Actually, something I thought was cool. Mapping the interval [0,1)⊂ℝ into the unit 1sphere S1⊂ℂ2 with the exponential function as such a(s)=e2πis. So this is a continuous bijective function, but its not a homeomorphism between [0,1) and S1⊂ℂ2 (its image space). Wait! What!? Does it make...
Well, I now find myself in similar circumstances. I want a textbook on the most general geometric objects possible, but I don't know how much more general you can get then Banach manifolds. I guess the algebraic stuff?
I hated the epsilons and deltas. I figured that was sort of my right of passage to learning the higher math. But, I'm not it for the theorems, I'm more interested in the philosophical aspects of math. So I was never really moved by any undergrad topics.
But, when I read that manifolds can be...
What does it mean when math text authors use the word "pathological"?
I have an example right in front of me in fact, but I'm sure you have seen this word before. I've seen it in a few other textbooks, and I'm pretty sure those books were also grad level math related subjects, just can't recall...
It's been a long time since I had to open up R and do some calculations, so my memory is a little bit rusty in statistical modeling. But I was just watching a review of the new Silent Hill HD Collection, that is ostensibly an HD remake of two older Silent Hill games. Of course this is but one HD...
A course in modern mathematical physics: groups, hilbert space, and differential geometry
I've only borrowed it from my library and read sections, but its pretty good. I'm going to buy it soon.
I thought this was kind of funny: in Lee's Intro to Topological Manifolds on page 2 there is a diagram of space curves. Just a couple of squiggly little R3 lines. Just seems like a retarded waste of space to me. But so far as I've gotten in this book, there are too many diagrams, many just...
Definitely not a textbook. If you went through 1,000s of math/phys books, paraphrasingly extracted all the little side notes, motivations, informal comments on the significance/implication of some theorem or formula, historical notes, and other bodies of information that's more expositional...