Objective: This course will introduce students to elements of mathematical analysis and of probability theory with a special emphasis on methods that are important in economics.
Economists use mathematical models to think about social and economic interactions, develop predictions about the outcomes of those interactions, and design policy interventions. This course will introduce some of the standard mathematical tools that are used in economics. The course will focus on the maths rather than on the economics, but examples will be used throughout to illustrate how mathematical tools are useful for tackling economic questions.
The course is divided into two parts: mathematical analysis and probability theory.
The topics that will be covered in mathematical analysis include logic and proofs, sets, relations, functions, sequences and limits, continuity, and differentiability. The focus will not be on proving results in mathematical analysis but rather on understanding key results in mathematical analysis and seeing how they are useful in tackling economic questions. Examples will draw on elements of decision theory and of game theory.
The topics that will be covered in probability theory include the probability axioms, independence, conditional probability and Bayes’ rule, discrete and continuous distributions, expectations and moments, correlation, the law of large numbers, and the central limit theorem. Examples will include decisions under risk and mitigation of risk.
The tools that students acquire in this course will be essential for tackling Introduction to Econometrics.