How to read course descriptions

MATHEMATICS (MATH)

118. Plane Trigonometry 2 (2) I II Not applicable to the mathematics major or minor. Students with credit in 120 obtain one unit of graduation credit for 118. P, acceptable score on Math Readiness Assessment Test.

119. Finite Mathematics 1 (3) I II Elements of set theory and counting techniques, probability theory, linear systems of equations, matrix algebra; linear programming with simplex method, Markov chains. P, MATH 121, acceptable score on Math Readiness Assessment Test.

120R. Calculus Preparation 2 (4) I II 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 both MATH 121 and MATH 118 will receive no credit for MATH 120. Students with credit in MATH 118, but not MATH 121, will receive three units of graduation credit for MATH 120. Students with credit in MATH 121 or 117R/S, but not MATH 118, will receive one unit of graduation credit for MATH 120. P, acceptable score on Math Readiness Assessment Test. Graphing calculators are required in this course.

121. Collegiate Algebra 2 (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. MATH 121 may be substituted for MATH 117 in any University requirement or prerequisite. P, acceptable score on Mathematics Readiness Assessment 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, acceptable score on Mathematics Readiness Assessment Test.

123. Elements of Calculus 2,4 (3) I II Introductory topics in differential and integral calculus. P, MATH 121 or acceptable score on Mathematics Readiness Assessment Test. Credit allowed for only one of the following courses: MATH 123, MATH 124, or MATH 125A.

124. Calculus with Applications 2,4 (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. P, MATH 120 or MATH 121 and MATH 118, MATH 117R/S and MATH 118, or an acceptable score on the Mathematics Readiness Assessment Test. Credit allowed for only one of the following courses: MATH 123, MATH 124, or MATH 125A.

125A. Calculus 2,4 (3) I II 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, acceptable score on Mathematics Readiness Assessment Test. Credit allowed for only one of the following courses: MATH 123, MATH 124, or MATH 125A.

125B. Calculus 4 (3) II 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, MATH 124 or MATH 125A.

160. Introduction to Statistics (3) I II 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, MATH 121 or MATH 117R/S.

199. Independent Study (1-4) [Rpt./]

199H. Honors Independent Study (1-6) [Rpt./] I II

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

215. Introduction to Linear Algebra (3) I II Vector spaces, linear transformations and matrices. There is some emphasis on the writing of proofs. P, MATH 125B.

223. Vector Calculus (4) I II Vectors, differential and integral calculus of several variables. P, MATH 125B.

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

254. Introduction to Ordinary Differential Equations 4 (3) I II Solution methods for ordinary differential equations, qualitative techniques; includes matrix methods approach to systems of linear equations and series solutions. P, MATH 223. Credit allowed for only one of these courses: MATH 254, MATH 355.

263. Statistical Methods in Biological Sciences (3) I II 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, MATH 121 or MATH 117R/S.

294. Practicum

a. Problem Solving Laboratory (1) [Rpt./] I II

299. Independent Study (2-4) [Rpt./]

299H. Honors Independent Study (1-3) [Rpt./] I

301. Understanding Elementary Mathematics (4) I II Development of a basis for understanding the common processes in elementary mathematics related to the concepts of number, measurement, geometry and probability. P, MATH 121 or MATH 122 or MATH 117R/S. Open to elementary education majors only.

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

322. Mathematical Analysis for Engineers (3) I II Complex functions and integration, line and surface integrals, Fourier series, partial differential equations. P, MATH 254 or MATH 355. Credit allowed for only one of these courses: MATH 322, MATH 422A.

323. Formal Mathematical Reasoning and Writing (3) I II 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, sequence a and limits of sequences and functions; the emphasis throughout is on proving theorems. P, MATH 215. Writing-Emphasis Course*.

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

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

355. Analysis of Ordinary Differential Equations 4 (3) I II Linear and nonlinear equations; basic solution techniques; qualitative and numerical methods; systems of equations; computer studies; applications drawn from physical, biological and social sciences. P, MATH 215. Credit allowed for only one of these courses: MATH 355, MATH 254.

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

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

397. Workshop

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

399. Independent Study (1-5) [Rpt./]

399H. Honors Independent Study (3) [Rpt./] I II

401B. Symbolic Logic (3) I (Identical with PHIL 401A-401B, which is home).

402. Mathematical Logic (3) I Sentential calculus, predicate calculus; consistency, independence, completeness, and the decision problem. Designed to be of interest to majors in mathematics or philosophy. P, MATH 124 or MATH 125B. Credit allowed for: MATH 402 or MATH 409A, but not for both. (Identical with C SC 402, PHIL 402).

403. Foundations of Mathematics (3) II 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, MATH 215. (Identical with PHIL 403). May be convened with MATH 503.

404. History of Mathematics (3) I 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, MATH 215 or MATH 223. May be convened with MATH 504.

405. Mathematics in the Secondary School (3) II (Identical with TTE 405, which is home).

409B. Symbolic Logic (3) I (Identical with PHIL 409A-409B, which is home). Change course number to: MATH 401A - MATH 401B. Spring 99

410. Matrix Analysis 4 (3) I II General introductory course in the theory of matrices. P, MATH 254 or MATH 355; knowledge of matrix operations (as contained in, for example, MATH 215 or SIE 270). Credit allowed for only one of these courses: MATH 410, MATH 413.

413. Linear Algebra 4 (3) I II Vector spaces, linear transformations and matrices, eigenvalues, bilinear forms, orthogonal and unitary transformations. P, MATH 323. Credit allowed for only one of these courses: MATH 413, MATH 410. May be convened with MATH 513.

415A. Introduction to Abstract Algebra (3) I Introduction to groups, rings, and fields. May be convened with MATH 515A.

415B. Second Course in Abstract Algebra (3) II A continuation of 415A. Topics may include Galois theory, linear and multilinear algebra, finite fields and coding theory. Polya enumeration. P, MATH 415A. May be convened with MATH 515B.

422B. Advanced Analysis For Engineers 3 (3) I Laplace transforms, Fourier series, partial differential equations, vector analysis, integral theorems, complex variables. P, MATH 254 or MATH 355. Credit allowed for only one of these courses: MATH 422A, MATH 322. Credit allowed for only one of these courses: MATH 422B, MATH 424. May be convened with MATH 522A-522B.

424. Elements of Complex Variables 3 (3) I II Complex numbers and functions, conformal mapping, calculus of residues. P, MATH 223. May be convened with MATH 524.

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

425B. Real Analysis of Several Variables (3) II Continuity and differentiation in higher dimensions, curves and surfaces; change of coordinates; theorems of Green, Gauss and Stokes; exact differentials. P, MATH 425A. May be convened with MATH 525B.

430. Second Course in Geometry (3) II 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, MATH 215. May be convened with MATH 530.

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

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

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

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

454. Ordinary Differential Equations and Stability Theory (3) I General theory of initial value problems, linear systems and phase portraits, linearization of nonlinear systems, stability and bifurcation theory, limit cycles and Poincare-Bendixson theory, an introduction to chaotic dynamics. P, MATH 243 or MATH 355.

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

461. Elements of Statistics (3) I II Probability spaces, random variables, standard distributions, point and interval estimation, tests of hypotheses; includes use of standard Statistical software package. P, MATH 223.

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

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

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

473. Automata, Grammars and Languages (3) I (Identical with C SC 473, which is home).

475A. Mathematical Principles of Numerical Analysis (3) I Analysis of errors in numerical computations, solution of linear algebraic systems of equations, matrix inversion, eigenvalues, roots of nonlinear equations, interpolation and approximation. P, MATH 254 or MATH 355; MATH 215, knowledge of a scientific programming language. (Identical with C SC 475A).

475B. Mathematical Principles of Numerical Analysis (3) II Numerical integration, solution of systems of ordinary differential equations, initial value and boundary value problems. (Identical with C SC 475B).

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

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

496. Seminar

b. Mathematical Software (3) [Rpt./ 1] I P, MATH 254 or MATH 355; knowledge of "C" programming language. May be convened with MATH 596B.

498. Senior Capstone (1-3) I II

498H. Honors Thesis (3) [Rpt./ 2] I II

499. Independent Study (1-5) [Rpt./]

499H. Honors Independent Study (3) [Rpt./] I II

*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).

500. History of Mathematics for Elementary (3) II Topics will include the history of numbers, numerals, and computation, and the history of elementary geometry, algebra, statistics, probability, computing devices and other topics appropriate to the elementary school mathematics curriculum.

501B. Symbolic Logic (3) I (Identical with PHIL 501A-501B, which is home).

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

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

504. History of Mathematics (3) I For a description of course topics see MATH 404. Graduate-level requirements include more extensive problem sets or advanced projects. P, MATH 215 or MATH 223. Not applicable to M.A., M.S., or Ph.D. degrees for math majors except for the M.A. teaching option. May be convened with MATH 404.

505. Arithmetic and Number Theory for Elementary Teachers (3) I Elementary school teachers will be introduced to creative mathematics through a series of exploratory problems. The problems are designed to give teachers insight into problem solving as well as ideas to use in their own classrooms. Solving problems using elementary arithmetic will be used to examine the two main facets of mathematics: abstract thinking and concrete modeling.

506. Geometry for Elementary School (1-3) [Rpt./ 4 units] I S Various topics in geometry for elementary and middle school teachers, such as tesselations, 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) I II 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, MATH 121 or MATH 117R/S. (Identical with GENE 509, PCOL 509).

510. Algebra for Elementary School (3) I The course aims at strengthening teachers' understanding of algebra (focusing on a study of patterns and functions), to explore algebra and pre-algebra activities appropriate for K-8, and to discuss research issues related to the learning and teaching of algebra in these grades.

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

513. Linear Algebra (3) II For a description of course topics see MATH 413. For a description of course topics see 413. Graduate-level requirements include more extensive problem sets or advanced projects. P, MATH 323. May be convened with MATH 413.

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

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

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

518. Topics in Algebra (3) [Rpt./ 11] I II Advanced topics in groups, rings, fields, algebras; content varies.

519. Topics in Number Theory and Combinatorics (3) [Rpt./ 11] I II Advanced topics in algebraic number theory, analytic number theory, class fields, combinatorics; content varies.

520A. Complex Analysis (3) I Analyticity, Cauchy's integral formula, residues, infinite products, conformal mapping, Dirichlet problem, Riemann mapping theorem. P, MATH 424.

520B. Complex Analysis (3) II Rudiments of Riemann surfaces. P, MATH 520A or MATH 582.

522B. Advanced Analysis For Engineers (3-3) I II For a description of course topics see MATH 422A-422B. Graduate-level requirements include more extensive problem sets or advanced projects. May be convened with MATH 422A-422B.

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

524. Elements of Complex Variables (3) I II For a description of course topics see MATH 424. Graduate-level requirements include more extensive problem sets or advanced project. May be convened with MATH 424.

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

525B. Real Analysis of Several Variables (3) II For a description of course topics see MATH 425B. Graduate-level requirements include more extensive problem sets or advanced projects. P, MATH 425A or 525A. May be convened with MATH 25B.

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, MATH 410, MATH 424, differential equation course.

528B. Banach and Hilbert Spaces (3-3) I II 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, MATH 527B or MATH 583; MATH 523A.

529. Topics in Modern Analysis (3) I II 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) II For a description of course topics see MATH 430. Graduate-level requirements include more extensive problem sets or advanced projects. May be convened with MATH 430.

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

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, MATH 415A and MATH 425A.

536B. Algebraic Geometry (3-3) I II 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, MATH 511, MATH 520A, MATH 534A.

537B. Global Differential Geometry (3-3) I II 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, MATH 534A, MATH 534B.

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

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

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

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

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

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

553B. Partial Differential Equations (3-3) I II 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, MATH 523B or MATH 527B or MATH 583B.

554. Ordinary Differential Equations (3) I 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, MATH 413 or consent of instructor.

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

557B. Dynamical Systems and Chaos (3-3) I II 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, MATH 422B or MATH 454; MATH 422A.

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

560. Elementary School Probability (1-3) [Rpt./ 3 units] II S 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 experience or consent of instructor.

561. Regression and Multivariate Analysis (3) I 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, MATH 410 or MATH 413; one of MATH 461, MATH 466, or MATH 509.

562. Time Series Analysis (3) I 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.

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) I II For a description of course topics see MATH 464. Graduate-level requirements include more extensive problem sets or advanced projects. May be convened with MATH 464.

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

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

567B. Theoretical Statistics (3-3) I II 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, MATH 466.

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

569. Nonparametric Statistics (3) II 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, MATH 461, MATH 466 or MATH 509.

570. Categorical Data Analysis (3) II 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, MATH 461, MATH 466 or MATH 509.

571. Design of Experiments (3) II 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, MATH 223, MATH 461 or MATH 509.

572. Statistical Consulting (3) I Course provides instruction and experience in all aspects of statistical consulting. The class is organized as a small consulting lab with instructor acting as director. Students interact with actual clients from university and local business communities. P, two semesters of statistics and consent of instructor.

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

574. Introduction to Geostatistics (3) I 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.

575B. Numerical Analysis (3-3) I II 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, MATH 475B or MATH 456. (Identical with C SC 575A-575B).

576A. Numerical Analysis PDE (3) I Finite difference, finite element and spectral discretization methods; semidiscrete, matrix and Fourier analysis. P, MATH 413, MATH 456, MATH 575B.

576B. Numerical Analysis PDE (3) II Well-posedness, numerical boundary conditions, nonlinear instability, time-split algorithms, special methods for stiff and singular problems. P, MATH 413, MATH 456, MATH 575B.

577. Topics in Applied Mathematics (3) I II [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) II 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, MATH 415A and knowledge of a scientific computer programming language. (Identical with C SC 578).

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

580. Calculators and Computers for Elementary Teachers (3) II Students will use calculators & computers to explore various mathematical topics such as elementary number theory, probability, statistics, geometry, and so on. Emphasis will be placed on how and when to use technology, on becoming comfortable with both calculators and computers, on what are good and poor activities with technology, and on the importance of estimation and good judgment when using technology. Students will be introduced to computer activities using BASIC, LOGO, and appropriate pre-packaged software.

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

583B. Principles and Methods of Applied Mathematics (3-3) I II 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, MATH 422B or MATH 424 or MATH 520A.

585. Mathematical Modeling (3) II For a description of course topics see MATH 485. Graduate-level requirements include more advanced projects. May be convened with MATH 485.

586. Case Studies in Applied Mathematics (1-3) [Rpt./ 6 units] I II 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) I Regular and singular perturbations, boundary layer theory, multiscale and averaging methods for nonlinear waves and oscillators. P, MATH 422A, MATH 422B or MATH 454.

588. Topics is Mathematical Physics (3) [Rpt./ 11] I II Advanced topics in field theories, mathematical theory of quantum mechanics, mathematical theory of statistical mechanics; content varies.

593. Internship (1-3) [Rpt./] I II

595. Colloquium

a. Math Instruction (1) [Rpt./ 11] I II

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

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

596. Seminar

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

b. Mathematical Software (3) [Rpt./ 1] I For a description of course topics see MATH 496B. May be convened with MATH 496B.

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

d. Initiating Reform in the Schools (1) [Rpt./3] S P, acceptance into NSF-funded grant program, PRIME.

597. Workshop

a. Numbers, Algebra and Functions (1-2) S P, acceptance into NSF-funded grant program, PRIME.

599. Independent Study (1-6) [Rpt./]

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

697. Workshop

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

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

699. Independent Study (1-6) [Rpt./] I II

900. Research (2-8) [Rpt./]

910. Thesis (3-6) [Rpt./]

920. Dissertation (1-9) [Rpt./]

930. Supplementary Registration (1-9) [Rpt./]

1.Students without university credit in the prerequisites for these courses will be required to have an appropriate score on the Math Readiness Assessment 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.


Academic Policies|College Information|Department Information|List of Courses|Undergraduate Majors|Undergraduate Minors|Academic Program Requirements Reports|Minor Requirement Reports|Academic Calendar|Schedule of Classes|Important Deadlines|List of Faculty|Accreditations and Affiliations|Graduate Catalog|Previous Catalogs|Order a Catalog|Student Responsibility|Home

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