Concise texts for studying and overviewing mathematics with the goal of applying these concepts to physics

Question

First of all, I apologize if this is not the place to ask such questions.

Background

I am trying to study mathematics in my free time, but I find it very time-consuming. Don't get me wrong, I am very willing to put in the effort, but I find it very hard to sit down to do only $10$ pages a day of a $600$-page Calculus 1 textbook for example. I am planning to study analysis, algebra, differential geometry and topology for physics which doesn't relate to what I am currently studying. I already have somewhat of a good idea about all of these but I just want a very brief text to study from.

For example, let's say I am studying Calculus 1, why bother with distance, velocity and time applications, when you can just tell me that we want to calculate the slope at a point and we do this by approaching it from a secant line. And for integrals, we just do Riemann sums. Then for infinite series, we do partial sums and convergence tests and we are done. This would take no more than $50$ pages and I can already move to Calculus 2.

Question

So to make my question clear, I want to know whether there are concise, short texts (that just directly talk about the ideas with derivations of the different theorems etc) for the subjects I mentioned.

Thank you in advance.

Answer 1

"All the Mathematics you missed [but need to know for Graduate School]" by Thomas Garrity

This book is an excellent resource that isn't focused on any particular areas of mathematics. It's designed to fill in any knowledge gaps when bridging from an undergraduate to a graduate course. The idea is just to give an overview of the key ideas in many of the big areas studied as an undergraduate. For example, the book covers areas such as topology, complex analysis, and differential equations. Of course, you should bear in mind the fact that the course is targeted at students who have completed their undergraduate studies. The author doesn't expect you to have studied a course on all of the areas he writes about, but there is a certain level of general mathematical understanding and pacing that might make the book more challenging for those who aren't part of the target audience.