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The University of Texas at Austin Department of

Math-Econ Track

The Math-Econ Track offers a specialized course of study for economics majors wanting to build analytical and quantitative skills for graduate study or careers in economics and business. The Math-Econ coursework satisfies economics major, math minor, and general elective requirements. A letter of recognition from the Economics Department is awarded to students who successfully complete the track.

Required Economics Coursework:

THREE upper division economics courses from the approved list below. These courses can count toward the economics major or as upper division general electives. See course descriptions and prerequisites on reverse side.

Three courses from this approved list:  341K Introduction to (required)  350K Topic 4: Advanced Econometrics  350K Topic 6: Advanced Microeconomic Theory  350K Topic 7: Applied Economic Analysis  350K Applied  350K Selected topics (upon dept approval-- see advisor)  354K Introductory  362M Mathematics for  363C  Selected ECO graduate courses (upon dept approval-- see advisor)

Required Math Coursework:

THREE upper division math courses from the approved list below. These courses can count toward a minor in math or as upper division general electives. See course descriptions and prerequisites on reverse side.

Three courses from this approved list:  M325K Discrete Math  M427K Advanced Calculus for Applications 1  M328K Intro to Number Theory  M340L Matrices and Matrix Calculations OR M341 Linear Algebra and Matrix Theory  M361K Intro to Real Analysis OR M365C Real Analysis  M362K Probability 1  M378K Intro to Math

*******************************************************Cut here************************************************************ To join the Math-Econ Track submit this section to the Economics Undergraduate Advising Center, BRB 1.114, Ph#512-471-2973, Email: [email protected]

Name ______E-ID ______Expected Graduating Semester/Yr ____ APPROVED ECONOMICS COURSES 341K Introduction to Econometrics Introduces the student to standard regression procedures of parameter estimation and hypothesis testing in economics. Prerequisite: Economics 420K and 329 with a grade of at least C- in each; Mathematics 408D is recommended. 350K Topic 4: Advanced Econometrics Theory of the linear regression model used widely in economic applications, including model specification, least squares and maximum likelihood estimation, hypothesis testing, multicollinearity, dummy variables, heteroskedasticity, and discrete choice models. Prerequisite: Economics 329 with a grade of at least C-, and Mathematics 408D, 340L, or 341. Economics 341K or Mathematics 362K is recommended. 350K Topic 6: Advanced Microeconomic Theory Modern theory of the consumer and the firm. Topics include an analysis of and demand functions, the theory of supply, cost and functions, duality theory, consumer surplus, choice under , and analysis. Emphasis on both economic principles and quantitative methods, especially static and dynamic optimization models. Prerequisite: Economics 329 with a grade of at least C-, and Mathematics 408D, 340L, or 341. 350K Topic 7: Applied Economic Analysis Major issues in applied economics, including relevant theoretical and empirical models. Prerequisite: Economics 329 with a grade of at least C-, and Mathematics 408D, 340L, or 341. Economics 341K or Mathematics 362K is recommended. 350K Advanced Topics in Economics Topics vary—approval for the Math-Econ Track depends on the topic—see advisor. Designed primarily for economics majors. Topics may include in-depth analysis of problems in economic theory, applications, and . Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Economics 330T and 350K may not both be counted unless the topics vary. Prerequisite: Economics 420K with a grade of at least C. Additional prerequisites may vary with the topic and are given in the Course Schedule. 354K Introductory Game Theory Introduction to the formal study of interdependent decision making. Applications of game theory include pricing and advertising strategies, labor-management bargaining, and tariff negotiations. Prerequisite: Economics 420K and 329 with a grade of at least C- in each. 362M Mathematics for Economists Application of mathematics in economic analysis. Prerequisite: Economics 420K and Mathematics 408D with a grade of at least C- in each. 363C Computational Economics The course will emphasize creativity in projects rather than feedback on exams and will use a series of computer models to focus on economics. The course provides base models and help in modifying the models in directions that reflect the students' . Prerequisite: Economics 420K or 320L with a grade of at least C-.

APPROVED MATH COURSES M325K Discrete Math Prerequisite: One of M408D, M408L, or M408S, with a grade of at least C-, or consent of instructor. This is a first course that emphasizes understanding and creating proofs. Therefore, it provides a transition from the problem-solving approach of calculus to the entirely rigorous approach of advanced courses such as M365C or M373K. The number of topics required for coverage has been kept modest so as to allow adequate time for students to develop theorem-proving skills M427K Advanced Calculus for Applications I Prerequisite: The prerequisite is one of 408D, M408L or M408S, with a grade of at least C-. M427K is a basic course in ordinary and partial differential equations, with Fourier series. It should be taken before most other upper division, applied mathematics courses. Geared to the audience primarily consisting of engineering and science students, the course aims to teach the basic techniques for solving differential equations which arise in applications. The approach is problem-oriented and not particularly theoretical. Most of the time is devoted to first and second order ordinary differential equations with an introduction to Fourier series and partial differential equations at the end. Depending on the instructor, some time may be spent on applications, Laplace transformations, or numerical methods. M328K Intro to Number Theory Prerequisite: M341 or M325K, with a grade of at least C-. This is a first course that emphasizes understanding and creating proofs; therefore, it must provide a transition from the problem-solving approach of calculus to the entirely rigorous approach of advanced courses such as M365C or M373K. The number of topics required for coverage has been kept modest so as to allow instructors adequate time to concentrate on developing the students theorem-proving skills. M340L Matrices & Matrix Calculations Prerequisite: The prerequisite is one semester of calculus (either M408C, M408K, or M408N) with grade of at least C-, or consent of instructor. Only one of M341 and M340L may be counted. The goal of M340L is to present the many uses of matrices and the many techniques and concepts needed in such uses. The emphasis is on concrete concepts and understanding and using techniques, rather than on learning proofs and abstractions. The course is designed for applications-oriented students such as those in the natural and social sciences, engineering, and business. Topics might include matrix operations, systems of linear equations, introductory vector-space concepts (e.g., linear dependence and independence, basis, dimension), determinants, introductory concepts of eigensystems, introductory linear programming, and least square problems. OR M341 Linear Algebra and Matrix Theory Prerequisite: The prerequisite is one of M408D, M408M, M408S or the equivalent, with a grade of at least C-, or consent of instructor. (Credit may not be received for both M341 and M340L. Majors with a 'math' advising code must register for M341 rather than for M340L; majors without a 'math' advising code must register for M340L. Math majors must make a grade of at least C in M341.) The emphasis in this course is on understanding the concepts and learning to use the tools of linear algebra and matrices. Some time should be devoted to teaching students to do proofs. M361K Intro to Real Analysis Prerequisite: Either consent of faculty undergraduate advisor, or two of the following courses, with grade of at least C- in each: M341, 328K, 325K (Philosophy 313K may be substituted for M325K), with a grade of at least C. May not be counted by students with credit for M365K with a grade of C- or better. This is 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. OR M365C Real Analysis I Prerequisite: Either consent of Mathematics Advisor, or two of M341, 328K, 325K (Philosophy 313K may be substituted for M325K), with a grade of at least C-. Students who receive a grade of C in M325K or M328K are advised to take M361K before attempting M365C. Students who have received a grade of C- or better in Mathematics 365C may not take Mathematics 361K. This course is an introduction to Analysis. Analysis, together with Algebra and Topology, form the central core of modern mathematics. Beginning with the notion of limit from calculus and continuing with ideas about and the concept of function that arose with the description of heat flow using Fourier series, analysis is primarily concerned with infinite processes, the study of spaces and their geometry where these processes act and the application of differential and integral to problems that arise in geometry, pde, physics and probability. 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. M362K Probability I Prerequisite: One of M408D, M408S, 408L, with a grade of at least C-. 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. M378K Intro to Math Stats Prerequisite: Mathematics 362K with a grade of at least C. Students taking this course are usually majoring in mathematics, actuarial science, or one of the natural sciences. M362K, 358K, and 378K form the core sequence for students in 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.

JLC updated 5/07, revised 8/10, updated 6/11