Introduction to Topological Manifolds by John Lee (prereqs)

[FallenApple]

I'm interested in this subject. This is a graduate text and I believe the prereqs are mostly a math degree, which I somewhat have(B.S in Applied Math from a few years back). The thing is, I forgot details about things. For example, I know how to do an epsilon delta proof and can read one when presented, but I don't remember the particular theorems/definitions( uniform convergence, ratiotests etc), I remember the philosophy behind a vector space/subspace of linear algebra, but I don't remember all the details of factorizations of matricies, all the theorems etc.

Is it possible to study this book while just looking up the needed details on the side as I go along?

 

[Cruz Martinez]

Yes, it is definitely possible. I read much of this book and worked through a considerable portion of the problems before finishing my physics degree. It is pretty self contained, it even has an appendix with some prereq. results from set theory, metric spaces and group theory. The presentation of the material in the book is also really very good, it provides a lot of motivation for the theory.

 

[micromass]

I'm interested in this subject. This is a graduate text and I believe the prereqs are mostly a math degree, which I somewhat have(B.S in Applied Math from a few years back). The thing is, I forgot details about things. For example, I know how to do an epsilon delta proof and can read one when presented, but I don't remember the particular theorems/definitions( uniform convergence, ratiotests etc), I remember the philosophy behind a vector space/subspace of linear algebra, but I don't remember all the details of factorizations of matricies, all the theorems etc.

Is it possible to study this book while just looking up the needed details on the side as I go along?

Don't worry, you're fine. The book is extremely good, and the best thing is that it requires very very little prereqs. I have guided multiple people through this excellent book, most of which never had any formal proof-based math courses. Everything you need is detailed in the appendix which you should read first and should be pretty well-known to you. Don't make a mistake though, the book is not easy, it just has very little prereqs.

 

[FallenApple]

Don't worry, you're fine. The book is extremely good, and the best thing is that it requires very very little prereqs. I have guided multiple people through this excellent book, most of which never had any formal proof-based math courses. Everything you need is detailed in the appendix which you should read first and should be pretty well-known to you. Don't make a mistake though, the book is not easy, it just has very little prereqs.

Thanks. Do you have any suggestions on how I should pace myself? This is mostly for casual self study.

I don't want to put so much time that wouldn't be able to work/study other subjects. But at the same time, putting in very little daily time really wouldn't make it stick.

How hard is this compared to say, real analysis on the level of Ross?

 

[FallenApple]

Yes, it is definitely possible. I read much of this book and worked through a considerable portion of the problems before finishing my physics degree. It is pretty self contained, it even has an appendix with some prereq. results from set theory, metric spaces and group theory. The presentation of the material in the book is also really very good, it provides a lot of motivation for the theory.

Thanks for the input. How much time did take you to get through the book? Was it helpful for understanding physics that uses manifolds?