What are your goals? What are your constraints? This is off-topic, but without those, we can’t give much advice anyways.
EDIT: Here is some generic advice.
Buy a copy of the Princeton Companion to Mathematics. It will serve you well. In particular, it will give you a good global understanding of math and how topics inter-relate. If you don’t know what you are interested in, this book is a good place to learn.
If you want a technical understanding, buy a couple Dover books on vital topics like algebra or analysis. Work through them a page or two at a time, checking you remember definitions and theorems after you read. Do the problems. Not every single one, but enough that the material is actually sinking in. Fraliegh’s First course in abstract algebra happens to have exemplary exercises.
When taking classes, the professor matters more for how interesting it is than the subject. Unless you need that particular subject, find out who is engaging and motivates their material well.
Strongly agree that anyone who’s seriously interested in mathematics should read the Princeton Companion. Until you do something like this, your impression of what parts of mathematics look cool and interesting is largely determined by what parts of mathematics you’ve heard about.
What are your goals? What are your constraints? This is off-topic, but without those, we can’t give much advice anyways.
EDIT: Here is some generic advice.
Buy a copy of the Princeton Companion to Mathematics. It will serve you well. In particular, it will give you a good global understanding of math and how topics inter-relate. If you don’t know what you are interested in, this book is a good place to learn.
If you want a technical understanding, buy a couple Dover books on vital topics like algebra or analysis. Work through them a page or two at a time, checking you remember definitions and theorems after you read. Do the problems. Not every single one, but enough that the material is actually sinking in. Fraliegh’s First course in abstract algebra happens to have exemplary exercises.
When taking classes, the professor matters more for how interesting it is than the subject. Unless you need that particular subject, find out who is engaging and motivates their material well.
Strongly agree that anyone who’s seriously interested in mathematics should read the Princeton Companion. Until you do something like this, your impression of what parts of mathematics look cool and interesting is largely determined by what parts of mathematics you’ve heard about.