Other Should I Become a Mathematician?

[pivoxa15]

Yes. The university business seems to be dumb and frustrating, and I don't understand why I keep aiming at getting there.

Maybe because other instutitions are even more frustrating like private businesses. Moreover only an institution like a university can you do some genuine learning.

 

[pivoxa15]

Mathwonk, I have the serious problem that I pretty much cannot do any of the problems in my pure maths subject unless I take a peak at the solution. Is that a sign that I should quit pure maths? That especially goes for topology. I did poorly in the prereqs as well so that could be the root to my problems.

 

[mathwonk]

it probably means you lack some background. just start further back as you say with perhaps topology. or get an easier book. i don't see why you should quit. we all have the same problem of finding the right entry level treatment of a new topic.

or it may mean you are not learning the material well eneough before trying the problems. or that you need more practice solving such problems. when trying to do a problem that does not yield, just make the problem easier and solve the easier one. then try to work back up.

 

[JasonRox]

I loooovvveee topology.

I can't wait to learn more this Fall.

 

[Jaden]

Mathwonk, do you know a good derivation of the normal distribution. It's used so often everywhere and it bothers me that I have to take something for granted which does not look obvious like 1+1.

 

[Kummer]

Mathwonk, do you know a good derivation of the normal distribution. It's used so often everywhere and it bothers me that I have to take something for granted which does not look obvious like 1+1.

Did you try looking in a standard (mathematical level) probability book.

I say mathematical level one because there are some easier ones used by other majors which need probability theory. In those books the normal distribution is mentioned but not much is developed in theory.

 

[Werg22]

The question is ambiguous. It is of course possible to prove that the integration from minus infinity to infinity of the normal distribution function gives 1. However, as to how to go from "I am looking for a function whose integration from -infinity to infinity is 1 and that is even" to an actual answer, I do not know.

 

[mathwonk]

i did not even know what the question means, but i could ask somebody more knowledgeable, is that the question? prove the integral of something over R is 1? or what? i have not taken probability since 1963, and only got a B+ then. (I think it was discrete probability too.)

 

[pivoxa15]

it probably means you lack some background. just start further back as you say with perhaps topology. or get an easier book. i don't see why you should quit. we all have the same problem of finding the right entry level treatment of a new topic.

or it may eman you are not learning the material well eneough before trying the problems. or that you need mroe practice solving such problems. when trying to doa problem that does not yield, just make the problem easier and solve the easier one. then try to work back up.

But the class is progressing and if I can't do the assignments then that is a problem. The worst thing is that the difficulty is getting to the point where I am actaully trying to avoid the problems which is a 'deadly' sign.

 

[mathwonk]

you may not learn the stuff this time around. that's fine. it'll come later.

or if you are committed to getting it this time, institute a crash plan. When i was flunking diff eq i bought a schaum's outline series in d.e. and began working all the problems until i caught up.

or post some questions on here in the appropriate forum. we'll help you get the ideas. start with one or two here. i love topology. when i was a senior i took kelley's general topology book and read it over the summer and worked the problems. it isn't very hard core or fun topology but it gives you the basic abstract point set stuff.

and i always found Simmons one of the clearest expositors of analysis. Sterling K. Berberian is also excellent.

 

[Jaden]

Can you recommend me a textbook which explains in a more simple way where the normal distribution function comes from ?

 

[mathwonk]

have you read wikipedia?

 

[pivoxa15]

you may not learn the stuff this time around. that's fine. it'll come later.

or if you are committed to getting it this time, institute a crSH PLAN. WHEN i was flunking diff eq i bought a schaums outline series in d.e. and began working all the problems until i caught up.

or post some questions on here in the appropriate forum. we'll help you get the ideas. start with one or two here. i love topology. when i was a senior i took kelleys general topology and read it over the summer and worked the problems. it isn't very hard core or fun topology but it gives you the basic abstract point set stuff.

and i alwAYS FOUND SIMMONS ONE OF THE VERY CLEAREST EXPOSITORS of analysis. sterling k berberian was also excellent.

I flunked point set topology actually and now I am enrolled in a 'proper'? topology course with 'Topics include topological spaces and continuous maps; quotient spaces; homotopy and fundamental groups; surfaces; covering spaces; and an introduction to homology theory'.

So you can see why I am struggling. The contents in the course dosen't seem to be rigorous which dosen't help. Plus my algebra isn't strong either. My brain seem to want to 'turn off' whenever I try to get into a problem which is a big worry.

 

[mathwonk]

well that's a lot of stuff, so just try to learn some of it. covering spaces are nice. for fundamental groups, the best intro is by andrew wallace, in a little book called intro to alg top. unfortunately he wrote more than one book by that title, it seems, but all his books are good. i think this is the one i learned from. he makes it so clear you almost canot fail to follow. and i recall it was still hard to catch onto at first for me.

An introduction to algebraic topology (ISBN: 0486457869)
Andrew H Wallace
Bookseller: Zubal Books
(Cleveland, OH, U.S.A.)
Bookseller Rating:
Price: US$ 6.59
[Convert Currency]
Quantity: 1 Shipping within U.S.A.:
US$ 7.50
[Rates & Speeds]
Book Description: Pergamon Press 1961, 1961. NOTE: THIS IS THE 1961 HARDCOVER EDITION! 198 pp., hardback, bookplate to front pastedown, minor underlining & notes in pencil to a few pages else v.g. Bookseller Inventory # ZB552817

 

[pivoxa15]

Do you think it might be better to get a better grounding in point set topology first ( I got a 51% on that exam) and then revisit more advanced topology? This would mean quiting the topology course I am doing now.

 

[quasar987]

I did a course with exactly that syllabus last semester pivoxa15.

For one, there obviously wasn't that much time spent on general topology, because of all the other topics to cover, and the rest of the subjects do not have that much to do with point set topology.

In my case also, the professor was rather sloppy in his proofs and statements of thm, because I suppose, he meant for us to understand that problems in topology & algebraic topology are not solved by writing "Let e>0. Then, ... Then,... Then,... QED!". On the opposite, they are solved in your head by visualizing the problem first, and then by moving stuff around in your head until VLAM, you see it. Then, it is only a formality to formalize the solution by writing it down in proper mathematical language.

So for every definition and theorem, you should spend as much time as it take to form a visual idea of what the def./thm. is saying. Use the R^n case for these visualizations; usually, they are adequate for more general spaces too.

But that does not mean I did not take time to transcribe the notes I took in class into a clean, organized, rigourous and massively commented compilation.

Also, remember that you are not restricted to what's written on the black board! Rent as many relevant books as you can (Munkres & Massey come to mind!). Personally, I used only Munkres occasionally and Wikipedia permanently.

 

[pivoxa15]

Just finished the first assignment for topology. It wasn't as bad as I expected. Things are coming back to me and I will continue to be enrolled in this subject. Hopefully one day it will all come to me.

 

[quasar987]

Is there an algebraic geometer around?

I am looking at the page of a professor and he has a list of suggested topics for masters thesis in the field of geometric groups. This is the one that, based on their brief descriptions, interests me the most:

"Algebraic geometry over a free group.
One can define a Zariski topology on F^n taking solution sets of equations as closed sets.
We plan to develop a notion of dimension in F^n."

Would you be able to explain what this is about more precisely?

 

[mathwonk]

he is trying to define dimension in the space F^n by analogy with the definition in k^n where k is a field or maybe algebraically closed field.

in that case a parallel is drawn between prime ideals of k[X1,...,Xn] and irreducible closed sets of k^n, and then the length of chains of these sets, or equivalently ideals, is used to define dimension.

e.g. in a vector space one can define dimension of a subspace as the length of a maximal chain of contained subspaces.

since the free group F has very little commutativity, the analogs are not at all clear to me.

 

[strings235]

mathwonk, I'm currently still a high school student and I've recently finished the two volumes by tom apostol through self-study. I haven't had any significant problems and wonder whether I should continue this by studying ode's, linear/abstract algebra, real analysis, etc, or simply turn to mathematics competitions and stay there until college. I've gotten advice that one shouldn't replace education with competitions, yet finding a university professor for tutoring is difficult because of transportation problems. Would I be able to self-study with success?

Thanks

 

[mathwonk]

just do what you enjoy. self study is very useful, but you will find when you get a teacher that you will gain more insight on the same things you have self studied. if you like competitions then do them. I did. it made me feel i was talented and gave me motivation to do more math.

but take advantage of the free time you have now to read those great books. if you could read apostol and do the probolems with little difficulty, then you are very strong. If you are having fun, keep going and enjoy. And keep in touch.

I suggest next ted shifrin's linear algebra book, actually the one by shifrin and adams. but it costs money, if you want a free one, try mine, off my web page. if you are really strong and motivated to work hard on your own, you may be able to read my 15 page linear algebra book. but if it is too hard don't feel bad, so far no one has said they could read it. but maybe you would be first!

for analysis at a a high level. try to get hold of a copy of Dieudonne's foundations of modern analysis.

heres a nice looking copy for $20. buy it by all means! you will never see a better bargain in your life.

https://www.amazon.com/dp/B0006AWGOM/?tag=pfamazon01-20

 

[MrJB]

Hi. I'd like to be a mathematician, but I'm not sure how to get there.
I graduated in '06 with a BS in Physics, GPA ~2.93. Only realized after graduating that I loved math more than physics. Not sure how to convince a grad school admissions committee that I'm both willing to work hard, and able to do the math. I took some math classes in undergrad, though not enough to be a complete background prep for grad school.
So, I'm wondering what my best options are?
Any advice would be appreciated.

 

[strings235]

great. could you give me the link to your book? and also, would you recommend michael artin's book on linear and abstract algebra?

 

[quasar987]

What is so great about Dieudonne's book?

And what does it cover?

 

[Emmanuel114]

http://www.archive.org/search.php?query=dieudonne

Online version?

 

[quasar987]

Great. The DJVU file doesn't work for me but at least I got to see the table of content.

 

[mathwonk]

please forgive brief answers as work has begun again. feel free to ask for more details. my links are on my public profile, or search math dept uga,

Dieudonne was a brilliant member of the famous bourbaki math group and wrote one of the first books in the early 1960's which went well beyond the traditional books on advanced calculus to rpesent the modern point of view on analysis.

he also wrote up the works of grothendieck, arguably the most famous mathematician of the last 50 years.

as to how to become a mathematician, I myself after a checkered career, just read the books and taught the courses and went and sat for the prelim exams at the university of washington, apparently outperformed the students there, and got an offer from them.

 

[ekrim]

hey mathematicians, i was wondering if its too late for me to live the math dream. I'm a junior math/mech eng major, and I've taken cal1,2,3, linear alg, diff eq, and complex analysis. I will be taking partial diff eq this fall. However, I have no training in proofs and had to use my own crackpot proofs on complex analysis tests. I also never paid too much attention and just studied the night before to con an A out of the class. Naturally, I've forgotten everything even though i have a 4.0. What should I do to make myself grad school worthy despite my ineptitude?

also, I say "math" rather than "maths." Could this be holding me back?

thanks

 

[leakin99]

Hey guys, first time posting in this thread. I am an undergrad math student who is mostly interested in applied math/medical physics. Anyway…I found this great website with a free ebook called “Intro to Methods of Applied Mathematics”. When I opened it, my eyes just lit up. It has everything! Well, at least for the undergraduate level. It’s 2000+ pages and about 9mb so it takes a bit to load up. I have not gone through the whole thing, but from what I’ve seen so far, it seems example based. Just thought I share this since I found it so amazing lol. Sorry if it has already been posted…

http://www.cacr.caltech.edu/~sean/applied_math.pdf

 

[mathwonk]

mike artin's book algebra is probably the best out there for those who are ready for it. i would not have written my book if i had been better acquainted with it, i would have just used his book in my class.