What is mathematics?
The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not real understanding or greater intellectual independence. The new edition of this classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. "Lucid... easily understandable".--Albert Einstein. 301 linecuts.
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- First impression from this list is that Russia has a lot of mathematicians!
From the list, I have only read What is Mathematics? by Courant, which is a well-known and excellent book. I’d add Princeton Companion to Mathematics as a more advanced version, and Mathematical Methods in the Physical Sciences by Mary Boas as a more detailed alternative to What is Mathematics, to the list. Other titles on the list, such as those on probability or linear algebra, are perhaps less well-known.
- Thank you so much for reading that paper and writing this comment.
There definitely are resources that I can recommend. Can't do this at the moment (work awaits!), but will come back to this in the evening.
One book that did a lot for me was What Is Mathematics?[1] by Courant and Robbins. Godel, Escher, Bach[2], while not strictly a math book (and not a book I actually finished reading), was another. These would be my go-to recommendations without thinking much.
There are also many more playful mathematics books that might be an even better fit for what you want, but I'd need to go through my bookshelf to pick some.
> It wasn't until after collage that I stumbled across some gifs showing how/why various formulas in geometry are what they are, and I was really upset that those types of things weren't shown in school.
I know, right? Me too.
BTW, if you have ever stumbled into this one:
https://www.reddit.com/r/math/comments/g15ei/tan_demystified...
...I made it for that exact reason. I need to come back to this stuff.
- I suggest starting with "What is Mathematics?" by Richard Courant (a book, not an online course). It has an excellent overview of mathematics for a young person who one day may want to become a mathematician. Later, it depends on which part of mathematics one loves the most.
- What is Mathematics by Courant and Robbins is surprisingly good. For something a little more specific Pinter's A Book of Abstract Algebra would fit the bill.
- I know Calculus so Strogatz's Infinite Powers created no interest in me. On the other hand What is Mathematics by Courant and Robbins was a delightful read.
Similarly I have only read a part of Road to Reality by Penrose and it was also fascinating.
Which popular non-fiction books in your subject domain did you like and dislike?
- Recursion is basically the other side of the coin for mathematical induction. I would suggest that you learn a functional programming language and mathematical induction.
You can try out: How to Design Programs at https://htdp.org/ if you want to learn more about how recursion is used in programming and where.
For mathematical induction you make read:
1. What is Mathematics by Courant and Robbins
2. Introduction to Mathematical Thinking by Keith Devlin
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