**Any experimental courses offered by MATH can be found at:****registrar.iastate.edu/faculty-staff/courses/explistings/**

## Courses

**Courses primarily for undergraduates:**

(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*

Permutations, combinations, probability, expected value, and applications. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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*

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. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.

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

*Prereq: Satisfactory performance on placement assessment*

Math concepts to provide supplemental assistance with course topics of MATH 140. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
Offered on a satisfactory-fail basis only.

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

*Prereq: Satisfactory performance on placement assessment or concurrent enrollment in MATH 139*

Coordinate geometry, quadratic and polynomial equations, functions, graphing, rational functions, exponential and logarithmic functions, inverse functions, quadratic inequalities, systems of linear equations. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.

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

*Prereq: Satisfactory performance on placement assessment or MATH 140*

Preparation for MATH 160 or MATH 165. Functions, graphing, basic trigonometry, logarithms, exponentials. Emphasis on co-variational reasoning. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
Only one of MATH 143 and MATH 145 may count toward graduation.

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

*Prereq: Satisfactory performance on placement assessment 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. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
Only one of MATH 143 and MATH 145 may count toward graduation.

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

*Prereq: Satisfactory performance on placement assessment*

Math concepts to provide supplemental assistance with course topics of MATH 150. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
Offered on a satisfactory-fail basis only.

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

*Prereq: Satisfactory performance on placement assessment or concurrent enrollment in MATH 149*

Linear equations and inequalities, matrix algebra, linear programming, discrete probability. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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*

Differential calculus, applications to max-min problems, integral calculus and applications. Will not serve as prerequisite for MATH 265 or MATH 266. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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 or minimum of C- in (MATH 140 or 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. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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.SS.

*Prereq: Satisfactory performance on placement assessment or minimum of C- in MATH 143*

Differential calculus, applications of the derivative, introduction to integral calculus. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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 satisfactory performance on placement assessments*

Integral calculus, applications of the integral, parametric curves and polar coordinates, power series and Taylor series. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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: Minimum of C- in MATH 165 or satisfactory performance on placement assessments*

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. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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; Early or Elementary Education major*

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. Satisfactory placement scores can be found at https://math.iastate.edu/academics/undergraduate/aleks/placement/.
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; Early or Elementary Education major*

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.

(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: MATH 166*

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; MATH 165); ENGL 150*

Concepts in discrete mathematics as applied to computer science. Logic, set theory, functions, relations, cardinality of sets, combinatorics, 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.

*Prereq: Permission of Instructor; 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.
Credit for either MATH 267 or the MATH 266, 268 pair of courses, but not both, may be applied toward graduation. Credit for only one of the following courses may be applied toward graduation: MATH 267, MATH 266, MATH 269.

(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.
Credit for either MATH 267 or the MATH 266, 268 pair of courses, but not both, may be applied toward graduation. Credit for only one of the following courses may be applied toward graduation: MATH 267, MATH 266, MATH 269.

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

*Prereq: MATH 266; Department Permission*

Laplace transforms and power series solutions to ordinary differential equations.
Credit for either MATH 267 or the MATH 266, 268 pair of courses, but not both, may be applied toward graduation.

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

*Prereq: Department Permission*

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. Familiarity with ordinary differential equations of first and second order required.
Students with credit in MATH 266 or MATH 267 may not earn credit in MATH 269.

Cr. 1-3. Repeatable.

*Prereq: Permission of Instructor*

Independent study.

Cr. 1-3. Repeatable.

*Prereq: Permission of Instructor*

Independent study.

(2-2) Cr. 3. F.

*Prereq: Minimum of C- in MATH 196; Early or Elementary Education major*

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; minimum of C- 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 COM S 230 or CPR E 310)*

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 COM S 230 or CPR E 310)*

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 concurrent enrollment in MATH 201 or COM S 230 or CPR E 310*

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: (MATH 207 or MATH 317); (STAT 101 or STAT 104 or STAT 105 or STAT 201 or STAT 226 or STAT 231 or STAT 305 or STAT 322 or STAT 330); STAT 341*

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: COM S 230 or CPR E 310 or MATH 201*

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; (MATH 266 or 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.

Cr. R. Repeatable, maximum of 2 times. F.S.SS.

*Prereq: Junior classification; Permission of Department Cooperative Education Coordinator*

Required of all cooperative education students. Students must register for this course prior to commencing each work period.

(Dual-listed with MATH 503). (3-0) Cr. 3. S.

*Prereq: 403: Minimum of C in MATH 301, 503: Not taken MATH 504 or MATH 505*

Properties of groups and rings, subgroups, ideals, and quotients, homomorphisms, structure theory for finite groups. PIDs, UFDs, and Euclidean Domains. Field extensions and finite fields. Selected applications.

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

*Prereq: MATH 317 or (MATH 207; MATH 201)*

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 COM S 230 or CPR E 310 or MATH 201*

A rigorous development of calculus of functions of one real variable: real number properties and topology, limits, continuity, differentiation, integration, series.

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

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

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.

(Dual-listed with MATH 523). (3-0) Cr. 3. F.

*Prereq: MATH 266 or MATH 267*

Introduction to mathematical techniques for modeling and simulation, parameter identification, and analysis of biological systems. Applications drawn from many branches of biology and medicine. Apply differential equations, difference equations, and dynamical systems theory to a wide array of biological problems. MATH 265 or equivalent recommended.

(3-0) Cr. 3. F.

*Prereq: (COM S 230 or CPR E 310 or 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: (COM S 230 or CPR E 310 or 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. 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 569). (3-0) Cr. 3. S.

*Prereq: (MATH 207 or MATH 317); (MATH 304 or MATH 314)*

Combinatorial counting, double-counting, generating functions, graph structure, planar graphs, probabilistic proofs, points in general positions, polytopes, Farkas lemma, linear programming and duality.

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

*Prereq: MATH 265; (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 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.

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.

**Courses primarily for graduate students, open to qualified undergraduates:**

(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.

(Dual-listed with MATH 403). (3-0) Cr. 3. S.

*Prereq: 403: Minimum of C in MATH 301, 503: Not taken MATH 504 or MATH 505*

Properties of groups and rings, subgroups, ideals, and quotients, homomorphisms, structure theory for finite groups. PIDs, UFDs, and Euclidean Domains. Field extensions and finite fields. Selected applications.

(3-0) Cr. 3. F.

*Prereq: MATH 302*

Algebraic systems and their morphisms, with emphasis on groups and rings.

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

*Prereq: MATH 317 or (MATH 207; MATH 201)*

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 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. S.

*Prereq: MATH 414, MATH 415*

Basic theory of ordinary differential equations, existence and uniqueness theorems, linear systems, linearization and stability, mathematical models in biology and physics, modeling with ordinary and partial differential equations, dynamical systems techniques.

(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.

(Dual-listed with MATH 423). (Cross-listed with BCB, BCBIO). (3-0) Cr. 3. F.

*Prereq: MATH 266 or MATH 267*

Introduction to mathematical techniques for modeling and simulation, parameter identification, and analysis of biological systems. Applications drawn from many branches of biology and medicine. Apply differential equations, difference equations, and dynamical systems theory to a wide array of biological problems. MATH 265 or equivalent recommended.

(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: 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.

(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. Alt. F., offered irregularly.

*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. 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.

(Dual-listed with MATH 469). (3-0) Cr. 3. S.

*Prereq: (MATH 207 or MATH 317); (MATH 304 or MATH 314)*

Combinatorial counting, double-counting, generating functions, graph structure, planar graphs, probabilistic proofs, points in general positions, polytopes, Farkas lemma, linear programming and duality.

(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; (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.

**Courses for graduate students:**

(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 even-numbered years.

*Prereq: MATH 601*

Topics in model theory, computability theory, and set theory such as infinitary logic, non-standard models of arithmetic, ultraproducts, and independence results.

(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*

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. F., offered odd-numbered years.

*Prereq: MATH 505.*

Detailed study of commutative rings with applications to number theory and algebraic geometry, including prime ideals, Going Up and Going Down theorems, exact sequences, Ext and Tor, modules of fractions, primary decomposition, rings of integers, dimension theory.

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

*Prereq: MATH 504; and MATH 507 or MATH 510*

Nilpotent and solvable Lie algebras. Root systems and the classification of finite-dimensional complex semi-simple Lie algebras. The universal enveloping algebra. Representation theory including Weyl's theorem, Verma modules, highest weight theory.

(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. Types and characterizations of convergence for random variables. Sums of independent random variables, empirical distributions, weak and strong laws of large numbers. Convergence in distribution and its formulations, tightness, characteristic functions, central limit theorems and Lindeberg-Feller conditions. Conditional probability and expectation, discrete parameter martingales.

(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. 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.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

(3-0) Cr. 3. Repeatable.

Cr. arr. Repeatable.