UA Courses | Mathematics

Winter 99/Spring 00 Course Descriptions
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Mathematics (MATH) Dept Info - College Info

MATH 105 Mathematics in Modern Society (3) I II 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. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Formerly MATH 122. P, acceptable score on the UA Math Readiness Test.

MATH 110 Collegiate Algebra (4) I II 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 110 may be substituted for MATH 117 in any university requirement or prerequisite. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics 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. Formerly MATH 121. P, acceptable score on Math Readiness Test.

MATH 111 Plane Trigonometry (2) I II Not applicable to the mathematics major or minor. Students with credit in MATH 120R or MATH 120S obtain one unit of graduation credit for MATH 111. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics 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. Formerly MATH 118. P, acceptable score on the UA Math Readiness Test.

MATH 113 Elements of Calculus (3) I II Introductory topics in differential and integral calculus. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Formerly MATH 123. P, MATH 110 or acceptable score on UA Math Readiness Test. Credit allowed for only one of the following courses: MATH 113, MATH 124, or MATH 125.

MATH 114 Finite Mathematics (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. Registration in math courses numbered 125 and below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Formerly MATH 119. P, MATH 110 or acceptable score on the UA Math Readiness Test.

MATH 120R Calculus Preparation (4) I II Reviews algebra and trigonometry; study of functions including polynomial, 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 UA Math Readiness Test to enter calculus. Students with credit in both MATH 110 and MATH 111 receive no credit for MATH 120R. Students with credit in MATH 111, but not MATH 110, receive three units of graduation credit for MATH 120R. Students with credit in MATH 110 but not MATH 111, will receive one unit of graduation credit for MATH 120R. Graphing calculators are required in this course. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics 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. P, acceptable score on UA Math Readiness Test.

MATH 120S Calculus Prep, Self-Study (2) I A self-study course designed for students registered in MATH 124 who need more review of algebra, functions, graphs, trigonometry. Students can drop MATH 124 and add MATH 120S at a time designated by the Mathematics Department. P, consent of current MATH 124 instructor. Credit allowed for only one of MATH 120S, MATH 110, MATH 111 or MATH 120R.

MATH 124 Calculus with Applications (5) I II 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. A graphing calculator is required in this course. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics 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. P, MATH 120R, or MATH 110 and MATH 111, or an acceptable score on the UA Math Readiness Test. Credit allowed for only one of the following courses: MATH 113, MATH 124, or MATH 125.

MATH 125 Calculus (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. A graphing calculator is required for this course. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Math Readiness Test. Credit will not be given for this course if the student has credit in a higher level math course; these students will be dropped from the course. Students with unusual circumstances can petition the Mathematics 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. Formerly MATH 125A. P, acceptable score on UA Mathematics Readiness Test. Credit allowed for only one of the following courses: MATH 113, MATH 124, or MATH 125.

MATH 129 Calculus (3) I II Continuation of 124 or 125. 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. A graphing calculator is required for this course. Formerly MATH 125B. P, MATH 124 or MATH 125. Credit allowed for only one of the following: MATH 129 or MATH 250A.

MATH 160 Basic Statistics (3) I II Organizing data: displaying distributions, measures of center, measures of spread, scatterplots, correlation, regression, and their interpretation. Design of experiments: simple random samples and their sampling distribution, models from probability, normal distributions, and normal approximations. Statistical inference: confidence intervals and hypothesis testing, t procedures and chi-square tests. Not intended for those who plan further studies in statistics. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Mathematics Readiness Test. P, MATH 121 or an acceptable score on the UA Mathematics Readiness Test. Credit allowed for only one of the following: MATH 160 or MATH 263.

MATH 195B From the Pendulum to the Lynx and the Hare (1) I P, simultaneous enrollment in calculus recommended. (Identical with ECOL 195B, which is home).

MATH 197A Basic Statistical Computation (1) I II Statistical computation using computer software. Projects accompany material in Math 160 and Math 263.

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

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

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

MATH 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 129 or MATH 250A.

MATH 223 Vector Calculus (4) I II Vectors, differential and integral calculus of several variables. P, MATH 129 or MATH 250A.

MATH 243 Discrete Mathematics in Computer Science (3) I II Set theory, logic, algebraic structures; induction and recursion; graphs and networks. P, MATH 129 or MATH 250A.

MATH 250A Calculus and Differential Equations I (3) I Integral calculus with applications, techniques of integration, solving first order differential equations using separation of variables, introduction to autonomous first order differential equations. The sequence MATH 250A-250B substitutes for the pair of courses MATH 129-254 or the pair MATH 129-355; however, MATH 250A alone does not substitute for MATH 129. P, score of 4 or 5 on the "AB" Advanced Placement Calculus Exam, consent of instructor. Credit allowed for only one of the following: MATH 250A or MATH 129.

MATH 250B Calculus and Differential Equations II (3) II First order differential equations and modeling, approximations and series, second order differential equations, linear and nonlinear autonomous systems. The sequence MATH 250A-250B substitutes for the pair of courses MATH 129-254 or the pair MATH 129-355; however, MATH 250B alone does not substitute for MATH 254 or MATH 355. P, MATH 250A with a passing grade. Credit allowed for only one of the following: MATH 250B, MATH 254, or MATH 355.

MATH 254 Introduction to Ordinary Differential Equations (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 or MATH 250B.

MATH 263 Introduction to Statistics and Biostatistics (3) I II Organizing data; distributions, measures of center and spread, scatterplots, nonlinear models and transformations, correlation, regression. Design of experiments: models from probability, discrete and continuous random variables, normal distributions, sampling distributions, the central limit theorem. Statistical inference; confidence intervals and test of significance, t procedures, inference for count data, two-way tables and chi-square procedures, inference for regression, analysis of variance. Registration in math courses numbered 125 or below, 160, and 263, requires all students, including transfer students with or without college level math credit, to take the UA Mathematics Readiness Test. P, MATH 110 or an acceptable score on the UA Math Readiness Test. Credit allowed for only one of MATH 160 or MATH 263.

MATH 294A Problem-Solving Laboratory (1) [Rpt./] I II

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

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

MATH 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 110 or MATH 105. Open to elementary education majors only.

MATH 310 Harmonic Analysis (3) II The course treats the interplay between algebra and analysis in a way that enhances both subjects. Specific examples of functions and the groups related to them will be discussed. P, MATH 129 or MATH 250A, MATH 215.

MATH 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.

MATH 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 or MATH 250B. Credit allowed for only one of the following: MATH 322 or MATH 422.

MATH 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 functions, 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 and limits of sequences and functions; the emphasis throughout is on proving theorems. Writing Emphasis Course. P, MATH 215.

MATH 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.

MATH 344 Foundations of Computing (3) P, MATH 243. (Identical with C SC 344, which is home).

MATH 355 Analysis of Ordinary Differential Equations (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.

MATH 362 Introduction to Probability Theory (3) I II Sample spaces, random variables and their properties, with considerable emphasis on applications. P, MATH 113, MATH 129, or MATH 250A.

MATH 380 Math Models In Biology (3) I P, MATH 223 or consent of instructor. (Identical with ECOL 380, which is home).

MATH 397A Mathematics Education (1) I II P, MATH 315 or MATH 330. Open to teaching majors in mathematics only.

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

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

MATH 401A Symbolic Logic (3) I (Identical with PHIL 401A, which is home). May be convened with MATH 501A.

MATH 401B Symbolic Logic (3) II (Identical with PHIL 401B, which is home). May be convened with MATH 501B.

MATH 402 Mathematical Logic (3) I [Taught alternate years 1999 - 2000] Sentential calculus, predicate calculus; consistency, independence, completeness, and the decision problem. Designed to be of interest to majors in mathematics or philosophy. (Identical with C SC 402, PHIL 402). May be convened with MATH 502.

MATH 403 Foundations of Mathematics (3) II [Taught alternate years 1999 - 2000] 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.

MATH 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.

MATH 405 Mathematics in the Secondary School (3) II P, or CR, MATH 315, MATH 330, MATH 362. (Identical with TTE 405, which is home).

MATH 410 Matrix Analysis (3) I II General introductory course in the theory of matrices. P, MATH 254 or MATH 355 or MATH 250B; knowledge of matrix operations (as contained in, for example, MATH 215 or SIE 270). Credit allowed for only one of the following: MATH 410, MATH 413.

MATH 413 Linear Algebra (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 the following: MATH 413, MATH 410. May be convened with MATH 513.

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

MATH 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 421A. May be convened with MATH 515B.

MATH 421 Complex Variables with Applications (3) II Complex numbers, analytic functions, harmonic functions, elementary functions, complex integration, Cauchy's integral theorem, series representations for analytic functions, residue theory, conformal mapping, applications to steady-state temperature and oscillating systems. P, MATH 254 or MATH 355 or MATH 250B. Credit allowed for only one of the following: MATH 421 or MATH 424. May be convened with MATH 521.

MATH 422 Advanced Applied Analysis (3) I Review of multivariable calculus, series solutions of differential equations, Laplace transforms, Fourier series, introduction to partial differential equations. P, MATH 254 or MATH 355, or MATH 250B. Credit allowed for only one of the following: MATH 422 or MATH 322. May be convened with MATH 522.

MATH 424 Theory of Complex Variables (3) I II Complex numbers, complex-valued functions, analytic functions, elementary functions, series, residues and poles, mapping by elementary functions, conformal mapping, the Schwarz-Christoffel transformation, integral formulas of Poisson type. MATH 421-422 will not be considered a two-semester course at the 400 level in the Master of Arts degree program. P, MATH 323 or consent of instructor. Credit allowed for only one of the following: MATH 424 or MATH 421. May be convened with MATH 524.

MATH 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 323. May be convened with MATH 525A.

MATH 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.

MATH 430 Second Course in Geometry (3) II [Taught alternate years 2000 - 2001] 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.

MATH 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.

MATH 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.

MATH 446 Theory of Numbers (3) II [Taught alternate years 2000 - 2001] Divisibility properties of integers, primes, congruencies, quadratic residues, number-theoretic functions. P, MATH 215. May be convened with MATH 546.

MATH 447 Combinatorial Mathematics (3) II [Taught alternate years 2000 - 2001] 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.

MATH 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 254 or MATH 355 or MATH 250B.

MATH 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 422. May be convened with MATH 556.

MATH 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.

MATH 464 Theory of Probability (3) I 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.

MATH 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.

MATH 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.

MATH 473 Automata, Grammars and Languages (3) I Writing Emphasis Course. P, C SC 344. (Identical with C SC 473, which is home).

MATH 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 or MATH 250B; MATH 215. Knowledge of a scientific programming language. (Identical with C SC 475A).

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

MATH 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.

MATH 481 Basic of Scientific Computing (2) I II Covers essentials of modern computing environment and tools, for both Windows and Unix-based environments. Course includes classroom and hands-on instruction. No computing experience necessary. May be convened with MATH 581.

MATH 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. Writing Emphasis Course. P, MATH 422. May be convened with MATH 585.

MATH 496B Mathematical Software (3) [Rpt./ 1] I P, MATH 254 or MATH 355 or MATH 250B; knowledge of "C" programming language. May be convened with MATH 596B.

MATH 498 Senior Capstone (1-3) I II

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

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

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

MATH 500 History of Mathematics for Elementary School (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. This course is applicable to the MA in TTE (with Specialization in Elementary Mathematics). It is not applicable to graduate degree programs in mathematics.

MATH 501A Symbolic Logic (3) I (Identical with PHIL 501A, which is home). May be convened with MATH 401A.

MATH 501B Symbolic Logic (3) II (Identical with PHIL 501B, which is home). May be convened with MATH 401B.

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

MATH 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.

MATH 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, 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.

MATH 505 Arithmetic and Number Theory for Elementary Teachers (3) Elementary school teachers will be introduced to creative mathematics through a series of exploratory problems. The problems are designed to give the teachers an 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. This course is applicable to the MA in TTE (with Specialization in Elementary Mathematics). It is not applicable to graduate degree programs in mathematics.

MATH 506 Geometry for Elementary School (1-3) [Rpt./ 4 units] Various topics in geometry for elementary and middle school teachers, such as tessellations, 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.

MATH 507 Problem Solving in High School (3) I Exploratory problems in algebra, geometry, and number theory will be worked on, written up, and presented to the class. Students will be encouraged to work in groups. Basic principles of problem solving will be discussed throughout. This course is only for M.A. in Math (Teaching Option) and M.A. in TTE P, open only to M.A. in Math (Teaching Option) and M.A. in TTE.

MATH 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. (Identical with PCOL 509, GENE 509).

MATH 510 Algebra for Elementary School (3) 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 tot he learning and teaching of algebra in these grades.

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

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

MATH 512 Modern Algebra for Secondary Teachers (3) II The course studies fields, specifically the rationals, the reals and the complex numbers. Specific topics include The Fundamental Theorem of Algebra, factoring, Rolle's Theorem, Descartes' Rule of Signs and Sturm's Algorithm for root separation. P, open only to M.A. in Math (Teaching Option) and M.A. in TTE.

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

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

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

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

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

MATH 517A Group Theory (3) [Rpt./ 4] I Selections from such topics as finite groups, abelian groups, characters and representations. P, MATH 511B.

MATH 517B Group Theory (3) [Rpt./ 4] II Selections from such topics as finite groups, abelian groups, characters and representations. P, MATH 511B.

MATH 518 Topics in Algebra (3) [Rpt./ 4] I II Advanced topics in groups, rings, fields, algebras; content varies.

MATH 519 Topics in Number Theory and Combinatorics (3) [Rpt./ 4] I II Advanced topics in algebraic number theory, analytic number theory, class fields, combinatorics; content varies.

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

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

MATH 521 Complex Variables with Applications (3) II For a description of course topics see MATH 421. Graduate-level requirements include more extensive problem sets or advanced projects. May be convened with MATH 421.

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

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

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

MATH 524 Theory 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.

MATH 525A Real Analysis of One Variable (3) I 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.

MATH 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. May be convened with MATH 425B.

MATH 527A Principles of Analysis (3) I 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, and a differential equations course.

MATH 527B Principles of Analysis (3) II 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, and a differential equations course.

MATH 528A Banach and Hilbert Spaces (3) I 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.

MATH 528B Banach and Hilbert Spaces (3) 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.

MATH 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.

MATH 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.

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

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

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

MATH 536A Algebraic Geometry (3) I 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.

MATH 536B Algebraic Geometry (3) 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.

MATH 537A Global Differential Geometry (3) I 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.

MATH 537B Global Differential Geometry (3) 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.

MATH 538 Topics in Geometry and Topology (3) [Rpt./ 4] I II Advanced topics in point set and algebraic topology, algebraic geometry, differential geometry; content varies.

MATH 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).

MATH 543 Theory of Graphs and Networks (3) I 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.

MATH 546 Theory of Numbers (3) II 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.

MATH 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.

MATH 550 Mathematical Population Dynamics (4) II 3R, 3L. P, ordinary differential equations as MATH 254 or MATH 355, full calculus sequence, upper-division ecology course (ECOL 302). (Identical with ECOL 550, which is home).

MATH 553A Partial Differential Equations (3) I 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.

MATH 553B Partial Differential Equations (3) 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.

MATH 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.

MATH 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 MATH 456.

MATH 557A Dynamical Systems and Chaos (3) I 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 422.

MATH 557B Dynamical Systems and Chaos (3) 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 422.

MATH 558 Probability and Statistics (3) I The course includes mathematical modeling, measures of central tendency and dispersion, discrete probability, applications, Bayes' theorem, Chebyshev's Inequality, binomial and normal distributions, hypothesis testing, and game theory. This course is only for M.A. in Math (Teaching Option) and M.A. in TTE. P, open only to M.A. in Math (Teaching Option) and M.A. in TTE.

MATH 559A Lie Groups and Lie Algebras (3) I 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.

MATH 559B Lie Groups and Lie Algebras (3) 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.

MATH 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 experience or consent of instructor.

MATH 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.

MATH 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.

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

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

MATH 564 Theory of Probability (3) I 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.

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

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

MATH 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.

MATH 567A Theoretical Statistics (3) I Basic decision theory. Bayes' rules for estimation. Admissibility and completeness. The minimax theorem. Sufficiency. Exponential families of distributions. 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.

MATH 567B Theoretical Statistics (3) II Basic decision theory. Bayes' rules for estimation. Admissibility and completeness. The minimax theorem. Sufficiency. Exponential families of distributions. 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.

MATH 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.

MATH 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.

MATH 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.

MATH 571 Design of Experiments (3) II Principles of designing experiments. Randomization, block designs, factorial experiments, response surface designs, repeated measures, analysis of contrasts, multiple comparisons, analysis of variance and covariance, variance components analysis. P, MATH 223, and one of MATH 461 or MATH 509.

MATH 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.

MATH 573 Theory of Computation (3) II P, C SC 473. (Identical with C SC 573, which is home).

MATH 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. (Identical with GEOG 574).

MATH 575A Numerical Analysis (3) I Error analysis, solution of linear systems and nonlinear equations, eigenvalue 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).

MATH 575B Numerical Analysis (3) II Error analysis, solution of linear systems and nonlinear equations, eigenvalue 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 575B).

MATH 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.

MATH 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.

MATH 577 Topics in Applied Mathematics (3) I II Advanced topics in asymptotics, numerical analysis, approximation theory, mathematical theory of mechanics, dynamical systems, differential equations and inequalities, mathematical theory of statistics; content varies.

MATH 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, knowledge of scientific computer programming language. (Identical with C SC 578).

MATH 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. (Identical with C SC 579). May be convened with MATH 479.

MATH 580 Calculators and Computers for Elementary Teachers (3) I S II Students will use calculators and 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. This course is applicable to the M.A. in TTE (with Specialization in Elementary Mathematics). It is not applicable to graduate degree programs in mathematics.

MATH 581 Basic Scientific Computing (2) I II For a description of course topics see MATH 481. Graduate-level requirements include 5 projects. May be convened with MATH 481.

MATH 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 421 or MATH 424.

MATH 583A Principles and Methods of Applied Mathematics (3) I 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 421 or MATH 424 or MATH 520A.

MATH 583B Principles and Methods of Applied Mathematics (3) 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 421 or MATH 424 or MATH 520A.

MATH 584 Technology in Secondary School (3) II Students will use computers and/or graphing calculators to explore various mathematical topics including number theory, geometry, precalculus, and calculus. Programming capabilities of the calculator or computer will be covered as appropriate. P, open only to M.A. in Math (Teaching Option) and M.A. in TTE.

MATH 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.

MATH 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.

MATH 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 422, MATH 4221 or MATH 454.

MATH 588 Topics in Mathematical Physics (3) [Rpt./ 4] I II Advanced topics in field theories, mathematical theory of quantum mechanics, mathematical theory of statistical mechanics; content varies.

MATH 589 Software Tools for Computational Science and Engineering (3) II Techniques and tools useful at the interface between mathematical and technical computing on the one hand, and the Internet on the other. Topics include scripting languages such as Perl and Tcl/Tk, graphics file formats, the mathematics of raster and vector graphics, and standard libraries and applications for numerical and symbolic computing. Also, the fundamentals of computer networking from a user's point of view. P, C SC 318 and ability to program in at least one modern high-level language. (Identical with C SC 589).

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

MATH 595A Math Instruction (1) [Rpt./ 11] I II

MATH 595B Research in Mathematics (1) [Rpt./ 4] I II

MATH 595C Research in Applied Mathematics (1) [Rpt./ 4] I II

MATH 596A Topics in Mathematics (1-3) [Rpt./ 12 units] S

MATH 596B Mathematical Software (3) [Rpt./ 1] I For a description of course topics see MATH 496B. May be convened with MATH 496B.

MATH 596E Topics in Mathematics for Secondary Teachers (1-4) [Rpt./ 4] II Mathematics appropriate for secondary mathematics teachers. Topics will vary.

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

MATH 636 Information Theory (3) II P, ECE 503. (Identical with ECE 636, which is home).

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

MATH 697B Applied Mathematics Laboratory (3) II S P, applied math core or equivalent. (Identical with PHYS 697B).

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

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

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

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

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

Page last updated: May 20, 2013