Self-Learning Geometry

Question

I'm an undergraduate senior wondering where he should start in learning geometry. My university unfortunately offers no such course. Should i begin with riemann geometry or differential geometry and can you recommend a textbook. I have taken 2 semesters of real analysis and algebra.

Answer 1

With the courses you have done, you will be able to do differential geometry and then learn topology along side it.

There are many resources avaliable to your disposal on OpenCourseWare, sponsored by MIT.

Answer 2

I learnt differential geometry from Pressley's Elementary Differential Geometry, and I highly recommend it. It's well-written and not too terse, and has good exercises with solutions. The only real drawback is that it is mainly focused on 2 and 3 dimensions, so if what you're mostly interested in is generalising to higher dimensions, then it's probably not for you. However, understanding the material in this book would also help you in understanding generalisations to higher dimensions.