Fall 2019 MATH 215A 001 LEC

Prerequisites: fluency in basic abstract algebra and point-set topology + appropriate level of "mathematical maturity". Experience from Math 214 could be useful.   Instructions for undergraduate students to request an enrollment permission can be found here:  https://tinyurl.com/F19GradEnrollPolicies 

Description: In this first semester of the Algebraic Topology sequence, we will follow the book "Homotopical topology" by A. Fomenko and D. Fuchs. The book is freely available in electronic form to UC Berkeley library patrons. The main difference of this text from Hatcher's (usually used for this course) is that it begins with homotopy groups, and introduces (co)homology only afterwards, mostly as a tool for computing the former. This seems conceptually more appropriate.  

The plan is to cover Introduction, Chapter 1, and the most of Chapter 2 - which means we will move quickly. To help with digesting the fair amount of material, I plan, if there is enough interest, to open a seminar which can function as both discussion section and office hours. 

I recommend those who plan to take this course to check their readiness by trying to read "Introduction" in advance, and to do exercises from it.

Also, you need to be willing to abandon the familiar mathematical environment, and immerse into some alien extra-terrestial universe (depicted by Fomenko's drawings found in the book) from which there might be no return.          

Office: 701 Evans

Office Hours: 

Required Text: see description above

Recommended Reading: yes, it is highly recommended

Grading: Letter grade.

Homework: yes

Course Webpage:  TBD