理论经济学数理教科书
集合理论，最优化理论，纳什均衡，的严密证明与图解。
适合经济学phd课程
介绍内容如下
We will start with a refresher on linear programming, particularly Lagrange Theory. The problems we
will encounter should provide the motivation for the rest of the first part of this course where we will
be concerned mainly with the mathematical foundations of optimisation theory. This includes a revision
of basic set theory, a look at functions, their continuity and their maximisation in n-dimensional vector
space (we will only occasionally glimpse beyond finite spaces). The main results are conceptual, that is,
not illustrated with numerical computation but composed of ideas that should be helpful to understand a
variety of key concepts in modern Microeconomics and Game Theory. We will look at two such results in
detail—both illustrating concepts from Game Theory: (i) that it is not rational to play a strictly dominated
strategy and (ii) Nash’s equilibrium existence theorem. We will not do many proofs throughout the course
but those we will do, we will do thoroughly and you will be asked to proof similar results in the exercises.
The course should provide you with the mathematical tools you will need to follow a master’s level
course in economic theory.