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MATH 532 - Modern Geometry Credits: 3
Projective geometry, theorem of Desargues, conics, transformation theory, affine geometry, Euclidean geometry, non-Euclidean geometries, and topology.
Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director
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MATH 533 - Elementary Geometric Topology Credits: 3
Topology of the line, plane, and space, Jordan curve theorem, Brouwer fixed point theorem, Euler characteristic of polyhedra, orientable and non-orientable surfaces, classification of surfaces, network topology.
Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director
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MATH 534 - Elements of General Topology Credits: 3
Elementary properties of sets, functions, spaces, maps, separation axioms, compactness, completeness, convergence, connectedness, path connectedness, embedding and extension theorems, metric spaces, and compactification.
Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director
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MATH 540 - Modern Applied Algebra Credits: 3
Finite structures useful in applied areas. Binary relations, Boolean algebras, applications to optimization, and realization of finite state machines.
Prerequisites: MATH 250 or 241
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MATH 541 - Algebraic Coding Theory Credits: 3
Error-correcting codes, polynomial rings, cyclic codes, finite fields, BCH codes.
Prerequisites: C or better in MATH 544 or in both MATH 300 and 344 or consent of the Undergraduate Director
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MATH 544 - Linear Algebra Credits: 3
Vectors, vector spaces, and subspaces; geometry of finite dimensional Euclidean space; linear transformations; eigenvalues on theoretical concepts, logic, and meethods.
Prerequisites: C or better in MATH 300, or consent of the Undergraduate Director
Note: MATH 544L is an optional laboratory course where additional applications will be discussed.
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MATH 544L - Linear Algebra Lab Credits: 1
Computer-based applications of linear algebra for mathematics students. Topics include numerical analysis of matrices, direct and indirect methods for solving linear systems, and least squares method (regression). Typical applications include theoretical and practical issues related to discrete Markov’s processes, image compression, and linear programming.
Prerequisites: Prereq or coreq: C or better or concurrent enrollment in MATH 544
Note: Credit not allowed for both MATH 344L and 544L
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MATH 546 - Algebraic Structures I Credits: 3
Permutation groups; abstract groups; introduction to algebraic structures through study of subgroups, quotient groups, homomorphisms, isomorphisms, direct product; decompositions; introduction to rings and fields.
Prerequisites: C or better in MATH 544 or consent of the Undergraduate Director
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MATH 547 - Algebraic Structures II Credits: 3
Rings, ideals, polynomial rings, unique factorization domains; structure of finite groups; topics from: fields, field extensions, Euclidean constructions, modules over principal ideal domains (canonical forms).
Prerequisites: C or better in MATH 546 or consent of the Undergraduate Director
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MATH 548 - Geometry, Algebra, and Algorithms Credits: 3
Polynomials and affine space, Grobner bases, elimination theory, varieties, and computer algebra systems.
Prerequisites: Math 300 and Math 544 or consent of the Undergraduate Director.
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MATH 550 - Vector Analysis Credits: 3
Vector fields, line and path integrals, orientation and parametrization of lines and surfaces, change of variables and Jacobians, oriented surface integrals, theorems of Green, Gauss, and Stokes; introduction to tensor analysis.
Prerequisites: C or better in MATH 241 or consent of the Undergraduate Director
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MATH 551 - Introduction to Differential Geometry Credits: 3
Parametrized curves, regular curves and surfaces, change of parameters, tangent planes, the differential of a map, the Gauss map, first and second fundamental forms, vector fields, geodesics, and the exponential map.
Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director
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MATH 552 - Applied Complex Variables Credits: 3
Complex integration, calculus of residues, conformal mapping, Taylor and Laurent Series expansions, applications.
Prerequisites: C or better in MATH 241 or consent of the Undergraduate Director
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MATH 554 - Analysis I Credits: 3
Least upper bound axiom, the real numbers, compactness, sequences, continuity, uniform continuity, differentiation, Riemann integral and fundamental theorem of calculus.
Prerequisites: C or better in MATH 300 and either at last one of 511, 520, 534, 550, or 552, or consent of the Undergraduate Director
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MATH 555 - Analysis II Credits: 3
Riemann-Stieltjes integral, infinite series, sequences and series of functions, uniform convergence, Weierstrass approximation theorem, selected topics from Fourier series or Lebesgue integration.
Prerequisites: C or better in MATH 554 or consent of the Undergraduate Director
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MATH 561 - Introduction to Mathematical Logic Credits: 3
Syntax and semantics of formal languages; sentential logic, proofs in first order logic; Godel’s completeness theorem; compactness theorem and applications; cardinals and ordinals; the Lowenheim-Skolem-Tarski theorem; Beth’s definability theorem; effectively computable functions; Godel’s incompleteness theorem; undecidable theories.
Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director
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MATH 562 - Theory of Computation Credits: 3
Basic theoretical principles of computer science as modeled by formal languages and automata; computability and computational complexity. Major credit may not be received for both CSCE 355 and CSCE 551.
Cross-listed Course: CSCE 551
Prerequisites: C or better in CSCE 350 or MATH 344or 544 or 574 or consent of the Undergraduate Director
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MATH 570 - Discrete Optimization Credits: 3
Discrete mathematical models. Applications to such problems as resource allocation and transportation. Topics include linear programming, integer programming, network analysis, and dynamic programming.
Prerequisites: C or better in MATH 344 or 544, or consent of the Undergraduate Director
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MATH 574 - Discrete Mathematics I Credits: 3
Mathematical models; mathematical reasoning; enumeration; induction and recursion; tree structures; networks and graphs; analysis of algorithms.
Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director
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MATH 575 - Discrete Mathematics II Credits: 3
A continuation of MATH 574. Inversion formulas; Polya counting; combinatorial designs; minimax theorems; probabilistic methods; Ramsey theory; other topics.
Prerequisites: C or better in MATH 574 or consent of the Undergraduate Director
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MATH 576 - Combinatorial Game Theory Credits: 3
Winning in certain combinatorial games such as Nim, Hackenbush, and Domineering. Equalities and inequalities among games, Sprague-Grundy theory of impartial games, games which are numbers.
Prerequisites: C or better in MATH 344, 544, or 574, or consent of the Undergraduate Director
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MATH 580 - Elementary Number Theory Credits: 3
Divisibility, primes, congruences, quadratic residues, numerical functions. Diophantine equations.
Prerequisites: C or better in MATH 300 or consent of the Undergraduate Director
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MATH 587 - Introduction to Cryptography Credits: 3
Design of secret codes for secure communication, including encryption and integrity verification: ciphers, cryptographic hashing, and public key cryptosystems such as RSA. Mathematical principles underlying encryption. Code-breaking techniques. Cryptographic protocols.
Cross-listed Course: CSCE 557
Prerequisites: C or better in CSCE 145 or in MATH 241, and in either CSCE 355 or MATH 574, or consent of the Undergraduate Director
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MATH 590 - Undergraduate Seminar Credits: 1-3
A review of literature in specific subject areas involving student presentations. Content varies and will be announced in the Master Schedule of Classes by suffix and title. Pass-fail grading. For undergraduate credit only.
Prerequisites: consent of instructor
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MATH 599 - Topics in Mathematics Credits: 1-3
Recent developments in pure and applied mathematics selected to meet current faculty and student interest.
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MATH 602 - An Inductive Approach to Geometry Credits: 3
This course is designed for middle-level pre-service mathematics teachers. This course covers geometric reasoning, Euclidean geometry, congruence, area, volume, similarity, symmetry, vectors, and transformations. Dynamic software will be utilized to explore geometry concepts.
Prerequisites: C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director
Note: This course cannot be used for credit toward a major in mathematics.
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MATH 603 - Inquiry Approach to Algebra Credits: 3
This course introduces basic concepts in number theory and modern algebra that provide the foundation for middle level arithmetic and algebra. Topics include: algebraic reasoning, patterns, inductive reasoning, deductive reasoning, arithmetic and algebra of integers, algebraic systems, algebraic modeling, and axiomatic mathematics. This course cannot be used for credit towards a major in mathematics.
Prerequisites: C or better in MATH 122 or 141 or equivalent, or consent of the Undergraduate Director
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MATH 650 - AP Calculus for Teachers Credits: 3
A thorough study of the topics to be presented in AP calculus, including limits of functions, differentiation, integration, infinite series, and applications. (Not intended for degree programs in mathematics.)
Prerequisites: current secondary high school teacher certification in mathematics and a C or better in at least 6 hours of calculus, or consent of the Undergraduate Director
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MATH 700 - Linear Algebra Credits: 3
Vector spaces, linear transformations, dual spaces, decompositions of spaces, and canonical forms.
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MATH 701 - Algebra I Credits: 3
Algebraic structures, sub-structures, products, homomorphisms, and quotient structures of groups, rings, and modules.
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MATH 701I - Foundations of Algebra I Credits: 3
An introduction to algebraic structures; group theory including subgroups, quotient groups, homomorphisms, isomorphisms, decomposition; introduction to rings and fields.
Prerequisites: MATH 241 or equivalent
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MATH 702 - Algebra II Credits: 3
Fields and field extensions. Galois theory, topics from, transcendental field extensions, algebraically closed fields, finite fields.
Prerequisites: MATH 701
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MATH 702I - Foundations of Algebra II Credits: 3
Theory of rings including ideals, polynomial rings, and unique factorization domains; structure of finite groups; fields; modules.
Prerequisites: MATH 701-I or equivalent
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MATH 703 - Analysis I Credits: 3
Compactness, completeness, continuous functions. Outer measures, measurable sets, extension theorem and Lebesgue-Stieltjes measure. Integration and convergence theorems. Product measures and Fubini’s theorem. Differentiation theory. Theorems of Egorov and Lusin. Lp-spaces. Analytic functions: Cauchy-Riemann equations, elementary special functions. Conformal mappings. Cauchy’s integral theorem and formula. Classification of singularities, Laurent series, the Argument Principle. Residue theorem, evaluation of integrals and series.
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MATH 703I - Foundations of Analysis I Credits: 3
The real numbers and least upper bound axiom; sequences and limits of sequences; infinite series; continuity; differentiation; the Riemann integral.
Prerequisites: MATH 241 or equivalent
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MATH 704 - Analysis II Credits: 3
Compactness, completeness, continuous functions. Outer measures, measurable sets, extension theorem and Lebesgue-Stieltjes measure. Integration and convergence theorems. Product measures and Fubini’s theorem. Differentiation theory. Theorems of Egorov and Lusin. Lp-spaces. Analytic functions: Cauchy-Riemann equations, elementary special functions. Conformal mappings. Cauchy’s integral theorem and formula. Classification of singularities, Laurent series, the Argument Principle. Residue theorem, evaluation of integrals and series.
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MATH 704I - Foundations of Analysis II Credits: 3
Sequences and series of functions; power series, uniform convergence; interchange of limits; limits and continuity in several variables.
Prerequisites: MATH 703-I or equivalent
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MATH 705 - Analysis III Credits: 3
Signed and complex measures, Radon-Nikodym theorem, decomposition theorems. Metric spaces and topology, Baire category, Stone-Weierstrass theorem, Arzela-Ascoli theorem. Introduction to Banach and Hilbert spaces, Riesz representation theorems.
Prerequisites: MATH 703, 704
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MATH 708 - Foundations of Computational Mathematics I Credits: 3
Approximation of functions by algebraic polynomials, splines, and trigonometric polynomials; numerical differentiation; numerical integration; orthogonal polynomials and Gaussian quadrature; numerical solution of nonlinear systems, unconstrained optimization.
Prerequisites: Math 554 or equivalent upper level undergraduate course in Real Analysis
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MATH 709 - Foundations of Computational Mathematics II Credits: 3
Vectors and matrices; QR factorization; conditioning and stability; solving systems of equations; eigenvalue/eigenvector problems; Krylov subspace iterative methods; singular value decomposition. Includes theoretical development of concepts and practical algorithm implementation.
Prerequisites: Math 544 or 526, or equivalent upper level undergraduate courses in Linear Algebra
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MATH 710 - Probability Theory I Credits: 3
Probability spaces, random variables and distributions, expectations, characteristic functions, laws of large numbers, and the central limit theorem.
Cross-listed Course: STAT 810
Prerequisites: STAT 511, 512, or MATH 703
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MATH 711 - Probability Theory II Credits: 3
More about distributions, limit theorems, Poisson approximations, conditioning, martingales, and random walks.
Cross-listed Course: STAT 811
Prerequisites: MATH 710
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MATH 712I - Probability and Statistics Credits: 3
This course will include a study of permutations and combinations; probability and its application to statistical inferences; elementary descriptive statistics of a sample of measurements; the binomial, Poisson, and normal distributions; correlation and regression.
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MATH 720 - Applied Mathematics I Credits: 3
Modeling and solution techniques for differential and integral equations from sciences and engineering, including a study of boundary and initial value problems, integral equations, and eigenvalue problems using transform techniques, Green’s
functions, and variational principles.
Prerequisites: MATH 555 and MATH 520 or equivalent
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MATH 721 - Applied Mathematics II Credits: 3
Foundations of approximation of functions by Fourier series in Hilbert space; fundamental PDEs in mathematical physics; fundamental equations for continua; integral and differential operators in Hilbert spaces. Basic modeling theory and solution techniques for stochastic differential equations.
Prerequisites: MATH 720
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MATH 722 - Numerical Optimization Credits: 3
Topics in optimization; includes linear programming, integer programming, gradient methods, least squares techniques, and discussion of existing mathematical software.
Prerequisites: graduate standing or consent of the department
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MATH 723 - Differential Equations Credits: 3
Elliptic equations: fundamental solutions, maximum principles, Green’s function, energy method and Dirichlet principle; Sobolev spaces: weak derivatives, extension and trace theorems; weak solutions and Fredholm alternative, regularity, eigenvalues and eigenfunctions.
Prerequisites: Math 703/704 or permission of instructor
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MATH 724 - Differential Equations II Credits: 3
Detailed study of the following topics: method of characteristics; Hamilton-Jacobi equations; conservation laws; heat equation; wave equation; linear parabolic equations; linear hyperbolic equations.
Prerequisites: MATH 723
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MATH 725 - Approximation Theory Credits: 3
Approximation of functions; existence, uniqueness and characterization of best approximants; Chebyshev’s theorem; Chebyshev polynomials; degree of approximation; Jackson and Bernstein theorems; B-splines; approximation by splines; quasi-interpolants; spline interpolation.
Corequisite: Prereq or coreq: MATH 703
Prerequisites: Prereq or coreq: MATH 703
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MATH 726 - Numerical Differential Equations I Credits: 3
Elliptic equations: fundamental solutions, maximum principles, Green’s function, energy method and Dirichlet principle; Sobolev spaces: weak derivatives, extension and trace theorems; weak solutions and Fredholm alternative, regularity, eigenvalues and eigenfunctions.
Prerequisites: Math 708/709, or permission of instructor
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MATH 727 - Numerical Differential Equations II Credits: 3
Ritz and Galerkin weak formulation. Finite element, mixed finite element, collocation methods for elliptic, parabolic, and hyperbolic PDEs, including development, implementation, stability, consistency, convergence analysis, and error estimates.
Prerequisites: 726
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MATH 728 - Selected Topics in Applied Mathematics Credits: 3
Course content varies and will be announced in the schedule of classes by suffix and title.
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MATH 729 - Nonlinear Approximation Credits: 3
Nonlinear approximation from piecewise polynomial (spline) functions in the univariate and multivariate case, characterization of the approximation spaces via Besov spaces and interpolation, Newman’s and Popov’s theorems for rational approximation, characterization of the approximation spaces of rational approximation, nonlinear n-term approximation from bases in Hilbert spaces and from unconditional bases in Lp (p>1), greedy algorithms, application of nonlinear approximation to image compression.
Prerequisites: MATH 703
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MATH 730 - General Topology I Credits: 3
Topological spaces, filters, compact spaces, connected spaces, uniform spaces, complete spaces, topological groups, function spaces.
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MATH 731 - General Topology II Credits: 3
Topological spaces, filters, compact spaces, connected spaces, uniform spaces, complete spaces, topological groups, function spaces.
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MATH 732 - Algebraic Topology I Credits: 3
The fundamental group, homological algebra, simplicial complexes, homology and cohomology groups, cup-product, triangulable spaces.
Prerequisites: MATH 730 or 705, and 701
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MATH 733 - Algebraic Topology II Credits: 3
The fundamental group, homological algebra, simplicial complexes, homology and cohomology groups, cup-product, triangulable spaces.
Prerequisites: MATH 730 or 705, and 701
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MATH 734 - Differential Geometry Credits: 3
Differentiable manifolds; classical theory of surfaces and hypersurfaces in Euclidean space; tensors, forms and integration of forms; connections and covariant differentiation; Riemannian manifolds; geodesics and the exponential map; curvature; Jacobi fields and comparison theorems, generalized Gauss-Bonnet theorem.
Prerequisites: MATH 550
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MATH 735 - Lie Groups Credits: 3
Manifolds; topological groups, coverings and covering groups; Lie groups and their Lie algebras; closed subgroups of Lie groups; automorphism groups and representations; elementary theory of Lie algebras; simply connected Lie groups; semisimple Lie groups and their Lie algebras.
Prerequisites: MATH 705 or 730
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MATH 736I - Modern Geometry Credits: 3
Synthetic and analytic projective geometry, homothetic transformations, Euclidean geometry, non-Euclidean geometries, and topology.
Prerequisites: MATH 241 or equivalent
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MATH 737 - Introduction to Complex Geometry Credits: 3
Algebraic geometry over the complex numbers, using ideas from topology, complex variable theory, and differential geometry.
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MATH 738 - Selected Topics in Geometry and Topology Credits: 3
Course content varies and will be announced in the schedule of classes by suffix and title.
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MATH 739 - Introduction to Complex Geometry II Credits: 3
Algebraic geometry over the complex numbers, using ideas from topology, complex variable theory, and differential geometry.
Prerequisites: MATH 737
Note: Effective Spring 2017
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MATH 741 - Algebra III Credits: 3
Theory of groups, rings, modules, fields and division rings, bilinear forms, advanced topics in matrix theory, and homological techniques.
Prerequisites: MATH 702
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MATH 742 - Representation Theory Credits: 3
Representation and character theory of finite groups (especially the symmetric group) and/or the general linear group, Young tableaux, the Littlewood Richardson rule, and Schur functors.
Prerequisites: MATH 702
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MATH 743 - Lattice Theory Credits: 3
Sublattices, homomorphisms and direct products of lattices; freely generated lattices; modular lattices and projective geometries; the Priestley and Stone dualities for distributive and Boolean lattices; congruence relations on lattices.
Prerequisites: MATH 740
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MATH 744 - Matrix Theory Credits: 3
Extremal properties of positive definite and hermitian matrices, doubly stochastic matrices, totally non-negative matrices, eigenvalue monotonicity, Hadamard-Fisher determinantal inequalities.
Prerequisites: MATH 700
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MATH 746 - Communtative Algebra Credits: 3
Prime spectrum and Zariski topology; finite, integral, and flat extensions; dimension; depth; homological techniques, normal and regular rings.
Prerequisites: MATH 701
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MATH 747 - Algebraic Geometry Credits: 3
Properties of affine and projective varieties defined over algebraically closed fields, rational mappings, birational geometry and divisors especially on curves and surfaces, Bezout’s theorem, Riemann-Roch theorem for curves.
Prerequisites: MATH 701
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MATH 748 - Selected Topics in Algebra Credits: 3
Course content varies and will be announced in the schedule of classes by suffix and title.
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MATH 750 - Fourier Analysis Credits: 3
The Fourier transform on the circle and line, convergence of Fejer means; Parseval’s relation and the square summable theory, convergence and divergence at a point; conjugate Fourier series, the conjugate function and the Hilbert transform, the Hardy-Littlewood maximal operator and Hardy spaces.
Prerequisites: MATH 703 and 704
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MATH 751 - The Mathematical Theory of Wavelets Credits: 3
The L1 and L2 theory of the Fourier transform on the line, bandlimited functions and the Paley-Weiner theorem, Shannon-Whittacker Sampling Theorem, Riesz systems, Mallat-Meyer multiresolution analysis in Lebesgue spaces, scaling functions, wavelet constructions, wavelet representation and unconditional bases, nonlinear approximation, Riesz’s factorization lemma, and Daubechies’ compactly supported wavelets.
Prerequisites: MATH 703
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MATH 752 - Complex Analysis Credits: 3
Normal families, meromorphic functions, Weierstrass product theorem, conformal maps and the Riemann mapping theorem, analytic continuation and Riemann surfaces, harmonic and subharmonic functions.
Prerequisites: MATH 703, 704
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MATH 752I - Complex Variables Credits: 3
Properties of analytic functions, complex integration, calculus of residues, Taylor and Laurent series expansions, conformal mappings.
Prerequisites: MATH 241 or equivalent
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MATH 754 - Several Complex Variables Credits: 3
Properties of holomorphic functions of several variables, holomorphic mappings, plurisubharmonic functions, domains of convergence of power series, domains of holomorphy and pseudoconvex domains, harmonic analysis in several variables.
Prerequisites: MATH 703 and 704
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MATH 755 - Applied Functional Analysis Credits: 3
Banach spaces, Hilbert spaces, spectral theory of bounded linear operators, Fredholm alternatives, integral equations, fixed point theorems with applications, least square approximation.
Prerequisites: MATH 703
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MATH 756 - Functional Analysis I Credits: 3
Linear topological spaces; Hahn-Banach theorem; closed graph theorem; uniform boundedness principle; operator theory; spectral theory; topics from linear differential operators or Banach algebras.
Prerequisites: MATH 704
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MATH 757 - Functional Analysis II Credits: 3
Linear topological spaces; Hahn-Banach theorem; closed graph theorem; uniform boundedness principle; operator theory; spectral theory; topics from linear differential operators or Banach algebras.
Prerequisites: MATH 704
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MATH 758 - Selected Topics in Analysis Credits: 3
Course content varies and will be announced in the schedule of classes by suffix and title.
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MATH 760 - Set Theory Credits: 3
An axiomatic development of set theory: sets and classes; recursive definitions and inductive proofs; the axiom of choice and its consequences; ordinals; infinite cardinal arithmetic; combinatorial set theory.
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MATH 761 - The Theory of Computable Functions Credits: 3
Models of computation; recursive functions, random access machines, Turing machines, and Markov algorithms; Church’s Thesis; universal machines and recursively unsolvable problems; recursively enumerable sets; the recursion theorem; the undecidability of elementary arithmetic.
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MATH 762 - Model Theory Credits: 3
First order predicate calculus; elementary theories; models, satisfaction, and truth; the completeness, compactness, and omitting types theorems; countable models of complete theories; elementary extensions; interpolation and definability; preservation theorems; ultraproducts.
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MATH 768 - Selected Topics in Foundations of Mathematics Credits: 3
Course content varies and will be announced in the schedule of classes by suffix and title.
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MATH 770 - Discrete Optimization Credits: 3
The application and analysis of algorithms for linear programming problems, including the simplex algorithm, algorithms and complexity, network flows, and shortest path algorithms. No computer programming experience required.
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MATH 774 - Discrete Mathematics I Credits: 3
An introduction to the theory and applications of discrete mathematics. Topics include enumeration techniques, combinatorial identities, matching theory, basic graph theory, and combinatorial designs.
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MATH 775 - Discrete Mathematics II Credits: 3
A continuation of MATH 774. Additional topics will be selected from: the structure and extremal properties of partially ordered sets, matroids, combinatorical algorithms, matrices of zeros and ones, and coding theory.
Prerequisites: MATH 774 or consent of the instructor
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MATH 776 - Graph Theory I Credits: 3
The study of the structure and extremal properties of graphs, including Eulerian and Hamiltonian paths, connectivity, trees, Ramsey theory, graph coloring, and graph algorithms.
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MATH 777 - Graph Theory II Credits: 3
Continuation of MATH 776. Additional topics will be selected from: reconstruction problems, independence, genus, hypergraphs, perfect graphs, interval representations, and graph-theoretical models.
Prerequisites: MATH 776 or consent of instructor
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MATH 778 - Selected Topics in Discrete Mathematics Credits: 3
Course content varies and will be announced in the schedule of classes by suffix and title.
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MATH 780 - Elementary Number Theory Credits: 3
Diophantine equations, distribution of primes, factoring algorithms, higher power reciprocity, Schnirelmann density, and sieve methods.
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MATH 780I - Theory of Numbers Credits: 3
Elementary properties of integers, Diophantine equations, prime numbers, arithmetic functions, congruences, and the quadratic reciprocity law.
Prerequisites: MATH 241 or equivalent
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MATH 782 - Analytic Number Theory I Credits: 3
The prime number theorem, Dirichlet’s theorem, the Riemann zeta function, Dirichlet’s L-functions, exponential sums, Dirichlet series, Hardy-Littlewood method partitions, and Waring’s problem.
Prerequisites: MATH 580 and 552
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MATH 783 - Analytic Number Theory II Credits: 3
The prime number theorem, Dirichlet’s theorem, the Riemann zeta function, Dirichlet’s L-functions, exponential sums, Dirichlet series, Hardy-Littlewood method partitions, and Waring’s problem.
Prerequisites: MATH 580 and 552
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MATH 784 - Algebraic Number Theory Credits: 3
Algebraic integers, unique factorization of ideals, the ideal class group, Dirichlet’s unit theorem, application to Diophantine equations.
Prerequisites: MATH 546 and 580
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MATH 785 - Transcendental Number Theory Credits: 3
Thue-Siegel-Roth theorem, Hilbert’s seventh problem, diophantine approximation.
Prerequisites: MATH 580
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MATH 788 - Selected Topics in Number Theory Credits: 3
Course content varies and will be announced in the schedule of classes by suffix and title.
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MATH 790 - Graduate Seminar Credits: 1
Although this course is required of all candidates for the master’s degree it is not included in the total credit hours in the master’s program.
Note: Although this course is required of all candidates for the master’s degree it is not included in the total credit hours in the master’s program.
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MATH 791 - Mathematics Pedagogy I Credits: 0-1
First of two required math pedagogy courses for graduate assistants in the department.
Pedagogical topics include assessment theory, discourse, theory, lesson planning, and
classroom management. Applications assist graduate students with
syllabus/lesson/assessment creation, teacher questioning, midcourse evaluations, and
student learning and engagement.
Note: Pass/Fail Grading
Restricted to Mathematics graduate students teaching at some capacity
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MATH 792 - Mathematics Pedagogy II Credits: 0-1
Second of two required math pedagogy courses for graduate assistants in the
department. Pedagogical topics include student-learning and reflection theories, sociomathematical norms, and constructivism. Applications assist graduates with
lesson/revision/reflection, student-centered investigations, curriculum problem solving and
metacognition.
Prerequisites: Satisfactory grade in MATH 791
Note: Pass/Fail Grading
Restricted to Mathematics graduate students teaching at some capacity.
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MATH 797 - Mathematics into Print Credits: 3
The exposition of advanced mathematics emphasizing the organization of proofs and the formulation of concepts; computer typesetting systems for producing mathematical theses, books, and articles.
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