MATH 176: EXPLORATIONS IN TOPOLOGY AND ANALYSIS
The goal of this course is to explore the underpinnings of single- variable calculus, and to to develop some fundamental notions of topology in Euclidean space. The course will move towards proving theorems that are among the crowning jewels of these subjects: The fundamental theorems of calculus and the Brauer fixed-point theorem. It is intended for students who have had some exposure to calculus (AB or BC in high school), and would like to deepen their understanding of the subject. It will prepare them to continue with honors multivariable calculus, math 285. It can be seen as a continuation of Math 175, but more broadly it is a course for anyone interested to gain a deeper understanding of single-variable calculus.
The course will be taught in an IBL manner, and it will follow roughly the same format as Math 175.