Mathematics

(4-0) Cr. 0. F.S.

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 MATH 30 respectively depending on the level of material covered. Satisfactory completion of MATH 30 is recommended for students planning to take MATH 140, MATH 143, MATH 145, MATH 150, or MATH 151, while MATH 25 is sufficient for MATH 104, MATH 105, MATH 195, STAT 101 or STAT 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.

(4-0) Cr. 0. F.S.

Students should initially enroll in MATH 10. See description of MATH 10. Offered on a satisfactory-fail basis only.

(4-0) Cr. 0. F.S.

Students should initially enroll in MATH 10. See description of MATH 10. Offered on a satisfactory-fail basis only.

(1-0) Cr. 1. F.

A required orientation for all first-year and transfer students in mathematics. Provides information about campus resources and opportunities available to students, assists with transition to the University, and academic planning. Offered on a satisfactory/fail basis only. Offered on a satisfactory-fail basis only.

(3-0) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry
Permutations, combinations, probability, expected value, and applications. Either MATH 104 or MATH 150 may be counted toward graduation, but not both.

(3-0) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry.
Introduction to the use of basic mathematics to solve real-world problems in the areas of voting issues, measuring power in situations where people have different numbers of votes, apportionment, fair division, and elementary game theory. No prior background in politics or history is necessary for this course.

(3-1) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry; or MATH 30.
Coordinate geometry, quadratic and polynomial equations, functions, graphing, rational functions, exponential and logarithmic functions, inverse functions, quadratic inequalities, systems of linear equations. Prepares students for MATH 160.

(4-0) Cr. 4. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry; or MATH 140.
Preparation for MATH 160, MATH 165, and MATH 181. Functions, graphing, basic trigonometry, logarithms, exponentials. Emphasis on co-variational reasoning. Only one of MATH 143 and MATH 145 may count toward graduation.

(3-0) Cr. 3. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry; or minimum of C- in MATH 140.
Mathematical ideas regarding the conception of space. General trigonometry, with an emphasis on the calculation of lengths, areas, and angles. The Law of Sines and the Law of Cosines. Polar, cylindrical, and spherical coordinate systems. Conic sections and quadric surfaces. Only one of MATH 143 and MATH 145 may count toward graduation.

(2-1) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 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 MATH 150 may be counted toward graduation, but not both.

(2-1) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 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 MATH 265 or MATH 266. Only one of MATH 151, MATH 160, or the sequence MATH 165-MATH 166 may be counted towards graduation.

(4-0) Cr. 4. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of geometry; or minimum of C- in MATH 140; or minimum of C- in MATH 143
Analytic geometry, derivatives and integrals of elementary functions, simple differential equations, and applications. Will not serve as a prerequisite for MATH 265 or MATH 266. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or MATH 181 may be counted towards graduation.

(4-0) Cr. 4. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry; or minimum of C- in MATH 143
Differential calculus, applications of the derivative, introduction to integral calculus. Only one of MATH 151 or MATH 160 or the sequence MATH 165-MATH 166 may be counted towards graduation.

(4-0) Cr. 4. F.S.SS.

Prereq: Minimum of C- in MATH 165 or high math placement scores
Integral calculus, applications of the integral, parametric curves and polar coordinates, power series and Taylor series. Only one of MATH 151, MATH 160, or the sequence MATH 165-MATH 166 may be counted towards graduation.

(4-0) Cr. 4. F.

Prereq: Permission of instructor and minimum C- in MATH 165 or high math placement scores
Integral calculus, applications of the integral, parametric curves and polar coordinates, power series and Taylor 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 MATH 160, or the sequence MATH 165-MATH 166 may be counted towards graduation.

(2-2) Cr. 3. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years high school algebra, 1 year of high school geometry, enrollment in elementary education or early childhood education
Whole number operations through analysis of properties, theoretical and hands-on models, mathematical analysis of elementary students’ thinking; standard and non-standard algorithms; structure of the decimal system; linear measurement; two- and three-dimensional measurement, shapes and spatial sense; number theory; algebra as it relates to elementary curricula/teaching profession. Students in the College of Liberal Arts and Sciences may not count MATH 195 toward General Education Requirements.

(2-2) Cr. 3. F.S.

Prereq: Minimum of C- in MATH 195 and enrollment in elementary education or early childhood education.
Integer, fraction and decimal operations through analysis of properties, theoretical and hands-on models, mathematical analysis of elementary students’ thinking; standard and non-standard algorithms; continuation of two- and three-dimensional measurement, shapes and spatial sense; probability and statistics; proportional reasoning; algebra as it relates to elementary curricula/teaching profession.

(3-0) Cr. 3. F.S.

Prereq: MATH 166 or MATH 166H
Transition to advanced mathematics. Communicating mathematics. Logical arguments; techniques of proofs regarding sets, numbers (natural and real), functions, relations, and limits.

(Cross-listed with STAT). Cr. 1. S.

Career development in the mathematics and statistics disciplines with an emphasis on contemporary social issues. Presentations by professionals in STEM fields about occupations, decision-making strategies, and career goal implementation; development of job searching, resume writing, negotiating, and interviewing techniques. Offered on a satisfactory-fail basis only.

(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 applications and techniques. Only one of MATH 207 and MATH 317 may be counted toward graduation.

(Cross-listed with COM S). (3-1) Cr. 3. F.S.SS.

Prereq: Minimum of C- in COM S 227 and MATH 165; ENGL 150
Concepts in discrete mathematics as applied to computer science. Logic, set theory, functions, relations, combinatorics, discrete probability, graph theory and number theory. Proof techniques, induction and recursion.

(3-0) Cr. 3. F.S.

Prereq: MATH 166
Interest rates, time value of money, annuities. Loans, bonds, yield rates. Term structure of interest rates, asset and liability management. Duration, convexity, immunization.

(4-0) Cr. 4. F.S.SS.

Prereq: Minimum of C- in MATH 166 or MATH 166H
Geometry of space and vectors, multivariable differential calculus, multivariable integral calculus, vector calculus.

(4-0) Cr. 4. F.S.

Prereq: Permission of the instructor; and minimum of C- in MATH 166 or MATH 166H
Geometry of space and vectors, multivariable differential calculus, multivariable integral calculus, 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.

(3-0) Cr. 3. F.S.SS.

Prereq: Minimum of C- in MATH 166 or MATH 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.

(4-0) Cr. 4. F.S.SS.

Prereq: Minimum of C- in MATH 166 or MATH 166H
Same as MATH 266 but also including Laplace transforms and power series solutions to ordinary differential equations.

(1-0) Cr. 1. F.S.SS.

Prereq: MATH 266
Laplace transforms and power series solutions to ordinary differential equations. Together, MATH 266 and MATH 268 are the same as MATH 267.

(1-0) Cr. 1. F.S.SS.

Prereq: Familiarity with ordinary differential equations of first and second order, permission of department.
Systems portion of MATH 266 and MATH 267: Eigenvalue methods for systems of first order linear equations. Introduction to stability and phase plane analysis. For students supplementing transfer courses in differential equations in order to earn credit in MATH 266 or 267. Students with credit in MATH 266 or MATH 267 may not earn credit in MATH 269.

Cr. 1-3. Repeatable.

Prereq: Permission of the instructor.
Independent study.

Cr. 1-3. Repeatable.

Prereq: Permission of the instructor.
Independent study.

(2-2) Cr. 3. F.

Prereq: Enrollment in elementary education and minimum of C- in MATH 196
Mathematical reasoning and topics in Euclidean and non-Euclidean geometry, including transformations, congruence, and similarity; exploration of probability with simulations; linearity and connections to Calculus; fractals and fractal dimension.

(3-0) Cr. 3. F.S.

Prereq: MATH 166 or MATH 166H, MATH 317, and grade of C- or better in MATH 201
Basic properties of integers, divisibility and unique factorization. Polynomial rings over a field. Congruence. Introduction to abstract rings, homomorphisms, ideals. Roots and irreducibility of polynomials. Introduction to groups. Emphasis on proofs.

(3-0) Cr. 3. F.

Prereq: MATH 166 or MATH 166H; MATH 201 or experience with proofs
Enumeration strategies involving permutations, combinations, partitions, binomial coefficients, inclusion-exclusion principle, recurrence relations, generating functions. Additional topics selected from probability, algebraic combinatorics, and applications.

(3-0) Cr. 3. S.

Prereq: MATH 166 or MATH 166H; MATH 201 or experience with proofs
Structure and extremal properties of graphs. Topics are selected from: trees, networks, colorings, paths and cycles, connectivity, planarity, directed graphs, matchings, Ramsey theory, forbidden structures, enumeration, applications.

(4-0) Cr. 4. F.S.

Prereq: Credit or enrollment in MATH 201
Systems of linear equations, determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors. Emphasis on writing proofs and results. Only one of MATH 207 and MATH 317 may be counted toward graduation.

(Cross-listed with STAT). (3-2) Cr. 4. F.S.

Prereq: MATH 265 (or MATH 265H)
Probability; distribution functions and their properties; classical discrete and continuous distribution functions; multivariate probability distributions and their properties; moment generating functions; transformations of random variables; simulation of random variables and use of the R statistical package. Credit for only one of the following courses may be applied toward graduation: STAT 341, STAT 347, STAT 447, or STAT 588.

(Cross-listed with STAT). (3-2) Cr. 4. F.S.

Prereq: STAT 201 or equivalent; STAT 341; MATH 207 or MATH 317
Sampling distributions; confidence intervals and hypothesis testing; theory of estimation and hypothesis tests; linear model theory; resampling methods; introduction to Bayesian inference; use of the R statistical package for simulation and data analysis.

(Cross-listed with COM S). (3-0) Cr. 3. S.

Prereq: MATH 201 or COM S 230
Divisibility, integer representations, primes and divisors, linear diophantine equations, congruences, and multiplicative functions. Applications to cryptography. Additional topics, chosen at the discretion of the instructor.

(3-0) Cr. 3. S.

Prereq: MATH 265
Functions of a complex variable, including differentiation, integration, series, residues, and conformal mappings.

(3-0) Cr. 3. F.

Prereq: MATH 265
Vector and matrix programming and graphing in MATLAB for scientific applications. Polynomial interpolation and approximation. Systems of linear equations and numerical linear algebra. Numerical differentiation and integration. Root-finding methods for 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.

(3-0) Cr. 3. F.S.

Prereq: MATH 265 and one of MATH 266, MATH 267
Method of separation of variables for linear partial differential equations, including heat equation, Poisson equation, and wave equation. Topics from Fourier series, Sturm-Liouville theory, Bessel functions, spherical harmonics, and method of characteristics.

(2-2) Cr. 3. S.

Prereq: MATH 201, MATH 301
Coursework in university mathematics including calculus, abstract algebra, discrete mathematics, geometry, and other topics as it relates to teaching mathematics in grades 5-12.

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.

(Dual-listed with MATH 507). (3-0) Cr. 3. F.

Prereq: MATH 317; or MATH 207 and experience writing proofs
Advanced topics in applied linear algebra including eigenvalues, eigenvalue localization, singular value decomposition, symmetric and Hermitian matrices, nonnegative and stochastic matrices, matrix norms, canonical forms, matrix functions. Applications to mathematical and physical sciences, engineering, and other fields.

(3-0) Cr. 3. F.S.SS.

Prereq: Minimum of C- in MATH 201
A rigorous development of calculus of functions of one real variable: real number properties and topology, limits, continuity, differentiation, integration, series.

(3-0) Cr. 3. S.

Prereq: MATH 414; MATH 265; and MATH 317 or MATH 407
Sequences and series of functions of a real variable, uniform convergence, power series, metric spaces, calculus of functions of two or more real variables.

(Cross-listed with COM S). (3-0) Cr. 3.

Prereq: MATH 301 or MATH 207 or MATH 317 or COM S 230 or CPR E 310
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.

(Cross-listed with COM S, CPR E). (2-2) Cr. 3. F.

Prereq: MATH 265; MATH 207 or MATH 317; or permission of instructor.
Unix, serial programming of scientific applications, OpenMP for shared-memory parallelization. No Unix, Fortran or C experience required.

(3-0) Cr. 3. F.

Prereq: MATH 201; MATH 207 or MATH 317
Euclidean geometry of triangles, circles, and parallelograms, studied from several points of view, chosen from: synthetic, analytic, axiomatic, transformational, complex numbers, or vector methods. Possible and impossible constructions with compass and straightedge.

(3-0) Cr. 3. S.

Prereq: MATH 201; MATH 207 or MATH 317
Foundations of Euclidean geometry and the axiomatic method, including the use of models. The history, logical consistency, and basic theorems of non-Euclidean geometries, such as hyperbolic, elliptic, and projective geometry.

Cr. 3. F.

Prereq: MATH 240, credit or coenrollment in MATH 265
Topics in life insurance for the Actuarial Sciences I: single life annuities, benefits premiums and reserves.

Cr. 3. S.

Prereq: MATH 441
Topics in life insurance for the Actuarial Sciences II: multiple life functions, multiple decrement models, pension plan valuation, insurance models, applications.

(Dual-listed with MATH 581). (Cross-listed with COM S). (3-0) Cr. 3. S.

Prereq: MATH 265 and either MATH 266 or MATH 267
First order Euler method, high order Runge-Kutta methods, and multistep methods 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. Computer programming required.

Cr. 1-3. Repeatable, maximum of 9 credits.

Prereq: Permission of instructor.
No more than 9 credits of Math 490 or Math 490H may be counted toward graduation.

Cr. 1-3. Repeatable, maximum of 9 credits.

Prereq: Permission of the instructor.
No more than 9 credits of Math 490 or 490H may be counted toward graduation.

Cr. 2-3.

Writing and presenting a formal mathematics paper. Upon approval by the department, the paper will satisfy the departmental advanced English requirement.

(2-0) Cr. 2. F.S.

Prereq: MATH 317 or MATH 407
Introduction to independent mathematical thought, with emphasis on oral communication of an advanced topic. Seminar content varies.

Cr. arr. Repeatable, maximum of 9 credits.

Prereq: Permission of instructor
Topics of current interest.

(Cross-listed with EDUC). (3-0) Cr. 3. F.

Prereq: 15 credits in college mathematics. Admitted to the Educator Preparation Program.
Develop an understanding of instructional planning, lesson implementation, and assessment in grades 5-12 mathematics, with a focus on reform-based mathematics, equity, and conceptual understanding.

(3-0) Cr. 3. F.

Prereq: MATH 265 and (MATH 207 or MATH 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.

(3-0) Cr. 3. S.

Prereq: MATH 414 or MATH 501
Introduction to general topology. Topological spaces, continuous functions, connectedness, compactness. Topics selected from countability and separation axioms, metrization, and complete metric spaces. Topics in algebraic topology.

(3-0) Cr. 3. F.

Prereq: MATH 302
Algebraic systems and their morphisms, with emphasis on groups and rings.

(3-0) Cr. 3. S.

Prereq: MATH 504
Continuation of MATH 504. Algebraic systems and their morphisms, with emphasis on modules and fields.

(Dual-listed with MATH 407). (3-0) Cr. 3. F.

Prereq: MATH 317; or MATH 207 and experience writing proofs
Advanced topics in applied linear algebra including eigenvalues, eigenvalue localization, singular value decomposition, symmetric and Hermitian matrices, nonnegative and stochastic matrices, matrix norms, canonical forms, matrix functions. Applications to mathematical and physical sciences, engineering, and other fields.

(3-0) Cr. 3. S.

Prereq: MATH 317 or MATH 407 or (MATH 207 and one of MATH 301 or MATH 414)
Advanced topics in linear algebra including canonical forms; unitary, normal, Hermitian and positive-definite matrices; variational characterizations of eigenvalues.

(3-0) Cr. 3. S.

Prereq: MATH 414 or MATH 501
Theory of analytic functions, integration, topology of the extended complex plane, singularities and residue theory, maximum principle, conformal mapping, meromorphic functions, argument principle.

(3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501
Lebesgue measure and Lebesgue integral, one variable differentiation theory, Fubini and Tonelli theorems in R^n, Lp spaces.

(3-0) Cr. 3. S.

Prereq: MATH 515
Metric spaces, topological spaces, compactness, abstract theory of measure and integral, differentiation of measures, Banach spaces.

(3-0) Cr. 3. S.

Prereq: MATH 481 or MATH 561
Finite difference methods for partial differential equations. Methods for elliptic equations; explicit and implicit methods for parabolic and hyperbolic equations; stability, accuracy, and convergence theory, including von Neumann analysis, modified equations, and the Courant-Friedrichs-Lewy condition.

(3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501
Techniques of classical and functional analysis with applications to differential equations and 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.

(3-0) Cr. 3. S.

Prereq: MATH 519
Continuation of MATH 519. 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.

(Cross-listed with COM S, CPR E). (3-0) Cr. 3. S.

Prereq: CPR E 308 or MATH 481; experience in scientific programming; knowledge of FORTRAN or C
Introduction to parallelization techniques and numerical methods for distributed memory high performance computers. A semester project in an area related to each student’s research interests is required.

(Cross-listed with CPR E, CYBSC). (3-0) Cr. 3. S.

Prereq: MATH 301 or CPR E 310 or COM S 230
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.

(Cross-listed with CPR E, CYBSC). (3-0) Cr. 3. S.

Prereq: E E 524 or MATH 317 or MATH 407 or COM S 230
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.

(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. Students in MSM take each of 540A, 540B, and 540C. Topics are offered on a 3-year cycle. A. Assessment, equity, and teaching of statistics. Offered SS 2017. B. Geometry and discrete mathematics, and problem solving. Offered SS 2018. C. Teaching of analysis, algebra, and the use of technology. Offered SS 2016.

(1-0) Cr. 1.

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. Offered SS 2017.

(1-0) Cr. 1.

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. Offered on a 3-year cycle. Offered SS 2018.

(1-0) Cr. 1.

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. Offered SS 2016.

(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. 2016. The fundamental concepts of calculus which are critical to the effective understanding of the material in first year calculus. Emphasis is on a constructivist approach to learning, cooperative groups, problem solving, and use of technology.

(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. 2016. The use of technology in secondary mathematics with an emphasis on the exploration, creation, and implementation of algorithms.

(4-0) Cr. 4.

Prereq: Enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2018. Applications of graph theory, game theory, voting theory, recursion, combinatorics, and algebraic structures. Issues in integrating discrete topics into the secondary curriculum. Use of the computer to explore discrete mathematics.

(3-0) Cr. 3.

Prereq: MATH 435 or equivalent and enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2018. 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.

(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.

(3-0) Cr. 3. F.

Prereq: MATH 415 or MATH 501
The initial-value problem, existence and uniqueness theorems, continuous dependence on parameters, linear systems, stability and asymptotic behavior of solutions, linearization, dynamical systems, bifurcations, and chaotic behavior.

(3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501
Approximation theory, including polynomial interpolation, spline interpolation and best approximation; numerical differentiation and integration; numerical methods for ordinary differential equations.

(3-0) Cr. 3. S.

Prereq: MATH 317
Numerical linear algebra including LU factorization, QR factorization, linear least squares, singular value decomposition, eigenvalue problems, and iterative methods for large linear systems.

(3-0) Cr. 3. S.

Prereq: MATH 265 and one of MATH 317, 507, 510
Theory and methods for constrained and unconstrained optimization. Steepest-descent, conjugate gradient, Newton and quasi-Newton, line search and trust-region, first and second order necessary and sufficient conditions, linear, quadratic and general nonlinear programming.

(3-0) Cr. 3. F.

Prereq: MATH 317 or MATH 507 or MATH 510
Algorithms for linear programming, integer and combinatorial optimization. Linear programming, duality theory, simplex algorithm; the solution of the shortest-path, minimum spanning tree, max-flow/min-cut, minimum cost flow, maximum matching, and traveling salesman problems; integer linear programming, branch-and-bound, local and global search algorithms; matroids and greedy algorithms.

(3-0) Cr. 3. F.

Prereq: MATH 317 or MATH 507 or MATH 510
Structural theory of graphs. Topics include basic structures (trees, paths, cycles and matchings), networks, colorings, connectivity, topological graph theory, Ramsey and Turan theory, spectral graph theory, introduction to probabilistic methods.

(3-0) Cr. 3. S.

Prereq: MATH 302 or MATH 504
Enumeration methods. Generating functions and sieve methods. Partially ordered sets, lattices, and Moebius inversion. Extremal set theory.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. F.

Prereq: E E 324 or AER E 331 or MATH 415; and MATH 207
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.

(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.

(Dual-listed with MATH 481). (3-0) Cr. 3. S.

Prereq: MATH 265 and either MATH 266 or MATH 267
First order Euler method, high order Runge-Kutta methods, and multistep methods 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. Computer programming required.

Cr. arr. Repeatable.

(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.

(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.

Cr. arr. Repeatable.

Cr. arr.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 504
Model theory of propositional and predicate logic, the Soundness Theorem, the Compactness Theorem, the Goedel-Henkin Completeness Theorem, the Incompleteness Theorem, computability theory. As time permits: modal and temporal logic, set theory (the continuum hypothesis). Emphasis on the relationship between `provable' and `true' and the relationship between `computable' and `definable'.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

Prereq: MATH 504
Combinatorial designs and algebraic codes. Construction methods including finite fields. Error-correcting codes. Adjacency matrices and algebraic combinatorics.

(3-0) Cr. 3. Alt. S., offered even-numbered years.

Prereq: MATH 567
Study of extremal graph problems and methods. Topics include probabilistic methods, generalizations of Turan’s theorem, Szemeredi's regularity lemma, random graph theory.

Cr. arr.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 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.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

Prereq: MATH 615
Continuation of MATH 615.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 504
Categories and functors and their applications.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

Prereq: MATH 504
Representations of algebraic structures. Content varies by semester.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

Prereq: MATH 501 or MATH 515
Topics selected from: Geometry of curves and surfaces. Manifolds, coordinate systems. Tangent and cotangent vectors, vector fields. Tensors, differential forms, Riemannian metrics. Connections, covariant differentiation, curvature tensors. Applications to physics and engineering.

Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 515
Fourier Series on an interval, approximate identities and summation, Gibb's phenomenon, Fourier transform on the line, uncertainty principle. Additional topics may include distributions, Hardy-Littlewood maximal function, boundedness of singular integral operators, arithmetic combinatorics, wavelet theory.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 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 the spectrum of an operator, analytic function theory, and modern operator theory.

(Cross-listed with STAT). (3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501 or equivalent course.
Sequences and set theory; Lebesgue measure, measurable functions. Absolute continuity of functions, integrability and the fundamental theorem of Lebesgue integration. General measure spaces, probability measure, extension theorem and construction of Lebesgue-Stieljes measures on Euclidean spaces. Measurable transformations and random variables, induced measures and probability distributions. General integration and expectation, Lp-spaces and integral inequalities. Uniform integrability and absolute continuity of measures. Probability densities and the Radon-Nikodym theorem. Product spaces and Fubini-Tonelli theorems.

(Cross-listed with STAT). (3-0) Cr. 3. S.

Prereq: STAT 641, or STAT 543 and MATH 515.
Probability spaces and random variables. Kolmogorov's consistency theorem. Independence, Borel-Cantelli lemmas and Kolmogorov's 0 - 1 Law. Comparing types of convergence for random variables. Sums of independent random variables, empirical distributions, weak and strong laws of large numbers. Convergence in distribution and its characterizations, tightness, characteristic functions, central limit theorems and Lindeberg-Feller conditions. Conditional probability and expectation. Discrete parameter martingales and their properties and applications.

(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.

(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.

(3-0) Cr. 3. F.

Prereq: MATH 515 or MATH 519
Study of model problems of elliptic, parabolic and hyperbolic types, first order equations, conservation laws, transform methods, introduction to linear partial differential equations of arbitrary order, fundamental solutions.

(3-0) Cr. 3. S.

Prereq: MATH 655
Sobolev spaces, general theory of second order linear elliptic, parabolic and hyperbolic partial differential equations, first order linear hyperbolic systems, variational methods, fixed point methods.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 516 or MATH 520 or MATH 561 or MATH 656
Weak and variational formulations of elliptic problems; weak derivatives and Sobolev spaces; Lax-Milgram theorem, Bramble-Hilbert lemma; examples of finite element spaces; polynomial approximation theory; error estimates for finite element methods; implementation issues; mixed finite element methods for Stokes problems; applications.

Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 561, MATH 562
Mathematical theory of weak/entropy solutions of nonlinear hyperbolic conservation laws; shock speed and Riemann problems; numerical methods for scalar equations and systems including Euler equations; conservative methods; approximate Riemann solvers; total variation stability; DG method.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. 3. Repeatable.

Cr. arr. Repeatable.