I'm aware that this question has been asked several times, but I have specific questions hence why I'm asking again.
I began to appreciate the beauty of mathematics when I glossed over the Fundamental theorem of calculus while taking a Calculus II course. The more I come across mathematical literature the more interested I become in learning it. I'd like to add that I enjoy self studying many different subjects (Physics, Chemistry, History, etc.) and it never feels forced. Its something that is genuinely enjoyable. However as much as mathematics interests me I find it hard to motivate myself to learn by reading books. My guess it that more so than many other subjects mathematical writing is incredibly dense.
Typical answers to this question usually result in people providing a list of topics to study, and perhaps a list of books to complement that. So I know what my entry point to this journey should be. Given my background, I would begin by learning Calculus with theory. After reading various similar questions these were the three names I heard the most; Spivak, Apostol, and Courant.
Spivak's writing was by far the most pleasant and I was able to acquire a copy of this book from a friend. However I also found that I felt that a lot information was omitted from each chapter and the reader was expected to fill in the gaps to be able to do the exercises. This is as instructive as it is time consuming. I'm willing to invest the time to self study, but the ratio of extra understanding gained of the subject to the extra time spent to understand just doesn't seem very efficient. Just my opinion. At a later point I may decide to go through Spivak after learning more about mathematics.
Apostol's book seemed right up my alley, and I found that I wanted to keep reading it (I found a preview of the first chapter online). Many people said of the three Apostol was the most dry. That may be true but I felt it had a good balance of being succinct, explaining the subject manner in a rigorous manner, while still making the subject matter feel intuitive. Unfortunately I could not find a friend with a copy of this book, the book is ridiculously expensive and there was no good copy available online.
Courant is the one I attempted to go through most recently. This was the book recommended for studying Applied Math and after going through the first chapter I can see why. I personally didn't like this book very much just because of how verbose it was. What took a whole paragraph could have been shortened to a sentence or two and I found it to be a chore to get through.
So my list of questions becomes the following:
- How do you develop and maintain the motivation to self study mathematics?
- If I were to read a book on Algorithms it becomes immediately applicable because I can just start by implementing that Algorithm in a language. Physics is immediately relevant being that physics is a natural science; I can read, do practice problems and even create physics simulations using code. But what approach should I take for math? I was planning to go about it by, reading, doing problems, and repeat the process, but I feel this is just setting myself up to lose interest in the subject.
- Lastly, what book should I start with? Alternatives to the books I mentioned would be great. A cross between Spivak and Apostol would make for the perfect introduction to calculus I think.