Department of Mathematics

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, twenty-eight hours of mathematics, and twelve hours of coursework in the College of Business Administration. Detailed information is available from the director of actuarial studies in the Department of Mathematics.

Prerequisites

Important advice on which entry-level mathematics course to take, based on the student's score on the Mathematics Level I test, is available from the Measurement and Evaluation Center and the Department of Mathematics.

In courses that have a minimum test score or course grade as a prerequisite, students will be dropped from the course on the twelfth class day if University records do not show that they have met the prerequisite. Students for whom the Mathematics Level I 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 test-result slip as the written proof; information about where to obtain the test-result slip is given at the time of the test.

Students who wish to enroll in conference courses in the Department of Mathematics must submit consent of instructor forms to the undergraduate adviser before registering. Forms are available in the department office.

Unless otherwise stated in the description below, each class meets for three lecture hours a week for one semester.

Actuarial Foundations: ACF

Lower-Division Courses

309. Theory of Interest.

Measurement of interest, present value, accumulated value, annuities, amortization, sinking funds, bonds, and securities. Includes syllabus for Society of Actuaries Exam 140. 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.

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 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

Lower-Division Courses

301. 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.

302. Introduction to Mathematics.

Intended primarily for general liberal arts students seeking knowledge of the role and nature of mathematics as well as training in mathematical thinking and problem solving. Topics include number theory, probability, and statistics; additional topics are chosen by the instructor. Mathematics 302 and 303D 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.

303D. Applicable Mathematics.

An entry-level 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 302 and 303D 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 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 test or Mathematics 301 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 304E and 305G may not both be counted. Mathematics 301, 304E, 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 test or Mathematics 301 with a grade of at least C.

408C. Differential and Integral Calculus.

Certain sections are designated as honors sections for well-prepared 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 test, or Mathematics 304E or 305G with a grade of at least C.

408D. Sequences, Series, and Multivariable Calculus.

Certain sections are designated as honors sections for well-prepared 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 well-prepared 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.

311. Linear Algebra and Matrix Theory.

Vector spaces, linear transformations, matrices, linear equations, determinants. Some emphasis on rigor and proofs. Mathematics 311 and 340L may not both be counted. Mathematics majors are expected to take Mathematics 311 immediately after 408D. Prerequisite: Mathematics 408D with a grade of at least C.

316. Elementary Statistical Methods.

Graphical presentation, frequency functions, distribution functions, averages, standard deviation, variance, curve-fitting, 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 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 303D, 304E, 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.

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.

Upper-Division Courses

325K. Discrete Mathematics.

Provides a transition from the problem-solving approach of Mathematics 408C and 408D to the rigorous approach of advanced courses. Topics include logic, set theory, relations and functions, combinatorics, graph theory and graph algorithms, matrix operations, and elementary linear algebra. Prerequisite: Mathematics 408D with a grade of at least C, or consent of instructor.

427K. Advanced Calculus for Applications I.

Infinite series, ordinary and partial differential equations. 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 problem-solving 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 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 long-session 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 to become a member of the Cooperative Mathematics Program; Computer Sciences 304P, Mathematics 408D, and a grade of at least C in two of the following courses: Mathematics 311, 325K, 427K, 362K, 378K; and consent of the undergraduate adviser.

333L. Structure of Modern Geometry.

Axiom systems, transformational geometry, introduction to non-Euclidean geometries, and other topics in geometry; use of these ideas in teaching geometry. Prerequisite: Mathematics 408D with a grade of at least C, or upper-division standing and consent of instructor.

340L. Matrices and Matrix Calculations.

Techniques of matrix calculations and applications of linear algebra. Mathematics 311 and 340L may not both be counted. Prerequisite: One semester of calculus with a grade of at least C or consent of instructor.

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 311 with a grade of at least C and either 325K or 328K with a grade of at least C.

360K. Topics in Modern Mathematics I.

Designed especially for applied learning and development majors with a mathematics concentration. May be repeated for credit when the topics vary. May not be counted toward the major requirement for any degree in mathematics. Prerequisite: Mathematics 408C and 316L with a grade of at least C in each, or written consent of the undergraduate mathematics education adviser.

Topic 1: Applications of Probability Theory. A problem-oriented, problem-solving approach to an in-depth development of discrete probability theory and the normal distribution. Only one of the following may be counted: Mathematics 316, 360K (Topic 1), 362K.

Topic 2: Number Theory. An investigative approach to classical number theory, closely paralleling its historical development, with emphasis on discovery and development. Mathematics 328K and 360K (Topic 2) may not both be counted.

Topic 3: Problem Solving. A study of problem solving, heuristics, strategies, pitfalls, and approaches to proofs. Emphasizes improving the ability to solve challenging problems.

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 real-valued 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 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 real-valued 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 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 Mathematics for Applications.

Introduction to numerical methods for applied problems in science and engineering. Topics include linear equations, approximation, differential equations. Only one of the following may be counted: Computer Sciences 367, Mathematics 368K, Physics 329. Prerequisite: A grade of at least C in Mathematics 427K and in either 311 or 340L, and knowledge of FORTRAN programming.

369E. Applied Statistical Methods for Actuaries.

Introduction to analysis of variance, regression analysis, and time series. Includes the syllabus for the Society of Actuaries and Casualty Actuarial Society Exam 120. Prerequisite: A grade of at least C in Mathematics 378K and in either 340L or 311.

369G. Operations Research for Actuaries.

Introduction to linear programming, project scheduling, dynamic programming, queueing theory, decision analysis, and simulation of distributions. Includes the syllabus for the Society of Actuaries Exam 130. Prerequisite: A grade of at least C in Mathematics 362K and in either 340L or 311.

369J. Credibility Theory and Loss Distributions.

Introduction to statistical techniques for modeling and approximating the probabilistic distribution of insurance losses, including measuring the credibility of the resulting models. Includes the syllabus for the Casualty Actuarial Society Exam 4B. Prerequisite: Mathematics 378K with a grade of at least C.

469K. Actuarial Mathematics I.

Probabilistic theory of single-event losses, with applications to insurance. With Mathematics 469L, includes the syllabus for the Society of Actuaries Exam 150. Four lecture hours a week for one semester. Mathematics 469K and 389L may not both be counted. Prerequisite: Actuarial Foundations 309 and Mathematics 362K with a grade of at least C in each, and consent of the director of the concentration in actuarial studies.

469L. Actuarial Mathematics II.

Probabilistic theory of multiple-event losses, with applications to insurance. With Mathematics 469K, includes the syllabus for the Society of Actuaries Exam 150. Four lecture hours a week for one semester. Mathematics 469L and 389M may not both be counted. Prerequisite: Mathematics 469K with a grade of at least C, and consent of the director of the concentration in actuarial studies.

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.

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 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.

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.

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: Upper-division standing in mathematics and written consent of instructor.

375C. Conference Course (Computer-Assisted).

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: Upper-division standing in mathematics and written consent of instructor.

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.

28 August 1996. Registrar's Web Team
Comments to rgcat@utxdp.dp.utexas.edu