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All Graduate Math Courses
This is not necessarily the official description for the courses. For the official descriptions, consult the 2011 - 2012 graduate catalog.
Description: Taught on Mondays and Wednesdays. The Monday classes cover 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. The Wednesday classes cover the IT resources required for someone to become an effective member of our department.
Prerequisites: Open to graduate students in Mathematics, others with consent of instructor. May not be used to satisfy degree requirements.
Offered: Fall
Credits: 1
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Description: Advanced topics in analysis. With a change of content, this course is repeatable to a maximum of twelve credits.
Credits: 3
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Description: Advanced topics in analysis. With a change of content, this course is repeatable to a maximum of twelve credits.
Credits: 3
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Description: Advanced topics in probability theory, theory of random processes, mathematical statistics, and related fields. With a change of content, this course is repeatable to a maximum of twelve credits.
Credits: 3
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Description: An introduction to local fields and their connections to topics in number theory and analysis.
Prerequisites: MATH 5211
Offered: Fall
Credits: 3
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Description: Topics include, but may not be restricted to, Computability Theory, Model Theory, and Set Theory. With a change of content, this course is repeatable to a maximum of twelve credits.
Prerequisites: MATH 5260
Credits: 3
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Description: Advanced topics in Geometry and Topology. With a change of content, this course is repeatable to a maximum of twelve credits.
Credits: 3
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Description: Advanced topics in Geometry and Topology. With a change of content, this course is repeatable to a maximum of twelve credits.
Credits: 3
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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. With a change of content, this course is repeatable to a maximum of twelve credits.
Credits: 3
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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. With a change of content, this course is repeatable to a maximum of twelve credits.
Prerequisites: Instructor consent required.
Credits: 3
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Description: Functions of a complex variable, integration in the complex plane, conformal mapping. Not open to students who have passed MATH 3146. Open for master's credit but not doctoral credit toward degree in Mathematics.
Credits: 3
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Description: Introduction to the theory of functions of a real variable. Not open to students who have passed MATH 3150. Open for master's credit but not doctoral credit toward degree in Mathematics.
Offered: Spring
Credits: 3
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Description: Metric spaces, sequences and series, continuity, differentiation, the Riemann-Stielties integral, functions of several variables.
Offered: Spring
Credits: 3
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Description: General theory of measure and Lebesgue integration, Lp-spaces.
Prerequisites: MATH 5110
Offered: Spring
Credits: 3
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Description: An introduction to the theory of analytic functions, with emphasis on modern points of view.
Prerequisites: MATH 5110
Credits: 3
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Description: Advanced topics of contemporary interest. These include Riemann surfaces, Kleinian groups, entire functions, conformal mapping, several complex variables, and automorphic functions, among others. With a change of content this course may be repeatable to a maximum of twelve credits.
Prerequisites: MATH 5120
Credits: 3
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Description: Normed linear spaces and algebras, the theory of linear operators, spectral analysis.
Prerequisites: MATH 5111
Credits: 3
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Description: Normed linear spaces and algebras, the theory of linear operators,
spectral analysis.
Prerequisites: MATH 5111
Credits: 3
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Description: Foundations of harmonic analysis developed through the study of Fourier series and Fourier transforms.
Prerequisites: MATH 5111
Credits: 3
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Description: Harmonic analysis on various spaces such as Euclidean spaces, and abelian and non-abelian locally compact groups. With a change of content, this course is repeatable to a maximum of six credits.
Prerequisites: MATH 5111
Credits: 3
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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.
Prerequisites: MATH 5111
Credits: 3
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Description: 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.
With a change of content, this course is repeatable to a maximum of six credits.
Prerequisites: MATH 5160
Credits: 3
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Description: Group theory, ring theory and modules, and universal mapping properties.
Offered: Fall
Credits: 3
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Description: Linear and multilinear algebra, Galois theory, category theory, and commutative algebra.
Prerequisites: MATH 5210
Offered: Spring
Credits: 3
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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
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Description: Algebraic integers, ideal class group, ramification, Frobenius elements in Galois groups,
Dirichlet's unit theorem, localization, and completion. Further topics (zeta-functions, function fields, non-maximal orders) as time permits.
Prerequisites: MATH 5211
Credits: 3
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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
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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
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Description: Topological spaces, maps, induced topologies, separation axioms, compactness, connectedness, classification of surfaces, the fundamental group and its applications, covering spaces.
Prerequisites: MATH 5110, which may be taken concurrently.
Offered: Fall
Credits: 3
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Description: Smooth manifolds, vector fields, differential forms, de Rham cohomology, homology theory, singular (co)homology, Poincaré duality. With a change of content, this course is repeatable to a maximum of six credits.
Prerequisites: MATH 5310
Credits: 3
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Description: This course is an introduction to algebraic varieties: affine and projective varieties, dimension of varieties and subvarieties, algebraic curves, singular points, divisors and line bundles, differentials, intersections.
Prerequisites: MATH 5211 and MATH 5310, which may be taken concurrently.
Credits: 3
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Description: This course introduces further concepts and methods of modern algebraic geometry, including schemes and cohomology.
Prerequisites: MATH 5320
Credits: 3
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Description: This course is an introduction to the study of differentiable manifolds on which various differential and integral calculi are developed. The topics include covariant derivatives and connections, geodesics and exponential map, Riemannian metrics, curvature tensor, Ricci and scalar curvature.
Prerequisites: MATH 5310
Credits: 3
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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
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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
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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
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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
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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
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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
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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
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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
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Description: Numerical solution of elliptic, parabolic and hyperbolic partial differential equations by finite element solution methods. Applications.
Credits: 3
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Description: Numerical solution of elliptic, parabolic and hyperbolic partial differential equations by finite element solution methods. Applications.
Prerequisites: MATH 5520
Credits: 3
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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
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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
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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
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Description: The mathematics of measurement of interest, accumulation and discount, present value, annuities, loans, bonds, and other securities. Not open to students who have passed MATH 2620.
Credits: 3
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Description: The continuation of Math 5620, 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. Not open to students who have passed MATH 3650.
Credits: 4
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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. Not open to students who have passed MATH 3630.
Prerequisites: MATH 2620 or MATH 5620, which may be taken concurrently.
Offered: Fall
Credits: 4
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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. Not open to students who have passed MATH 3631.
Prerequisites: MATH 5630.
Credits: 4
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Description: Analysis, estimation, and validation of lifetime tables
Prerequisites: MATH 5630 or STAT 3445.
Credits: 3
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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. Not open to students who have passed MATH 4535, STAT 4535, or STAT 5535.
Credits: 3
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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
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Description: Survival models, mathematical graduation, or demography.
Credits: 3
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Description: Credibility theory or advanced theory of interest.
Credits: 3
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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
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Description: An introduction to tensor algebra and tensor calculus with applications chosen from the fields of the physical sciences and mathematics.
Credits: 3
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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
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Description: Vector algebra and vector calculus with particular emphasis on invariance. Classification of vector fields. Solution of the partial differential equations of field theory.
Credits: 3
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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
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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
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Description: Participation in internship and paper describing experiences.
Credits: 1 to 3
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Description: Seminar. Participation and presentation of mathematical papers in joint student faculty seminars. Variable topics
Credits: 1
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Description: Seminar.
Credits: 1
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Description: Seminar.
Prerequisites: MATH 5211
Credits: 1
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Description: Seminar.
Prerequisites: MATH 5260
Credits: 1
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Description: Seminar.
Credits: 1
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Description: Seminar.
Prerequisites: MATH 5310
Credits: 1
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Prerequisites: MATH 5360
Credits: 1
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Description: (Doctoral Level).
Credits: 3
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University of Connecticut | 
