/sci/ - Science & Math

>>5914455
Nope. Please learn math from actual experts before wading into the murky depths of crackpottery.

>>5913792
Why'd you not take comb and graph theory? At undergrad level they're basically free credits. Also, some of the most beautiful and inventive proofs come from combinatorics.

As a very basic application, you can sometimes prove things about specific formal power series by interpreting them as generating series of certain objects. And I'm sure you can imagine why that might come in handy.

Also, I think Gowers wrote something like a combinatorialists apology. Google "gowers two cultures." Please consider giving it a read.

the video is legit

it's from a university and a MD and stuff

would it be a bad idea to invest most of your unused money in silver or other semi-precious metals?

i don't really trust my dollars anymore.

>>5830598
True story, I developed a mental illness that I recovered out of, while doing a chemistry degree.

I obtained said chemistry degree, and not the kiddie tier chemistry either, but with a specialization in Inorganic and Computational Chemistry.

I had mediocre grades though, so I'm moving into business now, but it helped my confidence alot.

Schizophrenia doesn't prevent you from doing anything, it just adds some resistance to what your doing.

An engineering degree, with the exception of maybe chemical or electrical, is comparable in intensity to a chemistry or physics degree at full load.

You can do it if you apply yourself and just shut out social events. Which should be easy, since

1. Schizos tend not to like people; I didn't, and still don't, even though I recovered out of it.
2. You can spend your entire time studying if people avoid you because they think your crazy.

>>5765580
are you me?
I was just gonna make a thread about STDs.

>>5732335
Because when F = ma, then the Euler-Lagrange equations are satisfied.

>>5732382
Logic is a branch of logic. As is math.

>>5732391
Well then I'm probably good to go, unless there's some physics background I'm missing. Would you happen to know what physics I'd need (on top of the usual undergrad stuff).

Question: If I find an exact solution for a PDE which satisifies my boundary conditions, does that mean my solution is the only one satisfying those? Is there a uniqueness theorem for PDEs?

>>5701615
Time to read off a sizable chunk of my bookshelf, then.

Linear algebra:
- Axler, "Linear Algebra Done Right"

General algebra:
- Artin, "Algebra"
- Isaacs, "Algebra"
- Lang, "Algebra"

Analysis:
- Spivak, "Calculus"
- Rudin, "Principles of Mathematical Analysis"
- Rudin, "Real and Complex Analysis"
- Gamelin, "Complex Analysis"

Commutative algebra:
- Atiyah & MacDonald, "Introduction to Commutative Algebra"
- Eisenbud, "Commutative Algebra with a View Toward Algebraic Geometry"

Algebraic geometry:
- Smith et al., "An Invitation to Algebraic Geometry"
- Shafarevich, "Basic Algebraic Geometry"
- Harris, "Algebraic Geometry"
- Hartshorne, "Algebraic Geometry"
- Eisenbud & Harris, "The Geometry of Schemes"
- Vakil's "Foundations of Algebraic Geometry" notes: http://math.stanford.edu/~vakil/216blog/

Number theory:
- Serre, "A Course in Arithmetic"
- Ireland & Rosen, "A Classical Introduction to Modern Number Theory"

Also, lots of good recommendations here:
http://www.ocf.berkeley.edu/~abhishek/chicmath.htm

>>5701304
Yeah, Ellenberg seems like a great guy. Seems he has quite a good reputation, since like half the people I talk to about UW-Madison mention him.

>>5701273
...I think you got that backwards. I live in the States. Guessing you're British, then?

>>5701280
I'm going to UW-Madison. (By the way, if you don't mind telling me where you're going next year, I put a throwaway address in the email field.)

>>5701233
The answer OP gave here >>5701253 is also completely true of me.

Except I wouldn't use the phrase "sticky-wicket". And I don't really care if someone figures out who I am.

>>5701214
Right, good point. That ties in nicely to a few nice classes of objects where maps are injective if and only if they're surjective; finite sets of the same size (and therefore also finite groups, rings, fields, etc. of the same size) and finite-dimensional vector spaces of the same dimension are the two best-known examples.

There's also the closely related fact that distance-preserving maps from a compact metric space to itself are bijective. These three cases are discussed in depth (albeit in an extremely abstract way) here:
http://golem.ph.utexas.edu/category/2011/12/the_eventual_image.html

>>5701201
Er... right, of course kernels make sense for arbitrary groups. Thanks for catching that. I've been working through Hartshorne this semester, so my mind's in the commutative realm, and I was thinking of the natural generalization to modules and other abelian categories.

Actually, for (arbitrary) groups, it seems like enough of a fragment of the generalization would work to still make sense for checking surjectivity. The problem is just that f(G) might not be a normal subgroup, but even so, we can look at the cardinality of the set of (left or right) cosets H/f(G), which is 1 if and only if the map is surjective.

>>5701181
Stated that generally? Not really. In more specific contexts, possibly: for example, if you're working with homomorphisms of abelian groups (or anything else where you have a reasonable notion of "kernel"), then to show a homomorphism is injective, it's enough to show that the kernel is zero, i.e., only zero gets mapped to zero.

Oh, by the way, I'll be checking this thread every now and then; I can answer some questions, too, though I probably don't know as much as OP about some topics.

>>5694771
Let me just mention another useful characterization of compactness: A topological space X is compact if and only if, for all topological spaces Y, the projection <span class="math">X \times Y \to Y[/spoiler] is a closed map (i.e., it maps closed subsets to closed subsets).

Here is a proof:
http://ncatlab.org/toddtrimble/published/Characterizations+of+compactness

The reason this is a nice characterization comes from algebraic geometry: the correct generalization of compactness is a "proper map", which is defined in essentially the same way, but using the tensor product (or technically, the scheme-theoretic product, which is locally the tensor product of rings) instead of the topological product. (Literal topological compactness is fairly useless in algebraic geometry, because the spectrum of a ring is *always* compact.)

>>5683255
Fun fact: Waiters have better memory than mathematicians.

I got 94 % on my first try btw.

>I'm a mathematician and a part time quant.

>>5683844
>4chan
>any board
>worksafe

lel

I wanted to make a post saying

>inb4 hidden variables

but I see I'm already too late

>>5606961
Gray, P. (2011). Psychology (6th ed.)

This is the book used in a course called "introduction and cognition part A: Introduction to Psychology". It's a first semester course, so the book is probably on or below your level.

>>5606952
You're not being very helpful. Have you really studied psychology?

@OP
You should look at course descriptions of some university. Usually literature is included.

Hang on for a bit, I'll check mine.

>>5603972
That's exactly the first reply to this thread. Thanks for playing though.