/sci/ - Science & Math

[Anonymous No.5392221]

What should I learn over the winter break in mathematics?

I'm a junior undergraduate math major. I've already taken some abstract algebra and real analysis courses so I'm up for anything accessible at this level. It could be something fun and out of the way, or something fundamental for a mathematician to know.

Thanks for suggestions.

[Anonymous No.5392231]

Maybe combinatorics and/or graph theory?

[Anonymous No.5392245]

>>5392231

I second some sort of discrete combinatorics type thing.

[Anonymous No.5392250]

topology son.

[Anonymous No.5392252]

Modular forms.

[Anonymous No.5392254]

>>5392250
Taking it next semester and I've already previewed it a little.

[Anonymous No.5392288]

>>5392254
I'm in your exact situation. I took intro abstract algebra/real analysis last semester, then intro topology is coming in the spring. Where do you go to school?

[Anonymous No.5392630]

>>5392288
A state school

[Anonymous No.5392634]

>I'm a junior undergraduate math major. I've already taken some abstract algebra and real analysis courses
WTF, are you me?

[Anonymous No.5392652]

model theory
differential geometry
algebraic geometry

[Anonymous No.5392660]

fun and out of the way: generating functions.
http://www.math.upenn.edu/~wilf/DownldGF.html

[Anonymous No.5392676]

Time wait switches also allow pubs to activate heating only what time the outdoor corner is in exploit. These have been in operation in support of many living, used in take away frequented areas or those where entry and door is at different points. During the last only some time including Firefly full seasons a focus on energy efficiency, these have been revamped. Gone are the pneumatic timers that little by little unconfined earlier than cutting the rule, currently they are electronic and flng a concern intended instead of pubs and clubs indoors, as they seek to combat stale odors, which were previously masked by tobacco smoke. Food odors coming as of the kitchen, as well as smells as of toilets and stale beer spilled onto carpets, now need to be extruded out of the building, as cigarette smoke no longer masks these pungent aromas.

[Anonymous No.5392708]

>>5392660
>download gf
I wish it were so simple ;_;

[Anonymous No.5392870]

>>5392221
I'm a senior undergrad mathematics major. You could do what I'm doing and study Atiyah–MacDonald. Commutative algebra is pretty fundamental if you're going to do research in algebra, especially algebraic geometry. (It's also fundamental for me not getting killed by Hartshorne's "Algebraic Geometry" next semester.)

Or you could just pick a chapter of Lang's "Algebra", read it, and do some of the exercises. Most everything in there is fairly fundamental. (Except, his chapter on algebraic spaces is kind of weird, so maybe not that one.)

Maybe Lie groups? Those are interesting, and you could learn the basic stuff about them pretty quickly. My class used Kirillov's book, which is a good introduction; maybe you can find it somewhere.

Or how about number theory? Plenty of stuff to look at there.

[Anonymous No.5392882]

>>5392870
For now I'm reading through some of Milne's notes on Group Theory which is a nice review and some new concepts (since it's graduate level). I eventually would like to study some Algebraic Geometry though, so I'm going to need to find a good source of Commutative Algebra. That's mostly rings and modules, right? Do you have any recommendations?

[Anonymous No.5392904]

>>5392882
Milne's notes are all good, so you can look at his stuff on other topics, too.

For commutative algebra, Atiyah–MacDonald's "Introduction to Commutative Algebra" is the standard way of learning it. It's an exercise book — over 200 exercises in about 120 pages, light on exposition — so you learn most of the material by doing lots of problems. And yes, it's the theory of commutative rings and modules.

Matsumura's "Commutative Ring Theory" and Eisenbud's "Commutative Algebra with a View Toward Algebraic Geometry" are both very good references for learning commutative algebra at a more advanced level.

Check out this bibliography: http://www.ocf.berkeley.edu/~abhishek/chicmath.htm
Lots of good book recommendations there, including for commutative algebra.

[Anonymous No.5392916]

Physicist here

Are you thinking of sticking with pure math or do you plan on making the switch to applied at some point?

Just wondering.

[Anonymous No.5392932]

If you actually want a real job learn some numerical analysis.

[Anonymous No.5392945]

>>5392932

or stats

[Anonymous No.5392970]

>>5392916
I like pure math but I should probably be familiar with both.

[Anonymous No.5392982]

Category Theory.

[Anonymous No.5393031]

>>5392904
I've always been apprehensive about ring theory for some reason, but I have to face it eventually.

A lot of these free group and presentation proofs keep passing over my head. Should I try reading an easier source first or keep rereading Milne til I get it?

[Anonymous No.5393067]

>>5392870
>recommending reading Lang
wtf are you doing

[Anonymous No.5393111]

>>5393067
What? I've learned a lot by reading Lang. It's definitely not an introductory book, but it's quite good once you have enough background in abstract algebra.

>>5393031
I don't think the stuff involving free groups and presentations is all that essential for later things. If you're spending too long on it, maybe just move onto something else and come back to it later when you're more comfortable with groups. That's what I'd do, at least.

Also, if it's the stuff on universal properties you're having trouble with, Lang's explanation of universal properties in chapter 1 of "Algebra" really helped clarify things for me.

[Anonymous No.5393130]

>>5393111
Nobody reads Lang to learn. It's a reference book. When you're learning for the first time you want exercises appropriate to your level, and even if Lang's explanations aren't bad (although a bit short), the exercises are not intended for first time learners.

[Anonymous No.5393159]

>>5393130
I agree that it's not good for first learning a topic, but it's great for deepening your understanding. That counts as learning, too.

Anyway, point taken: OP, if you're going to read Lang's "Algebra", read a chapter on something where you're already comfortable with the basics.

[Anonymous No.5393246]

>>5392630
which state school? same with me.