# Recommended Mathematical Training to Prepare for Graduate School in Economics

Although economics graduate programs have varying admissions requirements, graduate training in economics is highly mathematical. Most economics PhD programs expect applicants to have had advanced calculus, differential equations, linear algebra, and basic probability theory. Many applicants have completed a course in real analysis. This means that undergraduates thinking about graduate school in economics should take 1-2 mathematics courses each semester. About half of the students entering PhD programs in economics earn a Master's degree beforehand. Many shore up their math preparation during this period.

Note: Different universities will title and number their math courses differently. This list is meant as a general guideline; students should check the math requirements of Master's and PhD programs to which they are applying for more specific guidelines.

### Minimal Recommendation for entrance into an Economics Master's program

__Calculus and Analytic Geometry (at least 2 semesters)__

Topics include functions, limits and continuity, differentiation, applications of the derivative, curve sketching, and integration theory, methods of integration, applications of the integral, Taylor's theorem, infinite sequences and series.

__Matrix Theory/Linear Algebra__

Topics include matrix algebra, systems of linear equations, determinants, vector algebra and geometry, eigenvalues, eigenvectors, vector spaces, subspaces, bases, and dimension, linear transformations, representation by matrices, nullity, rank, diagonalization, inner products, adjoints, unitary, and orthogonal transformations.

__Statistics (at least 2 semesters)__:

Topics include fundamentals of probability theory, confidence intervals, and tests of hypothesis for normal distributions, one- and two-sample tests and associated confidence intervals for means and proportions, analysis of variance, F-tests, correlation, regression, contingency tables, and statistical analysis using the computer.

### Additional Highly Recommended Courses for entrance into an Economics Master's program

__Calculus of Several Variables/Multivariable Calculus__

Topics include two and three dimensional geometry, manipulation and application of vectors, functions of several variables, contour maps, graphs, partial derivatives, gradients, double and triple integration, vector fields, line integrals, surface integrals.

__Methods for Data Analysis__

Topics include statistical inference and design, t-tools, non-parametric alternatives, one-way ANOVA, simple linear regression, multiple linear regression, and variable selection procedures, statistical thinking, appropriate inference, interpretation of results, and writing, principles of experimental design, multi-factor ANOVA, repeated measures, logistic regression, Poison log-linear regression, multivariate and time series analyses, graphical techniques, data collection plans, populations, samples, and sampling distributions, inferences on means and proportions, simple linear regression. Should include both theory and empirical components and use SAS, Stata, R, Matlab, or a similar statistical software program.

### Minimal Recommendation for entrance into a PhD program - the above, plus

__Differential Equations__

Topics include introduction to qualitative, quantitative, and numerical methods for ordinary differential equations, modeling via differential equations, linear and nonlinear first order differential equations and systems, transform techniques.

__Probability Theory__

Topics include discrete and continuous random variables, expected value, variance, joint, marginal and conditional distributions, conditional expectations, applications, simulation, central limit theorem, order statistics.

__Mathematical Statistics__

Topics include theory of point estimation, interval estimation, and hypothesis testing.

### Additional Recommended Courses for PhD preparation

__Methods of Proof__

Topics include reasoning and communication in mathematics, including logic, generalization, existence, definition, proof, and the language of mathematics, functions, relations, set theory, recursion, algebra, and number theory.

__Stochastic Processes__

Topics include conditional probability theory, discrete and continuous time markov chains, birth and death processes and long run behavior, Poisson processes, and system reliability.

__Real Analysis__

Topics include a rigorous development of calculus with formal proofs, functions, sequences, limits, continuity, differentiation, integration, rigorous development of multivariate calculus, differentiable functions, inversion theorem, multiple integrals, line and surface integrals, and infinite series.