# All Courses

MATH 2: Intermediate Mathematics (3
) U

Mathematics (primarily algebra) preparatory to MATH 101. Qualification: Two years of high school college preparatory mathematics, algebra and geometry, and a score of 16 or more on ACT mathematics; or a qualifying score on the mathematics placement test. MATH 002 is the lowest level mathematics course offered at the University of Kansas. Students not prepared for MATH 101 will be permitted to enroll in MATH 002. However, before enrolling in MATH 002, such students are encouraged to prepare by self-study or by completing a beginning algebra course in high school, community college, or correspondence study.

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MATH 101: College Algebra (3
) U

Coordinate systems, functions and their graphs; linear, quadratic, general polynomial, rational, exponential, and logarithmic functions;equations and inequalities; linear and non-linear systems and matrices. Not open to students with credit in MATH 104. Prerequisite: MATH 002, or two years of high school algebra and a score of 22 or higher on ACT mathematics, or a qualifying score on the mathematics placement test.

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MATH 103: Trigonometry (2
) U

The circular functions and their applications. Not open to students with credit in MATH 104. May not be used to fulfill the College mathematics requirement. Prerequisite: MATH 101, or two years of high school algebra and a score of 26 or higher on enhanced ACT mathematics, or a qualifying score on the mathematics placement test.

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MATH 104: Precalculus Mathematics (5
) U

An introduction to the elementary functions (polynomial, rational, exponential, logarithmic, and trigonometric) and their properties. Intended primarily for students intending to enroll in MATH 121. Open for only two hours credit for students with credit in MATH 101. Not open to students with credit in MATH 103. Prerequisite: MATH 002, or two years of high school algebra and a score of 22 or higher on ACT mathematics, or a qualifying score on the mathematics placement test.

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MATH 105: Introduction to Topics in Mathematics (3
) N

This course has two purposes. First, to provide the student with some experience and insight into several areas of mathematics not normally covered in elementary courses. Typical topics which may be covered are number theory, geometries, introductory calculus, introductory probability and statistics. Second, to provide the student with some skill in handling abstract mathematical concepts. The material will develop dually the intuitive and axiomatic approach. A high degree of manipulative skill is not required for this course. Prerequisite: MATH 101 or MATH 104, or two years of high school algebra and a score of 26 or higher on ACT mathematics, or a qualifying score on the mathematics placement test.

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MATH 109: Mathematics for Elementary School Teachers I (3
) U

This course is designed to give the prospective elementary school teacher an overview of several components of the elementary school mathematics curriculum, including number systems, estimation, inequalities and order, sequences and patterns, sets, and relations and functions. The class meets each week for three one-hour instruction sessions and one two-hour laboratory session. This course may not be used to satisfy the College mathematics requirement. Prerequisite: MATH 101 or equivalent placement.

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MATH 110: Mathematics for Elementary School Teachers II (3
) U

Continuation of MATH 109, including geometry (including transformations) and elementary probability and statistics. Class meets each week for three one-hour instruction sessions and one two-hour laboratory session. This course does not serve as a prerequisite for any mathematics course. It may not be used to satisfy the College mathematics requirement. Prerequisite: MATH 109.

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MATH 111: Matrix Algebra, Probability, and Statistics (3
) N

Introduction to topics in matrix algebra, probability, and statistics. Topics will include matrix operations, the use of matrices to solve systems of linear equations, elementary data analysis, elementary statistical procedures, sample spaces and probability measures, random variables, probability models, links between probability and statistics, and applications. Prerequisite: MATH 101 or MATH 104, or two years of high school algebra and a score of 26 or higher on the ACT mathematics, or a qualifying score on the mathematics placement test.

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MATH 115: Calculus I (3
) N

Elementary differential and integral calculus, with applications in management and the biological sciences. Not open to students with credit in MATH 121. Prerequisite: MATH 101 or MATH 104, or two years of high school algebra and a score of 26 or higher on ACT mathematics, or a qualifying score on the mathematics placement test.

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MATH 116: Calculus II (3
) NM N

Continuation of MATH 115 including exponential, logarithmic, and trigonometric functions, techniques of integration, and the calculus of functions of several variables. Not open to students with credit in MATH 122 or MATH 118. Prerequisite: MATH 115, plus a course in trigonometry, or MATH 121. MATH 103 may be taken concurrently.

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MATH 118: Trigonometry and Calculus (3-5
) N

A course combining the material of MATH 103 and MATH 116. Open for only three hours credit to students with credit in MATH 103 or MATH 104, or five hours credit for students who do not have credit in MATH 103 or MATH 104. Not open for credit for students with credit in MATH 116. Prerequisite: MATH 115.

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MATH 121: Calculus I (5
) N

Differentiation and integration of algebraic and trigonometric functions. Applications to physical sciences and engineering. Open for only two hours credit to students with credit in MATH 115. Prerequisite: MATH 104; or MATH 103; or three years of college preparatory mathematics including trigonometry and a score of 28 or higher on ACT mathematics; or a qualifying score on the mathematics placement test.

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MATH 122: Calculus II (5
) NM N

Continuation of MATH 121, emphasis on applications. Introduction to partial differentiation and multiple integration. Open only for three hours credit to students with credit in both MATH 121 and MATH 116. Prerequisite: MATH 121, MATH 141 or MATH 116.

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MATH 141: Calculus I: Honors (5
) N

Differential and integral calculus and applications. Prerequisite: Three years of college preparatory mathematics including trigonometry, plus either (1) a score of 34 or more on ACT mathematics and a cumulative high school grade-point average of at least 3.5, or (2) a score of 32 or more on ACT mathematics and a cumulative high school grade-point average of at least 3.7.

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MATH 142: Calculus II: Honors (5
) NM N

Transcendental functions, methods of integration, parametric equations, vector algebra and its applications to analytic geometry. Introduction to partial derivatives and multiple integration. Prerequisite: MATH 121, or equivalent, and invitation of the Department of Mathematics.

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MATH 143: Linear Algebra and Multivariable Calculus: Honors (5
) N

Linear spaces, linear transformations and matrices, determinants, eigenvalues and eigenvectors, differential calculus of vector-valued functions, multiple integrals, line integrals and surface integrals. Infinite series. Prerequisite: MATH 122 or MATH 142, or equivalent, and invitation of the Department of Mathematics.

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MATH 177: First Year Seminar: _____ (3
) NM

A limited-enrollment, seminar course for first-time freshmen, organized around current issues in math. May not contribute to major requirements in math. First year seminar topics are coordinated and approved through the Office of First Year Experiences. Prerequisite: First-time freshman status.

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MATH 197: Mathematical Workshops: _____ (1-3
) U

Offered to provide opportunities for deeper understanding of freshman-sophomore mathematics through interactive learning. Topics will vary. May be repeated for additional credit. Prerequisite: Variable.

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MATH 220: Applied Differential Equations (3
) N

Linear ordinary differential equations, laplace transforms, systems of equations, and applications. Not open to those who have taken MATH 320. Prerequisite: MATH 122 or MATH 142 or equivalent.

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MATH 221: Applied Differential Equations, Honors (3
) N

Linear Ordinary Differential Equations, Laplace Transforms, Systems of Equations, Enrichment Applications. Prerequisite: Math 122 or Math 142 or equivalent, and invitation from the Department of Mathematics. Not open to students with credit in Math 320.

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MATH 223: Vector Calculus (3
) N

Multivariable calculus, multiple integration, and vector calculus. Prerequisite: MATH 122 or MATH 142 or equivalent.

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MATH 243: Vector Calculus, Honors (3
) N

Multivariable Calculus, Multiple Integration, Vector Calculus, Enrichment Applications. Prerequisite: Math 122 or Math 142 or equivalent, and invitation from the Department of Mathematics.

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MATH 290: Elementary Linear Algebra (2
) N

Systems of linear equations, matrices, vector spaces, linear transformations, and applications. Not open to those who have taken MATH 590. Prerequisite: MATH 122 or MATH 142 or equivalent.

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MATH 291: Elementary Linear Algebra, Honors (2
) N

Systems of Linear Equations, Matrices, Vector Spaces, Linear Transformations, Enrichment Applications. Prerequisite: Math 122 or Math 142 or equivalent, and invitation from the Department of Mathematics. Not open to students who have taken MATH 590.

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MATH 296: Special Topics: _____ (1-3
) N

Designed for the study of special topics in mathematics at the freshman/sophomore level. May be repeated for additional credit; does not count toward the major or minor in mathematics. Prerequisite: Variable.

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MATH 299: Directed Reading (1-5
) N

Directed reading on a topic chosen by the student with the advice of an instructor. May be repeated for additional credit. Consent of the department required for enrollment.

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MATH 320: Elementary Differential Equations (3
) N

Linear ordinary differential equations, series solutions. Laplace transforms. Systems of equations. Not open to those who have taken MATH 220. Prerequisite: MATH 223 and MATH 290, or MATH 143.

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MATH 321: Differential Equations: Honors (3
) N

Linear differential equations with applications, Wronskian, power series solution, systems of differential equations. Prerequisite: MATH 223 and MATH 290 or MATH 143, or equivalent and invitation of the Department of Mathematics.

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MATH 365: Elementary Statistics (3
) N

Elementary descriptive statistics of a sample of measurements; probability; the binomial, Poisson, and normal distributions, populations and sampling from populations; simple problems of statistical inference. May not be counted for junior-senior credit toward a major in mathematics. Not open to students with credit in BUS 368, BIOL 570, MATH 465, MATH 526, or MATH 628. Prerequisite: MATH 101, MATH 104, or MATH 111.

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MATH 409: Topics in Geometry for Secondary and Middle School Teachers (2
) N

Study of selected topics from Euclidean, non-Euclidean, and transformation geometry chosen to give breadth to the mathematical background of secondary and middle school teachers. May not be counted for junior-senior credit towards a major in mathematics. Prerequisite: MATH 122. Students enrolled in MATH 409 must concurrently enroll in MATH 410.

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MATH 410: Topics in History of Mathematics for Secondary and Middle School Teachers (1
) N

Study of selected topics from mathematical history chosen to provide students with knowledge of major historical developments in mathematics including individual contributions and contributions from different cultures. These topics will include a historical development of Euclidean and non-Euclidean geometry. May not be counted for junior-senior credit towards a major in mathematics. Prerequisite: Math 122. Students enrolled in MATH 410 must concurrently enroll in MATH 409.

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MATH 450: Discrete Mathematics (3
) N

Basic topics in discrete mathematics including sets, logic, relations and functions, graphs and combinatorics. Advanced topics chosen from partially ordered sets and lattices, Boolean algebras, automata, game theory, coding theory, cryptography, optimization and enumeration. Prerequisite: MATH 290.

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MATH 470: Problem Solving (3
) N

An introduction to the general methods of solving mathematical problems. Particular techniques such as specialization, generalization, contradiction, and induction will be presented. Topics presented may vary from semester to semester. Prerequisite: MATH 122 or equivalent or concurrent enrollment in MATH 122.

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MATH 500: Intermediate Analysis (3
) N

A careful formulation of convergence and limits of sequences and functions; continuity and properties of continuous functions; differentiation; the Riemann integral; mean-value theorems and the fundamental theorem of calculus. Not open to students with credit in MATH 765. Prerequisite: MATH 223 and MATH 290, or MATH 143.

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MATH 510: Introduction to the Theory of Computing (3
) N

Finite state automata and regular expressions. Context-free grammars and push-down automata. Turing machines. Models of computable functions and undecidable problems. The course emphasis is on the theory of computability, especially on showing limits of computation. (Same as EECS 510.) Prerequisite: EECS 210 and upper-level EECS eligibility.

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MATH 520: Intermediate Logic (3
) N

Formal systems, propositional and predicate logic, completeness theorem, effective procedures, definability in number theory, Godel's incompleteness theorem. Prerequisite: MATH 450, or MATH 588, or MATH 590.

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MATH 526: Applied Mathematical Statistics I (3
) NM N

A first course in statistics for students with the techniques of calculus at their disposal. The following topics are studied with illustrations and problems drawn from various fields of applications: basic notions of probability and probability distributions; classical estimation and testing procedures for one and two sample problems; chi-square test. Not open to those with credit in MATH 628 or DSCI 301. Prerequisite: MATH 122 or MATH 116.

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MATH 530: Mathematical Models I (3
) N

An introduction to mathematical models useful in a large variety of scientific and technical endeavors. Topics include: model construction, Markov chain models, models for linear optimization, graphs as models, and game theory. Prerequisite: MATH 223 and MATH 290, or MATH 143.

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MATH 531: Mathematical Models II (3
) N

A continuation of MATH 530. Topics include: deterministic and stochastic models of growth processes, growth models for epidemics, rumors and queues; parameter estimation; and methods of comparing models. Prerequisite: MATH 530 and some probability.

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MATH 540: Elementary Number Theory (3
) N

Divisibility, primes and their distribution, the Euclidean algorithm, perfect numbers, Fermat's theorem, Diophantine equations, applications to cryptography. Prerequisite: MATH 122 or consent of instructor.

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MATH 542: Vector Analysis (2
) N

Vector algebra; vector and scalar fields; line and surface integrals; theorems of Gauss, Green, and Stokes. Curvilinear coordinates. Applications. Introduction to tensor analysis. Not open to those with credit in MATH 143. Prerequisite: MATH 223 and MATH 290.

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MATH 558: Introductory Modern Algebra (3
) N

Development of the number systems. Polynomials. Introduction to abstract number systems such as groups and fields. Not open to students with credit in MATH 791. Prerequisite: MATH 290.

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MATH 559: Modern Geometries (3
) N

Selected topics in Euclidean geometry. Synthetic and analytic projective geometry; duality, Desargues' theorem, perspectives, conics. Non-Euclidean and metric projective geometries. Prerequisite: MATH 122.

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MATH 562: Evolution of Mathematical Thought (3
) N

Development of selected topics from the mainstream of mathematics. Prerequisite: Senior standing and at least nine hours credit in mathematics courses numbered 450 or above.

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MATH 570: Undergraduate Honor Seminar (3
) N

A seminar for undergraduate students with a strong record in mathematics. Topics may vary. May not be taken twice for credit towards a major in mathematics. Prerequisite: MATH 143 or MATH 321 or permission of instructor.

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MATH 581: Numerical Methods (3
) N

An introduction to numerical methods and their application to engineering and science problems. Applied treatment of elementary algorithms selected from the subject areas: finding roots of a single nonlinear equation, numerical differentiation and integration, numerical solution of ordinary differential equations. Emphasis on implementing numerical algorithms using the computer. Not open to students with credit in MATH 781 or MATH 782. Prerequisite: MATH 220 and MATH 290, or MATH 320.

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MATH 590: Linear Algebra (3
) N

Vector spaces, linear transformations, and matrices. Canonical forms, Determinants. Hermitian, unitary and normal transformations. Not open to students with credit in MATH 792. Prerequisite: MATH 223 and MATH 290 or equivalent, or MATH 143.

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MATH 591: Applied Numerical Linear Algebra (3
) N

An introduction to numerical linear algebra. Possible topics include: applied canonical forms, matrix factorizations, perturbation theory, systems of linear equations, linear least squares, singular value decomposition, algebraic eigenvalue problems, matrix functions, and the use of computational software. Not open to students with credit in MATH 780 or MATH 782. Prerequisite: MATH 290. Recommended: EECS 138 or equivalent experience.

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MATH 596: Special Topics: _____ (1-3
) N

Arranged as needed to present appropriate material to groups of students. May be repeated for additional credit. Prerequisite: Variable.

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MATH 601: Algebraic Coding Theory (3
) N

An introduction to error correcting codes. Included are: linear codes, cyclic codes, BCH codes, and convolutional codes. Prerequisite: MATH 290.

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MATH 605: Applied Regression Analysis (3
) N

The matrix approach to regression. Weighted least squares, transformations, examination of residuals, model selection, and analysis of variance. Prerequisite: One calculus-based statistics course.

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MATH 611: Time Series Analysis (3
) N

An introduction to the theory and computational techniques in time series analysis. Descriptive techniques: trends, seasonality, autocorrelations. Time series models: autoregressive, moving average, ARIMA models; model specification and fitting, estimation, testing, residual analysis, forecasting. Stationary processes in the frequency domain: Fourier methods and the spectral density, periodograms, smoothing, spectral window. Prerequisite: MATH 122 and a calculus based statistics course.

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MATH 624: Discrete Probability (3
) N

Theory and applications of discrete probability models. Elementary combinatory analysis, random walks, urn models, occupancy problems, and the binomial and Poisson distributions. Prerequisite: MATH 223 and MATH 290, or MATH 143.

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MATH 627: Probability (3
) N

Introduction to mathematical probability; combinatorial analysis; the binomial, Poisson, and normal distributions; limit theorems; laws of large numbers. Prerequisite: MATH 223 and MATH 290 or equivalent, or MATH 143.

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MATH 628: Mathematical Theory of Statistics (3
) N

An introduction to sampling theory and statistical inference; special distributions; and other topics. Prerequisite: MATH 627.

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MATH 630: Actuarial Mathematics (3
) N

This course is an introduction to some of the notions and computations in actuarial mathematics. Many computations are associated with compound interest with applications to bank accounts, mortgages, pensions, bonds, and annuities. Life contingencies are considered for annuities and insurance. Some introduction to option pricing is given, particularly the Black-Scholes formula. This course provides the background material needed for some of the initial examinations given by the societies for actuaries, including the Financial Mathematics Exam. Prerequisite: MATH 526 or MATH 627 or a comparable course in probability.

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MATH 631: Operations Research (3
) N

An introduction to commonly applied techniques. Topics include linear programming, duality and sensitivity analysis, the transportation problem, networks, decision and game theory, inventory models and queueing systems. Prerequisite: A calculus-based statistics course or permission of instructor.

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MATH 646: Complex Variable and Applications (3
) N

Analytic functions of a complex variable, infinite series in the complex plane, theory of residues, conformal mapping and applications. Prerequisite: MATH 223.

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MATH 647: Applied Partial Differential Equations (3
) N

Boundary value problems; topics on partial differentiation; theory of characteristic curves; partial differential equations of mathematical physics. Prerequisite: MATH 220, MATH 223 and MATH 290; or MATH 320.

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MATH 648: Calculus of Variations and Integral Equations (3
) N

Topics in the calculus of variations, integral equations, and applications. Prerequisite: MATH 220, MATH 223 and MATH 290; or MATH 320.

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MATH 660: Geometry I (3
) N

An introduction to modern geometry. Differential geometry of curves and surfaces, the topological classification of closed surfaces, dynamical systems, and knots and their polynomials. Other topics as time permits. Prerequisite: MATH 223 and MATH 290, or equivalent, or MATH 143.

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MATH 661: Geometry II (3
) N

Continuation of Math 660. Prerequisite: MATH 660 or permission of instructor.

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MATH 696: Special Topics: _____ (1-3
) N

Arranged as needed to present appropriate material to groups of students. May be repeated for additional credit. Prerequisite: Variable.

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MATH 699: Directed Reading (1-3
) N

Directed reading on a topic chosen by the student with the advice of an instructor. May be repeated for additional credit. Consent of the department required for enrollment.

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MATH 701: Topics in Mathematics for Teachers: _____ (1-6
)

Material, including both mathematical content and teaching methodology, related to classroom use at various levels, elementary through secondary. Topics may vary. May not be counted for junior-senior credit towards a major in mathematics, nor for graduate credit towards a graduate degree in mathematics. Prerequisite: Permission of instructor.

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MATH 715: Sampling Techniques (3
)

Statistical methodology of survey sampling. Data analysis and estimation methods for various experimental designs; fixed or random sample sizes, pre-and/or post-stratified samples, and multistage sampling. Estimates of totals, means, ratios and proportions with methods of estimating variances of such estimates. Prerequisite: A post-calculus probability or statistics course.

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MATH 717: Nonparametric Statistics (3
)

Methods requiring few assumptions about the populations sampled. Topics include quantile tests, tolerance limits, the sign test, contingency tables, rank-sum tests, and rank correlation. Prerequisite: MATH 628 or permission of instructor.

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MATH 722: Mathematical Logic (3
)

Propositional calculus. First order theories and model theory. Elementary arithmetic and Godel's incompleteness theorems. (Same as EECS 722.) Prerequisite: MATH 665 or MATH 691, or equivalent evidence of mathematical maturity.

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MATH 724: Combinatorial Mathematics (3
)

Counting problems, with an introduction to Polya's theory; Mobius functions; transversal theory; Ramsey's theorem; Sperner's theorem and related results. Prerequisite: MATH 290 and a math course numbered 450 or higher.

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MATH 725: Graph Theory (3
)

Graphs; trees; connectivity; Menger's theorem; eulerian and hamiltonian graphs; planarity; coloring of graphs; factorization of graphs; matching theory; alternating chain methods; introduction to matroids with applications to graph theory. Prerequisite: MATH 290 and a math course numbered 450 or higher.

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MATH 727: Probability Theory (3
)

A mathematical introduction to premeasure-theoretic probability. Topics include probability spaces, conditional probabilities and independent events, random variables and probability distributions, special discrete and continuous distributions with emphasis on parametric families used in applications, the distribution problem for functions of random variables, sequences of independent random variables, laws of large numbers, and the central limit theorem. Prerequisite: MATH 223 and MATH 290, or equivalent.

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MATH 728: Statistical Theory (3
) N

Theory of point estimation and hypothesis testing with applications. Confidence region methodologies and relations to estimation and testing. Prerequisite: MATH 727 or equivalent.

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MATH 735: Optimal Control Theory (3
)

An examination of the mathematical methods of deterministic control theory is given by considering some specific examples and the general theory. The methods include dynamic programming, the calculus of variations, and Pontryagin's maximum principle. Various problems of linear control systems, e.g., the linear regulator problem, are solved. Prerequisite: MATH 320 or equivalent.

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MATH 740: Number Theory (3
)

Divisibility, the theory of congruences, primitive roots and indices, the quadratic reciprocity law, arithmetical functions and miscellaneous additional topics. Prerequisite: MATH 223 and MATH 290, or equivalent.

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MATH 750: Stochastic Adaptive Control (3
)

Stochastic adaptive control methods. Stochastic processes such as Markov chains and Brownian motion, stochastic integral, differential rule, stochastic differential equations, martingales and estimation techniques. Identification and control of discrete and continuous time linear stochastic systems. Specific applications and simulation results of stochastic adaptive control theory. Prerequisite: MATH 627 and some knowledge of control.

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MATH 765: Mathematical Analysis I (3
)

MATH 765 and MATH 766 are theoretical courses on the fundamental concepts of analysis and the methods of proof. These two courses include the concept of a real number; limits, continuity, and uniform convergence; derivatives and integrals of functions of one and of several real variables. Prerequisite: MATH 223 and MATH 290, or equivalent.

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MATH 780: Numerical Analysis of Linear Systems (3
)

Computational aspects of linear algebra, linear equations and matrices, direct and indirect methods, eigenvalues and eigenvectors of matrices, error analysis. Prerequisite: MATH 590 and MATH 781.

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MATH 781: Numerical Analysis I (3
)

Finite and divided differences. Interpolation, numerical differentiation, and integration. Gaussian quadrature. Numerical integration of ordinary differential equations. Curve fitting. (Same as EECS 781.) Prerequisite: MATH 320 and knowledge of a programming language.

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MATH 782: Numerical Analysis II (3
)

Direct and iterative methods for solving systems of linear equations. Numerical solution of partial differential equations. Numerical determination of eigenvectors and eigenvalues. Solution of nonlinear equations. (Same as EECS 782.) Prerequisite: MATH 781.

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MATH 783: Applied Numerical Methods for Partial Differential Equations (3
)

Finite difference methods applied to particular initial-value problems (both parabolic and hyperbolic), to illustrate the concepts of convergence and stability and to provide a background for treating more complicated problems arising in engineering and physics. Finite difference methods for elliptic boundary-value problems, with a discussion of convergence and methods for solving the resulting algebraic system. Variational methods for elliptic problems. Prerequisite: MATH 647 or equivalent.

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MATH 790: Linear Algebra II (3
)

A theoretical course on the fundamental concepts and theorems of linear algebra. Topics covered are: vector space, basis, dimension, subspace, norm, inner product, Banach space, Hilbert space, orthonormal basis, positive definite matrix, minimal polynomial, diagonalization and other canonical forms, Cayley-Hamilton, spectral radius, dual space, quotient space. Prerequisite: MATH 590.

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MATH 791: Modern Algebra (3
)

This course includes the following topics: multiplicative properties of the integers and introductions to group theory, ring theory and field theory. Prerequisite: MATH 223 and MATH 290, or equivalent.

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MATH 796: Special Topics: _____ (1-3
)

Arranged as needed to present appropriate material for groups of students. May be repeated for credit. Prerequisite: Variable.

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MATH 799: Directed Readings (1-3
)

Directed readings on a topic chosen by the student with the advice of an instructor. May be repeated for additional credit. Consent of the department required for enrollment.

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MATH 800: Complex Analysis I (3
)

Cauchy's theorem and contour integration; the argument principle; maximum modulus principle; Schwarz symmetry principle; analytic continuation; monodromy theorem; applications to the gamma function and Riemann's zeta function; entire and meromorphic functions; conformal mapping; Riemann mapping theorem; univalent functions. Prerequisite: MATH 766 or concurrently with MATH 766.

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MATH 802: Set Theory (3
)

Axiomatic set theory; transfinite induction; regularity and choice; ordinal and cardinal arithmetic; miscellaneous additional topics (e.g., extra axioms such as GCH or MA; infinite combinatorics; large cardinals). Prerequisite: MATH 765 or MATH 791, or concurrent enrollment in MATH 765 or MATH 791, or equivalent evidence of mathematical maturity.

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MATH 810: Real Analysis and Measure Theory I (3
)

Measurable spaces and functions. Measure spaces and integration. Extensions of set functions, outer measures, Lebesgue measure. Signed and complex measures. Differentiation of set functions. Miscellaneous additional topics and applications. Prerequisite: MATH 766.

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MATH 820: Introduction to Topology (3
)

General topology. Set theory; topological spaces; connected sets; continuous functions; generalized convergence; product and quotient spaces; embedding in cubes; metric spaces and metrization; compact spaces; function spaces. Prerequisite: MATH 765.

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MATH 821: Algebraic Topology I (3
)

The fundamental group and covering spaces (including classification); compact surfaces; homology theory, computations (including homotopy invariance) and applications (including Brouwer fixed point theorem); introduction to cohomology theory. Prerequisite: MATH 790 and MATH 791 and MATH 820, or permission of instructor.

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MATH 822: Algebraic Topology II (3
)

Review of simplicial homology; Lefschetz fixed point theorem and degree theory; singular, cellular, and axiomatic homology; Jordan Brouwer separation theorems; universal coefficient theorems, products in cohomology, homotopy groups, and the Hurewicz Theorem. Prerequisite: MATH 821.

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MATH 824: Algebraic Combinatorics (3
)

An introduction to the fundamental structures and methods of modern algebraic combinatorics. Topics include partially ordered sets and lattices, matroids, simplicial complexes, polytopes, hyperplane arrangements, partitions and tableaux, and symmetric functions. Prerequisite: MATH 724 and MATH 791, or permission of the instructor.

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MATH 830: Abstract Algebra (3
)

A study of some structures, theorems, and techniques in algebra whose use has become common in many branches of mathematics. Prerequisite: MATH 790 and MATH 791.

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MATH 840: Differentiable Manifolds (3
)

Multilinear algebra of finite dimensional vector spaces over fields; differentiable structures and tangent and tensor bundles; differentiable mappings and differentials; exterior differential forms; curves and surfaces as differentiable manifolds; affine connections and covariant differentiation; Riemannian manifolds. Prerequisite: MATH 765 and MATH 790.

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MATH 850: Differential Equations and Dynamical Systems (3
)

Discrete and differentiable dynamical systems with an emphasis on the qualitative theory. Topics to be covered include review of linear systems, existence and uniqueness theorems, flows and discrete dynamical systems, linearization (Hartman-Grobman theorem), stable and unstable manifolds, Poincare sections, normal forms, Hamiltonian systems, and an introduction to bifurcation theory and chaos. Prerequisite: MATH 320 and MATH 766, or permission of instructor.

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MATH 851: Topics in Dynamical Systems (3
)

Topics to be covered include complex dynamical systems, perturbation theory, nonlinear analysis of time series, chaotic dynamical systems, and numerical methods as dynamical systems. This course may be repeated for credit. Prerequisite: MATH 850 or permission of instructor.

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MATH 865: Stochastic Processes I (3
)

Markov chains; Markov processes; diffusion processes; stationary processes. Emphasis is placed on applications: random walks; branching theory; Brownian motion; Poisson process; birth and death processes. Prerequisite: MATH 627 and MATH 765.

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