All Graduate Math Courses
This is not necessarily the official description for the courses. For the official descriptions, consult the 2008 - 2009 graduate catalog.
Description: The theory and practice of teaching mathematics at the college level.
Basic skills, grading methods, cooperative learning, active learning, use
of technology, classroom problems, history of learning theory, reflective
practice.
Prerequisites: Open to graduate students in Mathematics, others with
consent of instructor. May not be used to satisfy degree requirements.
Offered: Fall
Credits: 1
|
Description: This course covers the IT resources required for someone to become an effective member of our department.
Offered: Fall
Credits: 0
|
Prerequisites: MATH 5110
Credits: 3
|
Prerequisites: MATH 5010
Credits: 3
|
Description: Advanced topics in stochastic processes: applications to PDE and integro-differential equations
This course will include many of the following topics:
- Stochastic differential equations
- Representing the solutions of PDE by means of diffusions
- Martingale problems - the uniqueness theory of Stroock and Varadhan
- Harnack inequalities - the methods of Krylov-Safonov
- Heat kernel estimates
- Jump processes and their stochastic calculus
- Harnack inequalities for integro-differential operators
- Potential theory for the fractional Laplacian
The material will be similar to what is covered in my lecture notes on
my web page; see "PDE from a probability point of view" and
"Lecture notes for the Cornell Summer School in Probability 2007."
Prerequisites: MATH 5161 or a background in stochastic calculus.
Credits: 3
|
Description: An introduction to linear algebraic groups over algebraically closed fields.
Prerequisites: MATH 5211
Credits: 3
|
Description: Topics include, but may not be restricted to, Computability Theory, Model Theory, and Set Theory.
Prerequisites: MATH 5210
Credits: 3
|
Description: Advanced topics from uniform spaces, topological groups, Lie groups, fiber spaces, theory of submanifolds, PL topology, differential topology, cohomology operations, complex manifolds, Riemannian manifolds, transformation groups, fixed point theory.
Credits: 3
|
Description: Advanced topics from uniform spaces, topological groups, Lie groups, fiber spaces, theory of submanifolds, PL topology, differential topology, cohomology operations, complex manifolds, Riemannian manifolds, transformation groups, fixed point theory.
Prerequisites: MATH 5030
Credits: 3
|
Description: Advanced topics from the theory of ordinary or partial differential equations. Other possible topics: integral equations, optimization theory, the calculus of variations, advanced approximation theory.
Credits: 3
|
Description: Advanced topics from the theory of ordinary or partial differential equations. Other possible topics: integral equations, optimization theory, the calculus of variations, advanced approximation theory.
Prerequisites: Instructor consent required.
Credits: 3
|
Description: Functions of a complex variable, integration in the complex plane, conformal mapping.
Prerequisites: Not open to students who have passed MATH 3146. Not open for graduate credit toward degrees in mathematics.
Offered: Spring
Credits: 3
|
Description: Introduction to the theory of functions of a real variable.
Prerequisites: Not open for students who have passed MATH 3150. Not open for graduate credit toward degrees in mathematics.
Credits: 3
|
Description: Metric spaces, sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, functions of several variables.
Offered: Fall
Credits: 3
|
Description: Lebesgue measure and integration, differentiation,
Lp-spaces. Banach spaces, general theory of measure and integration.
Prerequisites: MATH 5110
Offered: Spring
Credits: 3
|
Description: This class is an introduction to complex analysis at the graduate level. A practical purpose of the class is to prepare students to take the qualifying exams. Highlights of the course will be (not an exclusive list) analytic functions, meromorphic functions, the Cauchy Integral Formula, residues, maximum principle and the Schwartz Lemma.
For prelims, check out the Complex Analysis Study Guide.
Prerequisites: MATH 5110
Credits: 3
|
Description: Advanced topics of contemporary interest. These include Riemann surfaces, Kleinian groups, entire functions, conformal mapping, several complex variables, and automorphic functions, among others.
Prerequisites: MATH 5120. May be repeated for credit to a maximum of 12 credits with a change in content and consent of the instructor.
Credits: 3
|
Description: Normed linear spaces and algebras, the theory of linear operators, spectral analysis.
Prerequisites: MATH 5111 and MATH 5211
Credits: 3
|
Description: Normed linear spaces and algebras, the theory of linear operators, spectral analysis.
Prerequisites: MATH 5130
Credits: 3
|
Description: Foundations of harmonic analysis developed through the study of Fourier series and Fourier transforms.
Prerequisites: MATH 5111 and MATH 5121
Credits: 3
|
Prerequisites: MATH 5111 and MATH 5121
Credits: 3
|
Description: Convergence of random variables and their probability laws, maximal inequalities, series of independent random variables and laws of large numbers, central limit theorems, martingales, Brownian motion. Contemporary theory of stochastic processes, including stopping times, stochastic integration, stochastic differential equations and Markov processes, Gaussian processes, and empirical and related processes with applications in asymptotic statistics.
Prerequisites: MATH 5111
Credits: 3
|
Description: Convergence of random variables and their probability laws, maximal inequalities, series of independent random variables and laws of large numbers, central limit theorems, martingales, Brownian motion. Contemporary theory of stochastic processes, including stopping times, stochastic integration, stochastic differential equations and Markov processes, Gaussian processes, and empirical and related processes with applications in asymptotic statistics.
Prerequisites: MATH 5160
Credits: 3
|
Description: Group theory, ring theory and modules, and universal mapping properties.
Offered: Fall
Credits: 3
|
Description: Linear and multilinear algebra, Galois theory, category theory and commutative algebra.
Prerequisites: MATH 5210
Offered: Spring
Credits: 3
|
Description: Introduction to the representation theory of finite groups and Lie
algebras. Characters, induced representations, representations of the
symmetric and general linear groups, symmetric functions, Schur-Weyl
duality, representations of complex semi-simple Lie algebras, and the
Weyl character formulae.
Prerequisites: MATH 5210
Credits: 3
|
Description: Algebraic integers, ideal class group, Dirichlet unit theorem, applications to diophantine equations. Further topics (localization, Frobenius elements in Galois groups, zeta-functions) as time permits.
Prerequisites: MATH 5211
Credits: 3
|
Description: The LU, QR, symmetric, polar, and singular value matrix decompositions. Schur and Jordan normal forms. Symmetric, positive-definite, normal and unitary matrices. Perron-Frobenius theory and graph criteria in the theory of non-negative matrices.
Offered: Fall
Credits: 3
|
Description: Predicate calculus, completeness, compactness, Lowenheim-Skolem theorems, formal theories with applications to algebra, Godel's incompleteness theorem. Further topics chosen from: axiomatic set theory, model theory, recursion theory, computational complexity, automata theory and formal languages.
Prerequisites: MATH 5210
Credits: 3
|
Description: Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces.
Offered: Fall
Credits: 3
|
Description: Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces.
Prerequisites: MATH 5310
Offered: Spring
Credits: 3
|
Description: Complexes, homology and cohomology groups, homotopy theory.
Prerequisites: MATH 5211 and MATH 5310, which may be taken concurrently.
Credits: 3
|
Description: Complexes, homology and cohomology groups, homotopy theory.
Prerequisites: MATH 5320
Credits: 3
|
Description: An introduction to the study of differentiable manifolds on which various differential and integral calculi are developed. A special emphasis is placed on the global aspects of modern differential geometry.
Credits: 3
|
Description: Banach spaces, linear operator theory and application to differential equations, nonlinear operators, compact sets on Banach spaces, the adjoint operator on Hilbert space, linear compact operators, Fredholm alternative, fixed point theorems and application to differential equations, spectral theory, distributions.
Credits: 3
|
Description: Banach spaces, linear operator theory and application to differential equations, nonlinear operators, compact sets on Banach spaces, the adjoint operator on Hilbert space, linear compact operators, Fredholm alternative, fixed point theorems and application to differential equations, spectral theory, distributions.
Credits: 3
|
Description: Existence and uniqueness of solutions, stability and asymptotic behavior. If time permits: eigenvalue problems, dynamical systems, existence and stability of periodic solutions.
Prerequisites: MATH 5111
Credits: 3
|
Description: Convergence of Fourier Series, Legendre and Hermite polynomials, existence and uniqueness theorems, two-point boundary value problems and Green's functions.
Prerequisites: MATH 5111 and 5140 are helpful but not required.
Credits: 3
|
Description: Solution of first and second order partial differential equations with applications to engineering and science.
Prerequisites: Not open to students who have passed MATH 3435. Not open for graduate credit toward degrees in mathematics.
Credits: 3
|
Description: Cauchy Kowalewsky Theorem, classification of second order equations, systems of hyperbolic equations, the wave equation, the potential equation, the heat equation in Rn.
Prerequisites: MATH 5120
Credits: 3
|
Description: The study of convergence, numerical stability, roundoff error, and discretization error arising from the approximation of differential and integral operators.
Prerequisites: MATH 5110, which may be taken concurrently.
Offered: Fall
Credits: 3
|
Description: The study of convergence, numerical stability, roundoff error, and discretization error arising from the approximation of differential and integral operators.
Prerequisites: MATH 5510
Offered: Spring
Credits: 3
|
Description: Numerical solution of elliptic, parabolic and hyperbolic partial differential equations by finite element solution methods. Applications.
Credits: 3
|
Description: Numerical solution of elliptic, parabolic and hyperbolic partial differential equations by finite element solution methods. Applications.
Prerequisites: MATH 5520
Credits: 3
|
Description: Development of mathematical models emphasizing linear algebra, differential equations, graph theory and probability. In-depth study of the model to derive information about phenomena in applied work.
Credits: 3
|
Description: Development and computer-assisted analysis of mathematical models in chemistry, physics, and engineering. Topics include chemical equilibrium, reaction rates, particle scattering, vibrating systems, least squares analysis, quantum chemistry and physics.
Credits: 4
|
Description: Theory of linear programming: convexity, bases, simplex method, dual and integer programming, assignment, transportation, and flow problems. Theory of nonlinear programming: unconstrained local optimization, Lagrange multipliers, Kuhn-Tucker conditions, computational algorithms.
Credits: 3
|
Description: The mathematics of measurement of interest, accumulation and discount, present value, annuities, loans, bonds, and other securities.
Prerequisites: Not open to students who have passed MATH 2620Q.
Credits: 3
|
Description: The continuation of Math 365, focusing on the mathematics of finance: measurement of financial risk and the opportunity cost of capital, the mathematics of capital budgeting and securities valuation, mathematical analysis of financial decisions and capital structure, and option pricing theory. Provides VEE credit in the Corporate Finance subject area for Society of Actuaries and Casualty Actuarial Society requirements.
Credits: 3
|
Description: Survival distributions, claim frequency and severity distributions, life tables, life insurance, life annuities, net premiums, net premium reserves, multiple life functions, and multiple decrement models.
Prerequisites: MATH 2620 or MATH 5620, which may be taken concurrently. Not open to students who have passed MATH 3630.
Offered: Fall
Credits: 3
|
Description: Lecture. Survival distributions, claim frequency and severity distributions, life tables, life insurance, life annuities, net premiums, net premium reserves, multiple life functions, and multiple decrement models.
Prerequisites: MATH 5630. Not open to students who have passed MATH 3631.
Credits: 3
|
Description: Analysis, estimation, and validation of lifetime tables
Prerequisites: MATH 5630
Credits: 3
|
Description: Introduction to the use of mathematical and statistical techniques to solve a wide variety of organizational problems. Topics include linear programming, project scheduling, queuing theory, decision analysis, dynamic and integer programming and computer simulation.
Prerequisites: Not open to students who have passed MATH 4535, STAT 4535, or STAT 5535.
Credits: 3
|
Description: Individual and collective risk theory, distribution theory, ruin theory, stoploss, reinsurance and Monte Carlo methods. Emphasis is on problems in insurance.
Offered: Fall
Credits: 3
|
Description: . Lecture. Survival models, mathematical graduation, or demography.
Credits: 3
|
Description: Lecture. Credibility theory or advanced theory of interest.
Credits: 3
|
Description: An introduction to the standard models of modern financial mathematics including martingales, the binomial asset pricing model, Brownian motion, stochastic integrals, stochastic differential equations, continuous time financial models,
completeness of the financial market, the Black-Scholes formula, the fundamental theorem of finance, American options, and term structure models.
Offered: Spring
Credits: 3
|
Description: An introduction to tensor algebra and tensor calculus with applications chosen from the fields of the physical sciences and mathematics.
Credits: 3
|
Description: An introduction to tensor algebra and tensor calculus with applications chosen from the fields of the physical sciences and mathematics.
Prerequisites: MATH 5710
Credits: 3
|
Description: Vector algebra and vector calculus with particular emphasis on invariance. Classification of vector fields. Solution of the partial differential equations of field theory.
Prerequisites:
Credits: 3
|
Description: Vector algebra and vector calculus with particular emphasis on invariance. Classification of vector fields. Solution of the partial differential equations of field theory.
Prerequisites: MATH 5720
Credits: 3
|
Description: Students who have well defined mathematical problems worthy of investigation and advanced reading should submit to the department a semester work plan.
Prerequisites: Instructor consent required.
Credits: 1-6
|
Description: Participation in internship and paper describing experiences.
Credits: 1 to 3
|
Description: Seminar. Participation and presentation of mathematical papers in joint student faculty seminars. Variable topics
Credits: 1
|
Description: Seminar.
Credits: 1
|
Prerequisites: MATH 5211
Credits: 1
|
Description: Seminar.
Prerequisites: MATH 5260
Credits: 1
|
Description: Seminar.
Prerequisites: MATH 5310
Credits: 1
|
Description: Seminar.
Prerequisites: MATH 5321
Credits: 1
|
Prerequisites: MATH 5360
Credits: 1
|
Description: (Doctoral Level).
Credits: 3
|
|
