuation of an existing course. Prerequisite: at least one of MATH 326, MATH 327, MATH 328, MATH 329, or equivalent. Note: Upon approval by the Department of Mathematical and Statistical Sciences, this course may be taken for credit multiple times.

Students registered in this course are supervised by individual staff members in areas of interest of the staff members. Students will be allowed to take this course only in exceptional circumstances and with the permission of the Chairman of the Department. This course shall not be counted against the minimum course requirement for graduate students.

Credit for this course can be obtained twice.

Topics among: Incomplete markets; Models with imperfection (markets with transaction costs, constraints or defaults); Risk measures; Interplay between finance and insurance; Mathematical models for the term structure of interest rates. Prerequisites: MATH 520 or consent of the Department.

Credit for this course may be obtained more than once.

Open only to students taking the MSc non-thesis option in mathematics.

Open only to students taking the MSc non-thesis option in mathematics.

Open only to students taking the MSc non-thesis option in mathematics.

Les nombres, inéquations, fonctions, géométrie analytique, limite, continuité, dérivées et applications, polynôme de Taylor, fonctions exponentielles et logarithmiques, fonctions trigonométriques inverses et hyperboliques, différentielle et calculs approximatifs. Intégration et théorème fondamental du calcul intégral. Méthode des trapèzes et méthode de Simpson. Préalable(s): Mathématiques 30-1 ou l'équivalent et Mathématiques 31. Note(s): (1) Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 114 (ou 113), MATH 117, 134, 144 ou SCI 100. (2) Ce cours est normalement réservé aux étudiants de la Faculty of Engineering. (3) Les étudiants de la Faculty of Engineering qui suivent ce cours obtiendront 3.5 crédits.

Techniques d'intégration et applications du calcul d'intégrales: calcul de longueurs, aires, volumes et masses, intégrales impropres, équations différentielles ordinaires d'ordre un; séparables, linéaires, méthode d'Euler, applications. Séries infinies, séries de Taylor, séries de puissances et critère de convergence d'une série. Coordonnées polaires, rectangulaires, sphériques et cylindriques dans l'espace de trois dimensions, courbes paramétriques dans le plan et l'espace. Volume et aire d'une surface de révolution. Préalable: MATHQ 100. Note(s): (1) Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 115, MATH 118, 146 ou SCI 100. (2) Ce cours est normalement réservé aux étudiants de la Faculty of Engineering. (3) Les étudiants de la Faculty of Engineering qui suivent ce cours obtiendront 3.5 crédits.

Vecteurs et matrices; solution d'équations linéaires; équations de lignes et de plans; déterminants; algèbre matricielle; orthogonalité de GramSchmidt et applications; valeurs propres, vecteurs propres et applications; nombres complexes. Préalable ou concomitant: MATHQ 100. Note(s): (1) Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ 120, 125, MATH 125 ou 127. (2) Ce cours est normalement réservé aux étudiants de la Faculty of Engineering. (3) Les étudiants de la Faculty of Engineering qui suivent ce cours obtiendront 3.5 crédits.

Taux de variation et dérivées. Dérivation des fonctions élémentaires, trigonométriques, exponentielles et logarithmiques. L'intégrale définie comme sommation. L'intégration. Le théorème fondamental du calcul intégral. Applications dans le contexte des sciences de la vie ou des Sciences physique, ou des affaires et de l'économie. Préalable(s): Mathématiques 30-1. Note: Ce cours n'est pas accessible aux étudiants ayant ou postulant des crédits pour MATHQ ou MATH 100, 113, 114, 117, 134, 144, 154 ou SCI 100.