MATH 5001 - Introduction to Set Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Axioms of set theory, transfinite induction and recursion, cardinal numbers, cardinal arithmetic, ordinal numbers, ordinal arithmetic, Axiom of Choice, equivalent principles, closed unbounded and stationary sets, infinitary combinatorics. Prereq: 4547 (547), 4580 (580), graduate standing or permission of department. Not open to students with credit for 647 MATH 5051 - Introduction to Mathematical Logic Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Syntax and semantics of sentential logic, syntax and semantics of first-order logic, compactness of first-order logic, Goedel?s completeness theorem, theories and models of theories, Goedel?s incompleteness theorems; computability. Prereq: 4547 (547), 4580 (580), graduate standing, or permission of department. Not open to students with credit for 648 or 649. MATH 5101 - Linear Mathematics in Finite Dimensions Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Vector spaces; linear transformations; inner product spaces; eigenvalues and eigenvectors; Hermitian, unitary and normal matrices; quadratic forms; constraints; Rayleigh quotients; singular value decomposition; pseudo-inverse. Prereq: 2568 (568), 571, or grad standing. Not open to students with credit for 601. MATH 5102 - Linear Mathematics in Infinite Dimensions Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Sturm-Liouville systems, Hilbert spaces, Fourier and wavelet theory, Green's functions, Helmholtz's equation, cylinder and spherical harmonic solutions, interior and exterior boundary value problems, method of steepest descent and stationary phase. Prereq: 5101 (602). Not open to students with credit for 603.02. MATH 5111 - Algebra I Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Groups and homomorphisms, group actions and Sylow?s theorems, direct and semidirect products, rings and homomorphisms, factorizations in rings, polynomial rings. Prereq: Graduate standing or permission of department. Not open to students with credit for 670. MATH 5112 - Algebra II Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Modules and vector spaces, modules over a principal ideal domain, applications to linear algebra, field theory, Galois theory. Prereq: 5111 (671) or 591H. Not open to students with credit for 672. MATH 5152 - Introduction to Number Theory with Applications Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Divisibility, fundamental theorem of arithmetic, Fermat's theorem, congruences, Euler's formula, prime numbers, Euler's phi-function, counting primes, powers and roots mod m, quadratic reciprocity theorem, Diophantine approximation, Pell's theorem. Prereq: Both 5101 (602) and 4581 (582); or graduate standing. Not open to students with credit for 683. MATH 5168 - Introduction to the Finite Element Method Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Basic concepts, formulation, and application of finite element techniques for numerical solution of problems of engineering and scientific interest. Prereq: 2568 (568) or CivilEn 2060 (406), and CSE 1221. Not open to students with credit for both CivilEn 768 and MechEng 7068. Cross-listed in MechEng and CivilEn. MATH 5194 - Group Studies in Mathematics Course Detail Units Campus 1 - 9 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Designed to give groups of advanced undergraduate and beginning graduate students an opportunity to pursue special studies not otherwise offered. Prereq: Permission of department. Repeatable. MATH 5201 - Introduction to Real Analysis I Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Basic metric topology, sequences and series, continuous functions, differentiable functions of one variable, Riemann integration, uniform convergence, Fourier series. Prereq: Grad standing or permission of department. Not open to students with credit for 651. MATH 5202 - Introduction to Real Analysis II Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Continuation of Fourier series, differentiable functions of several variables, implicit function theorem and inverse function theorem, introduction to Lebesgue measure and Lebesgue integration, introduction to Hilbert spaces. Prereq: 5201 (652). Not open to students with credit for 653. MATH 5221 - Introduction to Complex Analysis Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Calculus of functions of a complex variable, series expansion and singularities of complex analytic functions, Cauchy's integral theorem, maximum principle, harmonic functions, differentials and residue theory, Weierstrass theorem. Prereq: 4547 (548). Not open to students with credit for 5251 (654). MATH 5251 - Complex Variables and Applications Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Complex numbers and complex differentiable functions, elementary analytic functions, complex integration, series, poles and residues, conformal mapping, applications of conformal mapping. Prereq: Both 2153.xx (254) and 4547 (548); or permission of department. Not open to students with credit for 4552 (552), 514, or 654. MATH 5401 - Applied Differential Equations I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Existence and uniqueness, linear ODE systems, 2x2, phase plane analysis, conservative and reversible systems, bifurcation analysis, limit cycles, perturbation theory. Prereq: 2255 (255)  and 2568 (568 or 572). Not open to students with credit for 615. MATH 5402 - Applied Differential Equations II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Steady state, heat equation, wave equation, PDEs in two dimensions, the Dirichlet problem, nonlinear evolution equations, wave equations by method of characteristic curve. Prereq: 5401 (616). Not open to students with credit for 617. MATH 5451 - Calculus of Variations and Tensor Calculus Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Euler-Lagrange equations, Hamilton's Principle, Lagrangian mechanics, Hamiltonian dynamics, Hamilton-Jacobi integration theory of dynamical systems, direct methods, tensor calculus, curvature and geometry of continuum mechanics. Prereq: 2415.xx (415) and 2568 (568 or 572). Not open to students with credit for 701. MATH 5576H - Honors Number Theory Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Enrollment Information Course Attributes: Honors Course Description Elementary analytic and algebraic number theory, tracing its unifying role in the development of mathematics through history. Au Sem of odd # years. Prereq: C- or better in 4191H, or C- or better in 2182H with coreq 3345, or credit for 264H, or credit for both 263H and 345, or permission of department. Not open to students with credit for 577H. MATH 5590H - Honors Abstract Algebra I Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Enrollment Information Course Attributes: Honors Course Description 5590H - 5591H includes elementary number theory, group theory, ring theory, abstract linear algebra, field theory, and Galois theory. Prereq: C- or better in 5520H, credit for 520H, or permission of department. Not open to students with credit for 591H. MATH 5591H - Honors Abstract Algebra II Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Enrollment Information Course Attributes: Honors Course Description Continuation of 5590H: elementary number theory, group theory, ring theory, abstract linear algebra, field theory, and Galois theory. Prereq: C- or better in 5590H, credit for 591H, or permission of department. Not open to students with credit for 592H. MATH 5601 - Essentials of Numerical Methods Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Systems of linear equations, linear least squares, eigenvalue problems, nonlinear equations and optimization, interpolation, numerical integration and differentiation, numerical solution for ODEs, IVPs and BVPs. Prereq: 4556 (556) and either 2568 (568) or 572. Not open to students with credit for 607. MATH 5602 - Computational Partial Differential Equations Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Parabolic PDEs: method of lines, stability and convergence; hyperbolic PDEs: shock capturing, flux limiters; elliptic PDEs: direct solvers and iterative methods. Prereq: Under semesters 5601 and either 4512 or 4557. Under quarters either 512 or 557; and 556;  and either 568 or 572. Not open to students with credit for 606. MATH 5603 - Numerical Linear Algebra Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Fundamentals of numerical linear algebra; solving square systems; QR factorization and least squares; calculation of eigenvalues; iterative methods for linear systems; iterative methods for eigenvalue problems. Prereq: Under semesters 2568 and one of 3607, 5601 or 5602. Under quarters either 568 or 571 and either 606 or 607. MATH 5630 - Life Contingencies I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Introduction to the mathematical theory of contingencies.  Includes material from examinations by the Society of Actuaries and the Casualty Actuarial Society. Coreq: 3618 (618), or prereq: C- or better in 3618, or credit for 618. Prereq: C- or better in 4530, 5530H, or Stat 4201; or credit for 530, 531H, or Stat 420; or permission of department. Open only to actuarial science majors, or to students in the MMS program in Financial Math. Not open to students with credit for 631. MATH 5631 - Life Contingencies II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Continuation of Math 5630: Mathematical Theory of Contingencies.  Includes material from examinations by the Society of Actuaries and the Casualty Actuarial Society. Prereq: C- or better in 5630 (631). Open only to actuarial science majors, and to MMS students specializing in Financial Math. Not open to students with credit for 632. MATH 5632 - Financial Economics for Actuaries Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Introduction to the evaluation of options, futures, and other derivatives, interest models and risk management techniques.  Includes material from examinations by the Society of Actuaries and the Casualty Actuarial Society. Rereq: C- or better in 3618, credit for 618, or permission of department. Open only to students majoring in Actuarial Science or in Mathematics, or who have graduate status. Not open to students with credit for 632. MATH 5633 - Loss Models I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Introduction to the construction and evaluation of actuarial models, with topics covered by examinations of the Society of Actuaries and the Casualty Actuarial Society. Prereq: Either a C- or better in Stat 4202 or credit for Stat 421; and either a C- or better in 4530, 5530H, or Stat 4201 or credit for 530, 531H, or Stat 420. Open only to actuarial science majors, and to MMS students specializing in Financial Math. MATH 5634 - Loss Models II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Continuation of 5633: introduction to the construction and evaluation of actuarial models, with topics covered by examinations of the Society of Actuaries and the Casualty Actuarial Society. Prereq: C- or better in 5633. Open only to actuarial science majors, and to MMS students specializing in Financial Math. MATH 5651 - Mathematical Modeling of Biological Processes Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Enzyme dynamics, predator-prey and competition model, spread of diseases, plant growth, cell cycle and cell differentiation, reaction-diffusion with advection, cancer models and cancer therapy, wound healing. Prereq: Grad standing; or either 4512 (512) or 557, and 4556 (556), and either 2568 (568) or 572. Not open to students with credit for 865. MATH 5660 - Integrated Molecular and Cellular Biology for Non-Biologists Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Overview of molecular and cellular biology of single cells, tissues, organisms and their interactions, including genetics and biochemistry of single cells. Prereq: Bio 1101 (101) or permission of instructor. Not open to students with credit for any one of MolGen 5660 (660), 4500 (500), 4606 (606), 605, or 661. Cross-listed in MolGen 5660. MATH 5702 - Curves and Surfaces in Euclidean Three Space Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Parametrized curves, curvature of curves; Frenet frames, curves with prescribed curvatures, curves on hypersurfaces; principal, Gaussian, and mean curvatures; surfaces in R^3,  triangulation and classification of surfaces, Gauss-Bonnet theorem. Prereq: Grad standing or 2153.01 (254) and either 2568 (568) or 572. Not open to students with credit for 642. MATH 5756 - Mathematical Methods in Relativity Theory I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special relativity as moving frames; tensors, exterior algebra and exterior calculus; differentiable manifolds and space time structures; parallel transport, torsion and curvatures, metric compatibility; structure equations of differential geometry. Prereq: 2153.xx (254) and one of 2568 (568) or 5101 (601) or 572. Not open to students with credit for 665. MATH 5757 - Mathematical Methods in Relativity Theory II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Gravitation via geometry; stress energy tensor, fluid dynamics; energy momentum conservation; Einstein's field equations, geodesic world lines via Hamilton-Jacobi theory; Schwarzschild spacetime; gauge invariant perturbation theory. Prereq: 5756 (665). Not open to students with credit for 666. MATH 5801 - General Topology and Knot Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Topological spaces; continuous maps and metric spaces; connectedness, compactness, countability axioms; metrization, compactification, and convergence; combinatorial, geometric, and algebraic techniques in knot theory; invariants of knots. Prereq: Grad standing; or 4547 (547) and either 2568 (568) or 572. Not open to students with credit for 640. MATH 6002 - Advanced Mathematical Logic II: Model Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Construction of models, compactness, Lowenheim-Skolem theorems, unions of elementary chains, omitting types; categoricity; saturation; model completeness, quantifier elimination; ultraproducts; definability. Prereq: 5051 (649) or permission of department. Not open to students with credit for 747. MATH 6003 - Advanced Mathematical Logic III: Set Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Axioms of set theory; ordinal and cardinal numbers; transitive models of ZFC; the constructible universe L and HOD; forcing; large cardinals; descriptive set theory. Prereq: 5051 (649) or permission of department. Not open to students with credit for 747. MATH 6004 - Advanced Mathematical Logic IV: Computability Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Relative recursion; Turing reducibility, structure of Turing degrees; structure of the recursively enumerable degrees and priority arguments; recursion in higher types; generalized recursion; Borel and projective sets; determinacy. Prereq: 5051 (649) or permission of department. Not open to students with credit for 747. MATH 6111 - Abstract Algebra I Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Group theory; complex representations of finite groups; introduction to category theory; ring theory; modules; elementary homological algebra. Prereq: Grad standing or 5112 (672). Not open to students with credit for 770. MATH 6112 - Abstract Algebra II Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Polynomial and Noetherian rings; field theory; finite Galois Theory; infinite Galois Theory; algebraic spaces. Prereq: 6111 (771). Not open to students with credit for th 772. MATH 6151 - Commutative Algebra Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Prime and primary ideals; rings and modules of fractions; integral dependence; chain conditions; valuation and Dedekind domains; completions; Dimension Theory. Prereq: 6112 (772). Not open to students with credit for 978. MATH 6152 - Non-Commutative Algebra Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Semisimple modules and rings and the Wedderburn Structure Theorem; Jacobson Radical; central simple algebras and the Noether-Skolem Theorem; Brauer Group; primitive rings, Density Theorem. Prereq: 6112 (772). Not open to students with credit for 982. MATH 6191 - Internship in Mathematical Sciences Course Detail Units Campus 1 - 5 units Columbus Grading Basis Career Satisfactory/Unsatisfactory Graduate Course Components: Field Experience Required         Description Internship and practical experiences, designed primarily for Master level students in the mathematical sciences. Prereq: Permission of department. This course is graded S/U. MATH 6193 - Individual Studies in Mathematics Course Detail Units Campus 1 - 9 units Columbus Grading Basis Career Satisfactory/Unsatisfactory Graduate Course Components: Independent Study Required         Description Individual studies. Prereq: Permission of department. Repeatable to a maximum of 99 cr hrs or 20 completions. This course is graded S/U. MATH 6194 - Group Studies in Mathematics Course Detail Units Campus 1 - 9 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Designed to give groups of PhD students an opportunity to pursue special studies not otherwise offered. Prereq: Permission of department. Repeatable to a maximum of 99 cr hrs or 20 completions. MATH 6211 - Real Analysis I Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Measures; integration; introduction to normed linear spaces; introduction to L^p spaces; Fourier analysis; signed measures and differentiation. Prereq: 5202 (653). Not open to students with credit for 750. MATH 6212 - Real Analysis II Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Elements of functional analysis; properties and relations of L^p spaces and Fourier analysis; elements of the theory of distributions; selected applications. Preerq: 6211 (751). Not open to students with credit for 752. MATH 6221 - Complex Analysis I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Basic Cauchy theory; harmonic functions; Riemann mapping theorem, conformal maps; analytic continuation; applications of residue calculus; counting theorems for entire and meromorphic functions. Prereq: 5202 (653). Not open to students with credit for 753. MATH 6222 - Complex Analysis II: Several Complex Variables Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Function spaces in complex analysis; applications to number theory and geometry; basic SCV: pseudoconvexity and extension phenomena; Cauchy-Riemann equations in several variables; complex manifolds. Prereq: 6221 (753). Not open to students with credit for 754. MATH 6251 - Theory of Probability I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Review of measures and integration; independence for events and for random variables; covariance and correlation for random variables; weak and strong laws of large numbers; Borel-Cantelli lemmas; Central Limit Theorems. Prereq: 5202 (653). Not open to students with credit for 722. MATH 6252 - Theory of Probability II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Central limit theorems; Poisson processes; random walks, Markov chains; martingales; Brownian motion; stochastic processes. Prereq: 6251 (723). Not open to students with credit for 724. MATH 6411 - Ordinary Differential Equations I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Existence, uniqueness and smooth dependence; linear systems; periodic and homoclinic orbits; stability, hyperbolicity; stable, unstable, and center invariant manifolds; bifurcations of equilibria and periodic orbits; chaos, strange attractors. Prereq: Both 5202 and either 2568 (568) or 572. Not open to students with credit for Math 715. MATH 6451 - Partial Differential Equations I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Second order linear equations; first order equations: conservation laws, Hamilton-Jacobi equations; Fourier and Laplace transform method, Hopf-Cole and Legendre transform, singular perturbation method; Cauchy-Kovalevskaya Theorem. Prereq: 6411 (715). Not open to students with credit for 717. MATH 6501 - Combinatorics and Graph Theory I Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Matching Theory; network flows; matroids; Ramsey Theory; extremal set theory and graph theory; planar graphs, embeddings on surfaces; graph connectivity. Prereq: 5112 (672). Not open to students with credit for 775. MATH 6502 - Combinatorics and Graph Theory II Course Detail Units Campus 5 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Combinatorial designs and geometries; coding theory; enumeration, Moebius inversion and Polya theory; algebraic graph theory, spectrum of graphs; association schemes; combinatorics of the symmetric groups; generating functions and q-series. Prereq: 6501 (776). Not open to students with credit for 777. MATH 6701 - Differentiable Manifolds Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Differentiable manifolds; vector bundles, existence theorem for ODE, flows, sprays; vector fields, differential operators, Lie and exterior derivatives; Poincare Lemma, Darboux's Theorem; Frobenius's Theorem, Lie groups; de Rham cohomology. Prereq: Grad standing or all of 5201 (652), and either 2568 (568) or 572, and 2153.01 (254). Not open to students with credit for 765. MATH 6702 - Differential Geometry Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Riemannian manifolds, distance, volume; covariant derivatives, Levi-Civita connection; geodesics, curvatures: sectional, Ricci, scalar; Jacobi fields, conjugate points; Rauch comparison, Hopf-Rinow, Hadamard, Preissman's and Berger's Sphere Theorems. Prereq: 6701 (765). Not open to students with credit for 766. MATH 6801 - Algebraic Topology I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Simplicial and CW- complexes, operations on spaces; homotopy and homeomorphism type; fundamental group, Seifert Van-Kampen Theorem; classification of covering spaces; singular and simplicial homology, chain maps, homotopy invariance, functoriality. Prereq: Grad standing or both 5801 (640) and 5111 (670). Not open to students with credit for 756. MATH 6802 - Algebraic Topology II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Homology of pairs, excision, axioms; Mayer-Vietoris, cellular homology; cohomology groups, Ext and Tor functors, universal coefficients; Kunneth Theorem; Orientation on manifolds; fundamental class; Poincare, Alexander, and Lefschetz duality. Prereq: 6801 (756). Not open to students with credit for 758. MATH 6998 - Graduate Research Course Detail Units Campus 1 - 16 units Columbus Grading Basis Career Satisfactory/Unsatisfactory Graduate Course Components: Independent Study Required         Description Graduate research, primarily for Masters and beginning PhD students participating in research projects other than their thesis work. Prereq: Permission of department. Repeatable to a maximum of 99 cr hrs or 20 completions. This course is graded S/U. MATH 6999 - Graduate Thesis Research Course Detail Units Campus 1 - 16 units Columbus Grading Basis Career Satisfactory/Unsatisfactory Graduate Course Components: Independent Study Required         Description Graduate research, primarily for students working on their master theses. Prereq: Permission of department. Repeatable to a maximum of 99 cr hrs or 20 completions. This course is graded S/U. MATH 7121 - Algebraic Number Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Algebraic integers, Dedekind domains, ideal class group; Galois theory of prime ideals, Frobenius automorphisms; geometry of numbers; cyclotomic fields, class field theory over Q; Gauss sums; quadratic fields; local fields; ideles and adeles. Prereq: 6112 (772) and 5221 (660). Not open to students with credit for 780. MATH 7122 - Analytic Number Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Properties and examples of L-functions; primes in arithmetic progression;  Riemann-Weil formula; non-vanishing theorem; analysis of L-functions on the critical line; principle of large sieve; Brauer-Siegel theorem, Ikehara-Tauberian theorem. Prereq: 7121 (781) and 6222 (754). Not open to students with credit for 782. MATH 7161 - Lie Algebras Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Nilpotent and solvable Lie algebras; structure and classification of simple Lie algebras; Levi-Malcev decomposition; root systems; Dynkin diagrams; introduction to representation of complex semi-simple Lie algebras; universal enveloping algebra. Prereq: Grad standing or 5112 (672). Not open to students with credit for 854. MATH 7162 - Lie Groups and Representation Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Basic group theory constructions; passage between a Lie group and its Lie algebra; homogeneous spaces; maximal tori; unitary trick and complete reducibility; classification of irreducible unitary representations; Cartan-Weyl theory. Prereq: 7161 (855) and either 6701 or 758. Not open to students with credit for 855. MATH 7193 - Individual Studies in Mathematics Course Detail Units Campus 1 - 9 units Columbus Grading Basis Career Satisfactory/Unsatisfactory Graduate Course Components: Independent Study Required         Description Individual studies. Prereq: Permission of department. Repeatable to a maximum of 99 cr hrs or 20 completions. This course is graded S/U. MATH 7194 - Group Studies in Mathematics Course Detail Units Campus 1 - 9 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Designed to give groups of advanced PhD students an opportunity to pursue special studies not otherwise offered. Prereq: Permission of department. Repeatable to a maximum of 99 cr hrs or 20 completions. MATH 7211 - Functional Analysis I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Linear spaces and linear maps; Hahn-Banach theorem and its applications; normed linear spaces and their duals; Hilbert spaces and applications; weak and weak* topologies; Choquet theorems; bounded linear maps. Prereq: 6212 (751). Not open to students with credit for 857. MATH 7212 - Functional Analysis II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Banach algebras, elementary spectral theory; Gelfand's theory of commutative Banach algebras; examples of families of operators; spectral theory of normal, unitary, self-adjoint operators; semigroups of operators; distributions; applications. Prereq: 7211 (857). Not open to students with credit for 961. MATH 7221 - Ergodic Theory I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Measure preserving transformations; isomorphism, conjugacy, spectral isomorphism; measure preserving systems with discrete spectrum; hierarchy of mixing properties; invariant measures for continuous transformations; topological and symbolic dynamics. Prereq: 6212 (752). Not open to students with credit for 931. MATH 7222 - Ergodic Theory II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Entropy; topological entropy; flows on homogeneous spaces; structure theory of measure preserving systems; applications to combinatorics and number theory. Prereq: 7221 (932). MATH 7412 - Ordinary Differential Equations II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Topological equivalence of nonlinear systems; normal forms of Poincare-Dulac-Birkhoff; classification of vector fields near critical points; local bifurcation theory; topological dynamics; limit sets; flows on the torus. Prereq: 6451 (716). Not open to students with credit for 820. MATH 7413 - Ordinary Differential Equations III Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Structural stability; singularity theory of Thom and Arnol'd; versal deformations; global deformations at separatrix cycle; Anosov diffeomorphisms; Axiom A; symbolic dynamics. Prereq: 7412 (821). Not open to students with credit for 822. MATH 7452 - Partial Differential Equations II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Sobolev spaces, Sobolev inequalities and embedding theorems; Lax-Milgram theorem, Fredholm alternatives, weak compactness; linear elliptic equations: existence, regularity, maximum principles; hyperbolic equations; first order hyperbolic systems. Prereq: 6451 (716) and 6212 (751). Not open to students with credit for 835. MATH 7453 - Partial Differential Equations III Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Harnack inequalities, De Giorgi-Nash-Moser theory; calculus of variations; monotonicity and sub-super solution methods, Pohozaev identity; hyperbolic conservation laws; quasilinear elliptic and parabolic equations; Schauder theory; strong solutions. Prereq: 7452 (835). Not open to students with credit for 836. MATH 7611 - Computational Partial Differential Equations I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Numerical methods for boundary value problems (BVP); extension to separable elliptic PDEs, fast solvers; irregular domains, variable coefficients; iterative methods; diffusion equations; error analysis; variable coefficients in nonlinear problems. Prereq: 6602 (709). Not open to students with credit for 807. MATH 7612 - Computational Partial Differential Equations II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Linear hyperbolic equations, finite difference methods; quasi-linear and non-linear equations with shock formation, Lax-Wendroff theorem; flux-limiters, WENO methods; multi-dimensional problems; transport equations; adaptive grids, grid generation. Prereq: 7611 (808). Not open to students with credit for 809. MATH 7651 - Applied Complex Variables and Asymptotics I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Contour integration, conformal mapping; asymptotics of integrals; asymptotic properties of Laplace and Fourier transforms; Riemann-Hilbert problems, applications to singular integral equations; introduction to the theory of elliptic functions. Prereq: 5251 (654) and 5201 (651) and 6451 (717). Not open to students with credit for 804. MATH 7652 - Applied Complex Variables and Asymptotics II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Asymptotic expansions; Watson's and Borel-Ritt lemma, stationary phase, steepest descent methods; contractive mapping methods; WKB and boundary layer methods; analyzable functions, transseries; Borel transform; Borel summability of solutions. Prereq: 7651 (805). Not open to students with credit for 806. MATH 7711 - Riemannian Geometry Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Comparison theorem for Laplacian; Ricci flow; differential sphere theorem; rigidity theory; Einstein metrics; topics in geometric analysis and Riemannian geometry. Prereq: 6702, 758. Not open to students with credit for 852. MATH 7721 - Kahler Geometry Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Complex manifolds, analytic varieties; divisors, analytic cycles; holomorphic vector bundles, sheaves, cohomology; compact surfaces; Kahler metrics; Hodge Theorem, Hodge decomposition, Kodaria Theorems; Hartshorne-Frankel and Calabi conjecture. Prereq: 6701 and 6221; or 757 and 753. MATH 7811 - Homotopy Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Homotopy groups, Whitehead's theorem, CW approximation; homotopy excision, Hurewicz theorem; fibrations, mapping path and loop spaces; fibre bundles, sphere bundles over spheres; obstruction theory, relation to cohomology; Postnikov towers. Prereq: 6802 (758). Not open to students with credit for 862. MATH 7851 - Differential Topology I Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Whitney Immersion and Embedding Theorems, transverse functions, jet-bundles, Thom transversality; classification of vector bundles, collars, tubular neighborhoods, intersection theory; Morse functions and lemma; surgery, Smale cancellation. Prereq: 6701 (765) and 6801 (757). Not open to students with credit for 866. MATH 7852 - Differential Topology II Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description DeRahm and Cech cohomology; deRahm Theorem; Grassmannians; Stiefel-Whitney, Euler, Chern, and Pontryagin classes; Gysin sequence, Thom isomorphism; characteristic numbers, multiplicative sequences, Hirzebruch signature theorem; Chern-Weil Theory. Prereq: 6702 (766) and 6802 (757) and 7851 (867). Not open to students with credit for 868. MATH 7998 - Graduate Research Course Detail Units Campus 1 - 16 units Columbus Grading Basis Career Satisfactory/Unsatisfactory Graduate Course Components: Independent Study Required         Description Graduate Research, primarily for intermediate PhD students participating in research projects other than their thesis work. Prereq: Permission of the department. Repeatable to a maximum of 99 cr hrs or 20 completions. This course is graded S/U. MATH 8000 - Topics in Foundations of Mathematics Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in foundations of mathematics chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8110 - Topics in Algebra Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in algebra chosen by the instructor. prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8120 - Topics in Number Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in number theory chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8140 - Topics in Algebraic Geometry Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in algebraic geometry chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8160 - Topics in Representation Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in representation theory chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8210 - Topics in Real Analysis Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in real analysis chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8220 - Topics in Complex Analysis Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in complex analysis chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8250 - Topics in Probability Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in probability theory chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8300 - Topics in Financial Mathematics Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in financial mathematics chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8410 - Topics in Ordinary Differential Equations Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in ordinary differential equations chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8420 - Topics in Partial Differential Equations Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in partial differential equations chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8500 - Topics in Combinatorics Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in combinatorics chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8610 - Topics in Applied Mathematics Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in applied mathematics chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8650 - Topics in Mathematical Biology Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in mathematical biology chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8710 - Topics in Differential Geometry Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in differential geometry chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8750 - Topics in Lie Theory Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in Lie theory chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. MATH 8800 - Topics in Topology Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Special topics in topology chosen by the instructor. Prereq: Permission of department. Repeatable to a maximum of 15 cr hrs or 5 completions. STAT 6301 - Probability for Statistical Inference Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Introduction to probability, random variables, and distribution theory; intended primarily for students in MAS degree program. Prereq: Math 4547 (548); or permission of instructor. Not open to students with credit for 6801 or 620 or 610 or Math 4530 or 5530H or 530 or 531. STAT 6302 - Theory of Statistical Analysis Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Estimation, hypothesis tests, best tests, likelihood ratio tests, confidence sets, sufficiency, efficient estimators; intended primarily for students in the MAS degree program. Prereq: 6301 (610) or 6801(620); or permission of instructor. Not open to students with credit for 6802 (621 or 622 or 623). STAT 6801 - Statistical Theory I Course Detail Units Campus 4 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Introduction to probability, random variables, distribution theory and principles of inference. Intended primarily for students in the PhD program in Statistics or Biostatistics. Prereq: Grad standing in Stat or Biostat; or permission of instructor. Not open to students with credit for 6301 or 620 or 610. STAT 6802 - Statistical Theory II Course Detail Units Campus 4 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Introduction to statistical inference: Estimation, hypothesis testing, confidence intervals, and decision theory. Intended primarily for students in the PhD program in Statistics or Biostatistics. Prereq: 6801 or permission of instructor. Not open to students with credit for 622. EDUTL 7717 - Teaching Mathematics Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Seminar Required         Description Designed to provide an expanded view of the teaching of mathematics in grades 7-16 and current theories regarding best practices. Prereq: Not open to students with credit for 802.03. EDUTL 7718 - Student Learning Processes in Mathematics Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Seminar Required         Description Student cognition and learning. The topics of arithmetic, algebra and geometry will be used to explore issues of student thinking. We will investigate how the nature of these topics affect students' reasoning and problem solving and thinking. Prereq: Not open to students with credit for 802.05. EDUTL 7742 - Knowledge Representations in STEM Learning Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Theory and classroom practices to promote various physical, visual, symbolic and mental representations of STEM knowledge structures. Prereq: Not open to students with credit for 802. EDUTL 7743 - Curriculum across Secondary and Post-Secondary STEM Education Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Seminar Required         Description Examining key ideas of Arithmetic, Algebra, Pre-calculus and calculus, Abstract algebra, Number theory, Linear Algebra and Geometry in order to trace the development trajectory of specific concepts. Prereq: Not open to students with credit for 802.02. EDUTL 7744 - Problem Solving in STEM Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Seminar Required         Description Help students gain a deeper understanding of the process of mathematical problem solving from an epistemological standpoint. Current theories and perspectives associated with teaching and learning problem solving will be studied. Prereq: Not open to students with credit for 802.04. EDUTL 7745 - Classroom Discourse in STEM Learning Course Detail Units Campus 3 units Columbus Grading Basis Career Graded Graduate Course Components: Lecture Required         Description Theory and practice on discourse patterns in STEM classrooms, including speaking, reading and writing to learn STEM subject matter in schools or colleges. Prereq: Not open to students with credit for 802.