mathematician here i study algebraic geometry. know a bit about

>>7934191
I'm thinking of taking algebraic geometry as one of my modules for my masters, any good references for it?

>>7934198
ravi vakil's book FoAG is easily the best book available in the subject, though it is quite long winded.

if you're a masochist, go with hartshorne.

for either, you'll need a strong commutative algebra background and eisenbud is really on the only game in town.

I prefer topology myself, but I find that algebraic geometry is quite popular. What attracts you to algebraic geometry?

>>7934203
Thanks.

>>7934205

honestly? it's reputation for being difficult and abstract was why i originally got into it. seemed like a challenge.

nowadays, i like that it serves as a unifying subject and a bridge between diverseareas like number theory, representation theory, and algebraic topology.

What number am I thinking of?

>>7934225

7. or 1728.

>>7934191
How many burgers do you flip per day?

>>7934240

none yet. one more year of my phd before i need to decide between mcdonalds and walmart.

>>7934191

What are the real life applications of your field of study?

>>7934246

there are applications to cryptography and algebraic statistics. but really, almost none.

>>7934191
Why is the moduli space of elliptic curves with a naive level 3 structure representable?

>>7934191
Why is algebraic geometry the most boring application of category theory ever?

>>7934260

because the level 3 structure ensures that the elliptic curves carry no automorphisms and thus we can use an algebraic space (in fact, a scheme i think) instead of a deligne-mumford stack.

How did you become good at it? Was it practice makes perfect or were you mathematically gifted by default?
When you read a problem, for example prove that something is an isomorphism of something else do you actually visualize the structures as geometric objects in your head?
I recently started abstract algebra and I have no idea how anyone could come up with all that. I feel exceptionally retarded when i fail to prove most theorems or see the connections and relations between structures and morphisms.

>>7934263

algebraic geometers don't use category theory for much other than establishing foundations. even the more sophisticated applications like etale cohomology only use it to set up the apparatus before turning to more concrete geometric calculations.

>>7934251
I thought there were a few applications to physics.

>>7934268

practice. that is all... the short story:i'm a high school dropout and i needed to prove to myself that i wasn't an idiot. i ended up doing math sort of by a fluke and i got really, really into it. mostly to appease my own ego. i can tell the long story if you're interested.

yes i can visualize abstract structures in my head - but that's because it is the *only* way to do this kind of math. without a picture, i am lost. it's a skill that i trained, not a gift or any such crap. give it time, and you'll develop the skill as well.

>>7934279

yes, there are applications to string theory. gromov-witten theory is a huge deal. i would not consider this a 'practical application'

>>7934281
Long story should be interesting. Why did you drop out of hs? what do you do for a iiving now?

>>7934191
Second year undergrad here.
Enjoyed the linear algebra and abstract algebra of the first year and further linear algebra of second year (free abelian groups, tensor products, Hilbert's third problem). Even did geometry from a linear algebra point of view. But I didn't enjoy the groups and ring theory of second year... I found it really dry, especially when it came to Sylow's theorems and EDs, UFDs, PIDs. Took a course in number theory too and found it incredibly dull.
Is there still hope for me later in algebra in terms of interest?

i'm still a phd student, in my fourth year. i'll copypasta the full story.

I had a fairly rough go at high school: I ended up dropping out when I was 15 since being trans fucking sucked - though I hadn't been attending class regularly for probably a year and a half up to that point. In any case, my parents gave me an ultimatum: Either I get a job or I go to community college. I ended up going with the latter and solidly screwing off for 2 more years, largely playing World of Warcraft. Despite that, I got good grades, but I didn't have any educational ambitions. The fucking off continued, completely unabated for sixteen months...

Then I took a precalculus class. It was sort of an online class deal, except there was actually a computer lab on campus where I could go and ask the instructor for help. So I went to that place one day and asked my instructor what was probably an incredibly stupid question - I was a giant moron back then - Anyways, I remember him just looking me like I was literal human garbage and addressed me in a way that made it clear he was barely hiding his contempt. I'm sure that wasn't the first time someone treated me like that - but that was the first time I felt so insulted by it.

>>7934306
part 2,

The next day, went on Amazon, and found the single hardest calculus textbook I could find (Spivak, obviously). I spent the entire summer afterwards studying it, at least 5-6 hours a day - barely playing any video games. I needed to prove something to myself, I think... Anyway, by the end of the summer, I'd sort of fallen in love with math: The precision, the reason, and the absolute correctness. The way things that seem so insurmountable can come to feel as obvious - and as inevitable as the sunset - with just the tiniest flicker on light in your head.

Early next semester, I told my mom that I wanted to get a PhD in it, I'm pretty sure she thought I was a tad delusional - I probably was - but I wanted that like I never wanted anything in my life. Anyways, I transferred to [DELETED] a year and a half later - did that for three years - then I applied to grad school and got into [DELETED].

Did you spend a lot of time learning the basics ?
I am interested in algebraic geometry, have had classes and I would like to do something related in my thesis (I like representation theory, galois theory, valuation theory so I think this would be a nice way to put everything together), however I am not very fond of commutative algebra so I would rather not spend years reading the EGA/FGA/SGA.
Did you just take a lot of time at the beginning of your thesis to learn all this stuff or learned it as you went ?

>>7934314
>spend years reading the EGA/FGA/SGA.

that is not how algebraic geometers learn algebraic geometry. you learn the basics and you pick up a lot of other stuff by osmosis. but mostlyyou just start working on a problems and refer back to literature as needed.

i spend a ridiculous amount of time obsessing over the basics in my first years of grad school, but in retrospect - it was mostly wasted effort. i use maybe 5% of that stuff on a day to day basis.

>>7934303

maybe? read a friendly survey of class field theory and see if it catches your interest. many fields in algebra are extremely compelling, but the axiomatic Bourbaki approach that it is taught in tends to leech out all of the beauty.

>>7934328
Yeah, that's what I thought but you hear such horror stories that it's nice to have other people confirm that stuff

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>>7934191
I tried to solve this integral but the answer says: 3tan(x)/2. What am i doing wrong?

>>7934367

you made a basic fractions error on line 2.

>>7934228
No, 72

>>7934373
i think you're lying. liar.

>>7934367
Line 2
[eqn]\frac{a}{ \left( \frac{b}{c} \right)} \neq \frac{ \left( \frac{a}{b} \right) }{c}
[/eqn]

how will you feel when automated theorem proving AI will take your place?

>>7934384
The key point is that they can't create new theorems.

>>7934384

ever read any of the culture novels? the Minds (sentient AI starships) are incomprehensibly smarter than most humans. But the humans who live on the ships still do math and science, largely for self-amusement.

tldr: math is still fun even if there are people (or machines) who can do it a lot better than you can.

>>7934390
care to elaborate?

>>7934191
do you know much about toposes/algebraic theories? probing before typing longish question

I, like you it seems, am compelled by algebraic geometry because it's usually heralded as the hardest subject. I'm still a second year student, but what tips can you give? What books should I read, or about what topics?


These are the topics my uni offers for 3rd and 4th year (most can be taken any year, the last two have prereqs from 3rd year):

>Analysis Iii
>Differential Geometry Iii
>Number Theory Iii
>Galois Theory Iii
>Approximation Theory & Solutions of Odes Iii
>Dynamical Systems Iii
>Geometry Iii
>Probability Iii
>Elliptic Functions Iii
>Solitons Iii
>Stochastic Processes Iii
>Topology Iii
>Partial Differential Equations Iii
>Algebraic Geometry Iii
>Representation Theory Iii


>Algebraic Topology Iv
>Riemannian Geometry Iv

>>7934423
i forgot to say, which of these should i pick?

>>7934281
thanks man. stories like yours give me hope and motivation.

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>>7934191
why are you studying such a gay ass field? p.s. geometry sucks dick OP

Also a mathematician, but I study mathematical physics (mostly linear representation theory + differential topology + differential geometry). Complex differential geometry is cool as shit though and I want to get into algebraic geometry, where should I start?

>>7934478
I've always been curious how physicists use representation theory. Could you explain? I've only applied it to group theory and combinatorics

>>7934494
I'd be happy to. For pedagogical reasons, how much background do you have in physics? And do you know what a fiber bundle is?

>>7934494
it's used to help solve problems. For example, you would represent a mass as a square and an inclined ramp as a diagonal line, and then put arrows representing forces on them.

>>7934494
An elementary particle is an irreducible representation of the gauge symmetry group of the theory.

>>7934514
i have some in my neck
>XD

>>7934533
Close. Representation theory classifies particles/fields, but you don't need to involve gauge fields for all theories. It works perfectly well for free particles of any statistics. In fact, for many free theories gauge fields don't even occur. It would be more accurate to say that an elementary particle is an irrep of the Poincaré algebra.

>>7934549
Gauge theories are the only ones with real physical significance for elementary particles.

>>7934191
I am just getting into rings and finished the homomorphism theorems, how do I understand rings well? Can you point me on the path to getting to you?

>>7934306
>being trans

Are you fucking kidding? The bullying or any other issue that this may have caused will be re-paid.

You will get a job as a tenured professor immediately just because of muh diversity.

EZ PZ. Maybe you should try to start your own field of mathematics and then prove the transitivity of the operators.

TELL ME ABOUT ARTIN STACKS

>>7934642

sort of like deligne-mumford stack, except you glue things with smooth covers instead of etale covers.

derived stacks are the cool ones.

>>7934599

im stealth so that is... not happening.

>>7934416

i know a bit about topos theory, yes. even a tiny bit about (infinity,1) topos theory. both are very pretty subjects, though i've never found a use for them in practice.

>>7934591
You're right, physically realistic theories of elementary particles are almost always gauge theories (I say "almost" because there's a time and place for theories of matter interacting with an effective background rather than properly coupling with a gauge field). I was just stating that, in fact, the given definition of an elementary particle isn't quite true.

>>7934875

Degenerate

>>7934191
what do you think about The Rising Sea?

>>7934191
Why does Hodges in "A Shorter Model Theory" refer to Model Theory as Algebraic Geometry without fields?

>>7935155
Not OP but classical algebraic geometry studies the solution sets of polynomial equations in a field k, which are the same as definable sets in the language of k-algebras.

>>7935142
see
>>7934203

>>7934281
What textbooks did you use anon? The only algebraic geometry students I know at my university do everything through brute forcing algebra techniques and can't into even basic visualization.

>>7935155

i don't really know. i know that people have proven some deep algebraic geometric results using model theory, though such results always depend on working over an algebraically closed field.

so my guess that is that the author is referring to the fact that grothendieck style algebraic geometry is done is over an arbitrary commutative ring (though often, we assume the rings are noetherian).

>>7935214

Ravi Vakil's book for the basics... but... the single best way to get geometric intuition is to read the books of Griffiths (in particular, the multiauthor books on algebraic curves give splendid geometric intuition). joe harris's undergraduate book has some really pretty stuff. mile's reid's lecture notes on algebraic surfaces are great. FGA explained is really nice, kleinman's introduction to the picard scheme is outstandingly beautiful and traces the history of the subject all the way back to abel. every graduate student of algebraic geometry or number theory should read through all of matt emerton's mathoverflow responses. silverman's elliptic curves textbook is incredible. i could go on all day.

>>7935282
e: i'm dumb. the model theory reference is most likely due to the fact - as

>>7935214

alluded to - model theory may been as the study of "the locus of truth" of some system of syntactic statements. a model may be seen as a solution to such a system. model theorists are often interested in making statements concerning the totality of all models

algebraic geometry is the study of the locus of zeroes of some system of polynomial equations. the grothendieck functor of points approach emphasizes studying the solutions to a set of equations over all possible rings.

that's the rough metaphor, i think...

>>7935282
Thanks, I'll have a look. I've been curious about the visual side of the topic but all I ever read/hear with regards to it is algebra (and not even in a modern category theoretic way).

Of course, it doesn't help that many people who get into it do it for pretentious reasons like "I heard it was hard".

>>7935299
Look who's talking, a guy who posts bear memes on a Bangladeshi cow painting site.

ELI5 the baum-connes conjecture

>>7935485
>baum-connes

wat that.

Both spivak and rudin say this obvious so I'm an idiot. So what ami missing?
[math] \forall x, y \in S : | x-y | < r \Rightarrow \sup S - \inf S \leq r [/math]
Pardon my drunkness

>>7935507

sup S is the smallest number large than all the numbers in S. inf S is largest number smaller than than all the numbers in S.

if sup S - inf S was bigger than r, you'd obtain an immediate contradiction by choosing x sufficiently close to sup S and y sufficiently close to inf S.

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>>7934191

Have you ever done DMT?

>>7935516
In laymans terms, what do algebraic geometry mathematicians do? Do you guys find better ways to draw shapes on a computer, find neat properties of triangles, etc?

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>>7934281
Damn, motivated revitalized. Thanks anon

>>7935519

no. only mushrooms.

>>7935521

i study generalizations of sets defined by polynomial equations (like y = x^2). for this class of objects, there is a dictionary that allows us to translate and transpose our geometric and algebraic intuition. the fact that equations are so simple leads to miraculous symmetries.

>>7934228
>1728
Underrated post.

I suppose you are a PhD student. I recently got accepted and I ended up not liking the school after visiting for stupid reasons. At this point, I am most likely not going to get any more acceptances (though i'm hoping i will). Do you have any advice to make the most out of grad school?

>>7934191
>>7934205

Do you have experience with modal logic?

>>7934191
How do I find the limit of this sequence? [math]a_0 = 1[/math], [math]a_{n+1} = \sqrt{2a_{n}}[/math]

>>7934423
number theory if youre looking for something easy.

>>7934598
> how do I understand rings well?
Atiyah and Macdonald.

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>>7935485

>he doesn't like bear memes

Why do all the people that claim they're doing PhDs on /sci/ always have such piss poor grammar and spelling?

>>7935995
Yeah, how did that rigorous grammar entrance exam not weed out all of the math PhD students?

I'm a final year A level student in Singapore, and intend on doing mathematics in uni when I've graduated. However, many people have said that there would be little to no job prospects in the future. What are your opinions?

>>7934191
What tricks could help you prove that one quotient of polynomial algebra is not isomorphic to the other quotient? Is there are list of these somewhere?

>>7934191
What about shafarevich?

>>7936710
There is no trick for this, you need to find a property of one of the rings that the other one doesn't have. Look for integrality, normality, factoriality, etc.

>>7935995
Maybe his language is other than English?

I need to find an intersection of k spheres in n-dimensional euclidean space. It leads to a system of equations of the form [math]\sum_{k=1}^n (x_k-c_{i,k})^2 = r_i^2[/math], [math]i=1,\ 2,\ ...,\ k[/math], where [math]c_i=(c_{i,1},\ ...,\ c_{i,n})[/math] is the center of the [math]i[/math]-th sphere of radius [math]r_i[/math]. It is a system of polynomial equations, something that algebraic geometry deals with. Can you recommend some book/paper/known technique that would help me out?

>>7936022

Not OP (a faggot)
It is not like you could generalise on a global scale.
But at least in USA maths graduates job market is by far the most expanding one and some say it will keep growing for a while.

But in the end nobody knows how the future will look like.

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>>7934191
Can a subset of [math]\mathbb {R}^n [/math] with boundary be an affine variety?

>>7936802
Yes

>>7936802
Affine varieties are closed subsets of some R^n. They all contain their boundary.

>>7935820
Show by induction that a_n=2^[(2^n-1)/2^n] so the limit is going to be 2.

>>7934191
Hey OP, could you please define a 'Kernel' in the mathematical context?

Cheers

>>7936971
[math] \ker \left( f \right) = \left\{ {x|f\left( x \right) = e} \right\} [/math]

>>7936019

That's not an excuse to write like a retard.

>>7936996
Could you/someone then explain what the notation,
x|f(x) = e means?

>>7937077
[eqn] \{ x \mid f(x) = e \}[/eqn] means

the [math]x[/math] such that f(x) is equal to e, where e is the identity element, such as the identity element in groups.

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>>7934191
is there more than 3 physical dimensions?
how do you describe or represent more than 3 dimensions with math or geometry?

>>7937077
>>7936996
kernel is what gets mapped to zero (or additive identity)

Algebraic geometry is a meme field. Tell us about your math knowledge outside of AG.

>>7934515
kek

>>7934191
I am starting grad school soon. Why should or should I not go into AG?

Meaning, what are ways of telling if that would be good or not for me?

>>7937092
If you don't know, [math] {\mathbb{R}^n} = \left\{ {\left( {{x_1},...,{x_n}} \right)|{x_i} \in \mathbb{R}} \right\} [/math]. i.e. R^n is the set of all n-component vectors such that each component is a real number.


Then we can define a n-dimensional manifold as a set [math] M [/math] such that M is the union of multiple sets U, [math] M = \bigcup\limits_\alpha {{U_\alpha }} [/math]. For each of these sets U, there exists a bijective continuous map (with continuous inverse) [math] {h_\alpha }:{U_\alpha } \to {\mathbb{R}^n}[/math].

This is how we define the dimension of a manifold. By the dimension of the euclidean space the sets that make up the manifold get mapped to.


(There is more to the def. of a manifold that I have omitted here)

>>7937092
Note: This "multi-dimension is 2abstract4me zero physical sense" is just a gigantic meme. Every time you use more than 2 numbers to describe something (which you do all the time, even in classical mechanics) you get multi-dimension.

should i go into AG or logic?

>>7937440
AG

>>7934191
Homological algebra after Weibel for someone who wants to do algebraic and differential topology?

And why is module theory so interesting and intuitive to me but more advanced ring theory makes me piss myself?

>>7934875
>trans
>stealth
Oi m8, just admit you're a faggit m8.
Transexuality is a modern invention anyway.
Not that there is anything wrong with wanting to dress like a female and suck cocks etc., but if you legitimately think that you are "born in the wrong body" you are mentally ill.

>>7937662
I'm not that anon but many human cultures have maintained extra genders for millenniums. The only thing that's new is that we've decided to study gender as a part social identity (with roles and so on) separately from sex (as the physiological component).

Either way, assuming you're correct, why are you getting buttblasted by something a pervert on 4chan says they do? It's somehow worse than the people who read cringy tumblr blogs and invest a lot of time telling everyone how mad they are about this thing they read on a tumblr blog.

When can I start call myself a mathematician? I got a B in my introduction to college algebra course. Can I start calling myself a mathematician now?

>>7938338
Not really, no.

>>7938338
I was thinking about this today.

I think being a mathematician starts when you are adept at algebraic manipulations and you know basic logic/proofs. That's really all you need to think like a mathematician.

Can you prove by induction some trivial fact? Do you know what iff means? etc.

Content doesn't really matter, just can you operate even in a trivial way like a mathematician.

>>7939441
Am I an engineer when I understand the most basic parts of a mechanics class? Why is mathematician the one profession everyone thinks they can call themselves?

>>7939447

Only someone actually employed as a mathematician can call himself a mathematician.

>>7939463

What about people who make huge break throughs on their own? Or retired mathematicians?

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>>7934191

what about ternary?

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>>7934203
>eisenbud is really on the only game in town
Is his better than Matsumura's? Matsumura makes me wanna cry.

Gonna take algebraic number theory and commutative algebra simultaneously
Is that doable actually?

>>7939463
That's what I'm trying to say.

>>7939593
Eisenbud is great if you want some commutative algebra with your geometry.

>>7939602
I did it

My commutative algebra was more geared towards a geometric/homological view though, so there wasn't an ideal amount of overlap.

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>>7939715
Well, I'd like to learn communist algebra somehow. Matsumura has a clear and compact exposition, but his style is not mine. Is Eisenbud too geometric for this cause?

>>7939463
In my school, you get a salary for being a student. Does it mean I'm a mathematician ?

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Is AG just a meme? What can you even prove with it?

>>7940295
This is nitpicking, but you get money for being a student, as you said. You don't get money from what you do.

>>7940298
Well, for one thing, it was the right language to formulate many interesting (and concrete) enumerative problems in geometry (how many lines are on a generic hypersurface of such and such degree ? how many curves of such and such degree pass through these points ? in how many points do curves intersect in general ?)

I've never done AG but it sounds like a huge meme. I was at a grad program for their prospective student weekend. The program is well known for their applied biomath (which I was there for) and their algebraic geometry. All the students there for AG were like new adherents of a cult. All of them sounded really interested in it but couldn't articulate what it was and why they were interested. I didn't enroll in the program so I won't see what becomes of them, but I'm sure it would have been interesting.

>>7934191
Yes, surely!

I'm in my first year, so far I find commutative, linear and homological algebra most fun and interesting subjects to study. Thinking about commiting largely towards algebraic topology or algebraic geometry.

Do you think algebraic geometry is rather algebra or geometry? I assume you are from USA. Did you find useful school-level geometry (that euclidean stuff with lines and circles and greek theorems) in any imaginable way? Did it affect your intuition, how you imagine stuff in your head?

What's the relation between your field and others, like, say, integral/differential calculus, discrete mathematics, dynamic systems etc? What do you think about differential geometry/topology? Are they useful for you? How far your field is from algebraic topology?

So curios!

>>7934191
I suck at doing proofs. Can you suggest some tips by which I can improve on this aspect of my math?
Aspiring mathematician here! Thanks anon!

>>7940348
read a lot of math texts. do a lot of proofs. write them out in full when you are a beginner even if you don't have to turn the homework in.

>>7939493
It was tried by a few early russian computer scientists but didnt really pay off.

Also that inverted and doesn't really make sense (in terms of output, how is it even and?)

>>7940348
When I started studying math I had the same problem.

start with proof by contradiction

Are algebraic areas of math more popular for pure mathematicians than analytic areas of math because algebraic areas of math are easier?

>>7934191
I want to study the generalized version of non-convex, simple (i.e. noncrossing) discrete polygons. How should I go about learning them? Which direction (topology/algebra/geometry) should I go about learning about that? Every approach I try leads to a dead end...

>>7941678
>start with proof by contradiction
Awful advice.

>>7940348
The book "How to Prove It" was really useful for me. Go to the Amazon page and look at similar books; they have most of the same basic techniques. Do all/many of the solved exercise until you understand how the technique works, then do more the next day to reinforce. When you come across a proof in a textbook, try to pin down "That's a proof by contradiction, let me try and find where the contradiction lies in the proof."

>>7940298
ECDSA is based on algebraic geometry. It's more trustworthy than mashing two big primes together and hoping for the best.

>>7941685
They are not, actually. They are more meme'd about but they are certainly not more popular. In my MSc, about 2/3 of the people went for PDE, probability and statistics and I think the trend these days is to do stats and PDE because these are very new fields where a lot remains to be done and because there are jobs on the other end of the tunnel (both in academia and in the private sector).
Besides, this distinction between "algebraic" and "analytic" parts of math really only makes sense at the undergraduate level maybe. After that, you use whichever tool you need to answer your question. For example, differential geometry uses both algebraic tools (cohomology, homotopy, etc) and "analytic" tools (metrics, currents, etc). Complex geometry relies on both analytic and algebraic tools and proofs using one approach sometimes cannot be reduced to the other approach. The same goes for number theory, arithmetic geometry, etc.

>>7936802
>>7937092
>>7939593
>>7940233
Take your pedophile cartoons back to >>>/a/.

>>7942503
Oh ok that's interesting. It seems like the vast majority , or infact virtually all PhD or post-doc discussion on sci is about algebraic geometry, category theory, Toppa theory, algebra and sometimes number theory and graph theory. Shelves, functors, bundles, schemes, etc.

While I've never seen sci talk at a PhD level about PDE , advanced variational calculus, sobolev soaces, Polish spaces and the like.

What does that say about the kind of maths students and mathematicians who visit /sci/?

>>7942600
>What does that say about the kind of maths students and mathematicians who visit /sci/?
They like algebra.

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>>7942600
>Toppa theory

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>>7942600
I really wonder why that might be..

>>7934191
Are you good at Linear Equations?

>>7934367
Line 2 there's a huge mistake. The fraction is in the numerator but you treated it as being in the denominator and ended up doing some reciprocal which would be valid if you did it against [math]\frac{a}{ \frac{b}{c} }[/math] but not [math]\frac{ \frac{a}{b} }{ c }[/math]

could 5=5 be simplified to any of these:-
a)0
b)1
c)5

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>>7942708
I'm trying to come up with a linear function for a simple indoor positioning app using multi-lateration.

pic is where I'm at. Doesn't seem very performance-friendly without using linear functions.

Would appreciate any input from you.

>>7942724
What is this?
You need function for coordinates of (x,y) in triangle with vertices [math](a_1,a_2),(b_1,b_2),(c_1,c_2)[/math] ?
Well, thats
[math]\lambda_1(a_1,a_2) + \lambda_2(b_1,b_2) + \lambda_3(b_1,b_2)[/math]
[math]\lambda_1 + \lambda_2 + \lambda_3 = 1, 0 \leq \lambda_i \leq 1[/math]

>>7934191
Which starter I should choose?
I like charizard, but i have a pair of them for previous runs, I could go for blastoise even when I have one too. Never choosen venosaur but he's ugly as fuck. What do you think?

>>7942867
>>>/vp/
and the bulbasaurs are the only good grass-types in the game and you know it

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>>7934191
How this thing is called when curve is constructed by dragging other curves through each other? Can this be studied with AG? Any books/papers?

>>7943347
There are a bunch of ways to make curves by rolling curves on other curves, but they are generically called roulette curves.

>>7943347
Not an expert but this kind of stuff is studied in (classical) differential geometry.

Does Matiyasevich's theorem imply that everything we can compute is a solution set to a diophantine equation?

>>7945858
>Matiyasevich's theorem
This only says there there exists no algorithm to determine whether an arbitrary Diophantine equation has rational integer solutions, it says nothing about 'everything we can compute'

>>7945889
>Matiyasevich's theorem
It says r.e. sets are diophantine

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>>7934191
What was your PhD Thesis on? (link to .pdf of it?)

How satisfying is your career?


I have known a few mathematicians who said it is vital to know and understand the problem or the underlying math of something but actually figuring is not so important. Ex: Knew one fellow who couldn't do basic arithamatic but was a PhD and worked for Atari and other Silicon Valley companies.

What are some of your favorite math books?

If American, whom do you support for President?


Thank you kindly

>>7934203
http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf