DESCRIPTIONS OF COURSES ALLOWED FOR ADDITIONAL UPPER DIVISION MATH HOURS FOR MATH BA-TEACHING OPTION
439J: Probability Models with Actuarial Applications
. Probability models with actuarial applications, including Markov chains, Brownian motion, the Black-Scholes formula, frequency-of-loss and severity-of-loss random variables, compound distributions, and ruin theory. Prerequisite: Mathematics 362K. This is a course designed for students interested in actuarial science (the mathematics of insurance). It can give you some examples of how mathematics (especially probability) is applied to the study of insurance.339U: Actuarial Contingent Payments I.
Simulation of random samples; single-status models; present-value random variables for life insurance and annuities. Prerequisite: Mathematics 362K. Actuarial Foundations 309 is recommended. Another a course designed for students interested in actuarial science (the mathematics of insurance). It can give you some examples of how mathematics (especially probability) is applied to the study of insurance.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.348: Scientific Computation in Numerical Analysis
. Introduction to mathematical properties of numerical methods and their applications in computational science and engineering. Introduction to object-oriented programming in an advanced language. Study and use of numerical methods for solutions of linear systems of equations; nonlinear least-squares 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.
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.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. (Note: This course is not offered very often.)365D: Real Analysis I
I. 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.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, two-point-boundary 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.373L: Algebraic Structures II
. 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.175
. This is a number that is used for a one-credit-hour math course that does not have another number. Usually each semester a course with number 175 called Seminar for Prospective Teachers is offered. The topics vary from semester to semester. Examples of course descriptions:This course may be counted more than once when topics vary. Other courses given under this course number might or might not count toward this requirement; check with the faculty advisor (Dr. Smith, mks@math.utexas.edu)