 Suggested Statistics and Mathematics Courses for Ph.D. Econometrics and Economic Theory

The following, written July 2017, lists potential courses in the Statistics and Mathematics departments that may be useful for Ph.D. Economics students interested in furthering their skills and background in econometrics beyond the 240 sequence, and for economic theory, especially microeconomic theory.

Before taking any of these courses you should consult with relevant economics faculty and, for the course to count towards your degree, the Director of Graduate Studies.

STATISTICS

It is best to take Ph.D. level courses or the more advanced Masters courses in Statistics. The basic Masters courses are if anything less advanced than the Ph.D. econometrics courses.
For the Masters in Statistics (see https://www.stat.ucdavis.edu/grad/ms.html
) the prerequisites for entrance into the master's program are as follows: a bachelor's degree with 3.0 overall grade-point average; one year of calculus; a course in linear algebra; facility with a programming language; and upper-division work in mathematics and/or statistics.

For the Ph.D. in Statistics see https://www.stat.ucdavis.edu/grad/phd.html

Department of Statistics courses are listed at  http://catalog.ucdavis.edu/programs/STA/STAcourses.html

Probability Theory

Statistics 235A-C (Probability Theory) cross-listed as Mathematics 235A-C. Prerequisite is Mathematics 125B (Real Analysis) and Math 135A (probability theory) or Statistics 131A (probability theory in the more advanced of the two upper-division probability and statistics sequences).

Note that Statistics 200A (Introduction to Probability Theory) is too light. It is for MA students and overlaps too much with ECN/ARE 239.

Statistical Theory

Statistics 231A-C  (Mathematical Statistics I-III) is the core PhD sequence. Requires Mathematics 125B (Real Analysis) and Statistics 131A-C.

Note that Statistics 200B-20C (Introduction to Mathematical Statistics I-II) is too light. It is for MA students and overlaps too much with ECN/ARE 239 and 240A.

Other Statistics Courses that may be useful for econometrics

Statistics 208 (Statistical Methods in Machine Learning) is a Masters level course but is okay as there is no other machine learning course.

Statistics 225 (Clinical Trials) requires Biostatistics 223 (Generalized Linear Models) which is a required Biostatistics PhD course.

Statistics 233 (Designed Experiments) may be too easy (requires Statistics 131C) and specialized. Statistics 225 may be better.
Statistics 240A (Nonparametric Inference) is a PhD level course.

Statistics 241 (Asymptotic Theory of Statistics) is a PhD level course.

Statistics 243 (Computational Statistics) has less lower prerequisites but is required for the Statistics PhD.

Statistics 251 (Topics in Statistical Methods and Models) is a PhD level course.

MATHEMATICS

Math courses are listed at http://catalog.ucdavis.edu/programs/MAT/MATcourses.html

And detailed syllabi are at https://www.math.ucdavis.edu/courses/syllabi/

Real Analysis

Beginning Fall 2018: Mathematics 125A-B-C (Real Analysis) is the upper division undergraduate s sequence which requires Math 21C (Calculus).
Before Fall 2018: Mathematics 125A-B (Real Analysis) is the upper division undergraduate s sequence which requires Math 25 (Advanced Calculus) which requires Math 21C (Calculus).

Mathematics 201A-C (Analysis) is a PhD in mathematics core requirement so is quite advanced.

Other Mathematics that may be useful for economic theory and/or econometrics

The following are courses of potential interest, depending on ones’ planned economics specialty. Talk to relevant economics professors for guidance.

This list is not exhaustive.

Mathematics 108 (Introduction to Abstract Mathematics)  This emphasizes proving theorems.
Mathematics 133 (Mathematical Finance)
Mathematics 135A (Probability)

Mathematics 135B (Stochastic Processes)

Mathematics 145 (Topology)

Mathematics 168 (Optimization)

Mathematics 206 (Measure Theory) Pre-requisite is Math 125B.

Mathematics 215A-C (Topology)

Mathematics 239 (Differential Topology)

Mathematics 235A-C (Probability Theory) Same as Statistics 235A-C.

Mathematics 236A-B (Stochastic Dynamics and Applications). Course 235A-C recommended so quite advanced. A. Colin Cameron / UC-Davis Economics /  http://cameron.econ.ucdavis.edu