Mathematics

12:22 AM

I'm trying to relate Axiom Systems to Formal systems, can anyone help me ?
I know any formal system has 3 constituents, a language, a set of axioms, and rules of inference
what about an axiom system ?
is it a set of axioms ? does it also require a language ?
is it a specific kind of formal system ?

Peter Tamaroff

@nerdy You seem to have many questions. Why not ask this on main?

nerdy

It's actually one question : How is an axiom system related to the concept of formal system eheh but i think i'll do that

Peter Tamaroff

@nerdy Maybe @BrianM.Scott can help? How is your headache Brian?

Tobias Kildetoft

1:49 AM

well, that concludes "figure out if the spider in the corner is dangerous". Conclusion: Probably not, but let's vacuum it up anyway.

Peter Tamaroff

2:13 AM

@TobiasKildetoft How mean.

robjohn

3:20 AM

@TobiasKildetoft I capture them in a jar and toss them in a bush outside, unless it's a black widow.

DanZimm

3:34 AM

@robjohn I've never actually seen a black widow IRL - are they terrifying as I have heard?

Islands

3:50 AM

nah

Cecile

Hello everyone, may I ask for your opinion on this question: "Shall I pursue a teaching career in Math, or shall I continue with PhD?" My deadline for paperwork is coming, and I still can't decide >_< I plan to work with Geometry for PhD, but I don't know about possible research topics on this field.

DanZimm

@Cecile what kind of geometry?

Cecile

I prefer Hyperbolic Geometry or Algebra Geometry, but I'm not sure on the difficulty level though. I just have the interest.

DanZimm

4:06 AM

@Cecile how much math have you studied thus far and from what country are you?

cyclochaotic

@DanZimm we have black widows where I live, they have lighting fast reaction time, very quick

Cecile

So far I learn almost all undergraduate courses, except differential geometry and complex analysis. The "geometry" that I know so far is only Euclidean and some Hyperbolic geometry (the Klein and Poincare models). I hesitate on doing PhD on this field 'cause I'm afraid that my knowledge is not enough >_<

DanZimm

@cyclochaotic eek small things that move scare me at first sight

when they move away quickly its even wrose

@Cecile what country are you from? and have you taken topology?

Cecile

I'm from the U.S. I'm taking an intro course for topology now.

DanZimm

diff geometry from what i understand is usually a first year grad course

@Cecile I wouldn't really be the guy to talk to about geometry, otherwise in general I would say go for the PHD

cyclochaotic

4:14 AM

@Cecile stay in school as long as you enjoy it

Islands

what is differential geometry

and why isnt it offered in undergrad

Cecile

it's offered in undergrad, but I didn't take it back then due to time issue (my classes all overlapped)

DanZimm

@Islands like calculus on manifolds (at least thats how i understand it) - from my experience that wasnt offered in undergrad

@Cecile you must go to a better school than i do xD

Islands

hm.. my school doesn't even offer it in grad

Cecile

I just keep thinking... if I really do apply for PhD, what would be a research topic that I can choose >_< I'm really uncertain on that. That's why I leave the option of teaching, but... ah, so hard to decide!

DanZimm

4:17 AM

@Islands technically mine doesn't either, by our math grad program is only masters

@Cecile do you have a favorite prof of math youve run into?

cyclochaotic

@Cecile go talk to a professor about cutting edge research topics

DanZimm

@cyclochaotic I did that and my prof said exactly what he's researching right now xD

seems biased based on who you ask :P

then again depends what you consider cutting edge

cutting edge with relation to what

:P

Cecile

Yeah, I do have a really nice professor, but his main field is ... differential geometry >_<

I ask him b4, and he said ... "that's hard to choose"

Islands

does anyone know about chabauty methods?

Bageer

@Cecile (I am not in grad school but I plan on going too grad school) I pretty sure you sort of figure out what you want, and will, research in grad school. Of course it probably helps to have an idea of what field you want to research before grad school.

cyclochaotic

4:20 AM

Perhaps read some preprints on arxiv.org to get some ideas

DanZimm

@Bageer just curious, what are you interested in studying?

Bageer

@DanZimm I am leaning towards algebraic type of subjects, last semester I did an independent study in geometric group theory.

@DanZimm I also really like the idea of category theory and topos theory, but I don't know much about them.

@DanZimm What are your interests?

Cecile

Does number theory seem to be the "easier" field? In my opinion, it's all about numbers, no topology or analysis is needed.

DanZimm

@Bageer ah very cool - all things I'm ignorant of

Islands

Cecile: what about all those easy-to-state, hard-to-solve problems?

DanZimm

4:24 AM

@Bageer I'm currently doing independant study with a prof on measure theory and specifically lebesgue theory and then onto analysis of modern PDEs

Islands

there's a lot of them and they are all from number theory

DanZimm

@Cecile I find number theory the most difficult

cyclochaotic

Here's a simple problem, prove than any non-prime even number is the sum of two primes :)

Jayesh Badwaik

@cyclochaotic heh...

Bageer

@Cecile Going to grad school just to study the "easy" subject seems misplaced. I think you should go because your passionate about the subject. (maybe I am just reading to much into what you have been typing)

DanZimm

4:27 AM

@cyclochaotic isnt that a conjecture?

Islands

I think this would be the most interesting problem to work on: en.wikipedia.org/wiki/Inverse_Galois_problem

cyclochaotic

Goldbach

DanZimm

ya

xD

cyclochaotic

We can't even generate arbitrarily large prime numbers.

Bageer

@DanZimm Hah, I know almost nothing about analysis. I plan on picking up some analysis and topology to do some sort of independent study on the gap conjecture (a conjecture in geometric group theory). It seems to have a lot of applications to differential geometry (I believe Milnor came up with the conjecture).

Cecile

4:30 AM

@Bageer my meaning of "easier" is in terms of research topics, but in terms of the materials, I think topology is good. 'cause it's more to set theory (ex: open sets) than the "epsilon-delta" as in real analysis

DanZimm

@Bageer it's my thing, I love it! My school doesn't offer any sort of category theory or group theory classes. we have abstract algebra and advanced abstract algebra, the former im taking next semester and the ladder the semester after that

cyclochaotic

$250,000 to the first individual or group who discovers a prime number with at least 1,000,000,000 decimal digits at the EFF

Islands

no group theory?

seems like a standard 3rd year class?

DanZimm

@Cecile you can get pretty deep into topology and it can get analysis-y xD

@Islands thats in the abstract algebra class

you learn about groups rings and cosets

Cecile

yeah, although I took a whole year of real analysis, I'm quite lost after things get to 3-dimensional or more.

Oh, my friend once said Complex Analysis is "easier" than Real analysis 'cause there is no "epsilon-delta" to deal with. Is he correct? Or maybe just 'cause he's taking it?

DanZimm

4:36 AM

@Cecile complex analysis can be "easier" depending on how the prof teaches it

it can be a very deep topic or a much more applied subject thats less analytic

@Cecile if youre ok with 2-dimension why not 3?

Cecile

'cause something like volume of a Hypersphere... I figured out the integral but have no visual picture in mind >_<

I also plan to pursue teaching credential in the morning ('cause I have to teach 2 classes), then do PhD from the afternoon. But my friends said that's too heavy of a workload. @_@

DanZimm

@Cecile gotcha - i suppose im more into general analysis as opposed to real analysis so I'm pretty used to the lack of visualization

@Cecile if you want to really understand that stuff topology helps

Cecile

I got freak out after going to the school website and seeing the requirement of "passing qualifying exam and core exam with MS grade level by the beginning of 2nd year". The topics are algebra, real & complex analysis, but I know nothing on complex analysis & shaky on real analysis >_<

DanZimm

@Cecile eek yea analysis will getcha

DanZimm

5:53 AM

merh

Ethan

@Alasdair Can you tell me exactly what you are trying to do?

I am having trouble reading your question

What exactly do the variables $x$ and $y$ represent?

Transcript for

$Mathematics$ Mathematics