Higher level math is a big part of any PhD program in economics -- to the extent that students with bachelors degrees in mathematics are more likely than students with bachelors degrees in economics to be admitted into economics PhD programs, according to the California State University website. Not all math is equally relevant to studying economics at the PhD level, though. The most important kinds of math for someone pursuing a PhD in economics are linear algebra, multivariable calculus, probability theory and real analysis.
Someone pursuing a PhD in economics should study linear algebra. Linear algebra uses linear equations in the study of multidimensional matrices. In economics, being able to create and manipulate matrices provides a means of analyzing how economic factors interact. For example, linear algebra techniques can be used to study how changing domestic production rates effect foreign trade, says Steve Levandusky of Bucknell University in Pennsylvania.
Multivariable calculus is also important to study early in preparation for an economics PhD. Multivariable calculus allows for non-linear rates of change and multiple variables, which, for economists, allows for very detailed analysis of how economic factors interact. According to professors from the School of International and Public Affairs at Columbia University, economists can use multivariable calculus to evaluate things like the factors consumers consider before making purchases, the tradeoffs between labor and capital and the potential value of increasing or decreasing the production rate of a product.
One of the more specialized kinds of math economists use is probability theory. Where algebra and calculus allow for the creation and analysis of known sets of data, probability theory allows analysis of the unknown. It considers known data along with elements of chance to predict outcomes. Economists might use this to help a company decide how much or whether to place a bid for a government contract, for example.
R analysis is often cited as the most important math course for economics PhD preparation, according the California State University website. The "real" refers to the discipline's focus on real numbers, which excludes imaginary numbers and infinity. Real analysis builds on calculus and provides a foundation for the kinds of applied mathematics that are useful in economic study. Real analysis is especially valued by economics PhD programs because of its emphasis on writing and understanding proofs.