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.