# Preparation

An undergraduate degree in economics is not required for admission to the Ph.D. program, provided that applicants have achieved an adequate background in economics and mathematics at the undergraduate level.

Economics
All applicants are expected to have completed intermediate math-based economic theory courses. Further education in economics and economic theory is helpful, but not required.

Math
Applicants must have knowledge of multivariate calculus, basic matrix algebra, and differential equations; completion of a two-year math sequence, which emphasizes proofs and derivations.  Some knowledge of statistics and elementary probability is highly desirable, as is additional coursework in algebra and real analysis.  Descriptions of the Math courses offered at UC Berkeley which fulfill this requirement are as follows:

MATH 1A:  An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

MATH 1B: Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

MATH 53: Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

MATH 54: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.

MATH 104:The real number system. Sequences, limits, and continuous functions in R and R. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.

MATH 110:Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QR factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals.

STAT 134: An introduction to probability, emphasizing concepts and applications. Conditional expectation, independence, laws of large numbers. Discrete and continuous random variables. Central limit theorem. Selected topics such as the Poisson process, Markov chains, characteristic functions.