modern foundations of mathematics

Youtube上由Richard Southwell讲述的一门课程。

主要目的是介绍「现代」的数学基础理论，从集合论和范畴论开始，过渡到类型论，以及目前很有前景的Homotopy Type Theory。

In this series we develop an understanding of the modern foundations of pure mathematics, starting from first principles. We start with intuitive ideas about set theory, and introduce notions from category theory, logic and type theory, until we are in a position to understand dependent type theory, and in particular, homotopy type theory, which promises to replace set theory as the foundation of modern mathematics. We also take an interest in computer science, and how to write computer programming languages to formalize mathematics.

第一部分：Introduction to Mathematics（集合论）

第二部分：Category Theory

第三部分：Universal Constructions

第四部分：Logic and Partially ordered sets（经典逻辑、偏序集、范畴之间的关系，Heyting Algebra）

第五部分：Intuitionistic Logic and Type Theory