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I notice this learning maths as an adult. A good intro to logic and proofs opened up a new world. After struggling with a proof, I came to the conclusion that I

by jwdunne 11y ago

I notice this learning maths as an adult. A good intro to logic and proofs opened up a new world. After struggling with a proof, I came to the conclusion that I needed to study the axioms I was obviously expected to know futher - most importantly, I wanted to. How did I want to study and understand them? By proof. I remember a similar course with programming, actually. One curiosity led to the next once I equipped myself with the tools to think and experiment with computers.

Jtsummers 11y ago
I will also say, and meant to mention in my original comment, good textbooks are beautiful things. Most textbooks by the time I got to HS (mid-1990s) were meh. And they seemed to be getting worse each year. Compared to the books my parents and previous generations experienced. (Specifically for math.) Older books tended to be small, concise and precise. Think Sipser's automata text, but for everything in math. Being a third generation mathematician certainly helped by providing me access to an older library of books than a lot of my high school and college peers realized were available.
- jwdunne 11y ago
  Thanks for the tip :) I'll explore that. Do you have any recommendations for textbooks to sink my teeth into?
  - Jtsummers 11y ago
    Unfortunately, not much. I was pondering that after my post. It's been a long time since I was a math student, and professionally it's had zero to do with my career. A lot of books ended up boxed up at my parents' home as I moved around a number of times right after college. I'll check my own home tonight to see what I still have, but my shelves these days are mostly filled with fiction, programming, RPG, and history books. EDIT: Off the top of my head, for CS: Introduction to Algorithms: https://mitpress.mit.edu/books/introduction-algorithms https://mitpress.mit.edu/books/introduction-algorithms Introduction to the Theory of Computation: http://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X http://www.amazon.com/Introduction-Theory-Computation-Michae... Math: Calculus Made Easy: http://www.amazon.com/gp/product/0312185480?ref_=cm_lmf_tit_5 http://www.amazon.com/gp/product/0312185480?ref_=cm_lmf_tit_... - I'm really not sure how good this one is for a beginner, I picked it up while assisting my sister in refreshing her calculus skills for grad school (Aerospace Engineering) I can't remember the algebra and geometry textbooks (my dad's or my grandfather's) that I used, in addition to the assigned text, in high school. Anything by Knuth. Seriously, one summer a professor and I just picked up copies of Concrete Mathematics and worked through large portions of it for fun. Technically I got some math credits for it, but it was really just because we wanted to. Actually, this one helped me a lot with understanding calculus. Somehow, up to that point while I knew calculus, may brain had never made the connection that integration was summation until I saw the discrete counterpart to continuous integration. I had a mechanical understanding, but no deep understanding until that moment.

by jwdunne 11y ago

Jtsummers 11y ago

I will also say, and meant to mention in my original comment, good textbooks are beautiful things. Most textbooks by the time I got to HS (mid-1990s) were meh. And they seemed to be getting worse each year. Compared to the books my parents and previous generations experienced. (Specifically for math.) Older books tended to be small, concise and precise. Think Sipser's automata text, but for everything in math. Being a third generation mathematician certainly helped by providing me access to an older library of books than a lot of my high school and college peers realized were available.

jwdunne 11y ago
Thanks for the tip :) I'll explore that. Do you have any recommendations for textbooks to sink my teeth into?
- Jtsummers 11y ago
  Unfortunately, not much. I was pondering that after my post. It's been a long time since I was a math student, and professionally it's had zero to do with my career. A lot of books ended up boxed up at my parents' home as I moved around a number of times right after college. I'll check my own home tonight to see what I still have, but my shelves these days are mostly filled with fiction, programming, RPG, and history books. EDIT: Off the top of my head, for CS: Introduction to Algorithms: https://mitpress.mit.edu/books/introduction-algorithms https://mitpress.mit.edu/books/introduction-algorithms Introduction to the Theory of Computation: http://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X http://www.amazon.com/Introduction-Theory-Computation-Michae... Math: Calculus Made Easy: http://www.amazon.com/gp/product/0312185480?ref_=cm_lmf_tit_5 http://www.amazon.com/gp/product/0312185480?ref_=cm_lmf_tit_... - I'm really not sure how good this one is for a beginner, I picked it up while assisting my sister in refreshing her calculus skills for grad school (Aerospace Engineering) I can't remember the algebra and geometry textbooks (my dad's or my grandfather's) that I used, in addition to the assigned text, in high school. Anything by Knuth. Seriously, one summer a professor and I just picked up copies of Concrete Mathematics and worked through large portions of it for fun. Technically I got some math credits for it, but it was really just because we wanted to. Actually, this one helped me a lot with understanding calculus. Somehow, up to that point while I knew calculus, may brain had never made the connection that integration was summation until I saw the discrete counterpart to continuous integration. I had a mechanical understanding, but no deep understanding until that moment.