Reddit reviews Berkeley Problems in Mathematics (Problem Books in Mathematics)

http://www.amazon.com/Berkeley-Problems-Mathematics-Paulo-Souza/dp/0387008926

This book in conjunction with this book should keep you busy.

Consider using Anki for stuff you want to review periodically and already understand.

I always had a copy of the Springer book Berkeley Problems in Mathematics. It's definitely more work than play but there is 0 text...just 100 some odd pages of problems (all proofs) then the solutions to check yourself are totally separated in the back. You should be able to do it by the end of undergrad but the thing I really like about it is that for almost all of them there is a cute trick that makes the problem really short so if you are brute forcing it then stop and think more.

For some more Challenging problems, some of the old preliminary problems of the UC Berkeley are online here. Some of these have even been published as collected problem-books with solutions (amazon). If your local math-department has a library, they might have it available. I would definitely recommend checking this book out.

The problems usually do not require you to know more than some basic analysis, algebra, linear algebra and theory of differential equations, in order to understand them, but can sometimes be quite tricky to solve.

At least give the website a look. If the material is above your level of expertise (I don't quite know how far in your studies you are), I would recommend that you take a look at these problems sometime after you've got some more coursers under your belt. Solving problems like these is a great way of gaining working knowledge of the mathematics you will have learned.

*edit: Spelling (hopefully all errors have been corrected).

For differential geometry a great book is: [Analysis and Algebra on Differentiable Manifolds] (https://www.amazon.com/Analysis-Algebra-Differentiable-Manifolds-Mathematics/dp/9400793308/ref=sr_1_6?ie=UTF8&qid=1484591942&sr=8-6&keywords=problems+differential+geometry+and+manifolds+springer). It maybe doesn't have tremendous creativity required to solve the problems, but it'll give you lots of good practice.

For linear algebra and abstract, if you're not satisfied using Dummit and Foote (with easily accessible solutions online) or Lang Algebra (with harder to find solutions), Lang has some great exercises by the way, then I recommend the [Berkeley Problems in Mathematics book] (https://www.amazon.com/Berkeley-Problems-Mathematics-Problem-Books/dp/0387008926/ref=sr_1_sc_2?ie=UTF8&qid=1484591875&sr=8-2-spell&keywords=problems+in+abstracct+algebra).

Both of these books have complete solutions for problems and should be very useful for you.

Maybe because this collection has been long ago turned into a book: http://www.amazon.com/Berkeley-Problems-Mathematics-Paulo-Souza/dp/0387008926/

IAMNOTA math student ... but you can get this book Berkeley Problems in Mathematics which is decades of problems from their qualifying exam, and then try to learn those.