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 hours of actuarial foundations, twentyeight hours of mathematics, and selected 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 Mathematics Level 1 test; therefore, many students planning to take a course in the department must first have taken the Mathematics Level 1 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 1 test, is available from the Division of Instructional Innovation and Assessment 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 1 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 Division of Instructional Innovation and Assessment. 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 below, each course meets for three lecture hours a week for one semester.
ACF  Actuarial Foundations
LowerDivision Courses
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.
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.
UpperDivision Course
329. Theory of Interest. Measurement of interest, present value, accumulated value, amortization of loans, sinking funds, and bonds. Covers the interesttheory portion of the syllabus for the exams of the Society of Actuaries and the Casualty Actuarial Society. Only one of the following may be counted: Actuarial Foundations 309, 329, Mathematics 389F. Prerequisite: Mathematics 408D or 408L with a grade of at least C.
M  Mathematics
The information in parentheses after a course number is the Texas Common Course Numbering (TCCN) designation. Only TCCN designations that are exact semesterhour equivalents of University courses are listed here. Additional TCCN information is given in Appendix A.
LowerDivision Courses
301 (TCCN: MATH 1314). College Algebra. Topics include a brief review of elementary algebra; linear, quadratic, exponential, and logarithmic functions; polynomials; systems of linear equations; applications. 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 Higher Education Assessment (THEA) test (or an appropriate assessment test).
302 (TCCN: MATH 1332). 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 Higher Education Assessment (THEA) test (or an appropriate assessment test).
303D (TCCN: MATH 1324). 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 score of at least 430 on the SAT Mathematics Level 1 test, or Mathematics 301 with a grade of at least C.
303F. Mathematics of Investment. Simple and compound interest, equivalent rates, equivalent values, annuities, amortization, sinking funds, bonds, depreciation. Mathematics 302 and 303F may not both be counted; 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. Prerequisite: Three units of high school mathematics at the level of Algebra I or higher.
403K (TCCN: MATH 1425). Calculus I for Business and Economics. Differential and integral calculus of algebraic, logarithmic, and exponential functions with applications. Three lecture hours and two discussion sessions a week for one semester. Only one of the following may be counted: Mathematics 403K, 408C, 408K (or 308K). 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 Mathematics Level 1 test, Mathematics 301 with a grade of at least B, or Mathematics 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. Mathematics 403L and 408L (or 308L) 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. Prerequisite: Mathematics 403K, 408C, or 308L with a grade of at least C.
305E. Analytic Geometry. Combines development of methods (including adequate treatment of theory) and acquisition of skills with applications. Mathematics 305E and 305K may not both be counted. Mathematics 305E and 305G may not both be counted toward the major requirement for the Bachelor of Arts, Plan I, degree with a major in Mathematics or towards the Bachelor of Science in Mathematics degree. Prerequisite: Mathematics 301.
305G (TCCN: MATH 2312). 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 305G and any collegelevel trigonometry course may not both be counted. 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 score of at least 480 on the SAT Mathematics Level 1 test, or Mathematics 301 with a grade of at least C.
408C (TCCN: MATH 2417). Differential and Integral 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. Only one of the following may be counted: Mathematics 403K, 408C, 408K (or 308K). Prerequisite: A score of at least 560 on the SAT Mathematics Level 1 test, or Mathematics 305G with a grade of at least C.
408D (TCCN: MATH 2419). Sequences, Series, and Multivariable Calculus. Certain sections of this course are designated as advanced placement or honors sections; they are restricted to students who have scored well on the AP/BC exam, are in the Engineering Honors Program, or have the consent of the mathematics adviser. Such sections and their restrictions are identified in the Course Schedule. 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, 408M (or 308M). Prerequisite: Mathematics 408C or the equivalent with a grade of at least C.
308K, 408K (TCCN: MATH 2413). 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. Three lecture hours and two discussion hours a week for one semester. Only one of the following may be counted: Mathematics 403K, 408C, 408K (or 308K). Prerequisite: A score of at least 520 on the SAT Mathematics Level 1 test, or Mathematics 305G with a grade of at least C.
308L, 408L (TCCN: MATH 2414). 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, sequences, and infinite series. For Mathematics 308L, three lecture hours a week for one semester; for 408L, three lecture hours and two discussion hours a week for one semester. Mathematics 403L and 408L (or 308L) may not both be counted. Prerequisite: Mathematics 408C or 408K or the equivalent with a grade of at least C.
308M, 408M (TCCN: MATH 2415). Multivariable Calculus. Each fall a section of this course is designated in the Course Schedule as an engineering honors section, for students who wish to investigate more thoroughly the foundations of calculus. Enrollment in this section is restricted to students in the Engineering Honors Program. Introduction to the theory and applications of differential and integral calculus of functions of several variables. Includes parametric equations, polar coordinates, vectors, vector calculus, functions of several variables, partial derivatives, gradients, and multiple integrals. For Mathematics 308M, three lecture hours a week for one semester; for 408M, three lecture hours and two discussion hours a week for one semester. Only one of the following may be counted: Mathematics 403L, 408D, 408M (or 308M). Prerequisite: Mathematics 408L 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. Some sections may not be counted toward any mathematics or science degree requirement; 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.
110T, 210T, 310T, 410T. Topics in Mathematics. One, two, three, or four lecture hours a week for one semester. May be repeated for credit when the topics vary.
315C. Functions and Modeling. Indepth study of topics in secondary school mathematics. Emphasis is on modeling with linear, exponential, and trigometric functions; curve fitting; discrete and continuous models. Use of appropriate technology is explored. Prerequisite: Enrollment in a teaching preparation program or consent of instructor.
316 (TCCN: MATH 1342, 2342). Elementary Statistical Methods. Graphical presentation, frequency functions, distribution functions, averages, standard deviation, variance, curvefitting, and related topics. May not be counted by students with credit for Mathematics 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 score of at least 430 on the SAT Mathematics Level 1 test, or Mathematics 301 with a grade of at least C.
316K (TCCN: MATH 1350). 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 (TCCN: MATH 1351). 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.
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 Center for Global Educational Opportunities. 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 or 408L with a grade of at least C, or consent of instructor.
326K. Foundations of Number Systems. Restricted to students in a teacher preparation program or who have consent of instructor. Study of numberrelated topics in middlegrade and secondary school mathematics. Topics include place value; meanings of arithmetic operations; analysis of computation methods; historical development of number concepts and notation; and rational, irrational, algebraic, transcendental, and complex numbers. Emphasis is on communicating mathematics, developing pedagogical understanding of concepts and notation, and using both informal reasoning and proof. Prerequisite: Mathematics 408D or 408L 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 or 408L 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. Prerequisite: Mathematics 341 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 Center for Global Educational Opportunities. 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 or 408L; a grade of at least C in two of the following courses: Mathematics 325K, 427K, 341, 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 or 408L with a grade of at least C, or upperdivision standing and consent of instructor.
339J. Probability Models with Actuarial Applications. Introductory actuarial models for life insurance, property insurance, and annuities. With Mathematics 449P, covers the syllabus for the professional actuarial exam on model construction. Prerequisite: Mathematics 358K or 378K with a grade of at least C.
139S. Seminar on Actuarial Practice. Presentations by working actuaries on current issues in actuarial practice. One lecture hour a week for one semester. Offered on the pass/fail basis only. Prerequisite: Actuarial Foundations 329 (or 309); Mathematics 339J or 339U with a grade of at least C; and credit with a grade of at least C or registration for one of the following: Mathematics 339J, 339U, 339V, 449P.
339U. Actuarial Contingent Payments I. Intermediate actuarial models for life insurance, property insurance, and annuities. Prerequisite: Mathematics 362K with a grade of at least C; credit with a grade of at least C or registration for Actuarial Foundations 329 (or 309); and credit with a grade of at least C or registration for Mathematics 340L or 341.
339V. Actuarial Contingent Payments II. Advanced actuarial models for life insurance, property insurance, and annuities. Prerequisite: Actuarial Foundations 329 and Mathematics 339U with a grade of at least C in each.
340L. Matrices and Matrix Calculations. Techniques of matrix calculations and applications of linear algebra. Mathematics 340L and 341 may not both be counted. 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. Mathematics 340L and 341 may not both be counted. 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: Consent of the undergraduate adviser, or two of the following courses with a grade of at least C in each: Mathematics 325K or Philosophy 313K, Mathematics 328K, Mathematics 341.
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.
343M. ErrorCorrecting Codes. Introduction to applications of algebra and number theory to errorcorrecting codes, including finite fields, errorcorrecting codes, vector spaces over finite fields, Hamming norm, coding, and decoding. Prerequisite: Mathematics 328K or 341 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 LöwenheimSkolem theorems), and further topics in logic. Prerequisite: Philosophy 313, 313K, or 313Q.
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, and Fourier series. Prerequisite: Mathematics 341 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: Computer Sciences 303E or the equivalent, and Mathematics 341 or 340L with a grade of at least C.
449P. Actuarial Statistical Estimates. Statistical estimation procedures for random variables and related quantities in actuarial models. With Mathematics 339J, covers the syllabus for the professional actuarial exam on model construction. Four lecture hours a week for one semester. Prerequisite: Mathematics 339J, and 341 or 340L, with a grade of at least C in each.
349R. Applied Regression and Time Series. Introduction to simple and multiple linear regression and to elementary timeseries models, including autoregressive and movingaverage models. Emphasizes fitting models to data, evaluating models, and interpreting results. Prerequisite: Consent of the director of the concentration in actuarial studies; students are expected to have a basic knowledge of statistics.
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, 341 or 340L, and 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 or 408L 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: Consent of the undergraduate adviser, or two of the following courses with a grade of at least C in each: Mathematics 325K or Philosophy 313K, Mathematics 328K, Mathematics 341.
362K. Probability I. An introductory course in the mathematical theory of probability, fundamental to further work in probability and statistics, includes basic probability properties, conditional probability and independence, various discrete and continuous random variables, expectation and variance, central limit theorem, and joint probability distributions. Prerequisite: Mathematics 408D or 408L 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: Consent of the undergraduate adviser, or two of the following courses with a grade of at least C in each: Mathematics 325K or Philosophy 313K, Mathematics 328K, Mathematics 341. Students who receive a grade of C in one of the prerequisite courses are advised to take Mathematics 361K before attempting 365C. Students planning to take Mathematics 365C and 373K concurrently should consult a mathematics adviser.
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.
365G. Curves and Surfaces. Calculus applied to curves and surfaces in three dimensions: curvature and torsion of space curves, Gauss map and curvature of surfaces, Gauss theorem, geodesics, and the GaussBonnet theorem. Prerequisite: Credit with a grade of at least C or registration for Mathematics 365C.
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: Consent of the undergraduate adviser, or two of the following courses with a grade of at least C in each: Mathematics 325K or Philosophy 313K, Mathematics 328K, Mathematics 341. Students who receive a grade of C in one of the prerequisite courses are advised to take Mathematics 343K before attempting 373K. Students planning to take Mathematics 365C and 373K concurrently should consult a mathematics adviser.
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 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 427K, and 341 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. Prerequisite: Upperdivision standing.
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: Varies with the topic and is given in the Course Schedule.
175T, 275T, 375T, 475T. Topics in Mathematics. One, two, three, or four lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Upperdivision standing; additional prerequisites may vary with the topic and are given in the Course Schedule.
376C. Methods of Applied Mathematics. Variational methods and related concepts from classical and modern applied mathematics. Models 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: Computer Sciences 303E or the equivalent, Mathematics 427K, and Mathematics 341 or 340L with a grade of at least C in each.
378K. Introduction to Mathematical Statistics. Sampling distributions of statistics, estimation of parameters (confidence intervals, method of moments, maximum likelihood, comparison of estimators using mean square error and efficiency, sufficient statistics), hypothesis tests (pvalues, power, likelihood ratio tests), and other topics. Mathematics 358K, 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; Mathematics 365C, 367K, 373K, or 374G with a grade of A, and another of these courses with a grade of at least B; and consent of the honors adviser.
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Undergraduate Catalog  20062008
College of Natural Sciences 
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