Part V: Theorems and Problems.

A chapter of the book "The Princeton Companion to Mathematics," edited by Timothy Gowers, is presented. It discusses several mathematical theorems including Cauchy's Theorem, Dirichlet's Theorem and Ergodic Theorems. Fixed Point Theorems including Brouwer's Fixed Point Theorem and Infinite-Dimensional Fixed Point Theorem and the Fundamental Theorem of Algebra, are discussed.