# Graduate Courses

- MATH 701 Topics in Mathematics for Teachers: _____
- Material, including both mathematical content and teaching methodology, related to classroom use at various levels, elementary through secondary. Topics may vary. May not be counted for junior-senior credit towards a major in mathematics, nor for graduate credit towards a graduate degree in mathematics. Prerequisite: Permission of instructor. RSH.
**The class is not offered for the Spring 2019 semester.** - MATH 715 Sampling Techniques
- Statistical methodology of survey sampling. Data analysis and estimation methods for various experimental designs; fixed or random sample sizes, pre-and/or post-stratified samples, and multistage sampling. Estimates of totals, means, ratios and proportions with methods of estimating variances of such estimates. Prerequisite: A post-calculus probability or statistics course. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 717 Nonparametric Statistics
- Methods requiring few assumptions about the populations sampled. Topics include quantile tests, tolerance limits, the sign test, contingency tables, rank-sum tests, and rank correlation. Prerequisite: MATH 628 or permission of instructor. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 722 Mathematical Logic
- Propositional calculus. First order theories and model theory. Elementary arithmetic and Godel's incompleteness theorems. (Same as EECS 722.) Prerequisite: MATH 665 or MATH 691, or equivalent evidence of mathematical maturity. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 724 Combinatorial Mathematics
- Counting problems, with an introduction to Polya's theory; Mobius functions; transversal theory; Ramsey's theorem; Sperner's theorem and related results. Prerequisite: MATH 290 and a math course numbered 450 or higher. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 725 Graph Theory
- Graphs; trees; connectivity; Menger's theorem; eulerian and hamiltonian graphs; planarity; coloring of graphs; factorization of graphs; matching theory; alternating chain methods; introduction to matroids with applications to graph theory. Prerequisite: MATH 290 and a math course numbered 450 or higher. LEC.
- MATH 727 Probability Theory
- A mathematical introduction to premeasure-theoretic probability. Topics include probability spaces, conditional probabilities and independent events, random variables and probability distributions, special discrete and continuous distributions with emphasis on parametric families used in applications, the distribution problem for functions of random variables, sequences of independent random variables, laws of large numbers, and the central limit theorem. Prerequisite: MATH 223 and MATH 290, or equivalent. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 728 Statistical Theory
- Theory of point estimation and hypothesis testing with applications. Confidence region methodologies and relations to estimation and testing. Prerequisite: MATH 727 or equivalent. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 735 Optimal Control Theory
- An examination of the mathematical methods of deterministic control theory is given by considering some specific examples and the general theory. The methods include dynamic programming, the calculus of variations, and Pontryagin's maximum principle. Various problems of linear control systems, e.g., the linear regulator problem, are solved. Prerequisite: MATH 320 or equivalent. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 740 Number Theory
- Divisibility, the theory of congruences, primitive roots and indices, the quadratic reciprocity law, arithmetical functions and miscellaneous additional topics. Prerequisite: MATH 223 and MATH 290, or equivalent. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 750 Stochastic Adaptive Control
- Stochastic adaptive control methods. Stochastic processes such as Markov chains and Brownian motion, stochastic integral, differential rule, stochastic differential equations, martingales and estimation techniques. Identification and control of discrete and continuous time linear stochastic systems. Specific applications and simulation results of stochastic adaptive control theory. Prerequisite: MATH 627 and some knowledge of control. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 765 Mathematical Analysis I
- MATH 765 and MATH 766 are theoretical courses on the fundamental concepts of analysis and the methods of proof. These two courses include the concept of a real number; limits, continuity, and uniform convergence; derivatives and integrals of functions of one and of several real variables. Prerequisite: MATH 223 and MATH 290, or equivalent. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 766 Mathematical Analysis II
- A continuation of MATH 765. Prerequisite: MATH 765. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Chen, Geng

MW 11:00-12:15 PM SNOW 564 - LAWRENCE

3 62127 - MATH 780 Numerical Analysis of Linear Systems
- Computational aspects of linear algebra, linear equations and matrices, direct and indirect methods, eigenvalues and eigenvectors of matrices, error analysis. Prerequisite: MATH 590 and MATH 781. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 781 Numerical Analysis I
- Finite and divided differences. Interpolation, numerical differentiation, and integration. Gaussian quadrature. Numerical integration of ordinary differential equations. Curve fitting. (Same as EECS 781.) Prerequisite: MATH 320 and knowledge of a programming language. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 782 Numerical Analysis II
- Direct and interactive methods for solving systems of linear equations. Numerical solution of partial differential equations. Numerical determination of eigenvectors and eigenvalues. Solution of nonlinear equations. (Same as EECS 782.) Prerequisite: EECS 781 or MATH 781. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Miedlar, Agnieszka

TuTh 01:00-02:15 PM SNOW 454 - LAWRENCE

3 67099 - MATH 783 Applied Numerical Methods for Partial Differential Equations
- Finite difference methods applied to particular initial-value problems (both parabolic and hyperbolic), to illustrate the concepts of convergence and stability and to provide a background for treating more complicated problems arising in engineering and physics. Finite difference methods for elliptic boundary-value problems, with a discussion of convergence and methods for solving the resulting algebraic system. Variational methods for elliptic problems. Prerequisite: MATH 647 or equivalent. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Van Vleck, Erik

TuTh 11:00-12:15 PM SNOW 456 - LAWRENCE

3 73894 - MATH 790 Linear Algebra II
- A theoretical course on the fundamental concepts and theorems of linear algebra. Topics covered are: vector space, basis, dimension, subspace, norm, inner product, Banach space, Hilbert space, orthonormal basis, positive definite matrix, minimal polynomial, diagonalization and other canonical forms, Cayley-Hamilton, spectral radius, dual space, quotient space. Prerequisite: MATH 590. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 791 Modern Algebra
- This course includes the following topics: multiplicative properties of the integers and introductions to group theory, ring theory and field theory. Prerequisite: MATH 223 and MATH 290, or equivalent. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Witt, Emily

TuTh 09:30-10:45 AM SNOW 301 - LAWRENCE

3 64159 - MATH 796 Special Topics: _____
- Arranged as needed to present appropriate material for groups of students. May be repeated for credit. Prerequisite: Variable. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 799 Directed Readings
- Directed readings on a topic chosen by the student with the advice of an instructor. May be repeated for additional credit. Consent of the department required for enrollment. RSH.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # RSH Bayer, Margaret

APPT- KULC APPT - LAWRENCE

1-3 62128 RSH Chen, Geng

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1-3 73907 RSH Dao, Hailong

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1-3 66915 RSH Duncan, Tyrone

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1-3 62129 RSH Feng, Jin

APPT- KULC APPT - LAWRENCE

1-3 65911 RSH Gavosto, Estela

APPT- KULC APPT - LAWRENCE

1-3 62130 RSH Gay, A.

APPT- KULC APPT - LAWRENCE

1-3 62131 RSH Hernandez, Daniel

APPT- KULC APPT - LAWRENCE

1-3 72307 RSH Huang, Weizhang

APPT- KULC APPT - LAWRENCE

1-3 62132 RSH Jiang, Yunfeng

APPT- KULC APPT - LAWRENCE

1-3 70188 RSH Johnson, Mathew

APPT- KULC APPT - LAWRENCE

1-3 68232 RSH Kachi, Yasuyuki

APPT- KULC APPT - LAWRENCE

1-3 66509 RSH Katz, Daniel

APPT- KULC APPT - LAWRENCE

1-3 62133 RSH Lang, Jeffrey

APPT- KULC APPT - LAWRENCE

1-3 62134 RSH Liu, Weishi

APPT- KULC APPT - LAWRENCE

1-3 62135 RSH Liu, Zhipeng

APPT- KULC APPT - LAWRENCE

1-3 73909 RSH Mandal, Satyagopal

APPT- KULC APPT - LAWRENCE

1-3 73908 RSH Mantzavinos, Dionysios

APPT- KULC APPT - LAWRENCE

1-3 62136 RSH Martin, Jeremy

APPT- KULC APPT - LAWRENCE

1-3 65269 RSH Miedlar, Agnieszka

APPT- KULC APPT - LAWRENCE

1-3 73910 RSH Nualart, David

APPT- KULC APPT - LAWRENCE

1-3 65248 RSH Oh, Myunghyun

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1-3 65995 RSH Pasik-Duncan, Bozenna

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1-3 62137 RSH Porter, Jack

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1-3 62138 RSH Purnaprajna, Bangere

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1-3 62139 RSH Shao, Shuanglin

APPT- KULC APPT - LAWRENCE

1-3 68233 RSH Sheu, Albert

APPT- KULC APPT - LAWRENCE

1-3 62140 RSH Soo, Terry

APPT- KULC APPT - LAWRENCE

1-3 70215 RSH Stanislavova, Milena

APPT- KULC APPT - LAWRENCE

1-3 65310 RSH Stefanov, Atanas

APPT- KULC APPT - LAWRENCE

1-3 65089 RSH Talata, Zsolt

APPT- KULC APPT - LAWRENCE

1-3 65996 RSH Torres, Rodolfo

APPT- KULC APPT - LAWRENCE

1-3 62141 RSH Tu, Xuemin

APPT- KULC APPT - LAWRENCE

1-3 68234 RSH Van Vleck, Erik

APPT- KULC APPT - LAWRENCE

1-3 64021 RSH Witt, Emily

APPT- KULC APPT - LAWRENCE

1-3 71140 RSH Xu, Hongguo

APPT- KULC APPT - LAWRENCE

1-3 66543 - MATH 800 Complex Analysis I
- Cauchy's theorem and contour integration; the argument principle; maximum modulus principle; Schwarz symmetry principle; analytic continuation; monodromy theorem; applications to the gamma function and Riemann's zeta function; entire and meromorphic functions; conformal mapping; Riemann mapping theorem; univalent functions. Prerequisite: MATH 766 or concurrently with MATH 766. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Stefanov, Atanas

TuTh 11:00-12:15 PM SNOW 454 - LAWRENCE

3 62142 - MATH 801 Complex Analysis II
- Continuation of MATH 800. Prerequisite: MATH 800. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 802 Set Theory
- Axiomatic set theory; transfinite induction; regularity and choice; ordinal and cardinal arithmetic; miscellaneous additional topics (e.g., extra axioms such as GCH or MA; infinite combinatorics; large cardinals). Prerequisite: MATH 765 or MATH 791, or concurrent enrollment in MATH 765 or MATH 791, or equivalent evidence of mathematical maturity. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 810 Real Analysis and Measure Theory I
- Measurable spaces and functions. Measure spaces and integration. Extensions of set functions, outer measures, Lebesgue measure. Signed and complex measures. Differentiation of set functions. Miscellaneous additional topics and applications. Prerequisite: MATH 766. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 811 Real Analysis and Measure Theory II
- Continuation of MATH 810. Prerequisite: MATH 810. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 820 Introduction to Topology
- General topology. Set theory; topological spaces; connected sets; continuous functions; generalized convergence; product and quotient spaces; embedding in cubes; metric spaces and metrization; compact spaces; function spaces. Prerequisite: MATH 765. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 821 Algebraic Topology I
- The fundamental group and covering spaces (including classification); compact surfaces; homology theory, computations (including homotopy invariance) and applications (including Brouwer fixed point theorem); introduction to cohomology theory. Prerequisite: MATH 790 and MATH 791 and MATH 820, or permission of instructor. LEC.
- MATH 822 Algebraic Topology II
- Review of simplicial homology; Lefschetz fixed point theorem and degree theory; singular, cellular, and axiomatic homology; Jordan Brouwer separation theorems; universal coefficient theorems, products in cohomology, homotopy groups, and the Hurewicz Theorem. Prerequisite: MATH 821. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 824 Algebraic Combinatorics
- An introduction to the fundamental structures and methods of modern algebraic combinatorics. Topics include partially ordered sets and lattices, matroids, simplicial complexes, polytopes, hyperplane arrangements, partitions and tableaux, and symmetric functions. Prerequisite: MATH 724 and MATH 791, or permission of the instructor. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 830 Abstract Algebra
- A study of some structures, theorems, and techniques in algebra whose use has become common in many branches of mathematics. Prerequisite: MATH 790 and MATH 791. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 831 Abstract Algebra
- Continuation of MATH 830. Prerequisite: MATH 830. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Dao, Hailong

MWF 01:00-01:50 PM SNOW 156 - LAWRENCE

3 75767 - MATH 840 Differentiable Manifolds
- Multilinear algebra of finite dimensional vector spaces over fields; differentiable structures and tangent and tensor bundles; differentiable mappings and differentials; exterior differential forms; curves and surfaces as differentiable manifolds; affine connections and covariant differentiation; Riemannian manifolds. Prerequisite: MATH 765 and MATH 790. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 850 Differential Equations and Dynamical Systems
- Discrete and differentiable dynamical systems with an emphasis on the qualitative theory. Topics to be covered include review of linear systems, existence and uniqueness theorems, flows and discrete dynamical systems, linearization (Hartman-Grobman theorem), stable and unstable manifolds, Poincare sections, normal forms, Hamiltonian systems, and an introduction to bifurcation theory and chaos. Prerequisite: MATH 320 and MATH 766, or permission of instructor. LEC.
- MATH 851 Topics in Dynamical Systems
- Topics to be covered include complex dynamical systems, perturbation theory, nonlinear analysis of time series, chaotic dynamical systems, and numerical methods as dynamical systems. This course may be repeated for credit. Prerequisite: MATH 850 or permission of instructor. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Mantzavinos, Dionysios

TuTh 09:30-10:45 AM SNOW 564 - LAWRENCE

3 75768 - MATH 865 Stochastic Processes I
- Markov chains; Markov processes; diffusion processes; stationary processes. Emphasis is placed on applications: random walks; branching theory; Brownian motion; Poisson process; birth and death processes. Prerequisite: MATH 627 and MATH 765. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Talata, Zsolt

TuTh 09:30-10:45 AM SNOW 456 - LAWRENCE

3 66924 - MATH 866 Stochastic Processes II
- This is a second course in stochastic processes, focused on stochastic calculus with respect to a large class of semi-martingales and its applications to topics selected from classical analysis (linear PDE), finance, engineering, and statistics. The course will start with basic properties of martingales and random walks and then develop into the core program on Ito's stochastic calculus and stochastic differential equations. These techniques provide useful and important tools and models in many pure and applied areas. Prerequisite: MATH 727 and MATH 865. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 870 The Analysis of Variance
- The general linear hypothesis with fixed effects; the Gauss-Markov theorem, confidence ellipsoids, and tests under normal theory; multiple comparisons and the effect of departures from the underlying assumptions; analysis of variance for various experimental designs and analysis of covariance. Prerequisite: MATH 628 or MATH 728, and either MATH 590 or MATH 790. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 872 Multivariate Statistical Analysis
- The multivariate normal distribution; tests of hypotheses on means and covariance matrices; estimation; correlation; multivariate analysis of variance; principal components; canonical correlation. Prerequisite: MATH 628 or MATH 728, and either MATH 590 or MATH 790. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 874 Statistical Decision Theory
- Game theory, admissible decision functions and complete class theorems; Bayes and minimax solutions; sufficiency; invariance; multiple decision problems; sequential decision problems. Prerequisite: MATH 628 and MATH 766. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 881 Advanced Numerical Linear Algebra
- Advanced topics in numerical linear algebra including pseudo-spectra, rounding error analysis and perturbation theory, numerical methods for problems with special structure, and numerical methods for large scale problems. Prerequisite: Math 781, 782, 790, or permission of the instructor. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 882 Advanced Numerical Differential Equations
- Advanced course in the numerical solution of ordinary and partial differential equations including modern numerical methods and the associated analysis. Prerequisite: MATH 781, 782, 783, or permission of the instructor. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Tu, Xuemin

MW 11:00-12:15 PM SNOW 456 - LAWRENCE

3 75769 - MATH 890 Fourier Analysis
- Introduction to modern techniques in Fourier Analysis in the Euclidean setting with emphasis in the study of functions spaces and operators acting on them. Topics may vary from year to year and include, among others, distribution theory, Sobolev spaces, estimates for fractional integrals and fractional derivatives, wavelets, and some elements of CalderÃ³n-Zygmund theory. Applications in other areas of mathematics, in particular partial differential equations and signal analysis, will be presented based on the instructor's and the students' interests. Prerequisite: Math 810 and Math 800, or instructor's permission. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Shao, Shuanglin

TuTh 01:00-02:15 PM SNOW 256 - LAWRENCE

3 75772 - MATH 896 Master's Research Component
- RSH.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # RSH Bayer, Margaret

APPT- KULC APPT - LAWRENCE

1-6 62143 RSH Chen, Geng

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1-6 73917 RSH Dao, Hailong

APPT- KULC APPT - LAWRENCE

1-6 66916 RSH Duncan, Tyrone

APPT- KULC APPT - LAWRENCE

1-6 62144 RSH Feng, Jin

APPT- KULC APPT - LAWRENCE

1-6 65912 RSH Gavosto, Estela

APPT- KULC APPT - LAWRENCE

1-6 62145 RSH Gay, A.

APPT- KULC APPT - LAWRENCE

1-6 62146 RSH Hernandez, Daniel

APPT- KULC APPT - LAWRENCE

1-6 72308 RSH Huang, Weizhang

APPT- KULC APPT - LAWRENCE

1-6 62147 RSH Jiang, Yunfeng

APPT- KULC APPT - LAWRENCE

1-6 70189 RSH Johnson, Mathew

APPT- KULC APPT - LAWRENCE

1-6 68236 RSH Kachi, Yasuyuki

APPT- KULC APPT - LAWRENCE

1-6 66510 RSH Katz, Daniel

APPT- KULC APPT - LAWRENCE

1-6 62148 RSH Lang, Jeffrey

APPT- KULC APPT - LAWRENCE

1-6 62149 RSH Liu, Weishi

APPT- KULC APPT - LAWRENCE

1-6 62150 RSH Liu, Zhipeng

APPT- KULC APPT - LAWRENCE

1-6 73918 RSH Mandal, Satyagopal

APPT- KULC APPT - LAWRENCE

1-6 62151 RSH Mantzavinos, Dionysios

APPT- KULC APPT - LAWRENCE

1-6 73919 RSH Martin, Jeremy

APPT- KULC APPT - LAWRENCE

1-6 65270 RSH Miedlar, Agnieszka

APPT- KULC APPT - LAWRENCE

1-6 73920 RSH Nualart, David

APPT- KULC APPT - LAWRENCE

1-6 65249 RSH Oh, Myunghyun

APPT- KULC APPT - LAWRENCE

1-6 65997 RSH Pasik-Duncan, Bozenna

APPT- KULC APPT - LAWRENCE

1-6 62152 RSH Porter, Jack

APPT- KULC APPT - LAWRENCE

1-6 62153 RSH Purnaprajna, Bangere

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1-6 62154 RSH Shao, Shuanglin

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1-6 68237 RSH Sheu, Albert

APPT- KULC APPT - LAWRENCE

1-6 62155 RSH Soo, Terry

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1-6 70216 RSH Stanislavova, Milena

APPT- KULC APPT - LAWRENCE

1-6 65311 RSH Stefanov, Atanas

APPT- KULC APPT - LAWRENCE

1-6 67652 RSH Talata, Zsolt

APPT- KULC APPT - LAWRENCE

1-6 65998 RSH Torres, Rodolfo

APPT- KULC APPT - LAWRENCE

1-6 62156 RSH Tu, Xuemin

APPT- KULC APPT - LAWRENCE

1-6 68238 RSH Van Vleck, Erik

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1-6 64022 RSH Witt, Emily

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1-6 71141 RSH Xu, Hongguo

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1-6 66544 - MATH 899 Master's Thesis
- THE.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # THE Bayer, Margaret

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1-10 69025 THE Chen, Geng

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1-10 73921 THE Dao, Hailong

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1-10 66917 THE Duncan, Tyrone

APPT- KULC APPT - LAWRENCE

1-10 62157 THE Feng, Jin

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1-10 65913 THE Gavosto, Estela

APPT- KULC APPT - LAWRENCE

1-10 62158 THE Gay, A.

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1-10 62159 THE Hernandez, Daniel

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1-10 72309 THE Huang, Weizhang

APPT- KULC APPT - LAWRENCE

1-10 62160 THE Jiang, Yunfeng

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1-10 70190 THE Johnson, Mathew

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1-10 68239 THE Kachi, Yasuyuki

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1-10 66511 THE Katz, Daniel

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1-10 62161 THE Lang, Jeffrey

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1-10 62162 THE Liu, Weishi

APPT- KULC APPT - LAWRENCE

1-10 62163 THE Liu, Zhipeng

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1-10 73922 THE Mandal, Satyagopal

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1-10 62164 THE Mantzavinos, Dionysios

APPT- KULC APPT - LAWRENCE

1-10 73923 THE Martin, Jeremy

APPT- KULC APPT - LAWRENCE

1-10 65271 THE Miedlar, Agnieszka

APPT- KULC APPT - LAWRENCE

1-10 73924 THE Nualart, David

APPT- KULC APPT - LAWRENCE

1-10 65250 THE Oh, Myunghyun

APPT- KULC APPT - LAWRENCE

1-10 65999 THE Pasik-Duncan, Bozenna

APPT- KULC APPT - LAWRENCE

1-10 62165 THE Porter, Jack

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1-10 62166 THE Purnaprajna, Bangere

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1-10 62167 THE Shao, Shuanglin

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1-10 68240 THE Sheu, Albert

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1-10 62168 THE Soo, Terry

APPT- KULC APPT - LAWRENCE

1-10 70217 THE Stanislavova, Milena

APPT- KULC APPT - LAWRENCE

1-10 65312 THE Stefanov, Atanas

APPT- KULC APPT - LAWRENCE

1-10 67653 THE Talata, Zsolt

APPT- KULC APPT - LAWRENCE

1-10 66000 THE Torres, Rodolfo

APPT- KULC APPT - LAWRENCE

1-10 62169 THE Tu, Xuemin

APPT- KULC APPT - LAWRENCE

1-10 68241 THE Van Vleck, Erik

APPT- KULC APPT - LAWRENCE

1-10 64023 THE Witt, Emily

APPT- KULC APPT - LAWRENCE

1-10 71142 THE Xu, Hongguo

APPT- KULC APPT - LAWRENCE

1-10 65030 - MATH 905 Several Complex Variables
- Holomorphic functions in several complex variables, Cauchy's integral for poly-discs, multivariable Taylor series, maximum modulus theorem. Further topics may include: removable singularities, extension theorems, Cauchy-Riemann operator, domains of holomorphy, special domains and algebraic properties of rings of analytic functions. Prerequisite: MATH 800. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 910 Algebraic Curves
- Algebraic sets, varieties, plane curves, morphisms and rational maps, resolution of singularities, Reimann-Roch theorem. Prerequisite: MATH 790 and MATH 791. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 915 Homological Algebra
- Injective and projective resolutions, homological dimension, chain complexes and derived functors (including Tor and Ext). Prerequisite: MATH 830 and MATH 831, or consent of instructor. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 920 Lie Groups and Lie Algebras
- General properties of Lie groups, closed subgroups, one-parameter subgroups, homogeneous spaces, Lie bracket, Lie algebras, exponential map, structure of semi-simple Lie algebras, invariant forms, Maurer-Cartan equation, covering groups, spinor groups. Prerequisite: MATH 766 and MATH 790 and MATH 791. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 930 Topics in General Topology
- Paracompact spaces, uniform spaces, topology of continua, Peano spaces, Hahn-Mazurkiewicz theorem, dimension theory, and theory of retracts. Prerequisite: MATH 820. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 940 Advanced Probability
- Probability measures, random variables, distribution functions, characteristic functions, types of convergence, central limit theorem. Laws of large numbers and other limit theorems. Conditional probability, Markov processes, and other topics in the theory of stochastic processes. Prerequisite: MATH 811. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 950 Partial Differential Equations
- Introduction; equations of mathematical physics; classification of linear equations and systems. Existence and uniqueness problems for elliptic, parabolic, and hyperbolic equations. Eigenvalue problems for elliptic operators; numerical methods. Prerequisite: MATH 766. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 951 Advanced Partial Differential Equations II
- The course uses functional analytic techniques to further develop various aspects of the modern framework of linear and nonlinear partial differential equations. Sobolev spaces, distributions and operator theory are used in the treatment of linear second-order elliptic, parabolic, and hyperbolic equations. In particular we discuss the kind of potential, diffusion and wave equations that arise in inhomogeneous media, with an emphasis on the solvability of equations with different initial/boundary conditions. Then, we will survey the theory of semigroup of operators, which is one of the main tools in the study of the long-time behavior of solutions to nonlinear PDE. The theories and applications encountered in this course will create a strong foundation for studying nonlinear equations and nonlinear science in general. Prerequisite: MATH 950 or permission of the instructor. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 960 Functional Analysis
- Topological vector spaces, Banach spaces, basic principles of functional analysis. Weak and weak-topologies, operators and adjoints. Hilbert spaces, elements of spectral theory. Locally convex spaces. Duality and related topics. Applications. Prerequisite: MATH 810 and MATH 820 or concurrent with MATH 820. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 961 Functional Analysis
- Continuation of MATH 960. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 963 C*-Algebras
- The basics of C*-algebras, approximately finite dimensional C*-algebras, irrational rotation algebras, C*-algebras of isometries, group C*-algebras, crossed products C*-algebras, extensions of C*-algebras and the BDF theory. Prerequisite: MATH 811 or MATH 960, or consent of instructor. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 970 Analytic K-Theory
- K0 for rings, spectral theory in Banach algebras, K1 for Banach algebras, Bott periodicity and six-term cyclic exact sequence. Prerequisite: MATH 790 and MATH 791 and MATH 960. LEC.
**The class is not offered for the Spring 2019 semester.** - MATH 990 Seminar: _____
- LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Witt, Emily

TuTh 02:30-03:20 PM SNOW 306 - LAWRENCE

1-10 62170 LEC Stefanov, Atanas

W 03:00-03:50 PM SNOW 306 - LAWRENCE

1-10 62171 LEC Duncan, Tyrone

Tu 04:00-04:50 PM SNOW 408 - LAWRENCE

1-10 65034 LEC Van Vleck, Erik

F 02:00-02:50 PM SNOW 306 - LAWRENCE

1-10 69026 LEC Martin, Jeremy

F 04:00-04:50 PM SNOW 408 - LAWRENCE

1-10 65445 LEC Miedlar, Agnieszka

W 02:00-02:50 PM SNOW 306 - LAWRENCE

1-10 65055 LEC Kachi, Yasuyuki

F 02:00-02:50 PM SNOW 408 - LAWRENCE

1-10 62172 LEC Nualart, David

W 04:00-04:50 PM SNOW 306 - LAWRENCE

1-10 65033 LEC Sheu, Albert

M 02:00-02:50 PM SNOW 306 - LAWRENCE

W 02:00-02:50 PM SNOW 408 - LAWRENCE

1-10 68909 LEC Pasik-Duncan, Bozenna

M 04:00-04:50 PM SNOW 306 - LAWRENCE

1-10 62173 - MATH 993 Readings in Mathematics
- RSH.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # RSH Bayer, Margaret

APPT- KULC APPT - LAWRENCE

1-10 62174 RSH Chen, Geng

APPT- KULC APPT - LAWRENCE

1-10 73925 RSH Dao, Hailong

APPT- KULC APPT - LAWRENCE

1-10 66918 RSH Duncan, Tyrone

APPT- KULC APPT - LAWRENCE

1-10 62175 RSH Feng, Jin

APPT- KULC APPT - LAWRENCE

1-10 65914 RSH Gavosto, Estela

APPT- KULC APPT - LAWRENCE

1-10 62176 RSH Hernandez, Daniel

APPT- KULC APPT - LAWRENCE

1-10 72310 RSH Huang, Weizhang

APPT- KULC APPT - LAWRENCE

1-10 62177 RSH Jiang, Yunfeng

APPT- KULC APPT - LAWRENCE

1-10 70191 RSH Johnson, Mathew

APPT- KULC APPT - LAWRENCE

1-10 68242 RSH Kachi, Yasuyuki

APPT- KULC APPT - LAWRENCE

1-10 66512 RSH Katz, Daniel

APPT- KULC APPT - LAWRENCE

1-10 62178 RSH Lang, Jeffrey

APPT- KULC APPT - LAWRENCE

1-10 62179 RSH Liu, Weishi

APPT- KULC APPT - LAWRENCE

1-10 62180 RSH Liu, Zhipeng

APPT- KULC APPT - LAWRENCE

1-10 73926 RSH Mandal, Satyagopal

APPT- KULC APPT - LAWRENCE

1-10 62181 RSH Mantzavinos, Dionysios

APPT- KULC APPT - LAWRENCE

1-10 73928 RSH Martin, Jeremy

APPT- KULC APPT - LAWRENCE

1-10 65273 RSH Miedlar, Agnieszka

APPT- KULC APPT - LAWRENCE

1-10 73927 RSH Nualart, David

APPT- KULC APPT - LAWRENCE

1-10 65251 RSH Oh, Myunghyun

APPT- KULC APPT - LAWRENCE

1-10 66001 RSH Pasik-Duncan, Bozenna

APPT- KULC APPT - LAWRENCE

1-10 62182 RSH Porter, Jack

APPT- KULC APPT - LAWRENCE

1-10 62183 RSH Purnaprajna, Bangere

APPT- KULC APPT - LAWRENCE

1-10 63960 RSH Shao, Shuanglin

APPT- KULC APPT - LAWRENCE

1-10 68243 RSH Sheu, Albert

APPT- KULC APPT - LAWRENCE

1-10 62184 RSH Soo, Terry

APPT- KULC APPT - LAWRENCE

1-10 70218 RSH Stanislavova, Milena

APPT- KULC APPT - LAWRENCE

1-10 65313 RSH Stefanov, Atanas

APPT- KULC APPT - LAWRENCE

1-10 65090 RSH Talata, Zsolt

APPT- KULC APPT - LAWRENCE

1-10 66002 RSH Torres, Rodolfo

APPT- KULC APPT - LAWRENCE

1-10 62185 RSH Tu, Xuemin

APPT- KULC APPT - LAWRENCE

1-10 68244 RSH Van Vleck, Erik

APPT- KULC APPT - LAWRENCE

1-10 64024 RSH Witt, Emily

APPT- KULC APPT - LAWRENCE

1-10 71143 RSH Xu, Hongguo

APPT- KULC APPT - LAWRENCE

1-10 66545 - MATH 996 Special Topics: _____
- Advanced courses on special topics; given as need arises. Prerequisite: Variable. LEC.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # LEC Liu, Zhipeng

TuTh 02:30-03:45 PM SNOW 456 - LAWRENCE

3 72305 LEC Gavosto, Estela

M 03:00-04:20 PM SNOW 256 - LAWRENCE

3 78940 LEC Martin, Jeremy

MWF 10:00-10:50 AM SNOW 302 - LAWRENCE

3 75774 - MATH 999 Doctoral Dissertation
- THE.
Spring 2019 Type Time/Place and Instructor Credit Hours Class # THE Bayer, Margaret

APPT- KULC APPT - LAWRENCE

1-10 62186 THE Dao, Hailong

APPT- KULC APPT - LAWRENCE

1-10 66919 THE Duncan, Tyrone

APPT- KULC APPT - LAWRENCE

1-10 62187 THE Feng, Jin

APPT- KULC APPT - LAWRENCE

1-10 65915 THE Gavosto, Estela

APPT- KULC APPT - LAWRENCE

1-10 62188 THE Huang, Weizhang

APPT- KULC APPT - LAWRENCE

1-10 62189 THE Johnson, Mathew

APPT- KULC APPT - LAWRENCE

1-10 68245 THE Kachi, Yasuyuki

APPT- KULC APPT - LAWRENCE

1-10 66513 THE Katz, Daniel

APPT- KULC APPT - LAWRENCE

1-10 62190 THE Lang, Jeffrey

APPT- KULC APPT - LAWRENCE

1-10 62191 THE Liu, Weishi

APPT- KULC APPT - LAWRENCE

1-10 68316 THE Liu, Zhipeng

APPT- KULC APPT - LAWRENCE

1-10 73931 THE Mandal, Satyagopal

APPT- KULC APPT - LAWRENCE

1-10 62192 THE Mantzavinos, Dionysios

APPT- KULC APPT - LAWRENCE

1-10 73932 THE Martin, Jeremy

APPT- KULC APPT - LAWRENCE

1-10 65272 THE Nualart, David

APPT- KULC APPT - LAWRENCE

1-10 65252 THE Oh, Myunghyun

APPT- KULC APPT - LAWRENCE

1-10 66003 THE Pasik-Duncan, Bozenna

APPT- KULC APPT - LAWRENCE

1-10 62193 THE Porter, Jack

APPT- KULC APPT - LAWRENCE

1-10 62194 THE Purnaprajna, Bangere

APPT- KULC APPT - LAWRENCE

1-10 69027 THE Shao, Shuanglin

APPT- KULC APPT - LAWRENCE

1-10 68246 THE Sheu, Albert

APPT- KULC APPT - LAWRENCE

1-10 62195 THE Soo, Terry

APPT- KULC APPT - LAWRENCE

1-10 75304 THE Stanislavova, Milena

APPT- KULC APPT - LAWRENCE

1-10 65314 THE Stefanov, Atanas

APPT- KULC APPT - LAWRENCE

1-10 67654 THE Talata, Zsolt

APPT- KULC APPT - LAWRENCE

1-10 66004 THE Torres, Rodolfo

APPT- KULC APPT - LAWRENCE

1-10 62196 THE Tu, Xuemin

APPT- KULC APPT - LAWRENCE

1-10 68247 THE Van Vleck, Erik

APPT- KULC APPT - LAWRENCE

1-10 64025 THE Xu, Hongguo

APPT- KULC APPT - LAWRENCE

1-10 66546