What's your favorite area of math?
Mine is graph theory.
>>7925329
Same. What's your favourite area of graph theory?
>>7925541
Math
>>7925541
The nodes
>>7925541
I like algorithms (especially combinatorial optimization) and I'm kinda fond of coloring
>>7925670
You seem to know graph theory well. What resources do you recommend?
>>7925329
>graph theory
>abstract algebra
>number theory
>synthetic geometry
>category theory
>topology
in about that order
>>7925677
Are you undergrad? Grad? If grad, what kind of stuff did you study to get to where you are? Did you do much stuff on non-combinatorial optimization? Or much stuff on integer/linear/non-linear/convex/quadratic/whatever-the-fuck programming? What kind of optimization stuff have you done? Was it more exact-value, or was it more approximation-schemes for hard problems?
>>7925689
Undergrad. I'm pretty babby tier so I can't really help much.
>>7925693
Oh. I'm undergrad as well and haven't taken a dedicated optimization course (let alone a combinatorial one..) so I was wondering what kind of stuff I should learn. Currently I've done like 3 graph theory courses in the math dept and 3 algorithms/graph algorithms courses (were about 30%, 50% and 100% graph theory respectively, rest other algorithm stuff) in the CS dept. I've done linear algebra/differential equations/vector calc, but I haven't taken any dedicated optimization things. Not sure what stuff I should be studying if I ever consider doing graph theory/combinatorial optimzation for grad school.
Differential geometry and dynamics.
>>7925708
Not him, but check this out:
https://en.wikipedia.org/wiki/Courcelle%27s_theorem
>In the study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth.[1][2][3] The result was first proved by Bruno Courcelle in 1990[4] and independently rediscovered by Borie, Parker & Tovey (1992).[5] It is considered the archetype of algorithmic meta-theorems.[6][7]
I find optimization (in the "programming" sense) boring and I'm not really sure how it would relate to graph theory, so I can't help you there.
>>7925715
>It is NP-complete to determine whether a given graph G has treewidth at most a given variable k
>>7925715
>I find optimization (in the "programming" sense) boring and I'm not really sure how it would relate to graph theory
Mostly finding better algorithms (in the asymptotic sense) and seeing whether you can decide or figure out certain properties of graphs (like whether you can colour them in k-colours, whether they have another graph as a minor, how connected they are, etc). Since a lot of problems like independent set, dominating set, colouring, etc are NP-hard, usually people try and find certain classes of graphs (bipartite, interval, planar, chordal, trees, cayley graphs, etc) where certain things can be found or decided in polynomial time. I guess that's what you meant by "programming", right?
>>7925329
I like numbers
>>7925741
No, what you just iterated sounds like simply new classes of graphs. By "programming" I meant optimization in the strict algebraic/linear sense, where you essentially have a pseudo-piecewise function and are trying to find local/global minima/maxima.
>>7925767
Oh, derp, I interpreted programming as algorithms since you put it in quotes, rather than programming in the vein of linear/etc programming.
That kind of stuff is of relevance in combinatorial optimzation though, since a lot of problems in it can be restated as a ___ programming solution. Pretty much any problem like max indep set, min dominating set, min vertex cover, etc can be stated as an integer programming problem, and you can also often state them as a linear or quadratic programming problem, and then take the output and process it for approximation schemes, since LP is like O(n^2) or something whereas IP is NP-hard.
>No, what you just iterated sounds like simply new classes of graphs
I was more talking about looking at existing classes of graphs and coming up with efficient (polytime) algorithms for problems on them, like how you can trivially minimally colour a bipartite graph in linear time, whereas in general it's NP-hard, although I guess that's an awful example since that's kind of what the definition of bipartite is. I guess a better example might be like how you can do lots of things like independent set on chordal graphs or something, when their classification has to do with cycles (although I guess the PEO definition has to do with cliques, which are kind of the opposite of independent sets...)
>>7925787
Hmm.. interesting. Well my link (Courcelle's Theorem) demonstrates something that I feel would be a great starting point for finding new classes of graphs that can be computed on in newly found ways. Personally I'm not very familiar with "higher-order" logics like 2nd-order logic, but I feel that the fields of Type Theory (which is generalized logic) and Combinatorics (which includes graph theory) are quickly converging into something very interesting.
>>7925787
>>7925796
Also undergrad; my undergraduate institution (top 5 in the US) has only offered two courses on graph theory in my time here. Where do you guys study that you have this many classes dedicated to graph theory?
I'm also interested in graph theory; however, formal graph theory tends to seem too woo-woo hand-wavy with the fancy names for simple concepts.
differential geometry is pretty neat
>>7925926
We only offer two here normally, but there was one special topics in discrete math course that got offered in a graph theory topic, although I've only seen that happen twice (different graph topics too, never seems to be the same ever) in the last 8 years, usually it gets offered in other areas.
Operational research has the coolest, funnest problems, I find.
Optimisation (variation sl calculus or other methods) is also a very satisfying set of problems to be able to solve.
>>7926007
Yes, I agree that it is "fun" but the naming conventions for Ops research is straight BS.
Optimization is fun, no matter the subfield
algebraic pretentious brainwank theory
>>7925756
Hiii wingding samurai
Number Theory
Can someone give me some literature or just references where to look on algebraic/category-theoretic graph theory?
>>7925329
Set theory.
>>7927636
Cantor's diagonal argument is pretty beautiful, I must admit.
>>7925329
I like calculus of variation.
>>7925329
stochastic calculus
It's the only math I'm really good at, on top of econometrics (statistics).
Specifically I like studying jump processes and their occurrence in financial markets (option theory).
>>7928314
This
numerical analysis
>>7928355
>analysis
Mcfucking kill yourself
Type theory.
>>7928371
Norman go to bed.
>>7929501
Nice beard and hair line for an old hag that into bird porn. If he wouldn't look as scared as a deer, he could pull of a sexy Connes.
Regarding the thread, it's hard for me to find a subject I don't like. Probably the non-analytic aspects of number theory is what I find least appealing.
you need a theory to tell you how to put dots on a screen op?
: /
>>7929513
Who's this semen demon?
>>7927636
I like finding other set theorists on /sci/. What areas are you into?
>>7929549
Alain Connes
>>7925329
Probability & Statistics
>>7929581
I've not learned enough to make preferences in areas.
I'm not a mathematician, I just had some classes about it and enjoyed it the most of all math classes. Especially things like constructing various numeric sets, countability, how set theory is supposed to be foundation for mathematics etc. But I guess these are just basics.
>>7925329
Co-ordinate geometry and trigonometry.
I love plotting points on a line and then making a triangle out of the points. It's very therapeutic, especially if it's in different colours.
