Hello from Michael Litzky
Hi folks. Here's my little intro.
I'm an odd combination of left and right brain. I make my living as a math and science tutor but I'm also a storyteller and writer. About fifteen years ago I got interested and started learning math and science from books. I've gone through multi-variable calculus using Stewart's book and thought I was ready to study tensors. But I discovered I really need Linear Algebra first and before that, I needed to firm up my grounding. So I'm reading Tom Apostol's Calculus book and working the exercises.
I'd breezed through the proofs in I 3.3 and I 3.5 (proofs of the field and order axioms) and hit a wall with I 3.12 (proofs of real number properties). My brain couldn't seem to make the links with the axioms and theorems so far. When I found a proof for one of the exercises online, it was complicated enough that, though I could follow it, I knew I couldn't have thought of it. And it seemed to make an unjustified assumption, but I couldn't be sure of that either.
Alright, I said, I've gotten good at Euclidian Geometric proofs through lots of practice and tutoring it for several years. I just need some more guidance (and I need to do about a hundred proofs) and I can get good (I hope) at these proofs too. But there didn't seem to be any books on doing proofs. Math books always just seem to assume that you're already good at it.
Well, in this forum I found a post by someone in my exact situation (in fact, I may reply to that thread and say, hey, how's it going two years later?). There were also some links to resources for getting better at proofs. So I have lots of material to explore.
What I hope to get from this forum: I'd like to post a few proofs I came up with and see if I'm missing anything. If I'm completely stuck, I'd like to ask for guidance. I'd also like to cast off this feeling that I'm studying all this completely on my own. When I'm floundering, it will be nice to connect with others who are working on the same thing.
You can learn more about me, if you want, at my website(s):
Tutoring: Michael Litzky, Friendly Math and Science Tutor
Storytelling: Wondrous Tales: Stories for Young and Old
Writing: Fiction and More | by Michael Litzky