What does /sci/ think about graph theory and combinatorics?

I hope to make it my field of study if I stay in academia

>>7992024
I think that is a kickass textbook.

Counting seems pretty hard and doesn't seem very useful once you get beyond the basics. Similar thoughts about graph theory desu.

I used to like these topics and other "discrete" math topics when I was undergrad, but now I see that differential geometry is way more interesting and useful.

I like it very much
but can't quite spend too much time learning it

Graph theory is probably my favourite branch of mathematics, although I'm not sure how I feel about combinatorics. I like some parts of combinatorics but not others.

It's a joke of "field" with no overarching themes and just a bunch of autists trying to get better estimates on things nobody cares about.

>>7993201
Sounds like most math beyond undergrad

Doing a PhD in graph, I love it but it's a hard field

>>7993208
Other fields have good stories. Combinatorics has a distinct lack of good stories.

>>7993232

Care to explain what you mean ? I don't understand what you are trying to say.

>>7993201
>with no overarching themes
this is what keeps me away from combinatorics and related fields like graph theory

they have cool problems but there doesn't seem to be a bigger theoretical framework to place everything in

I don't think any amount of study would make me feel like I "get" combinatorics in the same way I "get" something like group theory

>>7992024
What is there to graphs if you know Dijkstra?

>>7993280
What?

>>7993201
Graph theory is by no means a joke field. It's just that the fundamental underlying principles are very simple in nature (like Euler circuit requiring each vertex to have even # of edges). And the fact that it can be enhanced in certain ways (coloring edges, adding weights/directions) means some findings will have bearing on only a specific part of graph theory. I also think it's proven pretty applicable; though, I don't have a source for that.

>>7993307
was talking to a graduate student at my school who's specializing in graph theory and he says the folks at Google are pretty interested in people with an expertise in it. also a few profs at my school who use it for modelling biological phenomena, fluid dynamics, financial modelling, and other neat stuff. definitely a very vibrant and interesting field

>>7993316
Yea it's like a computer scientist's dream in terms of code-ability. Each node can simply be represented by its ID and an array of the other modes it's connected to. And I'd say, in contrast to the person I replied to, I find the lack of a clear arc fascinating. The next important proof in the field might relate to the reconstruction conjecture or it might be something extremely specific.

>>7993341
It's not just codability, but the fact that many of the problems you want to solve in CS are really graph problems, or can be transformed to a graph problem.

ITT: undegrad not knowing szemeredi regularity or the probabilistic method who think they know this field because they read about djikstra

>>7993201
>>7993268
I have this book by Aigner called Combinatorial Theory where he tries to build a general framework for combinatorics. I remember that when I first read it I thought that it lacked a lot of the fun of doing combinatorics (which is the simplicity of the basic principles).
Still, there is a lot of good stuff in there and it might be worth checking out

>>7993280
Why do you feel the need to comment when you are obviously completely ignorant about this field?

>>7993491
>szemeredi regularity

>In mathematics, the Szemerédi regularity lemma >states that every large enough graph can be >divided into subsets of about the same size so >that the edges between different subsets behave >almost randomly.

What is a 'large enough' graph and what does 'about the same size as' mean?

Also what does

>so that the edges between different subsets >behave almost randomly.

mean?

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166KB, 792x735px

>>7993598
>quotes Wikipedia
>text below quoted text immediately gives a concise elaboration and precise definition

Surely I'm having a bad day and my mood isn't good, but I really hate you guys.

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>>7993618
t-t-t-hanks. It is early in the morning and I didn't bother reading anything beyond the quote. my bad.

I'm a CS major and I'd like to explore graph teory beyond the basics. It seems to me that almost any problem can firstly be modeled as a graph

>>7993632
How much math have you done?

Anyway check out Diestel. There's a free online preview.

>>7993201

This.

Most mathematicians think combinatorics is boring because it lacks a main theory and has little interaction with the popular fields of mathematics. Personally, I find it interesting for optimization problems.

Oh, and people who study combinatorics are often WEIRD AS FUCK

>>7993477
>>7993341
>>7993316

Do you know which areas of graph theory Google was most interested in?

>>7994129
you probably mean most undergrads and not most professional mathematicians

non-trivial combinatorics show up everywhere in mathematics: geometry, algebra, number theory, etc.

once you get past early years of study you should quickly learn not to discriminate against certain fields

>>7992024
Infinitary combinatorics, which is actually more a branch of set theory than of combinatorics, is pretty fascinating, and the provisional existences of cardinals with certain combinatorial properties have huge implications to the universe of mathematics in often very unexpected ways that seem to have nothing to do with combinatorial principles.

Examples: Erdős cardinals, Ramsey cardinals

>>7992024
I don't like combinatorica since the moment I almost failed my Discrete Maths exam thanks to Polya theorem.

my calc 3 professor at the community college I am attending has a PHD in math(his thesis was something on graph theory) from auburn university and has a masters from USC.

Wonder why he works as a CC professor

>>7994915

Probably because academia is super-saturated. It's hard to get a job as a professor at a university. There's simply too many people for how many positions there are.

>>7994915
because its easy and the money is decent.

big 4 years work their faculty hard.

my physics professor had his PhD from Cornell and he was teaching sum of forces and free body diagrams.

he taught 4 hours a day, 6 on days he had office hours. aside from that, he was never there. grading papers took him less than 30 minutes.

he also didn't get drug tested there and i'm pretty sure he smoked weed every now and then.

all that for 75k$ a year? i can see it.