# Courses

##### Master course schedule by semester - Mathematical Sciences & Statistics

## MATH 50400 Real Analysis

- Credit Hours: 3
- Course Summary: Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the Riemann-Stieltjes integral, sequences and series of functions, uniform convergence, the Stone-Weierstrass theorem, equicontinuity, and the Arzela-Ascoli theorem. This is a second or intermediate course in analysis, with a fast review of introductory topics.
- Prerequisites: MATH 44400

## MATH 50500 Intermediate Abstract Algebra

- Credit Hours: 3
- Course Summary: Group theory with emphasis on concrete examples and applications. Field theory: ruler and compass constructions, Galois theory, and solvability of equations by radicals.
- Prerequisites: MATH 45300
- Semester(s) Offered: Summer(Even)
- Additional Information: Class only offered during Summer II of years ending in an even number.

## MATH 51000 Vector Calculus

- Credit Hours: 3
- Course Summary: Calculus of functions of several variables and of vector fields in orthogonal coordinate systems. Optimization problems, implicit function theorem, Green's theorem, Stokes's theorem, divergence theorems, and applications to engineering and the physical sciences.
- Prerequisites: MATH 26100
- Semester(s) Offered: as requested

## MATH 51100 Linear Algebra with Applications

- Credit Hours: 3
- Course Summary: Matrices, rank and inverse of a matrix, decomposition theorems, eigenvectors, unitary and similarity transformations on matrices.
- Prerequisites: MATH 26100
- Semester(s) Offered: Fall, Spring, Summer I
- Additional Information: Not open to students with credit in MATH 35100.

## STAT 51100 Statistical Methods I

- Credit Hours: 3
- Course Summary: Descriptive statistics; elementary probability; random variables and their distributions; expectation; normal, binomial, Poisson, and hypergeometric distributions; sampling distributions; estimation and testing of hypotheses; one-way analysis of variance; and correlation and regression.
- Prerequisites: MATH 16500
- Semester(s) Offered: Spring

## STAT 51200 Applied Regression Analysis

- Credit Hours: 3
- Course Summary: Inference in simple and multiple linear regression, estimation of model parameters, testing and prediction. Residual analysis, diagnostics and remedial measures. Multicollinearity. Model building, stepwise, and other model selection methods. Weighted least squares. Nonlinear regression. Models with qualitative independent variables. One-way analysis of variance. Orthogonal contrasts and multiple comparison tests. Use of existing statistical computing package.
- Prerequisites: STAT 51100
- Semester(s) Offered: Fall

## STAT 51300 Statistical Quality Control

- Credit Hours: 3
- Course Summary: Control charts and acceptance sampling, standard acceptance plans, continuous sampling plans, sequential analysis, and response surface analysis. Use of existing statistical computing packages.
- Prerequisites: STAT 51100
- Semester(s) Offered: Spring(Even)

## MATH 51400 Numerical Analysis

- Credit Hours: 3
- Course Summary: Numerical Analysis
- Prerequisites: MATH 26600
- Semester(s) Offered: Fall, Spring

## STAT 51400 Design of Experiments

- Credit Hours: 3
- Course Summary: Fundamentals, completely randomized design, and randomized complete blocks. Latin squares, multiclassification, factorial, nested factorial, incomplete blocks, fractional replications, confounding, general mixed factorial, split-plot, and optimum design. Use of existing statistical computing packages.
- Semester(s) Offered: Spring

## BIOS-S 515 Biostatistical Practicum

- Credit Hours: 1-3
- Course Summary: Real-world projects in biostatistics involving participation in consulting sessions, directed reading in the literature, research ethics, design of experiments, collection of data and applications of biostatistical methods. Detailed written and oral reports required.
- Prerequisites: STAT 52100; BIOS S527, S546; or consent of instructor
- Additional Information: May be repeated, up to 6 credits.

## STAT 51500 Statistical Consulting Problems

- Credit Hours: 1-3
- Course Summary: Consultation on real-world problems involving statistical analysis under the guidance of a faculty member. A detailed written report and an oral presentation are required. To earn credit for this course the project must have an academic component typically involving some creative application of statistical techniques in an on-going or recently concluded investigation under the supervision of a qualified researcher. To receive approval for this course, the student must write a short proposal describing the scope of the project, methodology to be used and the output to be developed. The student should also clearly state the exact role of all team members involved in the project and give a likely timetable for completion. The project supervisor must send a written consent to supervise the student's project and authorize dissemination of project results to the statistics faculty for their evaluation in determining grade.
- Prerequisites: Consent of advisor.
- Semester(s) Offered: Fall, Spring, Summer

## STAT 51600 Basic Probability and Applications

- Credit Hours: 3
- Course Summary: A first course in probability intended to serve as a foundation for statistics and other applications. Intuitive background; sample spaces and random variables; joint, conditional, and marginal distributions; special distributions of statistical importance; moments and moment generating functions; statement and application of limit theorems; and introduction to Markov chains.
- Prerequisites: MATH 26100; Instructor consent required for any undergraduate student
- Semester(s) Offered: Fall

## STAT 51700 Statistical Inference

- Credit Hours: 3
- Course Summary: A basic course in statistical theory covering standard statistical methods and their applications. Includes unbiased, maximum likelihood, and moment estimation; confidence intervals and regions; testing hypotheses for standard distributions and contingency tables; and introduction to nonparametric tests and linear regression.
- Prerequisites: STAT 51100 or 51600; Instructor consent required for any undergraduate student
- Semester(s) Offered: Spring

## MATH 51800 Advanced Discrete Mathematics

- Credit Hours: 3
- Course Summary: This course covers mathematics useful in analyzing computer algorithms. Topics include recurrence relations, evaluation of sums, integer functions, elementary number theory, binomial coefficients, generating functions, discrete probability, and asymptotic methods.
- Prerequisites: MATH 26600
- Additional Information: Course is offered in the Spring of odd numbered years.

## MATH 51900 Introduction to Probability (STAT 51900)

- Credit Hours: 3
- Course Summary: See STAT 51900.
- Prerequisites: MATH 26100
- Semester(s) Offered: Fall

## STAT 51900 Introduction to Probability

- Credit Hours: 3
- Course Summary: Sample spaces and axioms of probability, conditional probability, independence, random variables, distribution functions, moment generating and characteristics functions, special discrete and continuous distributions--univariate and multivariate cases, normal multivariate distributions, distribution of functions of random variables, modes of convergence and limit theorems, including laws of large numbers and central limit theorem.
- Prerequisites: MATH 26100
- Semester(s) Offered: Fall

## MATH 52000 Boundary Value Problems of Differential Equations

- Credit Hours: 3
- Course Summary: Sturm-Liouville theory, singular boundary conditions, orthogonal expansions, separation of variables in partial differential equations, and spherical harmonics.
- Prerequisites: MATH 26100 and 26600
- Semester(s) Offered: Spring

## STAT 52000 Time Series and Applications

- Credit Hours: 3
- Course Summary: A first course in stationary time series with applications in engineering, economics, and physical sciences. Stationarity, autocovariance function and spectrum; integral representation of a stationary time series and interpretation; linear filtering; transfer function models; estimation of spectrum; and multivariate time series. Use of existing statistical computing packages.
- Prerequisites: STAT 51900
- Semester(s) Offered: Spring

## STAT 52100 Statistical Computing

- Credit Hours: 3
- Semester(s) Offered: Fall

## MATH 52200 Qualitative Theory of Differential Equations

- Credit Hours: 3
- Course Summary: Nonlinear ODEs, critical points, stability and bifurcations, perturbations, averaging, nonlinear oscillations and chaos, and Hamiltonian systems.
- Prerequisites: MATH 26600 and MATH 35100
- Semester(s) Offered: Fall

## STAT 52200 Sampling and Survey Techniques

- Credit Hours: 3
- Course Summary: Survey designs; simple random, stratified, and systematic samples; systems of sampling; methods of estimation; ratio and regression estimates; and costs. Other related topics as time permits.
- Prerequisites: STAT 51200
- Semester(s) Offered: Fall

## MATH 52300 Introduction to Partial Differential Equations

- Credit Hours: 3
- Course Summary: Method of characteristics for quasilinear first-order equations, complete integral, Cauchy-Kowalewsky theory, classification of second-order equations in two variables, canonical forms, difference methods of hyperbolic and parabolic equations, and Poisson integral method for elliptic equations.
- Prerequisites: MATH 26600 and 26100 or 51000
- Semester(s) Offered: Fall

## STAT 52300 Categorical Data Analysis

- Credit Hours: 3
- Course Summary: Models generating binary and categorical response data, two-way classification tables, measures of association and agreement, goodness-of-fit tests, testing independence, large sample properties. General linear models, logistic regression, and probit and extreme value models. Loglinear models in two and higher dimensions; maximum likelihood estimation, testing goodness-of-fit, partitioning chi-square, and models for ordinal data. Model building, selection, and diagnostics. Other related topics as time permits. Computer applications using existing statistical software.
- Prerequisites: STAT 52800
- Semester(s) Offered: Spring

## STAT 52400 Applied Multivariate Analysis

- Credit Hours: 3
- Course Summary: Extension of univariate tests in normal populations to the multivariate case, equality of covariance matrices, multivariate analysis of variance, discriminant analysis and misclassification errors, canonical correlation, principal components, and factor analysis. Strong emphasis on the use of existing computer programs.
- Prerequisites: STAT 52800
- Semester(s) Offered: Fall

## MATH 52500 Introduction to Complex Analysis

- Credit Hours: 3
- Course Summary: Complex numbers and complex-valued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; and elementary conformal mapping. See Course Web Site for more information.
- Prerequisites: MATH 26100 and MATH 26600; Instructor consent required for any undergraduate student
- Semester(s) Offered: Fall

## STAT 52501 Generalized Linear Models

- Credit Hours: 3
- Course Summary: Generalized linear models, likelihood methods for data analysis, and diagnostic methods for assessing model assumptions. Methods covered include multiple regression, analysis of variance for completely randomized designs, binary and categorical response models, and hierarchical loglinear models for contingency tables.
- Prerequisites: STAT 52800
- Semester(s) Offered: Fall

## MATH 52600 Principles of Mathematical Modeling

- Credit Hours: 3
- Course Summary: Ordinary and partial differential equations of physical problems, simplification, dimensional analysis, scaling, regular and singular perturbation theory, variational formulation of physical problems, continuum mechanics, and fluid flow.
- Prerequisites: MATH 26600 and 42600
- Semester(s) Offered: Fall(Odd)

## BIOS-S 527 Introduction to Clinical Trials

- Credit Hours: 3
- Course Summary: Prepares biostatisticians for support of clinical trial projects. Topics: fundamental aspects of the appropriate design and conduct of medical experiments involving human subjects including ethics, design, sample size calculation, randomization, monitoring, data collection analysis and reporting of the results.
- Prerequisites: SSTAT 51200, exposure to survival analysis; or consent of instructor.
- Semester(s) Offered: Fall

## MATH 52800 Advanced Mathematics for Engineering and Physics II

- Credit Hours: 3
- Course Summary: Divergence theorem, Stokes's Theorem, complex variables, contour integration, calculus of residues and applications, conformal mapping, and potential theory.
- Prerequisites: MATH 53700
- Semester(s) Offered: Spring

## STAT 52800 Mathematical Statistics

- Credit Hours: 3
- Course Summary: Sufficiency and completeness, the exponential family of distributions, theory of point estimation, Cramer-Rao inequality, Rao-Blackwell Theorem with applications, maximum likelihood estimation, asymptotic distributions of ML estimators, hypothesis testing, Neyman-Pearson Lemma, UMP tests, generalized likelihood ratio test, asymptotic distribution of the GLR test, and sequential probability ratio test.
- Prerequisites: STAT 51900
- Semester(s) Offered: Spring

## STAT 52900 Applied Decision Theory and Bayesian Analysis

- Credit Hours: 3
- Course Summary: Foundation of statistical analysis, Bayesian and decision theoretic formulation of problems; construction of utility functions and quantifications of prior information; methods of Bayesian decision and inference, with applications; empirical Bayes; combination of evidence; and game theory and minimax rules, Bayesian design, and sequential analysis. Comparison of statistical paradigms.
- Prerequisites: STAT 52800
- Semester(s) Offered: Spring(Odd)

## BIOS-S 530 Statistical Methods in Bioinformatics and Computational Biology

- Credit Hours: 3
- Course Summary: Covers a broad range of statistical methods used in many areas of bioinformatics research, including sequence alignment, genome sequencing and gene finding, gene expression microarray analysis, transcriptional regulation and sequence motif finding, comparative genomics, and proteomics.
- Prerequisites: STAT 51200, 51900; or consent of instructor.
- Semester(s) Offered: Spring(Odd)

## MATH 53000 Functions of a Complex Variable I

- Credit Hours: 3
- Course Summary: Complex numbers, holomorphic functions, harmonic functions, and linear transformations. Power series, elementary functions, Riemann surfaces, contour integration, Cauchy's theorem, Taylor and Laurent series, and residues. Maximum and argument principles. Special topics. See Course Web Site for more information.
- Prerequisites: P or C: MATH 54400
- Semester(s) Offered: Spring

## MATH 53100 Functions of a Complex Variable II

- Credit Hours: 3
- Course Summary: Compactness and convergence in the space of analytic functions, Riemann mapping theorem, Weierstrass factorization theorem, Runge's theorem, Mittag-Leffler theorem, analytic continuation and Riemann surfaces, and Picard theorems.
- Prerequisites: MATH 53000
- Semester(s) Offered: Fall(Odd)
- Additional Information: Class is only offered during years ending in an even number.

## MATH 53200 Elements of Stochastic Processes (STAT 53200)

- Credit Hours: 3
- Course Summary: See course listing for STAT 53200.
- Prerequisites: STAT 51900
- Semester(s) Offered: Fall(Even)

## STAT 53200 Elements of Stochastic Processes

- Credit Hours: 3
- Course Summary: A basic course in stochastic models including discrete and continuous time processes, Markov chains, and Brownian motion. Introduction to topics such as Gaussian processes, queues and renewal processes, and Poisson processes. Application to economic models, epidemic models, and reliability problems.
- Prerequisites: STAT 51900
- Semester(s) Offered: Fall(Even)

## STAT 53300 Nonparametric Statistics

- Credit Hours: 3
- Course Summary: Binomial test for dichotomous data, confidence intervals for proportions, order statistics, one-sample signed Wilcoxon rank test, two-sample Wilcoxon test, two-sample rank tests for dispersion, and Kruskal-Wallis test for one-way layout. Runs test and Kendall test for independence, one- and two-sample Kolmogorov-Smirnov tests, and nonparametric regression.
- Prerequisites: STAT 51600
- Semester(s) Offered: Spring(Odd)

## MATH 53500 Theoretical Mechanics

- Credit Hours: 3
- Course Summary: Continuum mechanics deals with the analysis of the motion of materials modeled as a continuous mass rather than as discrete particles. Applications of continuum mechanics are ubiquitous in science and engineering, and are getting more and more popular in medicine too. The goal of this course is to study the basic principles of continuum mechanics for deformable bodies, including conservation laws and constitutive equations, while discussing the mathematical challenges in solving these equations analytically and/or numerically.
- Prerequisites: MATH 26600 and 35100 or 51100, or consent of the instructor
- Semester(s) Offered: Spring(Odd)

## STAT 53600 Introduction to Survival Analysis

- Credit Hours: 3
- Course Summary: Deals with the modern statistical methods for analyzing time-to-event data. Background theory is provided, but the emphasis is on the applications and the interpretations of results. Provides coverage of survivorship functions and censoring patterns; parametric models and likelihood methods, special life-time distributions; nonparametric inference, life-tables, estimation of cumulative hazard functions, and the Kaplan-Meier estimator; one- and two-sample nonparametric tests for censored data; and semiparametric proportional hazards regression Cox Regression, parameters' estimation, stratification, model fitting strategies, and model interpretations. Heavy use of statistical software such as Splus and SAS.
- Prerequisites: STAT 51700
- Semester(s) Offered: Spring

## MATH 53700 Applied Mathematics for Scientists and Engineers I

- Credit Hours: 3
- Course Summary: Covers theories, techniques, and applications of partial differential equations, Fourier transforms, and Laplace transforms. Overall emphasis is on applications to physical problems.
- Prerequisites: MATH 26100 and 26600
- Semester(s) Offered: Fall

## MATH 54400 Real Analysis and Measure Theory

- Credit Hours: 3
- Course Summary: Algebras of sets, real number system, Lebesgue measure, measurable functions, Lebesgue integration, differentiation, absolute continuity, Banach spaces, metric spaces, general measure and integration theory, and Riesz representation theorem.
- Prerequisites: MATH 44400
- Semester(s) Offered: Fall

## MATH 54500 Principles of Analysis II

- Credit Hours: 3
- Course Summary: Continues the study of measure theory begun in MATH 54400. See Course Web Site for more information.
- Prerequisites: MATH 54400
- Semester(s) Offered: Spring

## BIOS-S 546 Applied Logitudinal Data Analysis

- Credit Hours: 3
- Course Summary: Covers modern methods for analysis of repeated measures, correlated outcomes and longitudinal data. Topics: repeated measures ANOVA, random effects and growth curve models, generalized estimating equations (GEE) and generalized linear mixed models (GLMMs). Extensive use of statistical software, e.g. SAS, R.
- Prerequisites: STAT 51200, 51900; or consent of instructor.
- Semester(s) Offered: Spring

## MATH 54600 Introduction to Functional Analysis

- Credit Hours: 3
- Course Summary: Banach spaces, Hahn-Banach theorem, uniform boundedness principle, closed graph theorem, open mapping theorem, weak topology, and Hilbert spaces.
- Prerequisites: MATH 54500
- Semester(s) Offered: Fall (Odd)

## MATH 54700 Analysis for Teachers I

- Credit Hours: 3
- Course Summary: Set theory, logic, relations, functions, Cauchy's inequality, metric spaces, neighborhoods, and Cauchy sequence.
- Prerequisites: MATH 26100
- Semester(s) Offered: Summer (odd years) with sufficient student interest or as needed. See advisor.

## MATH 54900 Applied Mathematics for Secondary School Teachers

- Credit Hours: 3
- Course Summary: Applications of mathematics to problems in the physical sciences, social sciences, and the arts. Content varies.
- Prerequisites: MATH 26600 and MATH 35100
- Additional Information: May be repeated for credit with the consent of the instructor. Course is offered on an as needed basis.

## MATH 55200 Applied Computational Methods II

- Credit Hours: 3
- Course Summary: The first part of the course focuses on numerical integration techniques and methods for ODEs. The second part concentrates on numerical methods for PDEs based on finite difference techniques with brief surveys of finite element and spectral methods.
- Prerequisites: MATH 55900 and consent of instructor.
- Semester(s) Offered: Spring
- Additional Information: This course is available on an as-needed basis.

## MATH 55300 Introduction to Abstract Algebra

- Credit Hours: 3
- Course Summary: Group theory: finite abelian groups, symmetric groups, Sylow theorems, solvable groups, Jordan-H-lder theorem. Ring theory: prime and maximal ideals, unique factorization rings, principal ideal domains, Euclidean rings, and factorization in polynomial and Euclidean rings. Field theory: finite fields, Galois theory, and solvability by radicals.
- Prerequisites: MATH 45300
- Semester(s) Offered: Fall

## MATH 55400 Linear Algebra

- Credit Hours: 3
- Course Summary: Review of basics: vector spaces, dimension, linear maps, matrices, determinants, and linear equations. Bilinear forms, inner product spaces, spectral theory, and eigenvalues. Modules over principal ideal domain, finitely generated abelian groups, and Jordan and rational canonical forms for a linear transformation.
- Prerequisites: MATH 35100
- Semester(s) Offered: Spring

## MATH 55555 Introduction to Biomathematics

- Credit Hours: 3
- Course Summary: This course will broaden the horizon of pure and applied math graduate students in mathematical biosciences. Upon successful completion of this course, students will gain general knowledge of the mathematical methods used in various life-sciences applications. No special knowledge of biology is necessary, but students are expected to be familiar with ODE, PDE and linear algebra.
- Semester(s) Offered: Spring (Even)

## MATH 55900 Applied Computational Methods I

- Credit Hours: 3
- Course Summary: Computer arithmetic, interpolation methods, methods for nonlinear equations, methods for solving linear systems, special methods for special matrices, linear least square methods, methods for computing eigenvalues, iterative methods for linear systems; methods for systems of nonlinear equations.
- Prerequisites: MATH 26600 and MATH 35100 or MATH 51100
- Additional Information: Course is offered on an as needed basis.

## MATH 56100 Projective Geometry

- Credit Hours: 3
- Course Summary: Projective invariants, Desargues' theorem, cross-ratio, axiomatic foundation, duality, consistency, independence, coordinates, and conics.
- Prerequisites: MATH 35100
- Semester(s) Offered: Summer (Even) with sufficient student interest or as needed. See advisor.
- Additional Information: Class is available only during Summer II of years ending in an even number and alternates with MATH 56300.

## MATH 56200 Introduction to Differential Geometry and Topology

- Credit Hours: 3
- Course Summary: Smooth manifolds, tangent vectors, inverse and implicit function theorems, submanifolds, vector fields, integral curves, differential forms, the exterior derivative, DeRham cohomology groups, surfaces in E3, Gaussian curvature, two-dimensional Riemannian geometry, and Gauss-Bonnet and Poincare theorems on vector fields.
- Prerequisites: MATH 35100 and MATH 44500
- Semester(s) Offered: Spring(Even)

## MATH 56300 Advanced Geometry

- Credit Hours: 3
- Course Summary: Analysis of axiom systems, finite geometries, critique of Euclid; Hilbert's incidence, betweenness, congruence, and continuity axioms; non-Archimedean geometry, geometry over fields, segment arithmetic and area, non-Euclidean geometry.
- Prerequisites: MATH 30000 or consent of instructor.
- Semester(s) Offered: SummerII(Even)
- Additional Information: Class is available only during Summer II of years ending in an even number and alternates with MATH 56100.

## MATH 56700 Dynamical Systems I

- Credit Hours: 3
- Course Summary: Covers the basic notions and theorems of the theory of dynamical systems and their connections with other branches of mathematics. Topics covered include fundamental concepts and examples, one-dimensional systems, symbolic dynamics, topological entropy, hyperbolicity, structural stability, bifurcations, invariant measures, and ergodicity.
- Prerequisites: MATH 54500 and 57100
- Semester(s) Offered: Spring(Even)

## MATH 57100 Elementary Topology

- Credit Hours: 3
- Course Summary: Topological spaces, metric spaces, continuity, compactness, connectedness, separation axioms, nets, and function spaces.
- Prerequisites: MATH 44400
- Semester(s) Offered: Fall

## MATH 57200 Introduction to Algebraic Topology

- Credit Hours: 3
- Course Summary: Singular homology theory, Ellenberg-Steenrod axioms, simplicial and cell complexes, elementary homotopy theory, and Lefschetz fixed point theorem.
- Prerequisites: MATH 57100
- Semester(s) Offered: Spring (Odd)

## MATH 57400 Mathematical Physics I

- Credit Hours: 3
- Course Summary: Topics in special functions, representation theory, spectral theory, noncommutative geometry, mathematical foundations of statistical physics. The specific content of the course will vary from year to year, to be determined by the instructor.
- Prerequisites: MATH 54500 and 53000
- Semester(s) Offered: Fall

## MATH 57800 Mathematical Modeling of Physical Systems I

- Credit Hours: 3
- Course Summary: Linear systems modeling, mass-spring-damper systems, free and forced vibrations, applications to automobile suspension, accelerometer, seismograph, etc., RLC circuits, passive and active filters, applications to crossover networks and equalizers, nonlinear systems, stability and bifurcation, dynamics of a nonlinear pendulum, van der Pol oscillator, chemical reactor, etc., introduction to chaotic dynamics, identifying chaos, chaos suppression and control, computer simulations, and laboratory experiments.
- Prerequisites: MATH 26600, PHYS 15200, PHYS 25100, and consent of instructor
- Semester(s) Offered: Fall(Even)

## MATH 58100 Introduction to Logic for Teachers

- Credit Hours: 3
- Course Summary: Logical connectives, rules of sentential inference, quantifiers, bound and free variables, rules of inference, interpretations and validity, theorems in group theory, and introduction to set theory.
- Prerequisites: MATH 35100
- Semester(s) Offered: Summer (odd years) with sufficient student interest or as needed. See advisor.

## MATH 58300 History of Elementary Mathematics

- Credit Hours: 3
- Course Summary: A survey and treatment of the content of major developments of mathematics through the eighteenth century, with selected topics from more recent mathematics, including non-Euclidean geometry and the axiomatic method.
- Prerequisites: MATH 26100
- Semester(s) Offered: Spring (Even), Summer (Odd)

## MATH 58500 Mathematical Logic I

- Credit Hours: 3
- Course Summary: Formal theories for propositional and predicate calculus with study of models, completeness, and compactness. Formalization of elementary number theory; Turing machines, halting problem, and the undecidability of arithmetic.
- Prerequisites: MATH 35100 or an undergraduate proof course; MATH 58700 recommended

## MATH 58700 General Set Theory

- Credit Hours: 3
- Course Summary: An introduction to set theory, including both so-called "naive" and formal approaches, leading to a careful development using the Zermelo-Fraenkel axioms for set theory and an in-depth discussion of cardinal and ordinal numbers, the Axiom of Choice, and the Continuum Hypothesis. Proofs form a major part of the course and of the homework assignments.
- Prerequisites: MATH 35100 or an equivalent course in Linear Algebra

## MATH 58800 Mathematical Modeling of Physical Systems II

- Credit Hours: 3
- Course Summary: Depending on the interests of the students, the content may vary from year to year. Emphasis will be on mathematical modeling of a variety of physical systems. Topics will be chosen from the volumes Mathematics in Industrial Problems by Avner Friedman. Researchers from local industries will be invited to present real-world applications. Each student will undertake a project in consultation with one of the instructors or an industrial researcher.
- Prerequisites: MATH 57800

## BIOS-S 598 Topics in Biostatistical Methods

- Credit Hours: 1-3
- Course Summary: Directed study and reports for students who wish to undertake individual reading and study on approved topics.
- Prerequisites: Consent of advisor.

## MATH 59800 Topics in Mathematics

- Credit Hours: 1-5
- Course Summary: Directed study and reports for students who wish to undertake individual reading and study on approved topics.
- Prerequisites: By arrangement.
- Semester(s) Offered: Fall, Spring, Summer

## MATH 61100 Methods of Applied Mathematics I

- Credit Hours: 3
- Course Summary: Introduction to Banach and Hilbert spaces, linear operators, spectral theory of compact linear operators, applications to linear integral equations and to regular Sturm-Liouville problems for ordinary differential equations, boundary value problems, Green's functions, distributions, Fourier transforms, classical PDEs (Laplace, heat, wave equations) of mathematical physics, spectral theory integral equations, and Fredholm Theory.
- Prerequisites: MATH 26600 and 35100

## MATH 61200 Methods of Applied Mathematics II

- Credit Hours: 3
- Course Summary: Continuation of Banach and Hilbert spaces, linear operators, spectral theory of compact linear operators, applications to linear integral equations and to regular Sturm-Liouville problems for ordinary differential equations, boundary value problems, Green's functions, distributions, Fourier transforms, classical PDEs (Laplace, heat, wave equations) of mathematical physics, Fredholm theory.
- Prerequisites: MATH 61100

## STAT 61900 Probability Theory

- Credit Hours: 3
- Course Summary: Probability Theory is the Foundation of statistical methodologies, which is fundamental in the practice of science. From this course students will get a precise mathematical understanding of probabilities and sigma-algebras, random weak convergence, characteristic functions, the central limit theorem, Lobesgue decomposition, conditioning and martingales.
- Prerequisites: STAT 51900
- Semester(s) Offered: Fall

## BIOS-S 621 Advanced Statistical Computing

- Credit Hours: 3
- Course Summary: This course covers selected computational techniques useful in advanced statistical applications and statistical research, such as methods for solving linear equations, numerical optimization, numerical integration, Bayesion methods, bootstrap methods and stochastic search algorithms.
- Prerequisites: STAT 52100; experience with R/S plus programming.
- Semester(s) Offered: Spring

## MATH 62600 Mathematical Formulation of Physical Problems I

- Credit Hours: 3
- Course Summary: Nature of applied mathematics, deterministic systems and ordinary differential equations, random processes and partial differential equations, Fourier analysis, dimensional analysis and scaling.
- Prerequisites: Advanced calculus or vector calculus, partial differential equations, linear algebra

## BIOS-S 627 Statistics in Pharmaceutical Research

- Credit Hours: 3
- Course Summary: An overview of the drug development process, including the various phases of development from pre-clinical to post-marketing. Topics: statistical issues in design, study monitoring, analysis and reporting. Additional topics may include regulatory and statistical aspects of population pharmacokinetics and real world applications.
- Prerequisites: STAT 51200; BIOS S527, S546.

## MATH 62700 Mathematical Formulation of Physical Problems II

- Credit Hours: 3
- Course Summary: Theories of continuous fields, continuous medium, field equations of continuum mechanics, inviscid fluid flow, viscous flow, turbulence. Additional topics to be dicussed include application of the theory of dynamical systems, methods for analysis of nonlinear ordinary and partial differential equations, and others. This course is an advancement of topics covered in MATH 62600.
- Prerequisites: MATH 62600

## STAT 62800 Advanced Statistical Inference

- Credit Hours: 3
- Course Summary: Real analysis for inference, statistics and subfields, conditional expectations and probability distributions, UMP tests with applications to normal distributions and confidence sets, invariance, asymptotic theory of estimation and likelihood based inference, U-statistics, Edgeworth expansions, saddle point method.
- Prerequisites: STAT 51900, 52800 Concurrent: STAT 61900
- Semester Offered: Spring - odd years

## BIOS-S 636 Advanced Survival Analysis

- Credit Hours: 3
- Course Summary: Discusses the theoretical basis of concepts and methodologies associated with survival data and censoring, nonparametric tests, and competing risk models. Much of the theory is developed using counting processes and martingale methods. Material is drawn from recent literature.
- Prerequisites: STAT 62800
- Semester(s) Offered: Spring

## BIOS-S 646 Advanced Generalized Linear Models

- Credit Hours: 3
- Course Summary: Presents classical and modern approaches to the analysis of multivariate observations, repeated measures, and longitudinal data. Topics include the multivariate normal distribution, Hotelling's T2, MANOVA, the multivariate linear model, random effects and growth curve models, generalized estimating equations, statistical analysis of multivariate categorical outcomes, and estimation with missing data. Discusses computational issues for both traditional and new methodologies.
- Prerequisites: BIOS S546
- Semester(s) Offered: Fall

## MATH 64600 Functional Analysis

- Credit Hours: 3
- Course Summary: Advanced topics in functional analysis, varying from year to year at the discretion of the instructor.
- Prerequisites: MATH 54600
- Semester(s) Offered: Spring(Even)

## MATH 66700 Dynamical Systems II

- Credit Hours: 3
- Course Summary: Topics in dynamics. Continuation of MATH 56700. See Course Web Site for more information.
- Prerequisites: MATH 56700
- Semester(s) Offered: Fall(Even)

## MATH 67200 Algebraic Topology I

- Credit Hours: 3
- Course Summary: Continuation of MATH 57200; cohomology, homotopy groups, fibrations, and further topics.
- Prerequisites: MATH 57200

## MATH 67300 Algebraic Topology II

- Credit Hours: 3
- Course Summary: Continuation of MATH 67200, covering further advanced topics in algebraic and differential topology such as K-theory and characteristic classes.
- Prerequisites: MATH 67200

## MATH 67400 Mathematical Physics II

- Credit Hours: 3
- Course Summary: Topics in inverse spectrum and scattering problems and their applications to the theory of solitons, spectral theory of difference equations and orthogonal polynomials, geometric quantization, and rigorous results in statistical physics, quantum field theory and random processes. The specific content of the course varies from year to year, to be determined by the instructor.
- Prerequisites: MATH 57400
- Semester(s) Offered: Spring

## MATH 69200 Topics in Applied Mathematics

- Credit Hours: 1-3
- Course Summary: Research topics of current interest in Applied Mathematics to be chosen by the instructor.

## MATH 69300 Topics in Analysis

- Credit Hours: 1-3
- Course Summary: Research topics of current interest in Analysis to be chosen by the instructor.

## MATH 69400 Topics in Differential Equations

- Credit Hours: 1-3
- Course Summary: Research topics in Differential Equations related to Physics and Engineering. Topics of current interest will be chosen by the instructor.

## MATH 69700 Topics in Topology

- Credit Hours: 1-3
- Course Summary: Research topics in Topology and their relationships to other branches of Mathematics. Topics of current interest will be chosen by the instructor.

## BIOS-S 698 Topics in Biostatistical Methods

- Credit Hours: 1-3
- Course Summary: Directed study and reports for students who wish to undertake individual reading and study on approved topics.
- Prerequisites: Consent of Instructor
- Semester(s) Offered: Fall, Spring, Summer

## STAT 69800 Research M.S. Thesis

- Credit Hours: 6
- Course Summary: M.S. thesis in Applied Statistics
- Prerequisites: Consent of Instructor
- Semester(s) Offered: Fall, Spring, Summer

## BIOS-S 699 Thesis/Research

- Credit Hours: 1-15
- Course Summary: Research required by the graduate students for the sole purpose of writing a Ph.D. Dissertation.
- Prerequisites: Must have been admitted to candidacy. See advisor for more information
- Semester(s) Offered: Fall, Spring, Summer

## MATH 69900 Research Ph.D. Thesis

- Credit Hours: Arranged
- Prerequisites: Consent of Instructor
- Semester(s) Offered: Fall, Spring, Summer

Music major makes noteworthy transition to math scholar

Karl Liechty 2010 Alumnus, Ph.D. Mathematics, Post-Doc, University of Michigan