MATHEMATICS (MATH)

116R .2 Introduction to College Algebra (3) Lecture. Not applicable to the mathematics major or minor. Basic concepts of algebra, linear equations and inequalities, relations and functions, quadratic equations, system of equations. P, two entrance units in algebra or an acceptable score on the math readiness test. This course will be offered for the last time in Fall 1997.

116S .2 Introduction to College Algebra (3) Self-Study. Identical to MATH 116R except taught in a self-study tutorial format. Not applicable to the mathematics major or minor. P, two entrance units in algebra or an acceptable score on the math readiness test. This course will be offered for the last time in Fall 1997.

117R .2,4 College Algebra (3) Lecture. Not applicable to the mathematics major or minor. Brief review and continuation of MATH 116R/S, functions, mathematical models, systems of equations and inequalities, exponential and logarithmic functions, polynomial and rational functions, sequences and series. Students with credit in 120 will obtain only two units of graduation credit for 117R. P, 116R or 116S or an acceptable score on the math readiness test. This course will be offered for the last time in Spring 1998.

117S .2,4 College Algebra (3) Self-Study. Identical to MATH 117R except taught in a self-study tutorial format. Not applicable to mathematics majors or minors. Students with credit in 120 will obtain only two units of graduation credit for 117S. P, 116R or 116S or an acceptable score on the math readiness test. This course will be offered for the last time in Spring 1998.

118. 1,2 Plane Trigonometry (2) Not applicable to the mathematics major or minor. Students with credit in 120 obtain one unit of graduation credit for 118. P, one entrance unit in geometry and either 1 1/2 entrance units in algebra, or 116R/S.

119. 1 Finite Mathematics (3) Elements of set theory and counting techniques, probability theory, linear systems of equations, matrix algebra; linear programming with simplex method, Markov chains. P, 121, 117R/S or acceptable score on math readiness test.

120. 1,2,4 Calculus Preparation (4) Reviews algebra and trigonometry; covers the study of functions including polynomials, rational, exponential, logarithmic and trigonometric. For students who have high school credit in college algebra and trigonometry but have not attained a sufficient score on the math readiness test to enter calculus. Students with credit in MATH 117R/S will obtain only two units of graduation credit for 117R/S. Students with credit in MATH 118 will obtain one unit of graduation credit for 118. Students with credit in MATH 121 will obtain only two units of graduation credit for MATH 120. Students with credit in MATH 118 will obtain only three units of graduation credit for 120. P, high school credit in college algebra and trigonometry, and an acceptable score on the math readiness test. Graphing calculators are required in this course.

121. Collegiate Algebra (4) Topics include properties of functions and graphs, polynomial functions, rational functions, exponential and logarithmic functions with applications, sequences and series, and systems of equations. Course includes an integrated review of important concepts in intermediate algebra. Students are expected to have a graphing calculator. Students with credit in MATH 120 will obtain only two units of graduation credit for MATH 121. P, an acceptable score on the math readiness test.

122. Mathematics in Modern Society (3) The course will examine topics such as voting schemes, apportionment problems, network problems, critical paths. Fibonacci numbers, population models, symmetry, fractals, data analysis, probability and statistics. P, two years of high school algebra and a satisfactory score on the Mathematics Readiness Assessment test.

123. 2,4 Elements of Calculus (3) Introductory topics in differential and integral calculus. Credit allowed for only one of the following courses: 123, 124, or 125a. P, 121, 117R/S or an acceptable score on math readiness test.

124. 2,4 Calculus with Applications (5) Introduction to calculus with an emphasis on understanding and problem solving. Concepts are presented graphically and numerically as well as algebraically. Elementary functions, their properties and uses in modeling; the key concepts of derivative and definite integral; techniques of differentiation, using the derivative to understand the behavior of functions; applications to optimization problems in physics, biology and economics. Graphing calculator will be required for this course. Credit allowed for only one of the following courses: 123, 124, or 125a. P, 120, or 121 and 118, 117R/S and 118, or acceptable score on math readiness test.

125a.2,4 Calculus (3) An accelerated version of 124. Introduction to calculus with an emphasis on understanding and problem solving. Concepts are presented graphically and numerically as well as algebraically. Elementary functions, their properties and uses in modeling; the key concepts of derivative and definite integral; techniques of differentiation, using the derivative to understand the behavior of functions; applications to optimization problems in physics, biology and economics. Graphing calculator will be required in this course. P, an acceptable score on math readiness test. Credit allowed for only one of the following courses: 123, 124, or 125a.

125b .4 Calculus (3) Continuation of 124 or 125a. Techniques of symbolic and numerical integration, applications of the definite integral to geometry, physics, economics, and probability; differential equations from a numerical, graphical, and algebraic point of view; modeling using differential equations, approximations by Taylor series. Graphing calculator will be required in this course. P, 124 or 125a.

129. Calculus with a Computer (2) Designed to supplement regular calculus courses. The use of computers to solve calculus problems emphasizing numerical and geometrical understanding of calculus. P or CR, 125b.

160. Introduction to Statistics (3) Descriptive statistics. Basic probability concepts and probability distributions, elementary sampling theory and techniques of estimation, hypothesis testing, regression and correlation. Some analysis of variance and nonparametric statistics if time permits. Students will utilize a statistical package for computational purposes. P, 117R/S.

202. Introduction to Symbolic Logic (3) (Identical with PHIL 202, which is home).

215. Introduction to Linear Algebra (3) Vector spaces, linear transformations and matrices. There is some emphasis on the writing of proof. P, 125b.

223. Vector Calculus (4) Vectors, differential and integral calculus of several variables. P, 125b.

243. Discrete Mathematics in Computer Science (3) Set theory, logic, algebraic structures; induction and recursion; graphs and networks. P, 125b.

254. 4 Introduction to Ordinary Differential Equations (3) Solution methods for ordinary differential equations, qualitative techniques; includes matrix methods approach to systems of linear equations and series solutions. Credit allowed for 254 or 355, but not for both. P, 223.

263. Statistical Methods in Biological Sciences (3) Organization and summarization of data, concepts of probability, probability distributions of discrete and continuous random variables, point and interval estimation, elements of hypothesis testing, regression and correlation analysis, chi-square distribution and analysis of frequencies, introduction to analysis of variance, with special emphasis on analysis of biological and clinical data. P, 117R/S.

294. Practicum

a. Problem-Solving Laboratory (1) [Rpt./4] P, 125b.

301. Understanding Elementary Mathematics (4) Development of a basis for understanding the common processes in elementary mathematics related to the concepts of number, measurement, geometry and probability. 3R, 3L. May not be applied to any mathematics major or minor, other than in elementary education. Open to elementary education majors only. P, 117R/S, or 121, or an acceptable score on the math readiness test.

315. Introduction to Number Theory and Modern Algebra (3) Elementary number theory, complex numbers, field axioms, polynomial rings; techniques for solving polynomial equations with integer and real coefficients. P, 323.

322. Mathematical Analysis for Engineers (3) Complex functions and integration, line and surface integrals, Fourier series, partial differential equations. Credit allowed for this course or 422a, but not for both. P, 254 or 355.

323. Formal Mathematical Reasoning and Writing (3) Elementary real analysis as an introduction to abstract mathematics and the use of mathematical language. Elementary logic and quantifiers; manipulations with sets, relations and function, including images and pre-images; properties of the real numbers; supremum and infimum; other topics selected from cardinality, the topology of the real line, sequences and limits of sequences and functions; the emphasis throughout is on proving theorems. P, 215. Writing-Emphasis Course.*

330. Topics in Geometry (3) Topics to be selected from 2- and 3-dimensional combinatorial geometry, postulational Euclidean geometry, Euclidean transformational geometry, symmetry, and 2-dimensional crystallography. P, 215.

344. Foundations of Computing (3) (Identical with C SC 344, which is home).

355. 4 Analysis of Ordinary Differential Equations (3) Linear and nonlinear equations; basic solution techniques; qualitative and numerical methods; systems of equations; computer studies; applications drawn from physical, biological and social sciences. Credit allowed for 254 or 355, but not for both. P, 215.

362. Introduction to Probability Theory (3) Sample spaces, random variables and their properties, with considerable emphasis on applications. P, 123 or 125b.

380. Math Models in Biology (3) (Identical with ECOL 380, which is home).

397. Workshop

a. Mathematics Education (1) Open only to teaching majors in MATH. P, 315 or 330.

402. Mathematical Logic (3) Sentential calculus, predicate calculus; consistency, independence, completeness, and the decision problem. Designed to be of interest to majors in mathematics or philosophy. Credit allowed for 402 or 411a, but not for both. P, 124 or 125a. (Identical with C SC 402 and PHIL 402). May be convened with 502.

403. Foundations of Mathematics (3) Topics in set theory such as functions, relations, direct products, transfinite induction and recursion, cardinal and ordinal arithmetic; related topics such as axiomatic systems, the development of the real number system, recursive functions. P, 215. (Identical with PHIL 403). May be convened with 503.

404. History of Mathematics (3) The development of mathematics from ancient times through the 17th century, with emphasis on problem solving. The study of selected topics from each field is extended to the 20th century. P, 125b. May be convened with 504.

405. Mathematics in the Secondary School (3) Not applicable to B.A. or B.S. degrees for math majors. (Identical with TTE 405).

409A - 409B. Symbolic Logic (3-3) (Identical with PHIL 409a-409b, which is home). May be convened with 509a-509b.

410. 4 Matrix Analysis (3) General introductory course in the theory of matrices. Credit allowed for 410 or 413, but not for both. P, 254 or 355.

413. 4 Linear Algebra (3) Vector spaces, linear transformations and matrices, eigenvalues, bilinear forms, orthogonal and unitary transformations. Credit allowed for 410 or 413, but not for both. P, 215. May be convened with 513.

415. Introduction to Abstract Algebra (3) Introduction to groups, rings, and fields. P, 323. May be convened with 515.

416. Second Course in Abstract Algebra (3) A continuation of 415. Topics may include Galois theory, linear and multilinear algebra, finite fields and coding theory. Polya enumeration. P, 415. May be convened with 516.

422A - 422B. 3 Advanced Analysis for Engineers (3-3) Laplace transforms, Fourier series, partial differential equations, vector analysis, integral theorems, complex variables. Credit allowed for 422a or 322, but not for both. Credit allowed for 422b or 424, but not for both. P, 254 or 355. 422a is not prerequisite to 422b. Both 422a and 422b are offered each semester. May be convened with 522a-522b.

424. 3 Elements of Complex Variables (3) Complex numbers and functions, conformal mapping, calculus of residues. Credit allowed for 422b or 424, but not for both. P, 223. May be convened with 524.

425. Real Analysis of One Variable (3) Continuity and differentiation of functions of one variable. Riemann integration, sequences of functions and uniform convergence. P, 223 and 323. May be convened with 525.

426. Real Analysis of Several Variables (3) Continuity and differentiation in higher dimensions, curves and surfaces; change of coordinates; theorems of Green, Gauss and Stokes; exact differentials. P, 425. May be convened with 526.

430. Second Course in Geometry (3) Topics may include low-dimensional topology; map coloring in the plane, networks (graphs) polyhedra, two-dimensional surfaces and their classification, map coloring on surfaces (Heawood's estimate, Ringel-Young theory), knots and links or projective geometry. P, 215. May be convened with 530.

434. Introduction to Topology (3) Properties of metric and topological spaces and their maps; topics selected from geometric and algebraic topology, including the fundamental group. P, 323.

443. Theory of Graphs and Networks (3) Undirected and directed graphs, connectivity, circuits, trees, partitions, planarity, coloring problems, matrix methods, applications in diverse disciplines. P, 323 or 243 or graduate standing. (Identical with C SC 443). May be convened with 543.

446. Theory of Numbers (3) Divisibility properties of integers, primes, congruences, quadratic residues, number-theoretic functions. P, 215. May be convened with 546.

447. Combinatorial Mathematics (3) Enumeration and construction of arrangements and designs; generating functions; principle of inclusion-exclusion; recurrence relations; a variety of applications. P, 215 or 243. May be convened with 547.

454. Intermediate Ordinary Differential Equations and Stability Theory (3) General theory of systems of ordinary differential equations, properties of linear systems, stability and boundedness of systems, perturbation of linear systems, Liapunov functions, periodic and almost periodic systems. P, 254 or 355.

456. Applied Partial Differential Equations (3) Properties of partial differential equations and techniques for their solution: Fourier methods, Green's functions, numerical methods. P, 322 or 421 or 422a. May be convened with 556.

461. Elements of Statistics (3) Probability spaces, random variables, standard distributions, point and interval estimation, tests of hypotheses; includes use of standard Statistical software package.

464. Theory of Probability (3) Probability spaces, random variables, weak law of large numbers, central limit theorem, various discrete and continuous probability distributions. P, 322 or 323. May be convened with 564.

466. Theory of Statistics (3) Sampling theory. Point estimation. Limiting distributions. Testing Hypotheses. Confidence intervals. Large sample methods. P, 464. May be convened with 566a.

468. Applied Stochastic Processes (3) Applications of Gaussian and Markov processes and renewal theory; Wiener and Poisson processes, queues. P, 464. May be convened with 568.

473. Automata, Grammars and Language (3) (Identical with C SC 473).

475A - 475B. Mathematical Principles of Numerical Analysis (3-3) 475a: Analysis of errors in numerical computations, solution of linear algebraic systems of equations, matrix inversion, eigenvalues, roots of nonlinear equations, interpolation and approximation. P, 215; 254 or 355; and a knowledge of a scientific computer programming language. 475b: Numerical integration, solution of systems of ordinary differential equations, initial value and boundary value problems. (Identical with C SC 475a-475b).

479. Game Theory and Mathematical Programming (3) Linear inequalities, games of strategy, minimax theorem, optimal strategies, duality theorems, simplex method. P, 410 or 413 or 415. (Identical with C SC 479) May be convened with 579.

485. Mathematical Modeling (3) Development, analysis, and evaluation of mathematical models for physical, biological, social, and technical problems; both analytical and numerical solution techniques are required. P, 422a. May be convened with 585. P, 422a. Writing Emphasis Course.*

496. Seminar

b. Mathematical Software (3) [Rpt.] P, 254 or 355, knowledge of "C" programming. May be convened with 596b.

*Writing-Emphasis Courses. P, satisfaction of the upper-division writing-proficiency requirement (see "Writing-Emphasis Courses" in the Academic Policies and Graduation Requirements section of this manual).

502. Mathematical Logic (3) For a description of course topics see 402. Graduate-level requirements include more extensive problem sets or advanced projects. P, 124 or 125a. (Identical with C SC 502 and PHIL 502). May be convened with 402.

503. Foundations of Mathematics (3) For a description of course topics see 403. Graduate-level requirements include more extensive problem sets or advanced projects. P, 215. (Identical with PHIL 503) May be convened with 403.

504. History of Mathematics (3) For a description of course topics see 404. Graduate-level requirements include more extensive problem sets or advanced projects. Not applicable to M.A., M.S., or Ph.D. degrees for math majors. P, 125b. May be convened with 404.

506. Geometry for Elementary School (1-3) [Rpt./4 units] Various topics in geometry for elementary and middle school teachers, such as tessalations, symmetry, length, area, volume, geometric constructions, polyhedra, efficiency of shapes, scale drawings taught with a variety of tools and approaches. Students will construct models, use hands-on materials, do laboratory activities, use the computer for geometric explorations and participate in geometric problem solving. P, certified elementary teachers with two or more years experience or consent of instructor.

509. Statistics for Research (4) Statistical concepts and methods applied to research in other scientific disciplines. Principles of estimation and hypothesis testing for standard one- and two-sample procedures. Correlation, linear regression. Contingency tables and analysis of variance. P, 117R/S. (Identical with GENE 509 and PCOL 509).

509A - 509B. Symbolic Logic (3-3) (Identical with PHIL 509a-509b, which is home). May be convened with 409a-409b.

511A - 511B. Algebra (3-3) Structure of groups, rings, modules, algebras; Galois theory. P, 415 and 416, or 413 and 415.

513. Linear Algebra (3) For a description of course topics see 413. Graduate-level requirements include more extensive problem sets or advanced projects. Not applicable to M.A., M.S., or Ph.D. degrees for math majors. P, 215. May be convened with 413.

514A - 514B. Algebraic Number Theory (3-3) Dedekind domains, complete fields, class groups and class numbers, Dirichlet unit theorem, algebraic function fields. P, 511b.

515. Introduction to Abstract Algebra (3) For a description of course topics see 415. Graduate-level requirements include more extensive problem sets or advanced projects. P, 323. May be convened with 415.

516. Second Course in Abstract Algebra (3) For a description of course topics see 416. Graduate-level requirements include more extensive problem sets or advanced projects. P, 415. May be convened with 416.

517A - 517B. Group Theory (3-3) Selections from such topics as finite groups, abelian groups, characters and representations. P, 511b.

518. Topics in Algebra (3) [Rpt./36 units] Advanced topics in groups, rings, fields, algebras; content varies.

519. Topics in Number Theory and Combinatorics (3) [Rpt./36 units] Advanced topics in algebraic number theory, analytic number theory, class fields, combinatorics; content varies.

520A - 520B. Complex Analysis (3-3) 520a: Analyticity, Cauchy's integral formula, residues, infinite products, conformal mapping, Dirichlet problem, Riemann mapping theorem. P, 424. 520b: Rudiments of Riemann surfaces. P, 520a or 582.

522A - 522B.3 Advanced Analysis for Engineers (3-3) For a description of course topics see 422a-422b. Graduate-level requirements include more extensive problem sets or advanced projects. Not applicable to M.A., M.S., or Ph.D. degrees for math majors. P, 254 or 355. May be convened with 422a-422b.

523A - 523B. Real Analysis (3-3) Lebesque measure and integration, differentiation, Radon-Nikodym theorem, Lp spaces, applications. P, 425.

524. 3 Elements of Complex Variables (3) For a description of course topics see 424. Graduate-level requirements include more extensive problem sets or advanced projects. P, 223. May be convened with 424.

525. Real Analysis of One Variable (3) For a description of course topics see 425. Graduate-level requirements include more extensive problem sets or advanced projects. P, 223 and 323. May be convened with 425.

526. Real Analysis of Several Variables (3) For a description of course topics see 426. Graduate-level requirements include more extensive problem sets or advanced projects. P, 425. May be convened with 426.

527A - 527B. Principles of Analysis (3-3) Advanced-level review of linear algebra and multivariable calculus; survey of real, complex and functional analysis, and differential geometry with emphasis on the needs of applied mathematics. P, 410, 424, and a differential equations course.

528A - 528B. Banach and Hilbert Spaces (3-3) Introduction to the theory of normed spaces, Banach spaces and Hilbert spaces, operators on Banach spaces, spectral theory of operators on Hilbert spaces, applications. P, 523a, 527b, or 583b.

529. Topics in Modern Analysis (3) [Rpt./36 units] Advanced topics in measure and integration, complex analysis in one and several complex variables, probability, functional analysis, operator theory; content varies.

530. Second Course in Geometry (3) For a description of course topics see 430. Graduate-level requirements include more extensive problem sets or advanced projects. P, 215. For persons enrolled in the Teaching Option. May be convened with 430.

531. Algebraic Topology (3) Poincare duality, fixed point theorems, characteristics classes, classification of principal bundles, homology of fiber bundles, higher homotopy groups, low dimensional manifolds. P, 534a-534b.

534A - 534B. Topology-Geometry (3-3) Point set topology, the fundamental group, calculus on manifolds. Homology, de Rham cohomology, other topics. Examples will be emphasized. P, 415 and 425.

536A - 536B. Algebraic Geometry (3-3) Affine and projective varieties, morphisms and rational maps. Dimension, degree and smoothness. Basic coherent sheaf theory and Cech cohomology. Line bundles, Riemann-Roch theorem. P, 511, 520a, 534a.

537A - 537B. Global Differential Geometry (3-3) Surfaces in R3, structure equations, curvature. Gauss-Bonnet theorem, parallel transport, geodesics, calculus of variations, Jacobi fields and conjugate points, topology and curvature; Riemannian geometry, connections, curvature tensor, Riemannian submanifolds and submersions, symmetric spaces, vector bundles. Morse theory, symplectic geometry. P, 534a-534b.

538. Topics in Geometry and Topology (3) [Rpt./36 units] Advanced topics in point set and algebraic topology, algebraic geometry, differential geometry; content varies.

539. Algebraic Coding Theory (3) Construction and properties of error correcting codes; encoding and decoding procedures and information rate for various codes. P, 415. (Identical with ECE 539)

543. Theory of Graphs and Networks (3) For a description of course topics see 443. Graduate-level requirements include more extensive problem sets or advanced projects. P, 215 or 223 or 243. (Identical with C SC 543) May be convened with 443.

546. Theory of Numbers (3) For a description of course topics see 446. Graduate-level requirements include more extensive problem sets or advanced projects. P, 215. May be convened with 446.

547. Combinatorial Mathematics (3) For a description of course topics see 447. Graduate-level requirements include more extensive problem sets or advanced projects. P, 215 or 243. May be convened with 447.

550. Mathematical Population Dynamics (4) (Identical with ECOL 550, which is home).

553A - 553B. Partial Differential Equations (3-3) Theory and examples of linear equations; characteristics, well-posed problems, regularity, variational properties, asymptotics. Topics in nonlinear equations, such as shock waves, diffusion waves, and estimates in Sobolev spaces. P, 523b or 527b or 583b.

554. Ordinary Differential Equations (3) General theory of linear systems, Foquet theory. Local theory of nonlinear systems, stable manifold and Hartman-Grobman theorems. Poincare-Bendixson theory, limit cycles, Poincare maps. Bifurcation theory, including the Hopf theorem. P, 413, 426 or consent of instructor.

556. Applied Partial Differential Equations (3) For a description of course topics see 456. Graduate-level requirements include more extensive problem sets or advanced projects. P, 322 or 421 or 422a. May be convened with 456.

557A - 557B. Dynamical Systems and Chaos (3-3) Qualitative theory of dynamical systems, phase space analysis, bifurcation, period doubling, universal scaling, onset of chaos. Applications drawn from atmospheric physics, biology, ecology, fluid mechanics and optics. P, 422a-422b or 454.

559A - 559B. Lie Groups and Lie Algebras (3-3) Correspondence between Lie groups and Lie algebras, structure and representation theory, applications to topology and geometry of homogeneous spaces, applications to harmonic analysis. P, 511a, 523a, 534a-534b, or consent of the instructor.

560. Elementary School Probability (1-3) [Rpt./3 units] Games and other activities that lead naturally to consideration of chance events and data analysis. Activities will relate to numeration and number systems, algebra, geometry and other topics in mathematics to emphasize the integrated nature of mathematics. Students work in groups to create and analyze activities. P, certified elementary teachers with two or more years of experience or consent of instructor.

561. Regression and Multivariate Analysis (3) Regression analysis including simple linear regression and multiple linear regression. Analysis of variance and covariance. Residual analysis. Variable selection techniques, collinearity, non-linear models and transformations. Cross-validation for model selection. Methods for analysis of multivariate observations. Multivariate expectations and covariance matrices. Multivariate normal distribution. Hotelling's T-square distribution. Principal components. Students will be expected to utilize standard statistical software packages for computational purposes. P, 410 or 413, and one of 461, 466, or 509.

562. Time Series Analysis (3) Methods for analysis of time series data. Time domain techniques. ARIMA models. Estimation of process mean and autocovariance. Model fitting. Forecasting methods. Missing data. Students will be expected to utilize standard statistical software packages for computational purposes. P, 461, 466 or 509.

563A. Probability Theory (3) I Introduction to measure theory, strong law of large numbers, charactersitic functions, the central limit theorem, conditional expectations, and discrete parameter martingales. P, MATH 464.

563B. Probability Theory (3) II A selection of topics in stochastic processes from Markov chains, Brownian motion, the funcional central limit theorem, diffusions and stochastic differential equations, martingales. P, MATH 563A; MATH 468 recommended.

564. Theory of Probability (3) For a description of course topics see 464. Graduate-level requirements include more extensive problem sets or advanced projects. P, 322 or 323. May be convened with 464.

565A - 565B. Stochastic Processes (3-3) Stationary processes, jump processes, diffusions, applications to problems in science and engineering. P, 468.

566. Theory of Statistics (3) For a description of course topics see 466. Gradaute-level requirements include more extensive problem sets or advanced projects. P, 464. May be convened with 466.

567A - 567B. Theoretical Statistics (3-3) Basic decision theory. Bays rules for estimation. Admissibility and completeness. The minimax theorem. Sufficiency. Exponential families of distribution. Complete sufficient statistics. Invariant decision problems. Location and scale parameters. Theory of nonparametric statistics. Hypothesis testing. Neyman-Pearson lemma. UMP and UMPU tests. Two-sided tests. Two-sample tests. Confidence sets. Multiple decision problems. P, 466.

568. Applied Stochastic Processes (3) For a description of course topics see 468. Graduate-level requirements include more extensive problem sets or advanced projects. P, 464. May be convened with 468.

569. Nonparametric Statistics (3) Distribution free statistical methods for nominal and ordinal data. Measures of association. Goodness of fit and runs tests. Analysis of one or more groups. Correlation and regression of ranked data. Rank order statistics. Applications of nonparametric statistical inference. Students will be expected to utilize standard statistical software packages for computational purposes. P, 461, 466, or 509.

570. Categorical Data Analysis (3) Two-way contingency tables. Logistic, probit and log-log regression. Loglinear models. Model selection techniques. Testing goodness of fit models. Numerical methods for finding MLE. Treatment of finding ordinal and nominal variables. Poisson and multinomial sampling. Students will be expected to utilize standard statistical software packages for computational purposes. P, 461, 466, or 509.

571. Experimental Design (3) Principles of designing experiments. Randomization, blocked designs, factorial experiments, response surface designs, repeated measures, analysis of contrasts, multiple comparisons, analysis of variance and covariance, variance components analysis. P, 223, 461, or 509. Change course title to: Design of Experiments. Spring '98

573. Theory of Computation (3) (Identical with C SC 573, which is home).

574. Introduction to Geostatistics (3) Exploratory spatial data analysis, random function models for spatial data, estimation and modeling of variograms and covariances, ordinary and universal kriging estimators and equations, regularization of variograms, estimation of spatial averages, non-linear estimators, includes use of geostatistical software. Application of hydrology, soil science, ecology, geography and related fields. P, linear algebra, basic course in probability and statistics, familiarity with DOS/Windows, UNIX.

575A - 575B. Numerical Analysis (3-3) Error analysis, solution of linear systems and nonlinear equations, eigenvalues interpolation and approximation, numerical integration, initial and boundary value problems for ordinary differential equations, optimization. P, 475b and 455 or 456. (Identical with C SC 575a-575b).

576A - 576B. Numerical Analysis PDE (3-3) 576a: Finite difference, finite element and spectral discretization methods; semidiscrete, matrix and Fourier analysis. 576b: Well-posedness, numerical boundary conditions, nonlinear instability, time-split algorithms, special methods for stiff and singular problems. P, 413, 456, 575b.

577. Topics in Applied Mathematics (3) [Rpt./36 units] Advanced topics in asymptotics, numerical analysis, approximation theory, mathematical theory of mechanics, dynamical systems, differential equations and inequalities, mathematical theory of statistics; content varies.

578. Computational Methods of Algebra (3) Applications of machine computation to various aspects of algebra, such as matrix algorithms, character tables and conjugacy classes for finite groups, coset enumeration, integral matrices, crystallographic groups. P, 415 and a knowledge of scientific computer programming language. (Identical with C SC 578).

579. Game Theory and Mathematical Programming (3) For a description of course topics see 479. Graduate-level requirements include more extensive problem sets or advanced projects. P, 410 or 413 or 415. (Identical with C SC 579). May be convened with 479.

582. Applied Complex Analysis (3) Representations of special functions, asymptotic methods for integrals and linear differential equations in the complex domain, applications of conformal mapping, Wiener-Hopf techniques. P, 422b or 424.

583A - 583B. Principles and Methods of Applied Mathematics (3-3) Boundary value problems; Green's functions, distributions, Fourier transforms, the classical partial differential equations (Laplace, heat, wave) of mathematical physics. Linear operators, spectral theory, integral equations, Fredholm theory. P, 424 or 422b or CR, 520a.

585. Mathematical Modeling (3) For a description of course topics see 485. Graduate-level requirements include more advanced projects. P, 422.

586. Case Studies in Applied Mathematics (1-3) [Rpt./6 units] In-depth treatment of several contemporary problems or problem areas from a variety of fields, but all involving mathematical modeling and analysis; content varies.

587. Perturbation Methods in Applied Mathematics (3) Regular and singular perturbations, boundary layer theory, multiscale and averaging methods for nonlinear waves and oscillators. P, 422a-422b or 454.

588. Topics in Mathematical Physics (3) [Rpt./36 units] Advanced topics in field theories, mathematical theory of quantum mechanics, mathematical theory of Statistical mechanics; content varies.

595. Colloquium

a. Math Instruction (1) [Rpt./12 units]

b. Research in Mathematics (1) [Rpt./4]

c. Research in Applied Mathematics (1) [Rpt./4]

596. Seminar

a. Topics in Mathematics (1-3) [Rpt./12]

b. Mathematical Software (3) [Rpt.] P, 254 or 355, knowledge of "C" programming. May be convened with 496b.

c. Research on Learning (1) [Rpt./3] P, must be accepted into NSF-funded grant program, PRIME.

d. Initiating Reform in the Schools (1) [Rpt./3] P, must be accepted into NSF-funded grant program.

597. Workshop

a. Numbers, Algebra and Functions (1-2) [Rpt./3] P, must be accepted into NSF-funded grant program, PRIME.

636. Information Theory (3) (Identical with ECE 636, which is home).

697. Workshop

a. Problems in Computational Science (3) [Rpt./1] (Identical with PHYS 697a).

b. Applied Mathematics Laboratory (3) P, Applied Mathematics core or equivalent. (Identical with PHYS 697b).

1.Students without university credit in the prerequisites for these courses will be required to have an appropriate score on the math readiness test to be enrolled in these courses.

2.Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped by the Registrar's Office. Students with unusual circumstances can petition the department for exemption from this rule. This policy does not infringe on the student's rights granted by the university policy on repeating a course.

3.Credit will be allowed for only one of 424 or 422b. 422a-422b will not be considered a two-semester course at the 400 level in the Master of Arts degree program.

4.Credit will be allowed for only one from each of the following groups: 123, 124 or 125a; 254 or 355; 410 or 413.


Page last updated:  May 20, 2013


Arizona Board of Regents © All rights reserved.
General Catalog  http://catalog.arizona.edu/
The University of Arizona


Page last updated:  May 20, 2013


Arizona Board of Regents © All rights reserved.
General Catalog  http://catalog.arizona.edu/
The University of Arizona


Page last updated:  May 20, 2013


Arizona Board of Regents © All rights reserved.
General Catalog  http://catalog.arizona.edu/
The University of Arizona