I apologize for asking this question since it has likely been asked around 100 times before, but I haven't found anything that quite suits me.
First, I wanted to revisit mathematics from the ground up (completely) because my mathematics education has been extremely hollow. I can solve problems but I take a long time because my foundations are essentially a fraction of what they should be. So I can work through for example baby Rudin (enough mathematical maturity) but I would take a lot longer than I should on parts because I don't know some of the elementary results readily, therefore I want to patch this up.
I kind of don't want to feel like I am bringing a exhausting miracle onto the paper that somehow is correct with the fraction of what I do know every time.
There are certain kinds of book styles I prefer which others tend to find very terse. In general there are 3 categories to these :
- Theorem-Proof books : State theorem, show proof.
- Problem books : Problems and Correct Solutions
- Encyclopedia/Reference/Axiom style books: What someone would call a reference of…
My personal interests are in Logic,Combinatorics, Topology,Geometry,Computation,Statistics,Probability,Analysis and Algebra.
I want to at least get a overly solid foundation ready to where it is appropriate to delve fully into any of the above areas.
The reason I don't want to use Khan (#2) for the above is because I prefer a more detailed book-based approach, I can't personally stand using videos.
Is there a better suited: book guide, series or sets of books for me?
Best Answer
I think your approach makes sense, especially when so many people suffer from the same problem now - fragmental mathematical knowledge. You might get a lot of book recommendations, and you'll need to process a lot of information - good luck!
Fortunately, such lists of books already exist - for example, this one looks comprehensive and sturdy.