Linear algebra is important in the study of economics. For example, in linear algebra one learns to calculate the slope of a graphed line, which represents elasticity of supply and demand. In economics, graphs are heavily utilized to display economic concepts. Elasticity refers to the sensitivity of consumers or sellers to price changes.
Statistics are centrally important to economics because the study of statistics displays concepts of correlation, probability and regression. The study of economics dovetails with the study of statistics because economic theories predict the behavior of the marketplace. Regression, probability and correlation concepts learned in statistics are heavily used in economics to describe the marketplace.
Calculus is the study of limits, functions and derivatives. While algebra solves static equations, calculus is the study of change. Functions are mathematical statements that describe outcomes dependent on a set of guidelines. For example, the function 3x = 9 means that x is a function of 3x. Calculus seeks to determine the differentiation, or derivatives of functions, relaxing the rules of functions based on limitations. This is important in economics due to the fact that economics is sometimes an inexact science, so finding the derivatives of functions leads to possible economic variations.
Game theory is the study of strategy. In economics, game theory assumes that participants in a society are rational and self-interested. The classic game theory example is the prisoner's dilemma, where two criminals that conspired to commit a crime are each offered the following deal: "The first to tell the truth will go free, while the other will receive ten years in jail." Game theory studies different interactions among participants in an economy to predict economic behavior. Game theory is useful in predicting behavior among competitors in an industry, among consumers and among lawmakers. Game theory is an abstract form of mathematical study, but applies mathematical concepts to the discipline.