This course introduces students to the most useful mathematical tools that will be applied in the remaining courses in economics and political science offered by the Center for Economics, Politics and History. Students learn each mathematical tool and how to apply it to an economic or political problem. Students will become familiar with the meaning and use of the following key concepts: functions; utility maximization under certainty and uncertainty; solving a system of equations; using derivatives in optimization problem solving; probability and the main families of probability distribution functions; conditional and unconditional probability; the law of large numbers; the central limit theorem; variance; covariance; correlation; projection; regression; stochastic processes; cooperative and noncooperative games; and Nash Equilibrium. Students also learn the basics of programming in R.