12. College of Natural Sciences

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. 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, twenty-eight 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.

Most entry-level courses in mathematics have as a prerequisite a specific minimum score on the SAT Subject Test in Mathematics Level 1; therefore, many students planning to take a course in the department must first have taken the test. Students should see the current Course Schedule or consult the Mathematics, Physics, and Astronomy Advising Center for the minimum score required.

Important advice on which entry-level 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 (DIIA) and the 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 DIIA. 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 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 before registering. Forms are available in the department office and the Advising Center.

The information in parentheses after a course number is the Texas Common Course Numbering (TCCN) designation. Only TCCN designations that are exact semester-hour equivalents of University courses are listed here. Additional TCCN information is published by the Office of Admissions.

Actuarial Foundations: ACF

Lower-Division 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.

Upper-Division Courses

329. Theory of Interest. Measurement of interest, present and accumulated value, amortization, sinking funds, bonds, duration, and immunization. Covers the interest-theory portion of an exam of the Society of Actuaries and the Casualty Actuarial Society. Three lecture hours a week for one semester. 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.

129D. Introductory Actuarial Financial Mathematics. Introductory analysis of financial derivatives. Covers the financial derivatives portion of the syllabus for the professional actuarial exam on financial mathematics. One lecture hour a week for one semester. Offered on the pass/fail basis only. Prerequisite: Credit with a grade of at least C or registration for Actuarial Foundations 329.

Mathematics: M

Lower-Division 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. 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. 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. Three lecture hours a week for one semester. 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. 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 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. Three lecture hours a week for one semester. 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.

Simple and compound interest, equivalent rates, equivalent values, annuities, amortization, sinking funds, bonds, depreciation. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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, 505G. Elementary Functions and Coordinate Geometry. Study of elementary functions, their graphs and applications, including polynomial, rational, and algebraic functions, exponential, logarithmic, and trigonometric functions. For 305G, three lecture hours a week for one semester; for 505G, three lecture hours and two discussion hours a week for one semester. Mathematics 305G, 505G and any college-level trigonometry course may not both be counted. Mathematics 301, 305G, 505G, 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, 505G 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 408L with a grade of at least C.

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 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 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 problem-solving laboratory for precalculus, calculus, or advanced calculus courses for students in the Emerging Scholars Program. Three two-hour laboratory sessions a week for one semester. May be repeated for credit. Offered on the pass/fail basis only.

310P. Modern Mathematics: Plan II. Restricted to Plan II students. Significant developments in modern mathematics. Topics may include fractals, the fourth dimension, statistics and society, and techniques for thinking about quantitative problems. Three lecture hours a week for one semester.

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. In-depth study of topics in secondary school mathematics. Emphasis is on modeling with linear, exponential, and trigonometric functions; curve fitting; discrete and continuous models. Use of appropriate technology is explored. Three lecture hours a week for one semester. Prerequisite: Enrollment in a teaching preparation program or consent of instructor.

316 (TCCN: MATH 1342). Elementary Statistical Methods. Graphical presentation, frequency functions, distribution functions, averages, standard deviation, variance, curve-fitting, and related topics. Three lecture hours a week for one semester. Only one of the following may be counted: Mathematics 316, Statistics and Scientific Computation 303, 304, 305, 306. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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, and graph theory and graph algorithms. Three lecture hours a week for one semester. 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 number-related topics in middle-grade 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. Three lecture hours a week for one semester. Prerequisite: Mathematics 408D or 408L 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 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. Three lecture hours a week for one semester. 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 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 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, or 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. Three lecture hours a week for one semester. Prerequisite: Mathematics 408D or 408L with a grade of at least C, or upper-division standing and consent of instructor.

339J. Probability Models with Actuarial Applications. Introductory actuarial models for life insurance, property insurance, and annuities. With Mathematics 349P, covers the syllabus for the professional actuarial exam on model construction. Three lecture hours a week for one semester. 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, 349P (or 449P).

339U. Actuarial Contingent Payments I. Intermediate actuarial models for life insurance, property insurance, and annuities. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. Prerequisite: Actuarial Foundations 329 and Mathematics 339U with a grade of at least C in each.

339W. Financial Mathematics for Actuarial Applications. Options and other financial derivatives, pricing models, stock price models, and interest-rate models for actuarial applications. Three lecture hours a week for one semester. Prerequisite: Actuarial Foundations 329 (or 309) with a grade of at least C; Actuarial Foundations 129D, or Finance 377 (Topic 2: Financial Risk Management) with a grade of at least C; and Mathematics 362K with a grade of at least C.

340L. Matrices and Matrix Calculations. Techniques of matrix calculations and applications of linear algebra. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. Prerequisite: Mathematics 328K or 343K with a grade of at least C.

343M. Error-Correcting Codes. Introduction to applications of algebra and number theory to error-correcting codes, including finite fields, error-correcting codes, vector spaces over finite fields, Hamming norm, coding, and decoding. Three lecture hours a week for one semester. Prerequisite: Mathematics 328K or 341 with a grade of at least C.

344K. Intermediate Symbolic Logic. Same as Philosophy 344K. A second-semester course in symbolic logic: formal syntax and semantics, basic metatheory (soundness, completeness, compactness, and Löwenheim-Skolem theorems), and further topics in logic. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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 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. Three lecture hours a week for one semester. Prerequisite: Computer Sciences 303E or 307, and Mathematics 341 or 340L with a grade of at least C.

349P. 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. Three 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 time-series models, including auto-regressive and moving-average models. Emphasizes fitting models to data, evaluating models, and interpreting results. Three lecture hours a week for one semester. 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 Survival-Model 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. Mathematics 358K and Statistics and Scientific Computation 321 may not both be counted. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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 Gauss-Bonnet theorem. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. Prerequisite: Mathematics 361K or 365C or consent of instructor.

367L. Topology II. Various topics in topology, primarily of a geometric nature. Three lecture hours a week for one semester. 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, two-point-boundary value problems, numerical approximation of partial differential equations, signal processing, optimization, and Monte Carlo methods. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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 second-order 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. 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. Three lecture hours a week for one semester. Prerequisite: Mathematics 374 with a grade of at least C.

474M. Mathematical Modeling in Science and Engineering. Tools for studying differential equations and optimization problems that arise in the engineering and physical sciences. Includes dimensional analysis and scaling, regular and singular perturbation methods, optimization and calculus of variations, and stability. Three lecture hours and two laboratory hours a week for one semester. Prerequisite: Mathematics 427K, and 340L or 341, with a grade of at least C in each; and some basic programming skills.

175, 275, 375, 475. Conference Course. Supervised study in mathematics, with hours to be arranged. May be repeated for credit. Prerequisite: Upper-division standing.

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: 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: Upper-division 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. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Computer Sciences 303E or 307, 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 (p-values, power, likelihood ratio tests), and other topics. Three lecture hours a week for one semester. 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.

Department of Physics

The information in parentheses after a course number is the Texas Common Course Numbering (TCCN) designation. Only TCCN designations that are exact semester-hour equivalents of University courses are listed here. Additional TCCN information is published by the Office of Admissions.

Physical Science: P S

Lower-Division Courses

303. Introductory Physical Science I: Mechanics and Heat. Designed for students with minimum prior preparation in mathematics and physics. Especially appropriate for prospective elementary school teachers. Inquiry laboratory approach to basic concepts of measurement, forces, motion, energy, temperature, and heat. Four hours of integrated laboratory and lecture a week for one semester.

304. Introductory Physical Science II: Electricity, Light, and Optics. Inquiry laboratory approach to electricity, magnetism, waves, light, and optical instruments. Four hours of integrated laboratory and lecture a week for one semester. Prerequisite: Physical Science 303.

Upper-Division Courses

350. Physical Science for Elementary and Middle School Teachers. Designed for kindergarten through sixth grade teachers with minimal preparation in mathematics (college algebra) and no preparation in physics. An inquiry laboratory in the basic concepts of light, electricity, and magnetism. Three hours of integrated laboratory and lecture a day for three weeks.

367M. Physical Science: Methods of Astronomy. Same as Astronomy 367M. An introductory, self-paced course in the methods of astronomy that emphasizes learning astronomical principles through observations. Six laboratory hours a week for one semester. May not be counted toward the Bachelor of Arts, Plan I, degree with a major in astronomy. Prerequisite: Upper-division standing and nine semester hours of coursework in mathematics and/or science, including one of the following: Physical Science 303, 304, Astronomy 301, 302, 303. Equivalent preparation in mathematics, physics, chemistry, or earth sciences may be substituted with written approval of the instructor.

375. Individual Study in Physical Science. Intended primarily for preservice and in-service teachers. Guided inquiry reading or laboratory research in physical science. Meets three times a week for one semester, for one hour each meeting. May be repeated for credit when the topics vary. Prerequisite: Upper-division standing and written consent of instructor.

Physics: PHY

Lower-Division Courses

301. Mechanics. Designed for students who intend to major in science or mathematics. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 301, 302K, 303K, 309K, 317K. Prerequisite: High school physics, Physics 306, or consent of the undergraduate adviser; Mathematics 408C, or 408K and concurrent enrollment in 408L; and credit or registration for Physics 101L.

101L. Laboratory for Physics 301. Three laboratory hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 101L, 102M, 103M, 117M. May not be counted toward a degree unless prerequisite is observed. Prerequisite: Credit or registration for Physics 301.

302K (TCCN: PHYS 1301). General Physics--Technical Course: Mechanics, Heat, and Sound. Noncalculus technical course in physics. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 301, 302K, 303K, 309K, 317K. Prerequisite: High school trigonometry or Mathematics 305G; and credit or registration for Physics 102M.

302L (TCCN: PHYS 1302). General Physics--Technical Course: Electricity and Magnetism, Light, Atomic and Nuclear Physics. Noncalculus technical course in physics. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 302L, 303L, 309L, 316, 317L. Prerequisite: Physics 302K and 102M and credit or registration for Physics 102N.

102M (TCCN: PHYS 1101). Laboratory for Physics 302K. Two laboratory hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 101L, 102M, 103M, 117M. May not be counted toward a degree unless prerequisite is observed. Prerequisite: Credit or registration for Physics 302K.

102N (TCCN: PHYS 1102). Laboratory for Physics 302L. Two laboratory hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 102N, 103N, 116L, 117N. May not be counted toward a degree unless prerequisite is observed. Prerequisite: Credit or registration for Physics 302L.

303K (TCCN: PHYS 2325). Engineering Physics I. A general survey of physics; primarily laws of motion, heat, and wave phenomena. Three lecture hours and one discussion hour a week for one semester. In most sections, examinations are given on Wednesday nights; see the Course Schedule for more information. Only one of the following may be counted without prior approval of the department: Physics 301, 302K, 303K, 309K, 317K. Prerequisite: A high school physics course, Physics 306, or consent of the undergraduate adviser; Mathematics 408C, or 408K and concurrent enrollment in 408L; and credit or registration for Physics 103M.

303L (TCCN: PHYS 2326). Engineering Physics II. Electricity and magnetism, optics, and atomic phenomena. Three lecture hours and one discussion hour a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 302L, 303L, 309L, 316, 317L. Prerequisite: Physics 303K and 103M; Mathematics 408D, or 408L and concurrent enrollment in 408M; and credit or registration in Physics 103N.

103M (TCCN: PHYS 2125). Laboratory for Physics 303K. Two laboratory hours a week for one semester. Only one of the following may be counted: Physics 101L, 102M, 103M, 117M. May not be counted toward a degree unless prerequisite is observed. Prerequisite: Credit or registration for Physics 303K.

103N (TCCN: PHYS 2126). Laboratory for Physics 303L. Two laboratory hours and one discussion hour a week for one semester. Only one of the following may be counted: Physics 102N, 103N, 116L, 117N. May not be counted toward a degree unless prerequisite is observed. Prerequisite: Credit or registration for Physics 303L.

104. Introductory Physics Seminar. Suggested for beginning physics majors. Discussion of the development of important ideas in physics, with emphasis on their relevance to contemporary research. One lecture hour a week for one semester. Offered on the pass/fail basis only.

306. Elementary Physics Methods. Designed for students who have not had high school physics, have weak problem-solving skills, and need preparation for Physics 301 or 303K. Three lecture hours a week for one semester. May not be counted toward any degree. Prerequisite: High school trigonometry or Mathematics 305G.

108. Introduction to Research. Introductory laboratory experience; use of tools and test equipment; beginning apprenticeship in active physics research. One class hour a week for one semester. May be repeated for credit. Offered on the pass/fail basis only. Prerequisite: Consent of instructor and approval of an undergraduate adviser.

309K (TCCN: PHYS 1305). Elementary Physics for Nontechnical Students. Designed for students who do not intend to do further work in natural sciences, engineering, mathematics, or medicine. Mechanics, heat, and sound. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 301, 302K, 303K, 309K, 317K.

309L (TCCN: PHYS 1307). Elementary Physics for Nontechnical Students. Designed for students who do not intend to do further work in natural sciences, engineering, mathematics, or medicine. Electricity and magnetism, light, atomic and nuclear physics. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 302L, 303L, 309L, 316, 317L. Prerequisite: Physics 309K.

110C. Conference Course. Supervised study of selected topics in physics, 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.

315. Wave Motion and Optics. Study of general properties of waves; examples include sound, electromagnetic, and mechanical waves; special emphasis on light and optics. Three lecture hours a week for one semester. Prerequisite: Mathematics 427K, Physics 316 and 116L, and credit or registration for Physics 115L.

115L. Laboratory for Physics 315. Three laboratory hours a week for one semester. May not be counted toward a degree unless prerequisite is observed. Prerequisite: Credit or registration for Physics 315.

316. Electricity and Magnetism. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 302L, 303L, 309L, 316, 317L. Prerequisite: Physics 301 and 101L; Mathematics 408D, or 408L and concurrent enrollment in 408M; and credit or registration for Physics 116L.

116L. Laboratory for Physics 316. Three laboratory hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 102N, 103N, 116L, 117N. May not be counted toward a degree unless prerequisite is observed. Prerequisite: Credit or registration for Physics 316.

317K. General Physics I. An introductory course designed and recommended primarily for premedical students and others in the biomedical sciences whose professional or preprofessional training includes an introductory course in calculus. Mechanics, heat, and sound, with biomedical applications. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 301, 302K, 303K, 309K, 317K. May not be counted toward the physics requirement for the degree of Bachelor of Science in Physics. Satisfies most medical and dental school requirements for physics. Prerequisite: A high school physics course, Physics 306, or consent of the undergraduate adviser; Mathematics 408C, or 408K and concurrent enrollment in 408L; and credit or registration for Physics 117M.

317L. General Physics II. Designed and recommended primarily for premedical students and others in the biomedical sciences whose professional or preprofessional training includes an introductory course in calculus. Electricity and magnetism, light, atomic and molecular physics, nuclear physics, and their biomedical applications. Three lecture hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 302L, 303L, 309L, 316, 317L. May not be counted toward the physics requirement for the degree of Bachelor of Science in Physics. Satisfies most medical and dental school requirements for physics. Prerequisite: Physics 317K and 117M and credit or registration for Physics 117N.

117M. Laboratory for Physics 317K. Three laboratory hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 101L, 102M, 103M, 117M. Prerequisite: Credit or registration for Physics 317K.

117N. Laboratory for Physics 317L. Three laboratory hours a week for one semester. Only one of the following may be counted without prior approval of the department: Physics 102N, 103N, 116L, 117N. Prerequisite: Credit or registration for Physics 317L.

119S, 219S, 319S, 419S, 519S, 619S, 719S, 819S, 919S. Topics in Physics. 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 Physics. 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

321. Modern Physics: Plan II. Restricted to Plan II students. Conceptual foundations of modern physics. Examines quantum mechanics, quantum field theory, relativity, and general relativity, including large-scale structure and cosmology; and the development of analytic problem-solving skills, including estimation. Three lecture hours a week for one semester. Prerequisite: Upper-division standing.

329. Introduction to Computational Physics. Computational methods for problem solving and research in physics; numerical analysis and computer simulation methods for physics applications using different types of computers. Three lecture hours a week for one semester. Only one of the following may be counted: Computer Sciences 367, Mathematics 368K, Physics 329. Prerequisite: Physics 315 and 115L, a programming course at the level of Computer Sciences 303E or consent of instructor, and credit or registration for Mathematics 341 or 340L.

129S, 229S, 329S, 429S, 529S, 629S, 729S, 829S, 929S. Topics in Physics. 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 Physics. 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 Physics. This course covers the work period of physics 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 Physics Program, Physics 316, and consent of the undergraduate adviser.

333. Modern Optics. Review of geometrical optics, polarization, interference, and optical instruments. Topics include Fourier optics, light propagation in fibers, quantum optics, and coherence. Three lecture hours a week for one semester. Prerequisite: Physics 315, 115L, and Mathematics 427K.

133L. Laboratory for Physics 333. Three laboratory hours a week for one semester. Prerequisite: Credit or registration for Physics 333.

336K. Classical Dynamics I. Elementary linear vector algebra, Newtonian mechanics, Lagrangian mechanics, central force motion, dynamics of rigid bodies, and theory of small oscillations. Three lecture hours a week for one semester. Prerequisite: Physics 315 and 115L, and Mathematics 427L or 364K.

336L. Fluid Dynamics. Fundamental concepts of fluid mechanics developed and applied to laminar and turbulent flows. Topics include the Navier-Stokes equations, pipe and channel flow, drag, boundary layers, convection, and rotating fluids. Three lecture hours a week for one semester. Prerequisite: Physics 336K.

338K. Electronic Techniques. Elementary circuit theory, amplifiers, feedback, pulse and digital techniques, signal processing, and microprocessors as applied to physics instrumentation. One and one-half lecture hours and three laboratory hours a week for one semester. Prerequisite: Physics 316 and 116L and Mathematics 427K.

341. Selected Topics in Physics. Three lecture hours a week for one semester. An additional one-hour problem session is required for some sections; these are identified in the Course Schedule. May be repeated for credit when the topics vary. May not be counted toward the Bachelor of Science in Physics degree without prior approval of the department. Prerequisite: Upper-division standing, three semester hours of coursework in a natural science, and three semester hours of coursework in mathematics.

• Topic 1: Energy Production.
• Topic 2: Great Men, Moments, and Ideas.
• Topic 3: Musical Acoustics.
• Topic 4: The Nature of Things.
• Topic 5: Pseudoscience.
• Topic 6: Writing.

352K. Classical Electrodynamics. Electrostatic fields, magnetostatic fields, derivation of Green's theorems and functions and of Maxwell's equations. Three lecture hours a week for one semester. Prerequisite: Physics 315 and 115L, and Mathematics 427L or 364K.

453. Modern Physics I: Introduction to Quantum Phenomena. Breakdown of classical physics for microscopic phenomena; absorption and emission spectra, the photoelectric effect, blackbody radiation, models of the atom, Compton effect, x-ray diffraction; Planck's hypothesis; deBroglie's hypothesis; the probability interpretation; the one-dimensional Schrödinger equation; special relativity; the uncertainty relation. Three lecture hours and three laboratory hours a week for one semester. Prerequisite: Physics 315 and 115L, or consent of instructor.

355. Modern Physics for Engineers. Modern physics, including relativity, quantum mechanics, and modern optics. Three lecture hours a week for one semester. Prerequisite: Physics 303L, 103N, and Mathematics 427K.

362K. Modern Physics III: Applications of Quantum Mechanics. The two-electron atom; spin and statistics; coupling schemes for many-electron atoms; atoms and the radiation field; perturbation methods for decay and collisions; thermal, electrical, and magnetic properties of solids; free-electron metal and band theory; if time permits, selected topics such as superconductivity, Josephson tunneling, and others. Three lecture hours a week for one semester. Prerequisite: Physics 373.

362L. Modern Physics IV: Subatomic Physics. Nuclei and nucleons, their gross properties; the hadrons; symmetries and conservation laws; nuclear stability; electromagnetic, weak, and hadronic interactions; nuclear reactions at low, medium, and high energies; nucleon structure; tools of experimental nuclear physics; models of theoretical nuclear physics; nuclear technology. Three lecture hours a week for one semester. Prerequisite: Physics 373; Physics 362K is recommended.

369. Thermodynamics and Statistical Mechanics. Basic concepts of thermal physics; entropy, enthalpy, free energy, phase transitions, equilibrium distribution functions, applications. Three lecture hours a week for one semester. Prerequisite: Credit or registration for Physics 373.

370C. Individual Study in Physics. Supervised reading or research in physics. 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: Physics 336K, credit or registration for Physics 352K, and consent of the undergraduate adviser.

670T. Senior Thesis. Individual research with faculty supervision. First half involves preparation of proposal; second involves completion of written thesis. Six hours of work a week for one semester, or three hours of work a week for two semesters. Only three semester hours may be counted toward the Bachelor of Science in Physics degree. Prerequisite: Upper-division standing and nine semester hours of upper-division coursework in physics.

373. Modern Physics II: Quantum Mechanics. Postulates of quantum mechanics; the bound states of the finite square well, the harmonic oscillator, operator-eigenvalue formulism and selected examples, the hydrogen atom, angular momentum, rigid rotor, spin, and, if time permits, simple scattering theory. Three lecture hours a week for one semester. Prerequisite: Physics 336K and 453, or consent of instructor.

474. Advanced Laboratory I. Modern experimental techniques, theory of error, and analysis of experiments; both modern and classical experiments in atomic and nuclear physics, electricity and magnetism, optics and heat. Three lecture hours and eight laboratory hours a week for one semester, with additional laboratory hours to be arranged. With consent of instructor, may be repeated for credit. Prerequisite: Physics 338K, 352K, and 453; or consent of the undergraduate adviser.

375P. Introductory Plasma Physics. Orbit theory and drifts, introduction to plasma stability and waves, applications to plasma confinement and heating. Three lecture hours a week for one semester. Prerequisite: Physics 352K and 369.

375R. Introduction to Relativity. Overview of the special and general theories of relativity, with emphasis on recent developments in gravitation. Three lecture hours a week for one semester. Prerequisite: Physics 352K.

375S. Introductory Solid-State Physics. Crystal structure, classification of solids, cohesion, thermal and electrical properties of solids, magnetic properties of solids, imperfections. Three lecture hours a week for one semester. Prerequisite: Physics 369 and 373.

379H. Honors Tutorial Course. Research project, resulting in a thesis, for outstanding students electing to take the honors program in physics. Conference course. Prerequisite: A University grade point average of at least 3.00, a grade point average in physics of at least 3.50, twelve semester hours of upper-division coursework in physics, and consent of the student's research supervisor and the departmental honors adviser.

Division of Statistics and scientific computation

Statistics and Scientific Computation: SSC

Lower-Division Courses

303. Statistics in Experimental Research. An introduction to the fundamental concepts and methods of statistics, with emphasis on applications in experimental science. Includes exploratory data analysis, correlation and regression, descriptive statistics, sampling distributions, confidence intervals, and hypothesis testing. Three lecture hours a week for one semester. Only one of the following may be counted: Mathematics 316, Statistics and Scientific Computation 303, 304, 305, 306.

304. Statistics in Health Care. An introduction to the fundamental concepts and methods of statistics, with emphasis on applications in the health sciences. Includes exploratory data analysis, correlation and regression, descriptive statistics, sampling distributions, confidence intervals, and hypothesis testing. Three lecture hours a week for one semester. Only one of the following may be counted: Mathematics 316, Statistics and Scientific Computation 303, 304, 305, 306.

305. Statistics in Policy Design. An introduction to the fundamental concepts and methods of statistics, with emphasis on applications in policy evaluation and design. Includes exploratory data analysis, correlation and regression, descriptive statistics, sampling distributions, confidence intervals, and hypothesis testing. Three lecture hours a week for one semester. Only one of the following may be counted: Mathematics 316, Statistics and Scientific Computation 303, 304, 305, 306.

306. Statistics in Market Analysis. An introduction to the fundamental concepts and methods of statistics, with emphasis on applications in the analysis of personal and group behaviors. Includes exploratory data analysis, correlation and regression, descriptive statistics, sampling distributions, confidence intervals, and hypothesis testing. Three lecture hours a week for one semester. Only one of the following may be counted: Mathematics 316, Statistics and Scientific Computation 303, 304, 305, 306.

110T, 210T, 310T, 410T. Topics in Statistics and Computation. For each semester hour of credit earned, one lecture hour a week for one semester. May be repeated for credit when the topics vary.

318. Introduction to Statistical and Scientific Computation. An introduction to quantitative analysis using fundamental concepts in statistics and scientific computation. Includes probability, distributions, sampling, interpolation, iteration, recursion, and visualization. Three lecture hours and one laboratory hour a week for one semester.

318M. Biostatistics. Introduction to methods of statistical analysis of biological data. Includes data analysis, basics of experimental design, statistical inference, interval estimation, and hypothesis testing. Three lecture hours and one discussion hour a week for one semester. Biology 318M and Statistics and Scientific Computation 318M may not both be counted. Prerequisite: Four semester hours of coursework in biology and either Mathematics 408D or 408L.

Upper-Division Courses

321. Introduction to Probability and Statistics. The basic theory of probability and statistics, with practical applications. Includes fundamentals of probability, distribution theory, sampling models, data analysis, experimental design, statistical inference, interval estimation, and hypothesis testing. Three lecture hours and one discussion hour a week for one semester. Mathematics 358K and Statistics and Scientific Computation 321 may not both be counted. Prerequisite: Mathematics 408D or 408L with a grade of at least C.

222. Introduction to Scientific Programming. Introduction to programming using both the C and Fortran (95/2003) languages, with applications to basic scientific problems. Covers common data types and structures, control structures, algorithms, performance measurement, and interoperability. Two lecture hours a week for one semester. Prerequisite: Credit or registration for Mathematics 408C or 408K.

329C. Practical Linear Algebra I. Matrix representations and properties of matrices; linear equations, eigenvalue problems and their physical interpretation; and linear least squares and elementary numerical analysis. Emphasis on physical interpretation, practical numerical algorithms, and proofs of fundamental principles. Three lecture hours a week for one semester. Prerequisite: Credit or registration for Mathematics 408C or 408K.

329D. Practical Linear Algebra II. Iterative solutions to linear equations and eigenvalue problems; properties of symmetric and nonsymmetric matrices, exploitation of parsity and diagonal dominance; introduction to multivariate nonlinear equations; numerical analysis; and selected applications and topics in the physical sciences. Three lecture hours a week for one semester. Prerequisite: Mathematics 340L, 341, or Statistics and Scientific Computation 329C.

335. Scientific and Technical Computing. A comprehensive introduction to computing techniques and methods applicable to many scientific disciplines and technical applications. Covers computer hardware and operating systems, systems software and tools, code development, numerical methods and math libraries, and basic visualization and data analysis tools. Three lecture hours a week for one semester. Prerequisite: Mathematics 408D or 408M, and prior programming experience.

339. Applied Computational Science. Concentrated study in a specific area or areas of application, with an emphasis on modeling and visualization. Areas may include computational biology, computational chemistry, computational applied mathematics, computational economics, computational physics, or computational geology. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Varies with the topic and is given in the Course Schedule.

150K. Data Analysis Applications. Introduction to the use of statistical or mathematical applications for data analysis. Two lecture hours a week for eight weeks. May be repeated for credit when the topics vary. Offered on the pass/fail basis only. Prerequisite: Varies with the topic and is given in the Course Schedule.

• Topic 1: SPSS Software. Prerequisite: Upper-division standing.
• Topic 2: SAS Software. Prerequisite: Upper-division standing.
• Topic 3: Stata Software. Prerequisite: Upper-division standing.
• Topic 4: The R Software Environment. Prerequisite: Upper-division standing.

352. Statistical Methods. Study of simple and multiple regression, fundamentals of experimental design, and analysis of variance methods. May include logistic regression, Poisson regression, resampling methods, introduction to Bayesian methods, and probability models. Includes substantial use of statistical software. Three lecture hours and one laboratory hour a week for one semester. Prerequisite: Mathematics 316, Statistics and Scientific Computation 303, 304, 305, or 306.

358. Special Topics in Statistics. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Upper-division standing. Additional prerequisites may vary with the topic and are given in the Course Schedule.

374C. Parallel Computing for Scientists and Engineers. Study of parallel computing principles, architectures, and technologies; and parallel application development, performance, and scalability. Designed to help prepare students to formulate and develop parallel algorithms to implement effective applications for parallel computing systems. Three lecture hours a week for one semester. Prerequisite: Mathematics 408D or 408M; Mathematics 340L; and prior programming experience using C or Fortran on Linux or Unix systems.

374D. Distributed and Grid Computing for Scientists and Engineers. Distributed and grid computing principles and technologies. Covers common modes of grid computing for scientific applications, development of grid-enabled applications, and future trends in grid computing. Three lecture hours a week for one semester. Prerequisite: Mathematics 408D or 408M; Mathematics 340L; and prior programming experience using C or Fortran on Linux or Unix systems.

374E. Visualization and Data Analysis for Scientists and Engineers. Scientific visualization principles, practices, and technologies, including remote and collaborative visualization. Introduces statistical analysis, data mining, and feature detection. Three lecture hours a week for one semester. Prerequisite: Mathematics 408D or 408M; Mathematics 340L; and prior programming experience using C or Fortran on Linux or Unix systems.

375. Special Topics in Scientific Computation. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Upper-division standing. Additional prerequisites may vary with the topic and are given in the Course Schedule.

379R. Undergraduate Research. Students complete an individual research project under the supervision of one or more faculty members. The equivalent of three lecture hours a week for one semester. May be repeated for credit. Prerequisite: Upper-division standing and consent of instructor.

UTeach-Natural Sciences

UTeach-Natural Sciences: UTS

Lower-Division Courses

101. Secondary Teacher Education Preparation: STEP 1. Introduction to mathematics, computer sciences, and science teaching as a career. Discussions include standards-based lesson design and various teaching and behavior management strategies. Fieldwork consists of planning and teaching four inquiry-based lessons to students in grades three to six in local elementary schools. One and one-half class hours a week for one semester; at least ten hours of fieldwork a semester are also required. Chemistry 107 (Topic: STEP 1--UTeach) and UTeach-Natural Sciences 101 may not both be counted. Prerequisite: Admission to the UTeach-Natural Sciences program.

110. Secondary Teacher Education Preparation: STEP 2. Topics may include routes to teacher certification in mathematics, computer sciences, and science teaching; various teaching methods that are designed to meet instructional goals; and learner outcomes. Students develop and teach three inquiry-based lessons in their field in a middle school, and participate in peer coaching. One and one-half class hours a week for one semester; at least twenty hours of fieldwork a semester are also required. Biology 101C (Topic: STEP 2) and UTeach-Natural Sciences 110 may not both be counted. Prerequisite: UTeach-Natural Sciences 101 or consent of the UTeach adviser in the College of Natural Sciences.

Upper-Division Courses

350. Knowing and Learning in Math and Science. Same as Curriculum and Instruction 365C. Restricted to students in the UTeach-Natural Sciences program. Psychological foundations of learning; problem solving in mathematics and science education utilizing technology; principles of expertise and novice understanding of subject matter; implications of high-stakes testing; and foundations of formative and summative assessment. Three lecture hours a week for one semester; additional hours may be required. Curriculum and Instruction 371 (Topic 21: Knowing and Learning in Math and Science) and UTeach-Natural Sciences 350 may not both be counted. Prerequisite: Credit with a grade of at least C or registration for UTeach-Natural Sciences 101.

355. Classroom Interactions. Same as Curriculum and Instruction 365D. Restricted to students in the UTeach-Natural Sciences program. Principles of delivering effective instruction in various formats (lecture, lab activity, collaborative settings); examination of gender, class, race, and culture in mathematics and science education; overview of policy related to mathematics and science education. Three lecture hours a week for one semester; additional hours may be required. Curriculum and Instruction 371 (Topic 20: Classroom Interactions) and UTeach-Natural Sciences 355 may not both be counted. Prerequisite: A University grade point average of at least 2.50, Curriculum and Instruction 365C or UTeach-Natural Sciences 350 with a grade of at least C, and UTeach-Natural Sciences 110 with a grade of at least C.

360. Project-Based Instruction. Same as Curriculum and Instruction 365E. Restricted to students in the UTeach-Natural Sciences program who have earned a passing score on the preliminary portfolio. Foundations of project-based, case-based, and problem-based learning environments; principles of project-based curriculum development in mathematics and science education; classroom management and organization of project-based learning classrooms. Three lecture hours a week for one semester with additional fieldwork hours to be arranged. Curriculum and Instruction 371 (Topic 22: Project-Based Instruction) and UTeach-Natural Sciences 360 may not both be counted. Prerequisite: A University grade point average of at least 2.50, and Curriculum and Instruction 365D or UTeach-Natural Sciences 355 with a grade of at least C.

170. Student Teaching Seminar. Restricted to students in the UTeach-Natural Sciences program who have earned a passing score on the preliminary portfolio. Discussions include student teaching experiences, contemporary critical issues in education, and preparation for the state certification exam. One class hour a week for one semester. Chemistry 107 (Topic: Special Topics Seminar) and UTeach-Natural Sciences 170 may not both be counted. Prerequisite: A University grade point average of at least 2.50, and credit or registration for Curriculum and Instruction 650S (or credit for 667S).

675. Student Teaching for Secondary and Middle Grades. Closely supervised field coursework in a cooperating school. Experience includes carrying out the duties of a secondary or middle grades teacher. Twenty hours of fieldwork a week for one semester. Offered on the pass/fail basis only. Prerequisite: A University grade point average of at least 2.50, approval of the preliminary portfolio by the College of Natural Sciences UTeach Program, consent of the UTeach adviser in the College of Natural Sciences, and concurrent enrollment in UTeach-Natural Sciences 170.