/mg/

Anime is maths

9548918
see

This is an off-topic post. Discuss math in the math thread

Any recommendations on how to get into differential geometry?

Math discussion belongs in /mg/. See

>Any recommendations on how to get into differential geometry?
Spivak volumes 1 through 5

Reminder to use projective geometry.
[math][t^{2}-1 : 2t : t^{2}+1 ] = \left[ \frac{ t^{2}-1}{t^{2}+1} : \frac{2t}{t^{2}+1} : 1 \right][/math]
gives a parametrization of the unit circle in affine co-ordinates using rational functions, [math]\alpha : \mathbb{R}\to S^{1} = Z_{aff}(x^{2}+y^{2}-1)[/math] by [math] \alpha(t) = (\frac{ t^{2}-1}{t^{2}+1} , \frac{2t}{t^{2}+1})[/math], which hits all points except (1,0).

Math discussion belongs solely in /mg/. See

>Are any of Wildberger's criticisms actually valid?
They're more of a Bishop Berkeley style critique then some kind of Edward Nelson proof. Whether this is "valid" to you I have no idea.

see

Also, by the same reasoning one uses to develop the rational parameterization of the circle, one can solve the age old problem of generating Pythagorean triples. [math]x^{2} + y^{2} = z^{2}[/math], [math]x,y,z\in \mathbb{Q}[/math] has the form [math](x,y,z) = \lambda(t^{2}-1,2t,t^{2}+1)[/math]. If we let [math]t=\frac{a}{b}\in\mathbb{Z}[/math] (with no common factors) we get
[math][x:y:z] = [\frac{a^{2}}{b^{2}}-1 : \frac{2a}{b} : \frac{a^{2}}{b^{2}}+1] = [a^{2}-b^{2} : 2ab : a^{2}+b^{2}][/math]. Thus all integer solutions to [math]x^{2} + y^{2} = z^{2}[/math], have form [math](x,y,z) = c(a^{2}-b^{2},2ab,a^{2}+b^{2})[/math], for integers, [math]a,b,c[/math] Letting b=c=1 and a=2 you see you get (3,4,5), etc, etc.

Thanks, I'll take a look.

How the heck do I visualize symmetric bilinear forms?

Looking for a Number Theory text. Does it matter if you start with analytic or algebraic? Should I be looking for a text that incorporates both, or neither?

What's your background? Have you already had any experience with elementary number theory?

>looking for a [X] text
buy some dover shit it's dirt cheap

I've read Epp's "Discrete Mathematics and Applications", and perused Lovasz's lectures notes and text "Discrete Mathematics: Elementary and Beyond" as well as "How to Prove It". I remember working with Peano's axioms from Terry Tao's "Analysis 1".

But no, I haven't read a cover to cover text on explicitly number theory. Sorry if this response was dumb, I don't know number theory so I don't know if these will cover my bases appropriately. Also I've yet to work through an Abstract Algebra text, but worked partially through Valenza's introductory LA text.

I'm going to pirate it anyway, so price doesn't matter. Plus my local library system is excellent.

I need to learn lie groups and diff geometry and don't know were to start, or what path to take. I'm reading Lee smooth manifolds, but it seems he assumes a lot of previous knowledge.