## Courses

### CPLX 701. Mathematical Foundations for Complex Systems (2)

*Prerequisite: Consent of the graduate advisor*. This course provides essential mathematical tools for the study of complex systems. Topics include vector calculus, linear algebra and aspects of differential equations and partial differential equations.

### CPLX 702. Physics Foundations for Complex Systems (2)

*Prerequisite: Consent of the graduate advisor*. This course introduces physical approaches to dealing with complex, many-body systems. Two distinct and complementary frameworks are presented: analytical mechanics and statistical physics. Core concepts include Lagrangian and Hamiltonian formulations of mechanics, phase space, nonlinear dynamics, chaos, fractals, free energy, entropy, partition functions and statistical ensembles.

### CPLX 703. Chemistry Foundations for Complex Systems (2)

*Prerequisite: Consent of the graduate advisor*. The first part of the course will cover nonlinear chemical kinetics, control of chemical reactions, self-assembly at microscopic and macroscopic levels, and development of new techniques for materials synthesis. In the second part, quantum chemical models for describing large systems and their interaction with the surroundings will be introduced.

### CPLX 704. Biology Foundations for Complex Systems (2)

*Prerequisite: Consent of the graduate advisor*. The course will explore how to analyze biology from a systems-level point of view. Students will explore design principles in biology, including plasticity, exploratory behavior, weak-linkage, constraints that deconstrain, robustness, (non)optimality and evolvability.

### CPLX 705. Computer Science Foundations for Complex Systems (2)

*Prerequisite: Consent of the graduate advisor*. Overview of computer science topics relevant to complex systems, including software development, design of algorithms, computer simulation, computer and sensor networks, social networks and agent-based systems.

### CPLX 706. Engineering Foundations for Complex Systems (2)

*Prerequisite: Consent of the graduate advisor*. This course introduces the principles and methods of complex systems engineering. The course is organized as a progression through the systems engineering processes of analysis, design, implementation and deployment with consideration of verification and validation throughout. Case studies and guest lectures in each phase present best practice in the field and both successes and failures are considered. Lectures will include modeling of engineering system performance and constraints; formulating systems of design rules; optimization algorithms; solver software. Students will work as an integrated conceptual design team. Complex systems engineering standards and selected journal articles will serve as a basis for readings. The course is relevant to all professions associated with the introduction of complex human-made systems.

### CPLX 710A. Complex Systems I (4)

*Prerequisites: Passing preliminary examination and graduate advisor consent*. This course provides an overview of complex systems and describes theoretical, numerical and computational approaches to defining, analyzing and solving applied problems in complex systems.

### CPLX 710B. Complex Systems II (4)

*Prerequisites: CPLX 710A, passing preliminary examination and graduate advisor consent*. Hands-on activities on complex systems topics. Examples of course project topics include complex networked systems (sensor networks and social networks) and agent-based modeling (genetic programming and evolutionary strategies).

### CPLX 791. Research Seminar (1)

*Prerequisites: Passing preliminary examination and graduate advisor consent*. Advanced studies in various subjects related to complex systems through special seminars, informal group studies of special problems, or group research on complete problems for analysis and experimentation.

### MATH 091B. Support Course for GE Mathematics (1)

*Corequisite: MATH 102 or MATH 103.* This is a credit/no credit pre-baccalaureate math class designed to support students in algebra intensive GE Math courses. It provides just in time remediation just prior to each of the linked GE Math lecture meetings, allowing students to have the prerequisites at their fingertips.

### MATH 102. Pre-Calculus I (3)

*Prerequisites: Listed in Table 1. *A preparation for the algebra necessary for calculus. This course is intended for computer science, engineering, mathematics, and natural science majors. It builds on student’s familiarity with linear, quadratic, and rational expressions to achieve fluent proficiency in analyzing the local and global behavior of functions involving such expressions. Not open to students who have credit in MATH 105. (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 102L. Pre-Calculus I Lab (1)

*Corequisite: MATH 102.* All students in MATH 102 are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 102. This course will include a self-paced, modular online component. 2 hours lab per week. (Credit/No Credit only)

### MATH 103. Mathematical Methods for Business (3)

*Prerequisites: Listed in Table 1. *Concepts and applications of algebra and calculus to business. Topics include functions, systems of equations, matrices, the derivative and business-related topics in calculus. (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 103L. Mathematics for Business Laboratory (1)

*Corequisite: MATH 103. *This self-paced, module-based laboratory is designed to give students additional exposure to the applications of college algebra to business and economics beyond what can be done in lecture. The additional hands-on problem-solving skills learned in this class enhance the lecture experience and strengthen the skills necessary for success in MATH 103 and subsequent courses in business majors. The lab environment allows students to both work at their own pace and receive small-group instruction with the laboratory instructor on all modules. 2 hours lab per week. (Credit/No Credit only)

### MATH 105. Pre-Calculus II (5)

*Prerequisites: Listed in Table 1. *A preparation for the trigonometric, exponential, and logarithmic functions used in calculus. This course is intended for computer science, engineering, mathematics, and natural science majors. This course builds on student’s familiarity with exponential, logarithmic, and trigonometric expressions to achieve proficiency in analyzing the local and global behavior of functions involving such expressions. (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 105L. Pre-Calculus II Lab (1)

*Corequisite: MATH 105.* All students in MATH 105 are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 105. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

### MATH 106. Mathematical Foundations for Non-Calculus Physics (5)

*Prerequisites: Listed in Table 1.* Mathematics applicable to problems in non-calculus based physics. Sets, inequalities; functions and graphs: polynomial, rational, exponential, logarithmic, trigonometric; introduction to vectors, angular velocity, and parametric equations. This course is not open to students who have credit in MATH 105 or MATH 255A. (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 131. Mathematical Ideas (3)

*Prerequisite: Multiple Measures Placement in GE-level Mathematics, or credit in MATH 093 or MATH 196QR or MATH 196S or equivalent. *General Education course intended to acquaint the student with basic mathematical ideas. (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 140. Introductory Statistics (4)

*Prerequisite: Multiple Measures Placement in GE-level Mathematics, or credit in MATH 093 or MATH 196QR or MATH 196S or equivalent.* Methods for displaying, describing and producing data. Normal distribution. Correlation and regression. Sampling distributions and probability. Statistical inference for means and proportions. Hybrid (part online) or fully online sections only. (Cross-listed with MATH 140BUS, MATH 140SCI, and MATH 141/L.) (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 140BUS. Introductory Statistics for Business (4)

*Prerequisite: Multiple Measures Placement in GE-level Mathematics, or credit in MATH 093 or MATH 196QR or MATH 196S or equivalent.* Methods for displaying, describing and producing data. Normal distribution. Correlation and regression. Sampling distributions and probability. Statistical inference for means and proportions. Applications to business. Open to students in the College of Business and Economics. Students who are exploratory majors may enroll in this course. (Cross-listed with MATH 140, MATH 140SCI, and MATH 141/L.) (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 140SCI. Introductory Statistics for STEM (4)

### MATH 141/L. Essentials of Statistics and Lab (3/1)

*Prerequisite: Multiple Measures Placement in GE-level Mathematics or concurrent enrollment in MATH 091S.* Basic statistical concepts and reasoning, including methods for displaying, summarizing, interpreting, and producing data. The normal model and variability in random samples. Statistical inference for means and proportions. The linear model: correlation and regression. This course is intended for students majoring in the social and behavioral sciences or in child and adolescent development. Students majoring in the arts, media, communications, the humanities, or those who are exploratory may also enroll. 3 hours lecture, 2 hours lab per week. (Cross-listed with MATH 140, MATH 140BUS, and MATH 140SCI.) (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 150A. Calculus I (5)

*Prerequisites: Listed in Table 1.* Limits, derivatives, and applications of differentiation. Definite and indefinite integrals. The fundamental theorem of calculus and applications of integration. (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 150AL. Calculus I Laboratory (1)

*Corequisite: MATH 150A.* All students in MATH 150A are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 150A. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

### MATH 150B. Calculus II (5)

*Prerequisites: Listed in Table 1. *Techniques of integration and improper integrals. Sequences and series. Power series and Taylor polynomials. Parametric and polar coordinates. Vectors and solid geometry.

### MATH 150BL. Calculus II Laboratory (1)

*Corequisite: MATH 150B.* All students in MATH 150B are encouraged to enroll in this course. This is a Credit/No Credit hybrid enrichment laboratory for students in MATH 150B. This course will include a self-paced, modular online component. 3 hours lab per week. (Credit/No Credit only)

### MATH 210. Basic Number Concepts (3)

*Prerequisites: Multiple Measures Placement in GE-level Mathematics, or credit in MATH 093 or MATH 196QR or MATH 196S or equivalent.* Language of sets, systems of numeration, nature of numbers and fundamentals of operations, relations and functions, domain of integers, and field of rational and real numbers. Designed primarily for students intending to teach in elementary or junior high school. Not available for credit toward the major or minor in Mathematics.

### MATH 211. Statistics and Probability for Elementary and Middle School Teachers (3)

*Prerequisite: Completion of MATH 210 with a grade of “C” or better.* Univariate and bivariate data analysis; probability and probability distributions; design of studies and concepts of inferential statistics; applications to procedures used to evaluate teaching and learning. Not available for credit toward a Mathematics major or minor.

### MATH 250. Calculus III (3)

*Prerequisite: Completion of MATH 150B with a grade of “C” or better. *Continuation of MATH 150B. Solid analytic geometry and space curves. Partial differentiation and applications. Multiple integrals. Line integrals and independence of path. Vector calculus including the divergence theorem and Stokes’ theorem.

### MATH 255A. Calculus for the Life Sciences I (3)

*Prerequisites: Listed in Table 1. Knowledge of trigonometry is assumed.* First semester of a brief course in calculus. Topics include calculus of functions of one real variable, techniques of differentiation, applications to graphing, optimization problems, and an introduction to integration. Applications to life sciences are emphasized. Not open for credit to students who have successfully completed MATH 150A. (Available for General Education, Basic Skills B4 Mathematics and Quantitative Reasoning.)

### MATH 255AL. Calculus for the Life Sciences I Lab (1)

*Corequisite: MATH 255A*. All students in MATH 255A are encouraged to enroll in this lab. This course will include a self-paced, modular outline component. 3 lab hours per week. (Credit/No Credit only)

### MATH 255B. Calculus for the Life Sciences II (3)

*Prerequisites: Listed in Table 1. *Second semester of a brief course in calculus. Topics include techniques of integration, introduction to differential equations, applications of calculus in probability, elements of multivariable calculus, and linear algebra. Applications to life sciences are emphasized. Not open for students who have successfully completed MATH 150AB.

### MATH 255BL. Calculus for the Life Sciences II Lab (1)

*Corequisite: MATH 255B*. All students in MATH 255B are encouraged to enroll in this course. This course will include a self-paced, modular online component. 3 lab hours per week. (Credit/No Credit only)

### MATH 262. Introduction to Linear Algebra (3)

*Prerequisite: Completion of MATH 150B with a grade of “C” or better.* Systems of linear equations, matrices, determinants, eigenvalues, vector spaces and linear transformations, as well as introduction to inner products on Rn and spectral theorem for symmetric matrices.

### MATH 280. Applied Differential Equations (3)

*Prerequisite: Completion of MATH 150B with a grade of “C” or better. Recommended Corequisite or Preparatory: MATH 250. *First order equations. Explicit solution methods, existence and uniqueness for initial value problems. Higher order linear equations. Undetermined coefficients and variation of parameters. Laplace transforms and transform solution methods. Linear first-order systems. Emphasis on engineering applications. Not available for students majoring in Mathematics.

### MATH 310. Basic Concepts of Geometry (3)

*Prerequisite: Completion of MATH 210 with a grade of “C” or better. Second course for students intending to teach in elementary or junior high school.* Geometry as a system; congruence and similarity through construction with straightedge and compass; transformational geometry; the nature of measurement, precision and accuracy. Not available for credit toward the major or minor in Mathematics.

### MATH 310L. Basic Concepts of Geometry Lab (1)

*Recommended Corequisite or Preparatory: MATH 310.* Problem solving using models and simulation in mathematics appropriate for the elementary-school classroom. 2 hours of activities per week. (Credit/No Credit only)

### MATH 312. Basic Algebraic Concepts (3)

*Prerequisites: Completion of MATH 210 and MATH 310 with grades of “C” or better, or instructor consent.* Topics selected from: abstract algebra and applied algebra using elementary mathematical models. Not available for credit toward the Mathematics major or minor.

### MATH 320. Foundations of Higher Mathematics (3)

*Prerequisite: Completion of MATH 150B with a grade of “C” or better.* The goal of this course is to help students transition from a primarily computational mode of doing mathematics to a more conceptual mode. The emphasis will be on proofs, which are taught in the context of elementary number theory, combinatorics and analysis; the language of sets, relations, order, equivalence classes, functions and cardinality is introduced. Students are expected to write large numbers of proofs and communicate mathematical ideas clearly.

### MATH 326. Discrete Mathematics (3)

*Prerequisites: ECE 320 or PHIL 230; Completion of MATH 150B with a grade of “C” or better. *Propositional calculus, predicate calculus, set algebra, relations, functions, mappings, fields and number systems.

### MATH 331. Mathematical Explorations (3)

*Prerequisites: Multiple Measures Placement in GE-level Mathematics, or credit in MATH 093 or MATH 196QR or MATH 196S. Completion of the lower division writing requirement; Upper division standing.* A course designed to give students an appreciation of the diversity of mathematics and the spirit in which it is employed in various applications. The character and origin of key topics from different branches of mathematics are explored. The contributions of various cultures to the field are studied, along with the use of mathematical models for physical problems. The development is conceptual rather than axiomatic, and includes several supervised reading and writing assignments. One significant writing assignment is required. Strongly recommended for prospective teachers in all fields. Not available for credit toward the major or minor in Mathematics. (Available for General Education, B5 Scientific Inquiry and Quantitative Reasoning.) (WI)

### MATH 340. Introduction to Probability and Statistics (4)

*Prerequisite: Completion of MATH 150B with a grade of “C” or better.* Sample spaces, probability rules, independence, conditional probability, Bayes Theorem, discrete random variables (binomial, Poisson, geometric, negative binomial), continuous random variables (normal, gamma, exponential, uniform), expectations, moment generating functions, joint, conditional and marginal distributions and conditional expectations, linear combinations of random variables, sampling distributions, Central Limit Theorem, inference for single means and for one and two proportions, and least squares regression.

### MATH 351. Differential Equations (3)

*Prerequisites: Completion of MATH 250 and MATH 262 with a grade of “C” or better. Not open to students who have credit for MATH 280.* First-order equations and explicit solution methods. The Picard-Lindelöf existence and uniqueness theorem. Higher order linear equations. Undetermined coefficients and variation of parameters. Power series solutions. Linear systems and eigenvector methods. Linearization and solution sketching for autonomous systems.

### MATH 360. Abstract Algebra I (3)

*Prerequisites: Completion of MATH 262 and MATH 320 with a grade of “C” or better.* Survey course in abstract algebra. Introduction to groups, rings, fields and vector spaces.

### MATH 366. Combinatorics (3)

*Corequisite: MATH 320 or MATH 326.* This is a one-semester introduction to combinatorics. Topics include enumerative combinatorics (inclusion-exclusion, generating functions, Polya’s Theorem, etc.) and combinatorial structures (graphs, designs, etc.).

### MATH 370. Foundations of Geometry (3)

*Prerequisite or Corequisite: MATH 320.* One of the goals of this course is to help students write rigorous proofs of results of plane Euclidean geometry. It is also expected that students visualize and develop geometric intuition through the use of dynamic geometry software. The content includes history, axiomatic structure and theorems of plane Euclidean geometry, geometric transformations of the plane, rigid motions, similarities, and inversion, coordinate geometry and an introduction to non-Euclidean geometries.

### MATH 382/L. Introduction to Scientific Computing and Lab (2/1)

*Corequisite: MATH 262.* This course gives students an introduction to basic numerical techniques and to programming using some of the common software packages used in mathematics. Students apply these techniques in projects from different branches of mathematics. (This course does not replace a rigorous course in numerical analysis.) 2 hours lecture, 2 hours lab.

### MATH 391. Field Experience in the Mathematics of the Public Schools (2)

*Prerequisites: Multiple Subject Candidates—MATH 210 and MATH 310 or corequisite with MATH 310. Single Subject Candidates—MATH 150A, MATH 150B; Junior standing. *Field experience course designed to give the prospective teacher an appreciation of a quality mathematics program in public schools. Requirements include 45 hours of participation in an assigned school and regular group meetings to discuss the classroom experience. (Credit/No Credit only)

### MATH 440A. Mathematical Statistics I (3)

*Prerequisites: Completion of MATH 262 and MATH 340 with a grade of “C” or better.* Point estimation, bias and mean squared error, optimality theory for estimates, maximum likelihood estimation, confidence intervals, test of hypotheses, power, and optimality theory for tests. Available for graduate credit.

### MATH 440B. Mathematical Statistics II (3)

*Prerequisite: Completion of MATH 440A with a grade of “C” or better.* Chi-square goodness of fit tests, simple and multiple linear regression, 1- and 2-way analysis of variance, and statistical analysis using the computer. Available for graduate credit.

### MATH 442A-Z. Topics in Mathematical Statistics (3)

*Prerequisite: Completion of MATH 340 with a grade of “C” or better, or MATH 440A with a grade of “C” or better.* Topics selected from statistics and/or probability, such as nonparametric statistics, multivariate statistics, experimental design, decision theory and advanced probability theory.

### MATH 443. Probability Theory and Stochastic Processes (3)

*Prerequisites: MATH 250, MATH 262, and MATH 340 all with grades of “C” or better.* This course focuses on more advanced but essential topics in probability theory and stochastic processes. Topics include joint probability distributions, functions of random variables, conditional probabilities, expectations and variances, probability inequalities, stochastic convergence, multivariate normal distribution, quadratic forms, random walks, Poisson process, and Markov chains. Available for graduate credit.

### MATH 444. Statistical Modeling (3)

*Prerequisite: MATH 340.* This course will cover the fundamental concepts of statistical model building, including inference, applied linear regression, multiple regression, prediction and variable selection, nonlinear and nonparametric regression, principal component analysis and factor analysis. Software and coding will be used to apply the theory to examples and real data sets, but no previous coding experience is required.

### MATH 445. Statistical Foundations to Machine Learning (3)

*Prerequisite: MATH 444 or MATH 440A or graduate standing with approval from the coordinator/instructor.* This course will cover concepts of linear models and prediction models including generalized linear models, supervised and unsupervised learning such as classification techniques and clustering. It also includes missing data techniques and concepts of time-series analysis. Software and coding will be used to apply the theory to examples and real data sets. Available for graduate credit.

### MATH 450A. Advanced Calculus I (3)

*Prerequisite: Completion of MATH 320 with a grade of “C” or better.* Brief exposure to real numbers including completeness, Bolzano Weierstrass theorem, countability of subsets; continuity and differentiability of real valued functions on the real line; the inverse function theorem on R; integration; the fundamental theorem of calculus; improper Riemann integration; infinite series; uniform convergence; power series and real analytic functions.

### MATH 450B. Advanced Calculus II (3)

*Prerequisite: Completion of MATH 450A with a grade of “C” or better.* Topics include topology on R^n, continuity and differentiability of functions from domains in R^m to R^n, Taylor’s formula, the inverse and implicit function theorems, integration of functions on Jordan regions, iterated integrals, the change of variables theorem, curves and surfaces in R^n, and the theorems of Green, Gauss, and Stokes. Available for graduate credit.

### MATH 455. Complex Variables (3)

*Prerequisite: Completion of MATH 450A with a grade of “C” or better.* Complex numbers, analytic functions, complex integration, Cauchy’s Theorem, power series, calculus of residues and conformal mappings. Available for graduate credit.

### MATH 460. Abstract Algebra II (3)

*Prerequisite: Completion of MATH 360 with a grade of “C” or better.* Second course in abstract algebra. Group theory, rings and modules, and field extensions. Available for graduate credit.

### MATH 462. Advanced Linear Algebra (3)

*Prerequisites: Completion of MATH 262 and MATH 320 with a grade of “C” or better. Recommended Corequisite or Preparatory: MATH 360.* This course covers vector spaces and linear transformations from a more theoretical perspective than that covered in MATH 262. The course begins with a review of abstract vector spaces, including the invariance of dimension of a finite dimensional vector space, the correspondence between linear transformations and matrices, similarity, as well as the definition and basic properties of determinants. The concepts of eigenvalues, eigenvectors, and diagonalization will be reviewed. The course will also cover real and complex inner product spaces, Hermitian operators, the spectral theorem, minimal and characteristic polynomials, the Cayley Hamilton theorem, and the Jordan canonical form.

### MATH 463. Number Theory (3)

*Prerequisite: Completion of MATH 320 with a grade of “C” or better. Recommended Corequisite or Preparatory: MATH 360.* Euclidean algorithm and the unique factorization theorem, congruences, primitive roots and indices, quadratic residues and the law of quadratic reciprocity, and distribution of primes. Available for graduate credit.

### MATH 480. Partial Differential Equations (3)

*Prerequisite: Completion of MATH 351 with a grade of “C” or better, or MATH 280 with a grade of “C” or better.* Orthogonal functions, Laplace’s equation, Poisson’s equation, Bessel’s equation, self-adjoint operators, Sturm-Liouville theory, Fourier series, separation of variables applied to the heat equation and wave equation, nonhomogeneous problems, Green’s functions for time-independent problems, and infinite domain problems. Available for graduate credit.

### MATH 481A. Numerical Analysis (3)

*Prerequisites: COMP 110/L; Completion of MATH 262 with a grade of “C” or better.* Techniques of applied mathematics, solution of equations, interpolation, numerical integration and numerical solution of differential equations. Available for graduate credit.

### MATH 482. Combinatorial Algorithms (3)

*Prerequisites: Completion of MATH 150B and MATH 262 with a grade of “C” or better; Some computer programming experience.* Computer-oriented study of seminumerical and non-numerical algorithms. Sorting, tree searching, generation of combinatorial structures, algorithm proof techniques, best algorithms and programming complexity. Available for graduate credit.

### MATH 483. Mathematical Modeling (3)

*Prerequisites: MATH 340 with a grade of “C” or better, and MATH 351 with a grade of “C” or better, or graduate standing.* Applications of mathematical techniques to solve selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering. Models discussed include deterministic, stochastic, optimization, static, and dynamic ones. Emphasis is placed on the initial phase of building mathematical models and the final phase of interpreting the solutions in terms of real-life applications. Available for graduate credit.

### MATH 490. Capstone Course (3)

*Prerequisite: Senior standing. *A course where prospective teachers see high-school level mathematics from a more advanced perspective, where there is considerably more emphasis on issues of pedagogy than in other content courses, and where students will see connections between the mathematics they have learned and some of the activities that they will themselves be engaged in as teachers. MATH 490 is required for the Secondary Teaching option, but a student may choose, in consultation with an advisor, to take the course a second time as an elective.

### MATH 493. Undergraduate Seminar in Mathematics (3)

*Prerequisite: Junior standing in the major.* Students will study current topics in mathematical and/or statistical literature and will prepare written summaries and give oral presentations to the class. Students will be active participants in all seminars by asking questions and providing written critiques and summaries of the presentations of other students.

### MATH 494. Practical Experience in Mathematics (3)

*Prerequisite: Junior standing in the major.* Students will gain practical experience in the profession by either participating in an internship doing mathematical/statistical work at an outside organization or by doing directed research within the department. All students are expected to work a minimum of 8 hours per week on this assignment and meet with the course instructor on a regular basis. All students are required to produce a written report on their work at the end of the semester. Students will give oral reports to the department and their peers.

### MATH 496A-Z. Experimental Topics in Modern Mathematics (3)

*Prerequisites: Senior standing and instructor consent.*

### MATH 499A-C. Independent Study (1-3)

See Independent Study under courses of study.

### MATH 501. Topology (3)

*Prerequisite: MATH 450A.* Metric spaces, topological spaces, compactness, completeness and connectedness. Introduction to function spaces, with emphasis on the uniform topology.

### MATH 540. Regression Analysis (3)

*Prerequisite: MATH 440A.* General linear model in matrix form, simple and multiple regression analysis, transformations, variable selection, multicollinearity, analysis of variance, robust regression, logistic regression, principal components and factor analysis. Statistical software utilized.

### MATH 541. Theoretical Statistical Inference (3)

*Prerequisites: MATH 340, MATH 450A and MATH 462.* Hogg-Craig Theorem, Cochran Theorem, convergence in probability and distribution, Cramer-Wold Theorem, Continuous Mapping Theorem, Weak-Law-of-Large-Numbers, Lindberg-Feller Central Limit Theorem (CLT), Lyapunov CLT, Regular Exponential families, Neyman-Factorization Criterion, the substitution principle, asymptotic relative efficiency, the method of the moments, the MLE and its asymptotic efficiency, Uniformly Minimum Variance Unbiased Estimation, Rao-Blackwell Theorem, Lehmann-Scheffe Theorem, minimal complete sufficient statistics, ancillary statistics, Basu Theorem, confidence regions, likelihood ratio tests, Wilk’s Theorem, Neyman-Pearson Lemma, Uniformly Most Powerful test, Karlin-Rubin Theorem, other large-sample tests.

### MATH 542. Nonparametric Statistics (3)

*Prerequisite: MATH 440A or MATH 541.* One, two and K sample location methods, the histogram estimator, kernel density estimation, the choice of the smoothing parameter, other density estimators: orthogonal basis, penalized maximum likelihood, nonparametric regression: Nadaraya-Watson, choice of smoothing parameter, k-nn, splines, bootstrap.

### MATH 543. Multivariate Statistics (3)

*Prerequisite: MATH 440A or MATH 541.* Multivariate normal distribution, multivariate data analysis, inference about a mean vector including Hotelling’s T2 and the likelihood ratio statistic, Wishart distribution, MANOVA, classification and discriminant analysis, principal components, factor analysis, canonical correlation, multidimensional scaling. Applications and use of statistical software.

### MATH 544. Stochastic Processes (3)

*Prerequisite: MATH 340.* Markov chains, first step analysis, recurrent and transient states, stationary and limiting distributions, random walks, branching processes, Poisson and birth and death processes, renewal theory, martingales, introduction to Brownian motion and related Gaussian processes.

### MATH 545. Probability Theory (3)

*Prerequisite: MATH 552.* Operations on sets and events, sigma algebras, probability measures, Lebesgue measure, measurable maps and random variables, independence, Borel-Cantelli lemmas, zero-one laws, integration with respect to a probability measure, convergence theorems for integral, product spaces, and Fubini’s theorem. Laws of large numbers, convergence in distribution, and the central limit theorem.

### MATH 546. Time Series Analysis (3)

*Prerequisite: MATH 440A or MATH 541.* Time series, stationary and nonstationary time series models, seasonal and nonseasonal time series models, trends, ARIMA (Box-Jenkins) models, smoothing methods, estimation, diagnostic checking, forecasting techniques, spectral domain, periodogram, filtering, spectral density.

### MATH 547. Categorical Data Analysis (3)

*Prerequisite: MATH 440A or MATH 541.* Inference and measures of association for categorical data, generalized linear model, logistic and Poisson regression, logit, probit and loglinear models, analysis of matched pairs.

### MATH 548. Statistical Computing (3)

*Prerequisite: MATH 440A or MATH 541.* Methods for generating random variables, Monte Carlo methods, Monte Carlo Integration and variance reduction, bootstrap and jackknife, optimization and solving nonlinear equations, EM algorithms, Fisher scoring method, and Markov Chain Monte Carlo methods.

### MATH 549A-E. Topics in Probability and Statistics (3-3)

*Prerequisite: MATH 440A or MATH 541 or consent of instructor.* This series will cover topics in probability and statistics not covered elsewhere in the program, as chosen by individual instructors. Up to two different courses within this series may be taken for credit.

Course |
Title |

MATH 549A | Bayesian Statistics |

MATH 549B | Linear Models |

MATH 549C | Functional Data Analysis |

MATH 549D | Advanced Probability |

MATH 549E | Current Topics in Statistics |

### MATH 550. Calculus on Manifolds (3)

*Prerequisites: MATH 450B and MATH 501.* Differentiable forms and exterior derivatives on R^n; line integrals on R^n; differentiable manifolds and differentiable forms; Stokes’ theorem and applications; additional topics as time permits.

### MATH 552. Real Analysis (3)

*Prerequisite: MATH 501.* Introduction to measure theory and Lebesgue integration, and their application to probability theory. Monotone and dominated convergence theorems, Fubini’s theorem, Fourier analysis and Banach spaces.

### MATH 560. Abstract Algebra III (3)

*Prerequisite: MATH 460.* Graduate course in abstract algebra. Group theory, Galois theory and other topics.

### MATH 570. Differential Geometry (3)

*Prerequisite: MATH 450B.* The local theory of regular curves in R3 and Frenet formulas. Regular surfaces in R3, the first and second fundamental forms, Gaussian and mean curvatures, and the Egregium Gauss theorem. Geodesics and the Gauss-Bonnet theorem.

### MATH 581. Numerical Methods for Linear Systems (3)

*Prerequisite: MATH 462.* Methods for solving large linear problems and eigenvalue problems are presented at an advanced level. Direct methods such as LU factorization, Cholesky factorization and the Least Squares method, and Iterative methods, such as the Jacobi, Gauss-Seidel, SOR and conjugate Gradient methods, are discussed in detail. Eigenvalue problems are solved via power iteration, the QR method and the Jacobi method.

### MATH 582A-D. Topics in Numerical Analysis (3-3-3-3)

*Prerequisite: MATH 581 or consent of instructor.* The course will cover topics in numerical analysis which are important in many applications and which are not covered elsewhere in the program. Part A usually covers numerical methods in optimization, Part B covers numerical methods for ordinary differential equations, and Part C covers numerical solution of partial differential equations. Part D covers a subject chosen by the instructor.

### MATH 589. Seminar in Mathematics (1)

*Prerequisite: Senior or graduate standing in the Mathematics Department.* Students will read about advanced topics in the recent literature in Mathematics and report on them in a lecture. This course may be taken up to two times with the consent of the advisor. (Credit/No Credit only)

### MATH 592A-C. Topics in Applied Mathematics (3-3-3)

*Prerequisite: MATH 552 or consent of instructor.* This course is devoted to a variety of important topics in applied mathematics that are not covered elsewhere in the program. In particular, Part A will cover the mathematical theory of partial differential equations, Part B covers mathematical optimization and operations research, and Part C covers mathematical biology.

### MATH 595A-Z. Experimental Topics (1-3)

*Prerequisite: Consent of instructor.* Specialized topics from a concentrated field of current interest presented at an advanced level.

### MATH 625. Advanced Mathematical Modeling (3)

Selected problems in ecology, biology, economics, finance, social sciences, life sciences, physical sciences and engineering are used to develop advanced techniques of mathematical modeling.

### MATH 651A-C. Advanced Topics in Analysis, Geometry and Topology (3-3-3)

*Prerequisite: Consent of instructor.* Advanced topics not covered in the previous classes on the subject. Part A covers topics in analysis, Part B covers topics in geometry, and Part C covers topics in topology. May be repeated with the consent of the advisor.

### MATH 655. Complex Analysis (3)

*Prerequisites: MATH 501, MATH 455.* Topics covered include the general Cauchy theorem, power series and analytic continuation, series and product expansions, conformal mapping and the Dirichlet problem.

### MATH 661A-C. Advanced Topics in Algebra, Number Theory and Discrete Mathematics (3-3-3)

*Prerequisite: Consent of instructor.* Advanced topics not covered in the previous classes on the subject. Part A covers topics in algebra, Part B covers topics in number theory, and Part C covers other topics in discrete mathematics. May be repeated with the consent of the advisor.

### MATH 662. Introduction to Commutative Algebra (3)

*Prerequisite: MATH 560 or consent of instructor.* Topics covered include modules, localization, integral dependence, chain conditions (Noetherian and Artinian), discrete valuation rings (DVRs) and Dedekind domains.

### MATH 680A. Applied Functional Analysis (3)

*Prerequisites: MATH 501, MATH 552.* This two-semester sequence gives an introduction to Banach and Hilbert spaces and their applications. Fixed Point Theorems and their applications to differential and integral equations and variational principles. Adjoint and self-adjoint operators and spectral theory of linear operators. MATH 680A is a prerequisite for MATH 680B.

### MATH 697A. Directed Comprehensive Studies (1)

Directed Comprehensive Studies

### MATH 698A-C. Thesis or Graduate Project (1-3)

Thesis or Graduate Project

### MATH 699A-C. Independent Study (1-3)

See Independent Study under courses of study.