CONTENTS
CHAPTER 1
The University
CHAPTER 2
School of Architecture
CHAPTER 3
Red McCombs School of Business
CHAPTER 4
College of Communication
CHAPTER 5
College of Education
CHAPTER 6
College of Engineering
CHAPTER 7
College of Fine Arts
CHAPTER 8
College of Liberal Arts
CHAPTER 9
College of Natural Sciences
CHAPTER 10
School of Nursing
CHAPTER 11
College of Pharmacy
CHAPTER 12
School of Social Work
CHAPTER 13
The Faculty
Texas Common Course Numbering System
(Appendix A)
APPENDIX B
Degree and Course Abbreviations



CHAPTER NINE CONTENTS
NEXT FILE IN CHAPTER NINE 
PREVIOUS FILE IN CHAPTER NINE
continued
Courses
The faculty has approval to offer the following courses in the
academic years 20002001 and 20012002; however, not all courses are
taught each semester or summer session. Students should consult the
Course
Schedule to determine which courses and topics will be
offered during a particular semester or summer session. The Course
Schedule may also reflect changes that have been made to the
courses listed here since this catalog was printed.
A full explanation of course numbers is given in General Information. In brief, the first digit of a course number
indicates the semester hour value of the course. The second and third
digits indicate the rank of the course: if they are 01 through 19,
the course is of lowerdivision rank; if 20 through 79, of
upperdivision rank; if 80 through 99, of graduate rank.
Department of Mathematics
The Department of Mathematics offers a wide variety of courses to
serve the needs of mathematics majors planning different careers and
to serve the mathematical needs of students in other fields. Students
majoring in mathematics should obtain a current copy of the Handbook
for Students from the department. For help planning a program of
study, students should consult an adviser in the Mathematics,
Physics, and Astronomy Advising Center, Robert Lee Moore Hall 4.101.
A concentration in actuarial studies is available to students
majoring in mathematics or another area. Typical programs include
three to seven hours of actuarial foundations, twentyeight hours of
mathematics, and twelve hours of coursework in the Red McCombs School
of Business. Detailed information is available from the director of
actuarial studies in the Department of Mathematics.
Prerequisites
Most entrylevel courses in the Department of Mathematics have as a
prerequisite a specific minimum score on the SAT II: Mathematics
Level IC test; therefore, many students planning to take a course in
the department must first have taken the Mathematics Level IC test.
See the current Course Schedule or consult the Advising Center for
the minimum score required.
Important advice on which entrylevel mathematics course to take,
based on the student's score on the Mathematics Level IC test, is
available from the Measurement and Evaluation Center and the
Mathematics, Physics, and Astronomy Advising Center.
In courses that have a minimum test score or course grade as a
prerequisite, students will be dropped from the course if University
records do not show that they have met the prerequisite. Students for
whom the Mathematics Level IC test score is required must be prepared
to present proof of their test score after classes have begun.
Students who took the test at a College Board test center must use
the official College Board score report as proof; students without
the score report can obtain alternate proof from the Measurement and
Evaluation Center. Students who took the test at the University must
use the testresult slip as the written proof; information about
where to obtain the testresult slip is given at the time of the test.
Students who plan to use transfer credit to meet a prerequisite must
submit a complete transcript to the Office of Admissions, so that the
credit can be added to University records. In addition to sending a
transcript, students are encouraged to bring a grade report to the
Advising Center as proof.
Students who wish to enroll in conference courses in the Department
of Mathematics must submit consent of instructor forms to the
Department of Mathematics before registering. Forms are available in
the department office and the Advising Center.
Unless otherwise stated in the description below, each class meets
for three lecture hours a week for one semester.
Actuarial Foundations: ACF
LowerDivision Courses
309. Theory of Interest.
Measurement of interest, present value,
accumulated value, annuities, amortization of loans, sinking funds,
and bonds. Covers the interesttheory portion of the syllabus for
exam #2 of the Society of Actuaries and the Casualty Actuarial
Society. Prerequisite: Credit or registration for Mathematics
408D.
110, 210, 310, 410. Conference Course.
Supervised study of selected
topics, by individual arrangement with department and instructor. May
be repeated for credit when the topics vary. Some sections are
offered on the pass/fail basis only; these are identified in the
Course Schedule. Prerequisite: Written consent of instructor.
110T. Conference Course: Texas Department of Insurance Internship.
Supervised internship at the Texas Department of Insurance. May be
repeated for credit. Admission by application only. Students must
apply to the director of the concentration in actuarial studies the
semester before they take the course.
112K. Actuarial Laboratory on Calculus and Linear Algebra.
Problems
and supplementary instruction in calculus, matrix algebra, and linear
algebra, especially as required for the Society of Actuaries and
Casualty Actuarial Society Exam 100. Three laboratory hours a week
for one semester. Prerequisite: Mathematics 408D with a grade
of at least C, and credit or registration for Mathematics 341 (or
311) or 340L.
112L. Actuarial Laboratory on Interest Theory.
Problems and
supplementary instruction in interest theory, especially as required
for the Society of Actuaries Exam 140. Three laboratory hours a week
for one semester. Prerequisite: Actuarial Foundations 309
with a grade of at least C and consent of the director of the
concentration in actuarial studies.
112M. Actuarial Laboratory on Probability and Statistics.
Problems
and supplementary instruction in probability and statistics,
especially as required for the Society of Actuaries and Casualty
Actuarial Society Exam 110. Three laboratory hours a week for one
semester. Prerequisite: Mathematics 362K, credit or
registration for Mathematics 378K, and consent of the director of the
concentration in actuarial studies.
112N. Actuarial Laboratory on Life Contingencies.
Problems and
supplementary instruction in actuarial mathematics and contingency
theory, especially as required for the Society of Actuaries Exam 150.
Three laboratory hours a week for one semester. Prerequisite:
Credit or registration for Mathematics 469L, and consent of the
director of the concentration in actuarial studies.
Mathematics: M
LowerDivision Courses
301. College Algebra.
Topics include a brief review of elementary
algebra; linear, quadratic, exponential, and logarithmic functions;
polynomials; systems of linear equations; applications. Three lecture
hours a week for one semester. Usually offered only in the summer
session. May not be counted toward the major requirement for the
Bachelor of Arts, Plan I, degree with a major in mathematics or
toward the Bachelor of Science in Mathematics degree. In some
colleges of the University, Mathematics 301 may not be counted toward
the Area C requirement or toward the total number of hours required
for a degree. Credit for Mathematics 301 may not be earned after a
student has received credit for any calculus course with a grade of C
or better. Prerequisite: A passing score on the mathematics
section of the Texas Academic Skills Program (TASP) test.
302. Introduction to Mathematics.
Intended primarily for general
liberal arts students seeking knowledge of the nature of mathematics
as well as training in mathematical thinking and problem solving.
Topics include number theory and probability; additional topics are
chosen by the instructor. Mathematics 302 and 303F may not both be
counted. A student may not earn credit for Mathematics 302 after
having received credit for any calculus course. May not be counted
toward the major requirement for the Bachelor of Arts, Plan I, degree
with a major in mathematics or toward the Bachelor of Science in
Mathematics degree. May be used to fulfill the Area C requirement for
the Bachelor of Arts, Plan I, degree or the mathematics requirement
for the Bachelor of Arts, Plan II, degree. Prerequisite:
Three units of high school mathematics at the level of Algebra I or
higher, and a passing score on the mathematics section of the Texas
Academic Skills Program (TASP) test.
303D. Applicable Mathematics.
An entrylevel course for the
nontechnical student, dealing with some of the techniques that allow
mathematics to be applied to a variety of problems. Topics include
linear and quadratic equations, systems of linear equations,
matrices, probability, statistics, exponential and logarithmic
functions, and mathematics of finance. Mathematics 303D and 303F may
not both be counted. May not be counted toward the major requirement
for the Bachelor of Arts, Plan I, degree with a major in mathematics
or toward the Bachelor of Science in Mathematics degree. A student
may not earn credit for Mathematics 303D after having received credit
for Mathematics 305G or any calculus course. Prerequisite: A
satisfactory score on the SAT II: Mathematics Level I or Level IC
test, or Mathematics 301 with a grade of at least C.
403K. Calculus I for Business and Economics.
Differential and
integral calculus of algebraic, logarithmic, and exponential
functions with applications; introduction to mathematics of finance.
Three lecture hours and two discussion sessions a week for one
semester. May not be counted by students with credit for Mathematics
408C, 308K, or 308L. May not be counted toward the major requirement
for the Bachelor of Arts, Plan I, degree with a major in mathematics
or toward the Bachelor of Science in Mathematics degree.
Prerequisite: A satisfactory score on the SAT II: Mathematics
Level I or Level IC test, Mathematics 301 with a grade of at least B,
or Mathematics 304E or 305G with a grade of at least C.
403L. Calculus II for Business and Economics.
Differential and
integral calculus of functions of several variables with
applications, infinite series, improper integrals; introductions to
probability, differential equations, matrices, systems of linear
equations, and linear programming. Three lecture hours and two
discussion sessions a week for one semester. Only one of the
following may be counted: Mathematics 403L, 408D, 308M. May not be
counted toward the major requirement for the Bachelor of Arts, Plan
I, degree with a major in mathematics or toward the Bachelor of
Science in Mathematics degree. Prerequisite: Mathematics
403K, 408C, or 308L with a grade of at least C.
305G. Elementary Functions and Coordinate Geometry.
Study of
elementary functions, their graphs and applications, including
polynomial, rational, and algebraic functions, exponential,
logarithmic, and trigonometric functions. Mathematics 301, 305G, and
equivalent courses may not be counted toward the total number of
hours required for the Bachelor of Arts, Plan I, degree with a major
in mathematics or the Bachelor of Science in Mathematics degree.
Credit for Mathematics 305G may not be earned after a student has
received credit for any calculus course with a grade of C or better.
Prerequisite: A satisfactory score on the SAT II: Mathematics
Level I or Level IC test, or Mathematics 301 with a grade of at least
C.
408C. Differential and Integral Calculus.
Certain sections are
designated as honors sections for wellprepared students of
mathematics and mathematically oriented sciences who wish to
investigate more thoroughly the foundations of calculus. Introduction
to the theory and applications of differential and integral calculus
of functions of one variable; topics include limits, continuity,
differentiation, the mean value theorem and its applications,
integration, the fundamental theorem of calculus, and transcendental
functions. Three lecture hours and two discussion hours a week for
one semester. May not be counted by students with credit for
Mathematics 403K, 308K, or 308L. Prerequisite: Four years of
high school mathematics and a satisfactory score on the SAT II:
Mathematics Level I or Level IC test, or Mathematics 305G with a
grade of at least C.
408D. Sequences, Series, and Multivariable Calculus.
Certain
sections are designated as honors sections for wellprepared students
of mathematics and mathematically oriented sciences who wish to
investigate more thoroughly the foundations of calculus. Introduction
to the theory and applications of sequences and infinite series,
including those involving functions of one variable, and to the
theory and applications of differential and integral calculus of
functions of several variables; topics include parametric equations,
sequences, infinite series, power series, vectors, vector calculus,
functions of several variables, partial derivatives, gradients, and
multiple integrals. Three lecture hours and two discussion hours a
week for one semester. Only one of the following may be counted:
Mathematics 403L, 408D, 308M. Prerequisite: Mathematics 408C
or the equivalent with a grade of at least C.
308K. Differential Calculus.
Introduction to the theory and
applications of differential calculus of functions of one variable;
topics include limits, continuity, differentiation, and the mean
value theorem and its applications. This course is available for
transfer credit but is not taught in residence. Only one of the
following may be counted: Mathematics 403K, 408C, 308K.
308L. Integral Calculus.
Introduction to the theory and applications
of integral calculus of functions of one variable; topics include
integration, the fundamental theorem of calculus, transcendental
functions, parametric equations, and sequences. Only one of the
following may be counted: Mathematics 403K, 408C, 308L.
Prerequisite: Mathematics 308K or the equivalent with a grade
of at least C.
308M. Multivariable Calculus.
Introduction to the theory and
applications of infinite series, including those involving functions
of one variable, and to the theory and applications of differential
and integral calculus of functions of several variables; topics
include infinite series, power series, vectors, vector calculus,
functions of several variables, partial derivatives, gradients, and
multiple integrals. Certain sections are designated as honors
sections for wellprepared students of mathematics and mathematically
oriented sciences who wish to investigate more thoroughly the
foundations of calculus. Only one of the following may be counted:
Mathematics 403L, 408D, 308M. Prerequisite: Mathematics 308L
or the equivalent with a grade of at least C.
110, 210, 310, 410. Conference Course.
Supervised study in
mathematics, with hours to be arranged. May be repeated for credit
when the topics vary. Some sections are offered on the pass/fail
basis only; these are identified in the Course Schedule.
Prerequisite: Written consent of instructor. Forms are
available in the department office or in the Mathematics, Physics,
and Astronomy Advising Center.
210E. Emerging Scholars Seminar.
Restricted to students in the
Emerging Scholars Program. Supplemental problemsolving laboratory
for precalculus, calculus, or advanced calculus courses for students
in the Emerging Scholars Program. Three twohour laboratory sessions
a week for one semester. May be repeated for credit. Offered on the
pass/fail basis only.
315C. Functions and Modeling.
Study in depth of topics in secondary
school mathematics that are used in teaching precalculus and in the
transition to calculus. Modeling with linear, exponential, and
trigonometric functions; curve fitting; discrete and continuous
models. Four laboratory hours a week for one semester.
Prerequisite: Enrollment in the UTeach program or consent of
instructor.
316. Elementary Statistical Methods.
Graphical presentation,
frequency functions, distribution functions, averages, standard
deviation, variance, curvefitting, and related topics. Only one of
the following may be counted: Mathematics 316, 360K (Topic 1:
Applications of Probability Theory), 362K. May not be counted toward
the major requirement for the Bachelor of Arts, Plan I, degree with a
major in mathematics or toward the Bachelor of Science in Mathematics
degree. Prerequisite: A satisfactory score on the SAT II:
Mathematics Level I or Level IC test, or Mathematics 301 with a grade
of at least C.
316K. Foundations of Arithmetic.
An analysis, from an advanced
perspective, of the concepts and algorithms of arithmetic, including
sets; numbers; numeration systems; definitions, properties, and
algorithms of arithmetic operations; and percents, ratios, and
proportions. Problem solving is stressed. May not be counted toward
the major requirement for the Bachelor of Arts, Plan I, degree with a
major in mathematics or toward the Bachelor of Science in Mathematics
degree. Credit for Mathematics 316K may not be earned after the
student has received credit for any calculus course with a grade of C
or better, unless the student is registered in the College of
Education. Prerequisite: Mathematics 302, 303D, 305G, or 316
with a grade of at least C.
316L. Foundations of Geometry, Statistics, and Probability.
An
analysis, from an advanced perspective, of the basic concepts and
methods of geometry, statistics, and probability, including
representation and analysis of data; discrete probability, random
events, and conditional probability; measurement; and geometry as
approached through similarity and congruence, through coordinates,
and through transformations. Problem solving is stressed. May not be
counted toward the major requirement for the Bachelor of Arts, Plan
I, degree with a major in mathematics or toward the Bachelor of
Science in Mathematics degree. Credit for Mathematics 316L may not be
earned after the student has received credit for any calculus course
with a grade of C or better, unless the student is registered in the
College of Education. Prerequisite: Mathematics 316K with a
grade of at least C.
318M. Introduction to Scientific Computing.
Introduction to the
computer as a basic tool in the sciences, mathematics, and
engineering. Fundamentals of computer hardware, operating systems,
networks, algorithms, and software. Beginning programming in an
advanced language. Introduction to applications of numerical methods
and computation in the mathematical sciences. Prerequisite:
Mathematics 408C or the equivalent with a grade of at least C.
119S, 219S, 319S, 419S, 519S, 619S, 719S, 819S, 919S. Topics in
Mathematics.
This course is used to record credit the student earns
while enrolled at another institution in a program administered by
the University's Study Abroad Office. Credit is recorded as assigned
by the study abroad adviser in the Department of Mathematics.
University credit is awarded for work in an exchange program; it may
be counted as coursework taken in residence. Transfer credit is
awarded for work in an affiliated studies program. May be repeated
for credit when the topics vary.
UpperDivision Courses
325K. Discrete Mathematics.
Provides a transition from the
problemsolving approach of Mathematics 408C and 408D to the rigorous
approach of advanced courses. Topics include logic, set theory,
relations and functions, combinatorics, and graph theory and graph
algorithms. Prerequisite: Mathematics 408D with a grade of at
least C, or consent of instructor.
326K. Foundations of Number Systems.
Intended to provide future
teachers with an understanding of certain concepts in school
mathematics. Includes place value and arithmetic operations
(including historical perspectives and analysis of both standard and
nonstandard algorithms); prime factorization and other properties of
integers; irrational and transcendental numbers; complex numbers;
properties of polynomials; and connections of these topics with other
areas of mathematics. Emphasis on conceptual understanding,
developing both formal proofs and informal explanations, looking at
concepts from multiple perspectives, and problem solving involving
these topics. Prerequisite: Mathematics 408D or the
equivalent with a grade of at least C.
427K. Advanced Calculus for Applications I.
Ordinary and partial
differential equations and Fourier series. Five class hours a week
for one semester. Prerequisite: Mathematics 408D with a grade
of at least C.
427L. Advanced Calculus for Applications II.
Matrices, elements of
vector analysis and calculus of functions of several variables,
including gradient, divergence, and curl of a vector field, multiple
integrals and chain rules, length and area, line and surface
integrals, Green's theorems in the plane and space, and, if time
permits, complex analysis. Five class hours a week for one semester.
Prerequisite: Mathematics 408D with a grade of at least C.
328K. Introduction to Number Theory.
Provides a transition from the
problemsolving approach of Mathematics 408C and 408D to the rigorous
approach of advanced courses. Properties of the integers,
divisibility, linear and quadratic forms, prime numbers, congruences
and residues, quadratic reciprocity, number theoretic functions.
Mathematics 328K and 360K (Topic 2: Number Theory) may not both be
counted. Prerequisite: Mathematics 341 (or 311) with a grade
of at least C.
129S, 229S, 329S, 429S, 529S, 629S, 729S, 829S, 929S. Topics in
Mathematics.
This course is used to record credit the student earns
while enrolled at another institution in a program administered by
the University's Study Abroad Office. Credit is recorded as assigned
by the study abroad adviser in the Department of Mathematics.
University credit is awarded for work in an exchange program; it may
be counted as coursework taken in residence. Transfer credit is
awarded for work in an affiliated studies program. May be repeated
for credit when the topics vary.
329W. Cooperative Mathematics.
This course covers the work period of
mathematics students in the Cooperative Education program, which
provides supervised work experience by arrangement with the employer
and the supervising instructor. Forty laboratory hours a week for one
semester. The student must repeat the course each work period and
must take it twice to receive credit toward the degree; at least one
of these registrations must be during a longsession semester. No
more than three semester hours may be counted toward the major
requirement; no more than six semester hours may be counted toward
the degree. The student's first registration must be on the pass/fail
basis. Prerequisite: Application through the College of
Natural Sciences Career Services Office; Mathematics 408D; a grade of
at least C in two of the following courses: Mathematics 325K, 427K,
341 (or 311), 362K, 378K; and consent of the undergraduate adviser.
333L. Structure of Modern Geometry.
Axiom systems, transformational
geometry, introduction to nonEuclidean geometries, and other topics
in geometry; use of these ideas in teaching geometry.
Prerequisite: Mathematics 408D with a grade of at least C, or
upperdivision standing and consent of instructor.
439J. Probability Models with Actuarial Applications.
Probability
models with actuarial applications, including Markov chains, Brownian
motion, the BlackScholes formula, frequencyofloss and severityofloss random variables, compound distributions, and ruin theory.
With Mathematics 339U and 439V, covers the syllabus for exam #3 of
the Society of Actuaries and the Casualty Actuarial Society. Four
lecture hours a week for one semester. Prerequisite:
Mathematics 362K.
339U. Actuarial Contingent Payments I.
Simulation of random samples;
singlestatus models; presentvalue random variables for life
insurance and annuities. With Mathematics 439J and 439V, covers the
syllabus for exam #3 of the Society of Actuaries and the Casualty
Actuarial Society. Prerequisite: Mathematics 362K. Actuarial
Foundations 309 is recommended.
439V. Actuarial Contingent Payments II.
Mathematical analysis of
insurance premiums, reserves, multiplestatus survival models,
multipledecrement survival models; applications to such areas as
life insurance and property/casualty insurance. With Mathematics 439J
and 339U, covers the syllabus for exam #3 of the Society of Actuaries
and the Casualty Actuarial Society. Four lecture hours a week for one
semester. Prerequisite: Mathematics 339U.
340L. Matrices and Matrix Calculations.
Techniques of matrix
calculations and applications of linear algebra. Only one of the
following may be counted: Mathematics 311, 340L, 341.
Prerequisite: One semester of calculus with a grade of at
least C or consent of instructor.
341. Linear Algebra and Matrix Theory.
Vector spaces, linear
transformations, matrices, linear equations, determinants. Some
emphasis on rigor and proofs. Only one of the following may be
counted: Mathematics 311, 340L, 341. Mathematics majors are expected
to take Mathematics 341 immediately after 408D. Prerequisite:
Mathematics 408D with a grade of at least C.
343K. Introduction to Algebraic Structures.
Elementary properties of
groups and rings, including symmetric groups, properties of the
integers, polynomial rings, elementary field theory. Students who
have received a grade of C or better in Mathematics 373K may not take
Mathematics 343K. Prerequisite: Mathematics 341 (or 311) with
a grade of at least C and either 325K or 328K with a grade of at
least C.
343L. Applied Number Theory.
Basic properties of integers, including
properties of prime numbers, congruences, and primitive roots.
Introduction to finite fields and their vector spaces with
applications to encryption systems and coding theory.
Prerequisite: Mathematics 328K or 343K with a grade of at
least C.
344K. Intermediate Symbolic Logic.
Same as Philosophy 344K. A
secondsemester course in symbolic logic: formal syntax and
semantics, basic metatheory (soundness, completeness, compactness,
and LowenheimSkolem theorems), and further topics in logic.
Prerequisite: Philosophy 313K or consent of instructor.
346. Applied Linear Algebra.
Emphasis on diagonalization of linear
operators and applications to dynamical systems and ordinary
differential equations. Other subjects include inner products and
orthogonality, normal mode expansions, vibrating strings and the wave
equation, Fourier series and Fourier integrals, and Green's
functions. Prerequisite: Mathematics 341 (or 311) or 340L
with a grade of at least C.
348. Scientific Computation in Numerical Analysis.
Introduction to
mathematical properties of numerical methods and their applications
in computational science and engineering. Introduction to
objectoriented programming in an advanced language. Study and use of
numerical methods for solutions of linear systems of equations;
nonlinear leastsquares data fitting; numerical integration; and
solutions of multidimensional nonlinear equations and systems of
initial value ordinary differential equations. Prerequisite:
Mathematics 318M, 427K, and 341 (or 311) or 340L with a grade of at
least C.
349P. Actuarial Statistical Estimates.
Statistical estimates for
frequencyofloss and severityofloss random variables; credibility
theory; statistics of simulation. Covers 40 percent of the syllabus
for exam #4 of the Society of Actuaries and the Casualty Actuarial
Society. Prerequisite: Mathematics 439J, and Mathematics 358K
or 378K.
349T. Time Series and SurvivalModel Estimation.
Introduction to the
probabilistic and statistical properties of time series; parameter
estimation and hypothesis testing for survival models. Covers 30
percent of the syllabus for exam #4 of the Society of Actuaries and
the Casualty Actuarial Society. Prerequisite: Mathematics
339U, and Mathematics 358K or 378K.
358K. Applied Statistics.
Exploratory data analysis, correlation and
regression, data collection, sampling distributions, confidence
intervals, and hypothesis testing. Prerequisite: Mathematics
362K with a grade of at least C.
360M. Mathematics as Problem Solving.
Discussion of heuristics,
strategies, and methods of evaluating problem solving, and extensive
practice in both group and individual problem solving. Communicating
mathematics, reasoning, and connections among topics in mathematics
are emphasized. Prerequisite: Mathematics 408D with a grade
of at least C and written consent of instructor.
361. Theory of Functions of a Complex Variable.
Elementary theory
and applications of analytic functions, series, contour integration,
and conformal mappings. Prerequisite: Mathematics 427K or
427L with a grade of at least C or consent of instructor.
361K. Introduction to Real Analysis.
A rigorous treatment of the
real number system, of real sequences, and of limits, continuity,
derivatives, and integrals of realvalued functions of one real
variable. Students who have received a grade of C or better in
Mathematics 365C may not take Mathematics 361K. Prerequisite:
Mathematics 341 (or 311) with a grade of at least C and either 325K
or 328K with a grade of at least C.
362K. Probability I.
An introductory course in the mathematical
theory of probability, fundamental to further work in probability and
statistics. Only one of the following may be counted: Mathematics
316, 360K (Topic 1: Applications of Probability Theory), 362K.
Prerequisite: Mathematics 408D with a grade of at least C.
362M. Introduction to Stochastic Processes.
Introduction to Markov
chains, birth and death processes, and other topics.
Prerequisite: Mathematics 362K with a grade of at least C.
364K. Vector and Tensor Analysis I.
Invariance, vector algebra and
calculus, integral theorems, general coordinates, introductory
differential geometry and tensor analysis, applications.
Prerequisite: Mathematics 427K or 427L with a grade of at
least C.
364L. Vector and Tensor Analysis II.
Continuation of Mathematics
364K, with emphasis on tensor and extensor analysis. Riemannian
geometry and invariance. Prerequisite: Mathematics 364K with
a grade of at least C.
365C. Real Analysis I.
A rigorous treatment of the real number
system, Euclidean spaces, metric spaces, continuity of functions in
metric spaces, differentiation and Riemann integration of realvalued
functions of one real variable, and uniform convergence of sequences
and series of functions. Students who have received a grade of C or
better in Mathematics 365C may not take Mathematics 361K.
Prerequisite: Mathematics 341 (or 311) with a grade of at
least C and either 325K or 328K with a grade of at least C. Students
who receive a grade of C in 325K or 328K are advised to take 361K
before attempting 365C.
365D. Real Analysis II.
Recommended for students planning to
undertake graduate work in mathematics. A rigorous treatment of
selected topics in real analysis, such as Lebesgue integration, or
multivariate integration and differential forms. Prerequisite:
Mathematics 365C with a grade of at least C.
367K. Topology I.
An introduction to topology, including sets,
functions, cardinal numbers, and the topology of metric spaces.
Prerequisite: Mathematics 361K or 365C or consent of
instructor.
367L. Topology II.
Various topics in topology, primarily of a
geometric nature. Prerequisite: Mathematics 367K with a grade
of at least C or consent of instructor.
368K. Numerical Methods for Applications.
Continuation of
Mathematics 348. Topics include splines, orthogonal polynomials and
smoothing of data, iterative solution of systems of linear equations,
approximation of eigenvalues, twopointboundary value problems,
numerical approximation of partial differential equations, signal
processing, optimization, and Monte Carlo methods. Only one of the
following may be counted: Computer Sciences 367, Mathematics 368K,
Physics 329. Prerequisite: Mathematics 348 with a grade of at
least C.
372. Fourier Series and Boundary Value Problems.
Discussion of
differential equations of mathematical physics and representation of
solutions by Green's functions and eigenfunction expansions.
Prerequisite: Mathematics 427K with a grade of at least C.
372K. Partial Differential Equations and Applications.
Partial
differential equations as basic models of flows, diffusion,
dispersion, and vibrations. Topics include first and secondorder
partial differential equations and classification (particularly the
wave, diffusion, and potential equations), and their origins in
applications and properties of solutions. Includes the study of
characteristics, maximum principles, Green's functions, eigenvalue
problems, and Fourier expansion methods. Prerequisite:
Mathematics 427K with a grade of at least C.
373K. Algebraic Structures I.
A study of groups, rings, and fields,
including structure theory of finite groups, isomorphism theorems,
polynomial rings, and principal ideal domains. Students who have
received a grade of C or better in Mathematics 373K may not take
Mathematics 343K. Prerequisite: Mathematics 341 (or 311) with
a grade of at least C and either 325K or 328K with a grade of at
least C, or consent of instructor. Students who receive a grade of C
in Mathematics 325K or 328K are advised to take 343K before
attempting 373K.
373L. Algebraic Structures II.
Recommended for students planning to
undertake graduate work in mathematics. Topics from vector spaces and
modules, including direct sum decompositions, dual spaces, canonical
forms, and multilinear algebra. Prerequisite: Mathematics
373K with a grade of at least C.
374. Fourier and Laplace Transforms.
Operational properties and
application of Laplace transforms; some properties of Fourier
transforms. Prerequisite: Mathematics 427K with a grade of at
least C.
374G. Linear Regression Analysis.
Fitting of linear models to data
by the method of least squares, choosing best subsets of predictors,
and related materials. Prerequisite: Mathematics 358K or 378K
with a grade of at least C, Mathematics 341 or 340L, and consent of
instructor.
374K. Fourier and Laplace Transforms.
Continuation of Mathematics 374. Introduction to other integral transforms, such as Hankel,
Laguerre, Mellin, Z. Prerequisite: Mathematics 374 with a
grade of at least C.
474M. Introduction to Mathematical Modeling and Industrial
Mathematics.
Some of the problems encountered in current industry,
and how mathematics can help solve them. Basic material in theory and
computation of ordinary and partial differential equations, integral
equations, calculus of variations and control theory. Specific
industrial applications. Three lecture hours and two laboratory hours
a week for one semester. Prerequisite: Mathematics 318M or
the equivalent, Mathematics 427K, and Mathematics 341 (or 311) or
340L with a grade of at least C in each.
175, 275, 375, 475. Conference Course.
Supervised study in
mathematics, with hours to be arranged. May be repeated for credit
when the topics vary. Prerequisite: Upperdivision standing
in mathematics and written consent of instructor.
375C. Conference Course (ComputerAssisted).
Supervised study in
mathematics on material requiring use of computing resources, with
hours to be arranged. May be repeated for credit when the topics
vary. Prerequisite: Upperdivision standing in mathematics
and written consent of instructor.
376C. Methods of Applied Mathematics.
Variational methods and related concepts from classical and modern applied mathematics. Model
s of conduction and vibration that lead to systems of linear
equations and ordinary differential equations, eigenvalue problems,
initial and boundary value problems for partial differential
equations. Topics may include a selection from diagonalization of
matrices, eigenfunctions and minimization, asymptotics of
eigenvalues, separation of variables, generalized solutions, and
approximation methods. May be repeated for credit when the topics
vary. Prerequisite: Mathematics 318M or the equivalent,
Mathematics 427K, and Mathematics 341 (or 311) or 340L with a grade
of at least C in each.
378K. Introduction to Mathematical Statistics.
Estimation of
parameters and testing of hypotheses. Mathematics 362K and 378K form
the core sequence for students in statistics. Prerequisite:
Mathematics 362K with a grade of at least C.
379H. Honors Tutorial Course.
Directed reading, research, and/or
projects, under the supervision of a faculty member, leading to an
honors thesis. Conference course. Prerequisite: Admission to
the Mathematics Honors Program, a grade point average of at least
3.50 in Mathematics 365C and 373K, and approval of the honors adviser.
