Mathematics

MATH 010. High School Algebra.

(4-0) Cr. arr. F.S.SS.
For students who do not have adequate facility with topics from high school algebra or do not meet the algebra admission requirement. The course is divided into tracks of one- and two-semester lengths. For most students a diagnostic exam will determine which track must be taken. Students will receive a grade in Math 25 or 30 respectively depending on the level of material covered. Satisfactory completion of Math 30 is recommended for students planning to take MATH 140 or 151, while Math 25 is sufficient for MATH 104, 105, 150, 195, Stat 101 or 105. Students must complete Math 30 to remove a deficiency in the algebra admission requirement. Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only.

MATH 025. High School Algebra.

(4-0) Cr. arr. F.S.SS.
Students should initially enroll in Math 10. See description of Math 10. Offered on a satisfactory-fail basis only.

MATH 030. High School Algebra.

(4-0) Cr. arr. F.S.SS.
Students should initially enroll in Math 10. See description of Math 10. Offered on a satisfactory-fail basis only.

MATH 101. Orientation in Mathematics.

Cr. R. F.
For new majors. Issues to consider in planning a program of study. Sources of general information and perspectives concerning mathematics. Discussion of possible areas of study and careers. Offered on a satisfactory-fail basis only.

MATH 104. Introduction to Probability and Matrices.

(3-0) Cr. 3. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry
Permutations, combinations, probability, binomial and multinomial theorems, matrices, expected value. Either Math 104 or 150 may be counted toward graduation, but not both.

MATH 105. Introduction to Mathematical Ideas.

(3-0) Cr. 3. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry
Topics from mathematics and mathematical applications with emphasis on their nontechnical content.

MATH 140. College Algebra.

(3-1) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra; 1 year of high school geometry
Coordinate geometry, quadratic and polynomial equations, functions, graphing, rational functions, exponential and logarithmic functions, inverse functions, quadratic inequalities. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements.

MATH 141. Trigonometry.

(2-0) Cr. 2. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra; 1 year of high school geometry, or enrollment in 140
May be taken concurrently with 140. Trigonometric functions and their inverses, solving triangles, trigonometric identities and equations, graphing. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements. Only one of Math 141, 142 may count toward graduation.

MATH 142. Trigonometry and Analytic Geometry.

(2-1) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry, or enrollment in 140
May be taken concurrently with 140. Trigonometric functions and their inverses, solving triangles, trigonometric identities and equations, graphing, polar coordinates, complex numbers, conic sections, parametric equations. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements. Only one of Math 141, 142 may count toward graduation.

MATH 150. Discrete Mathematics for Business and Social Sciences.

(2-1) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry
Linear equations and inequalities, matrix algebra, linear programming, discrete probability. Either Math 104 or 150 may be counted toward graduation, but not both.

MATH 151. Calculus for Business and Social Sciences.

(2-1) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry
Differential calculus, applications to max-min problems, integral calculus and applications. Will not serve as prerequisite for 265 or 266. Only one of Math 151, 160, the sequence 165-166, or the sequence 181-182 may be counted towards graduation.

MATH 160. Survey of Calculus.

(4-0) Cr. 4. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of geometry
Analytic geometry, derivatives and integrals of elementary functions, partial derivatives, and applications. Will not serve as a prerequisite for 265 or 266. Only one of Math 151, 160, the sequence 165-166, or the sequence 181-182 may be counted towards graduation.

MATH 165. Calculus I.

(4-0) Cr. 4. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry or enrollment in 141 or 142
Differential calculus, applications of the derivative, introduction to integral calculus. Only one of Math 151 or 160 or the sequence 165-166, or the sequence 181-182 may be counted towards graduation.

MATH 166. Calculus II.

(4-0) Cr. 4. F.S.SS. Prereq: Grade of C- or better in 165 or high math placement scores
Integral calculus, applications of the integral, infinite series. Only one of Math 151, 160, the sequence 165-166, or the sequence 181-182 may be counted towards graduation.

MATH 166H. Honors Calculus II.

(4-0) Cr. 4. F. Prereq: Permission of instructor and 165 or high math placement scores
Integral calculus, applications of the integral, infinite series. Additional material of a theoretical, conceptual, computational, or modeling nature. Some of the work may require more ingenuity than is required for MATH 166. Preference will be given to students in the University Honors Program. Only one of Math 151 or 160, the sequence 165-166, or the sequence 181-182 may be counted towards graduation.

MATH 181. Calculus and Mathematical Modeling for the Life Sciences I.

(4-0) Cr. 4. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry, 1 semester of trigonometry or enrollment in 141 or 142
Exponential and logarithm functions, difference equations, derivatives, and applications of the derivative. Examples taken from biology. Only one of Math 151, 160, the sequence 165-166, or the sequence 181-182 may be counted towards graduation.

MATH 182. Calculus and Mathematical Modeling for the Life Sciences II.

(4-0) Cr. 4. S. Prereq: 181
Integration, first and second order differential equations, applications of the definite integral, introduction to multivariable calculus. Examples taken from biology. Only one of 151, 160, the sequence 165-166, or the sequence 181-182 may be counted towards graduation.

MATH 195. Mathematics for Elementary Education I.

(2-2) Cr. 3. F.S. Prereq: Satisfactory performance on placement exam, 2 years high school algebra, 1 year of high school geometry, enrollment in elementary education or early childhood education
Theoretical and hands-on models, mathematical analysis of: elementary students? thinking, standard and non-standard algorithms, and properties related to whole numbers and whole number operations; linear measurement, and two- and three-dimensional geometric shapes and spatial sense; algebra as it relates to elementary curricula. Students in the College of Liberal Arts and Sciences may not count Math 140, 141, 142, or 195 toward Group III of the General Education Requirements.

MATH 196. Mathematics for Elementary Education II.

(2-2) Cr. 3. F.S. Prereq: Grade of C- or better in 195 and enrollment in elementary education or early childhood education.
Two- and three-dimensional measurement; probability, statistics, algebra as it relates to elementary curricula; theoretical and hands-on models, mathematical analysis of: elementary students? thinking, standard and non-standard algorithms, and properties related to integer, fraction, and decimal operations.

MATH 201. Introduction to Proofs.

(3-0) Cr. 3. F.S. Prereq: 166 or 166H
Reading and writing simple proofs, using logical reasoning, including quantifiers and truth tables. Proof techniques. Mathematical induction. Proofs in set theory, number theory, and calculus.

MATH 265. Calculus III.

(4-0) Cr. 4. F.S.SS. Prereq: Grade of C- or better in 166 or 166H
Analytic geometry and vectors, differential calculus of functions of several variables, multiple integrals, vector calculus.

MATH 265H. Honors Calculus III.

(4-0) Cr. 4. F.S. Prereq: Permission of the instructor; and 166 or 166H
Analytic geometry and vectors, differential calculus of functions of several variables, multiple integrals, vector calculus. Additional material of a theoretical, conceptual, computational, or modeling nature. Some of the work may require more ingenuity than is required in MATH 265. Preference will be given to students in the University Honors Program.

MATH 266. Elementary Differential Equations.

(3-0) Cr. 3. F.S.SS. Prereq: Grade of C- or better in 166 or 166H
Solution methods for ordinary differential equations. First order equations, linear equations, constant coefficient equations. Eigenvalue methods for systems of first order linear equations. Introduction to stability and phase plane analysis.

MATH 267. Elementary Differential Equations and Laplace Transforms.

(4-0) Cr. 4. F.S.SS. Prereq: Grade of C- or better in 166 or 166H
Same as 266 but also including Laplace transforms and series solutions to ordinary differential equations.

MATH 268. Laplace Transforms.

(1-0) Cr. 1. S. Prereq: 266
Laplace transforms and series solutions to ordinary differential equations. Together, Math 266 and 268 are the same as 267.

MATH 290. Independent Study.

Cr. 1-3. Repeatable.

MATH 297. Intermediate Topics for School Mathematics.

(2-2) Cr. 3. F. Prereq: Enrollment in elementary education and grade of C- or better in 196
Mathematical reasoning, data fitting, and topics in Euclidean and non-Euclidean geometry. Discrete mathematics topics selected from graphs, networks, recurrence relations, probability, Markov chains. Use of technology to learn and teach mathematics.

MATH 298. Cooperative Education.

Cr. R. Repeatable, maximum of 2 times. F.S.SS. Prereq: Permission of the department cooperative education coordinator; sophomore classification
Required of all cooperative education students. Students must register for this course prior to commencing each work period.

MATH 301. Abstract Algebra I.

(3-0) Cr. 3. F.S. Prereq: 166 or 166H, 307 or 317, and 201
Theory of groups. Homomorphisms. Quotient groups. Introduction to rings. Emphasis on writing proofs. Nonmajor graduate credit.

MATH 302. Abstract Algebra II.

(3-0) Cr. 3. S. Prereq: 301
Theory of rings and fields. Introduction to Galois theory. Emphasis on writing proofs. Nonmajor graduate credit.

MATH 304. Introductory Combinatorics.

(3-0) Cr. 3. Prereq: 166 or 166H; 201 or experience with proofs
Permutations, combinations, binomial coefficients, inclusion-exclusion principle, recurrence relations, generating functions. Additional topics selected from probability, random walks, and Markov chains. Nonmajor graduate credit.

MATH 307. Matrices and Linear Algebra.

(3-0) Cr. 3. F.S.SS. Prereq: 2 semesters of calculus
Systems of linear equations, determinants, vector spaces, linear transformations, orthogonality, least-squares methods, eigenvalues and eigenvectors. Emphasis on methods and techniques. Nonmajor graduate credit. Only one of Math 307, 317 may be counted toward graduation.

MATH 314. Graphs and Networks.

(3-0) Cr. 3. S. Prereq: 166 or 166H; 201 or experience with proofs
Structure and extremal properties of graphs. Topics are selected from: trees, networks, colorings, paths and cycles, connectivity, planarity, Ramsey theory, forbidden structures, enumeration, applications. Nonmajor graduate credit.

MATH 317. Theory of Linear Algebra.

(4-0) Cr. 4. F.S. Prereq: 166; credit or enrollment in 201
Systems of linear equations, determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors. Emphasis on writing proofs and results. Nonmajor graduate credit. Only one of Math 307, 317 may be counted toward graduation.

MATH 331. Topology.

(3-0) Cr. 3. Prereq: 307 or 317
Topological properties of metric spaces, including Euclidean n-space, continuous functions, homeomorphisms, and topological invariants. Examples from surfaces, knots, links, and three-dimensional manifolds. Nonmajor graduate credit.

MATH 341. Introduction to the Theory of Probability and Statistics I.

(Cross-listed with STAT). (3-0) Cr. 3. F.S. Prereq: MATH 265 (or 265H)
Probability; distribution functions and their properties; classical discrete and continuous distribution functions; multivariate probability distributions and their properties; moment generating functions; simulation of random variables and use of the R statistical package.

MATH 342. Introduction to the Theory of Probability and Statistics II.

(Cross-listed with STAT). (3-0) Cr. 3. S. Prereq: STAT 341; MATH 307 or 317
Transformations of random variables; sampling distributions; confidence intervals and hypothesis testing; theory of estimation and hypothesis tests; linear model theory, enumerative data; use of the R statistical package for simulation and data analysis.

MATH 350. Number Theory.

(Cross-listed with COM S). (3-0) Cr. 3. S. Prereq: 166
Divisibility, integer representations, primes and divisors, linear diophantine equations, congruences, and multiplicative functions. Applications to cryptography. Nonmajor graduate credit.

MATH 365. Complex Variables with Applications.

(3-0) Cr. 3. S. Prereq: 265
Functions of a complex variable, including differentiation, integration and series expansions, residues, evaluation of integrals, conformal mapping. Nonmajor graduate credit.

MATH 373. Introduction to Scientific Computing.

(3-0) Cr. 3. F. Prereq: 265
Vector, matrix, and graphics programming in MATLAB for scientific applications. Polynomial interpolation and approximation. Systems of linear equations and numerical linear algebra. Numerical differentiation and integration. Newton methods solving nonlinear equations and optimization in one and several variables. Fast Fourier transform. Emphasis on effective use of mathematical software and understanding of its strengths and limitations. Nonmajor graduate credit.

MATH 385. Introduction to Partial Differential Equations.

(3-0) Cr. 3. F.S. Prereq: 265 and one of 266, 267
Separation of variables methods for elliptic, parabolic, and hyperbolic partial differential equations. Fourier series, Sturm-Liouville theory, Bessel functions, and spherical harmonics. Nonmajor graduate credit.

MATH 397. Teaching Secondary Mathematics Using University Mathematics.

(2-2) Cr. 3. S. Prereq: 201, 301
Coursework in university mathematics including calculus, abstract algebra, discrete mathematics, geometry, and other topics as it relates to teaching mathematics in grades 7-12.

MATH 398. Cooperative Education.

Cr. R. Repeatable, maximum of 2 times. F.S.SS. Prereq: Permission of the department cooperative education coordinator; junior classification
Required of all cooperative education students. Students must register for this course prior to commencing each work period.

MATH 414. Analysis I.

(3-0) Cr. 3. F.S.SS. Prereq: 201; 265; and 307 or 317
Introduction to properties and basic topology of the real numbers. A careful development of calculus of functions of a real variable: limits, continuity, differentiation, integration, series. Nonmajor graduate credit.

MATH 415. Analysis II.

(3-0) Cr. 3. S. Prereq: 414
Sequences and series of functions of a real variable, uniform convergence, power series and Taylor series, Fourier series, topology of n-dimensional space, implicit function theorem, calculus of the plane and 3-dimensional space. Additional topics may include metric spaces or Stieltjes or Lebesgue integration. Nonmajor graduate credit.

MATH 421. Logic for Mathematics and Computer Science.

(Cross-listed with COM S). (3-0) Cr. 3. S. Prereq: MATH 301 or 307 or 317 or COM S 330
Propositional and predicate logic. Topics selected from Horn logic, equational logic, resolution and unification, foundations of logic programming, reasoning about programs, program specification and verification, model checking and binary decision diagrams, temporal logic and modal logic. Nonmajor graduate credit.

MATH 426. Mathematical Methods for the Physical Sciences.

(Cross-listed with PHYS). (3-0) Cr. 3. F. Prereq: 266 or 267
A fast-paced course primarily for first-year graduate students in physics and chemistry. Emphasis on techniques needed for quantum mechanics and electrodynamics. Functions of a complex variable and contour integration, integral transforms and applications, series methods for ordinary differential equations, Green's functions, Sturm-Liouville problems and orthogonal functions, boundary-value problems for partial differential equations. Nonmajor graduate credit.

MATH 435. Geometry I.

(3-0) Cr. 3. F. Prereq: 307 or 317
Euclidean geometry. Points, lines, circles, triangles, congruence, similarity, properties invariant under rigid motions. Synthetic, analytic, and axiomatic methods. Nonmajor graduate credit.

MATH 436. Geometry II.

(3-0) Cr. 3. S. Prereq: 435
Continuation of Euclidean geometry with topics from elliptic, projective, or hyperbolic geometry. Emphasis on analytic methods. Nonmajor graduate credit.

MATH 439. Mathematics of Fractals and Chaos.

(3-0) Cr. 3. Prereq: 265
Iterated function systems; periodic points; algorithms for generation of fractals; fractal dimension; Julia sets and the Mandelbrot set; chaos. Nonmajor graduate credit.

MATH 481. Numerical Methods for Differential Equations and Interpolation.

(Cross-listed with COM S). (3-0) Cr. 3. S. Prereq: MATH 265 and either MATH 266 or 267; knowledge of a programming language
First order Euler method, high order Runge-Kutta method, and multistep method for solving ordinary differential equations. Finite difference and finite element methods for solving partial differential equations. Local truncation error, stability, and convergence for finite difference method. Numerical solution space, polynomial approximation, and error estimate for finite element method. Nonmajor graduate credit.

MATH 490. Independent Study.

Cr. 1-3. Repeatable, maximum of 9 credits. Prereq: 301 or 317; 6 credits in mathematics
No more than 9 credits of Math 490 may be counted toward graduation.

MATH 491. Undergraduate Thesis.

Cr. 2-3.
Writing a formal mathematics paper. Upon approval by the department, the paper will satisfy the departmental advanced English requirement.

MATH 492. Undergraduate Seminar.

(2-0) Cr. 2. S. Prereq: Consent of instructor
Introduction to mathematics research, a participating seminar on advanced topics in mathematics. Mathematical literature search, reading a mathematical article with the guidance of the instructor, mathematical presentation. Seminar content varies.

MATH 497. Teaching Secondary School Mathematics.

(Cross-listed with C I). (3-0) Cr. 3. F. Prereq: 15 credits in college mathematics; if in a teacher licensure program, concurrent enrollment in C I 426 or 526
Theory and methods for teaching mathematics in grades 7-12. Includes critical examination of instructional strategies, curriculum materials, learning tools, assessment methods, National Standards in Mathematics Education, and equity issues.

MATH 498. Cooperative Education.

Cr. R. Repeatable, maximum of 2 credits. F.S.SS. Prereq: Permission of the department cooperative education coordinator; senior classification
Required of all cooperative education students. Students must register for this course prior to commencing each work period.

MATH 501. Introduction to Real Analysis.

(3-0) Cr. 3. F. Prereq: 265 and 307 or 317
A development of the real numbers. Study of metric spaces, completeness, compactness, sequences, and continuity of functions. Differentiation and integration of real-valued functions, sequences of functions, limits and convergence, equicontinuity.

MATH 504. Abstract Algebra I.

(3-0) Cr. 3. F. Prereq: 302
Algebraic systems and their morphisms, including groups, rings, modules, and fields.

MATH 505. Abstract Algebra II.

(3-0) Cr. 3. S. Prereq: 504
Continuation of MATH 504.

MATH 510. Linear Algebra.

(3-0) Cr. 3. F. Prereq: 307 or 317
Advanced topics in linear algebra including canonical forms; unitary, normal, Hermitian and positive-definite matrices; variational characterizations of eigenvalues, and applications to other branches of mathematics.

MATH 511. Functions of a Single Complex Variable.

(3-0) Cr. 3. S. Prereq: 414 or 501
Theory of analytic functions, integration, topology of the extended complex plane, singularities and residue theory, maximum principle.

MATH 515. Real Analysis I.

(3-0) Cr. 3. F. Prereq: 414 or 501
Lebesgue measure and Lebesgue integral, one variable differentiation theory, product integration, Lp spaces.

MATH 516. Real Analysis II.

(3-0) Cr. 3. S. Prereq: 515
Metric spaces, topological spaces, compactness, abstract theory of measure and integral, differentiation of measures, Banach spaces.

MATH 517. Finite Difference Methods.

(3-0) Cr. 3. S. Prereq: 481 or 561
Finite difference methods for partial differential equations, with emphasis on parabolic and hyperbolic equations, and other partial differential equations from application areas. Topics include convergence, stability and implementation issues.

MATH 519. Methods of Applied Mathematics I.

(3-0) Cr. 3. F. Prereq: 414 or 501
Techniques of classical and functional analysis with applications to partial differential equations, integral equations. Vector spaces, metric spaces, Hilbert and Banach spaces, Sobolev spaces and other function spaces, contraction mapping theorem, distributions, Fourier series and Fourier transform, linear operators, spectral theory of differential and integral operators, Green's functions and boundary value problems, weak solutions of partial differential equations and variational methods, calculus in Banach spaces and applications.

MATH 520. Methods of Applied Mathematics II.

(3-0) Cr. 3. S. Prereq: 519
Continuation of MATH 519.

MATH 525. Numerical Analysis of High Performance Computing.

(Cross-listed with COM S, CPR E). (3-0) Cr. 3. Alt. S., offered 2013. Prereq: CPR E 308, or one of Math 471, 481; experience in scientific programming; knowledge of FORTRAN or C
Development, analysis, and testing of efficient numerical methods for use on current state-of-the-art high performance computers. Applications of the methods to the students' areas of research.

MATH 533. Cryptography.

(Cross-listed with CPR E, INFAS). (3-0) Cr. 3. S. Prereq: MATH 301 or CPR E 310 or COM S 330
Basic concepts of secure communication, DES and AES, public-key cryptosystems, elliptic curves, hash algorithms, digital signatures, applications. Relevant material on number theory and finite fields.

MATH 535. Steganography and Digital Image Forensics.

(Cross-listed with CPR E, INFAS). (3-0) Cr. 3. S. Prereq: E E 524 or MATH 307 or COM S 330
Basic principles of covert communication, steganalysis, and forensic analysis for digital images. Steganographic security and capacity, matrix embedding, blind attacks, image forensic detection and device identification techniques. Related material on coding theory, statistics, image processing, pattern recognition.

MATH 540. Seminar in Mathematics Education.

(1-0) Cr. 1. SS. Prereq: Enrollment in the Master of School Mathematics program or professional studies in education
Research studies in mathematics learning and teaching, exemplary practices in mathematics education, and current state and national trends in the mathematics curriculum in grades K-12. Topics are offered on a 3-year cycle.

MATH 545. Intermediate Calculus.

(4-0) Cr. 4. Prereq: 3 semesters of calculus and enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2013. Further development of the fundamental concepts of calculus and their applications with an emphasis on a constructivist approach to learning, cooperative groups, problem solving, the use of technology.

MATH 546. Algorithms in Analysis and Their Computer Implementation.

(2-2) Cr. 3. Prereq: 3 semesters in calculus or concurrent enrollment in 545 and enrollment in the master of school mathematics program
Offered on a 3- year cycle, offered SS. 2013. The use of technology in secondary mathematics with an emphasis on the exploration and implementation of algorithms.

MATH 547. Discrete Mathematics and Applications.

(4-0) Cr. 4. Prereq: Enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2012. Applications of graph theory, game theory, linear programming, recursion, combinatorics and algebraic structures. Issues in integrating discrete topics into the secondary curriculum. Use of the computer to explore discrete mathematics.

MATH 549. Intermediate Geometry.

(3-0) Cr. 3. Prereq: 435 or equivalent and enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2012. A study of geometry with emphasis on metrics, the group of isometries, and the group of similarities. Specific spaces studied normally include the Euclidean plane, the 2-sphere, projective 2-space, and hyperbolic geometry. Emphasis on analytical methods. Incorporation of geometry software.

MATH 554. Introduction to Stochastic Processes.

(Cross-listed with STAT). (3-0) Cr. 3. F. Prereq: STAT 542
Markov chains on discrete spaces in discrete and continuous time (random walks, Poisson processes, birth and death processes) and their long-term behavior. Optional topics may include branching processes, renewal theory, introduction to Brownian motion.

MATH 557. Ordinary Differential Equations I.

(3-0) Cr. 3. F. Prereq: 415 or 501
The initial-value problem, existence and uniqueness theorems, continuous dependence on parameters, linear systems, stability and asymptotic behavior of solutions, linearization, topics from dynamical systems and two-point boundary-value problems.

MATH 561. Numerical Analysis I.

(3-0) Cr. 3. F. Prereq: 414 or 501
Approximation theory, including polynomial spline interpolation and best approximation; numerical differentiation and integration; numerical methods for ordinary differential equations.

MATH 562. Numerical Analysis II.

(3-0) Cr. 3. S. Prereq: 317
Numerical linear algebra including eigenvalue problems; numerical solution of nonlinear equations and optimization problems.

MATH 573. Random Signal Analysis and Kalman Filtering.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. F. Prereq: E E 324 or AER E 331 or M E 370 or M E 411 or MATH 341 or 395
Elementary notions of probability. Random processes. Autocorrelation and spectral functions. Estimation of spectrum from finite data. Response of linear systems to random inputs. Discrete and continuous Kalman filter theory and applications. Smoothing and prediction. Linearization of nonlinear dynamics.

MATH 574. Optimal Control.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. S. Prereq: E E 577
The optimal control problem. Variational approach. Pontryagin's principle. Hamilton-Jacobi equation. Dynamic programming. Time-optimal, minimum fuel, minimum energy control systems. The regulator problem. Structures and properties of optimal controls.

MATH 575. Introduction to Robust Control.

(Cross-listed with E E, M E, AER E). (3-0) Cr. 3. Prereq: E E 577
Introduction to modern robust control. Model and signal uncertainty in control systems. Uncertainty description. Stability and performance robustness to uncertainty. Solutions to the H2, Hoo, and l1 control problems. Tools for robustness analysis and synthesis.

MATH 576. Digital Feedback Control Systems.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. F. Prereq: E E 475 or AER E 432 or M E 411 or 414 or MATH 415; and MATH 267
Sampled-data, discrete data, and the z-transform. Design of digital control systems using transform methods: root locus, frequency response and direct design methods. Design using state-space methods. Controllability, observability, pole placement, state estimators. Digital filters in control systems. Microcomputer implementation of digital filters. Finite wordlength effects. Linear quadratic optimal control in digital control systems. Simulation of digital control systems.

MATH 577. Linear Systems.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. F. Prereq: E E 324 or AER E 331 or M E 414 or MATH 415; and MATH 307
Linear algebra review. Least square method and singular value decomposition. State space modeling of linear continuous-time systems. Solution of linear systems. Controllability and observability. Canonical description of linear equations. Stability of linear systems. State feedback and pole placements. Observer design for linear systems.

MATH 578. Nonlinear Systems.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. S. Prereq: E E 577
Linear vs nonlinear systems. Phase plane analysis. Bifurcation and center manifold theory. Lyapunov stability. Absolute stability of feedback systems. Input-output stability. Passivity theory and feedback linearization. Nonlinear control design techniques.

MATH 590. Independent Study.

Cr. arr. Repeatable.

MATH 591. Orientation for Mathematics Graduate Students I.

(0.5-0) Cr. 0.5. F.
Fall semester orientation seminar. Required for graduate students in Mathematics and Applied Mathematics. Topics include teaching at the university level and communication of mathematics. Offered on a satisfactory-fail basis only.

MATH 592. Orientation for Mathematics Graduate Students II.

(0.5-0) Cr. 0.5. S.
Spring semester orientation seminar. Required for graduate students in Mathematics and Applied Mathematics. Topics include teaching at the university level and communication of mathematics. Offered on a satisfactory-fail basis only.

MATH 595. Special Topics.

Cr. arr. Repeatable.

MATH 599. Creative Component.

Cr. arr.

MATH 601. Mathematical Logic I.

(3-0) Cr. 3. Alt. F., offered 2011. Prereq: 504
First semester of full-year course. Completeness and compactness of propositional and predicate logic, incompleteness and undecidability of set theory and arithmetic, Goedel's theorems, recursive functions, computability, models, ultraproducts, and ultralimits.

MATH 602. Mathematical Logic II.

(3-0) Cr. 3. Alt. S., offered 2012. Prereq: 601
Continuation of MATH 601.

MATH 605. Design Theory and Association Schemes.

(3-0) Cr. 3. Alt. F., offered 2012. Prereq: 504
Combinatorial designs and Latin squares. Construction methods including finite fields. Error-correcting codes. Adjacency matrices and algebraic combinatorics.

MATH 606. Enumerative Combinatorics and Ordered Sets.

(3-0) Cr. 3. Alt. S., offered 2013. Prereq: 504
Ordered sets and lattices. Generating functions. Moebius inversion and other enumeration methods.

MATH 607. Modern (Structural) Graph Theory.

(3-0) Cr. 3. Alt. F., offered 2011. Prereq: 504
Structural and extremal theory of graphs. Topics include basic structures (trees, paths and cycles), networks, colorings, connectivity, topological graph theory, Ramsey theory, forbidden graphs and minors, introduction to random graphs, applications.

MATH 608. Extremal Graph Theory.

(3-0) Cr. 3. Alt. S., offered 2012. Prereq: MATH 607
Study of extremal graph problems and methods. Topics include Szemeredi's regularity lemma, generalizations of the theorems of Turan and Ramsey, and the theory of random graphs.

MATH 610. Seminar.

Cr. arr.

MATH 615. General Theory of Algebraic Structures I.

(3-0) Cr. 3. Alt. F., offered 2012. Prereq: 504
First semester of full-year course. Subalgebras, homomorphisms, congruence relations, and direct products. Lattices and closure operators. Varieties and quasivarieties of algebras, free algebras, Birkhoff's theorems, clones, Mal'cev conditions. Advanced topics.

MATH 616. General Theory of Algebraic Structures II.

(3-0) Cr. 3. Alt. S., offered 2013. Prereq: 615
Continuation of MATH 615.

MATH 617. Category Theory.

(3-0) Cr. 3. Alt. F., offered 2011. Prereq: 504
Categories and functors and their applications.

MATH 618. Representation Theory.

(3-0) Cr. 3. Alt. S., offered 2012. Prereq: 504
Representations of algebraic structures. Content varies by semester.

MATH 621. Topology.

(3-0) Cr. 3. Alt. F., offered 2012. Prereq: Permission of instructor
Introduction to general topology. Topological spaces, continuous functions, connectedness, compactness. Topics selected from countability and separation axioms, metrization, and complete metric spaces.

MATH 622. Algebraic Topology.

(3-0) Cr. 3. Alt. S., offered 2013. Prereq: 504
Foundations of algebraic topology. The fundamental group, homology groups, relative homology groups, and long exact sequences.

MATH 624. Manifolds, Tensors and Differential Geometry.

(3-0) Cr. 3. Alt. F., offered 2012. Prereq: 501 or 515
Topics selected from: Geometry of curves and surfaces. Manifolds, coordinate systems. Tensors, differential forms, Riemannian metrics. Connections, covariant differentiation, curvature tensors.

MATH 633. Functional Analysis I.

(3-0) Cr. 3. Alt. F., offered 2011. Prereq: 515
Fundamental theory of normed linear spaces and algebras, such as topology and continuity, duality and spectral theory, emphasizing aspects that provide a framework for the study of boundary-value problems, eigenvalue problems, harmonic analysis, analytic function theory, and modern operator theory.

MATH 634. Functional Analysis II.

(3-0) Cr. 3. Alt. S., offered 2012. Prereq: 633
Continuation of MATH 633.

MATH 642. Advanced Probability Theory.

(Cross-listed with STAT). (4-0) Cr. 4. F. Prereq: STAT 542
Measure spaces, extension theorem and construction of Lebesgue-Stieltjes measures on Euclidean spaces, Lebesgue integration and the basic convergence theorems, Lp-spaces, absolute continuity of measures and the Radon-Nikodym theorem, absolute continuity of functions on R and the fundamental theorem of Lebesgue integration, product spaces and Fubini-Tonelli Theorems, convolutions. Fourier series and transforms, probability spaces; Kolmogorov's existence theorem for stochastic processes; expectation; Jensen's inequality and applications, independence, Borel-Cantelli lemmas; weak and strong laws of large numbers and applications, renewal theory.

MATH 645. Advanced Stochastic Processes.

(Cross-listed with STAT). (3-0) Cr. 3. S.
Weak convergence. Random walks and Brownian motion. Martingales. Stochastic integration and Ito's Formula. Stochastic differential equations and applications.

MATH 646. Mathematical Modeling of Complex Physical Systems.

(Cross-listed with PHYS). (3-0) Cr. 3. S.
Modeling of the dynamics of complex systems on multiple scales: Classical and dissipative molecular dynamics, stochastic modeling and Monte-Carlo simulation; coarse grained nonlinear dynamics, interface propagation and spatial pattern formation.

MATH 655. Partial Differential Equations I.

(3-0) Cr. 3. F. Prereq: 515 or 519
First order equations and systems, conservation laws, general theory of linear partial differential equations of elliptic, parabolic and hyperbolic types, maximum principles, fundamental solutions, Sobolev spaces, variational and Hilbert space methods.

MATH 656. Partial Differential Equations II.

(3-0) Cr. 3. S. Prereq: 655
Continuation of MATH 655.

MATH 658. Dynamical Systems.

(3-0) Cr. 3. Alt. S., offered 2013. Prereq: 501 or 515 or 557
Smooth mappings and flows. Fixed points, stable, unstable and center manifolds, normal forms. Structural stability, bifurcations. Horseshoe maps, introduction to chaotic behavior.

MATH 666. Finite Element Methods.

(3-0) Cr. 3. F. Prereq: 516 or 520 or 561 or 656
Elements of functional analysis; Sobolev spaces; variational principles and weak formulations; approximation theory in finite element spaces; analysis of finite element methods; implementation issues; applications.

MATH 680. Advanced Topics.

Cr. 3. Repeatable.

MATH 699. Research.

Cr. arr. Repeatable.