Other Should I Become a Mathematician?

[future_phd]

I am thinking of picking up Spivak's Calculus because we used Stewart's Calculus for our calc 1 and 2 and it really doesn't look like it prepares you well for Analysis courses or Pure Math in general.

Am I right in picking Spivak or is there another one I should pick instead? I want to be prepared for when I take my first Real Analysis class (next September). Also I haven't really self studied up to this point so I am wondering if there are any tips on good tips/habbits for self studying and also should I start at page 1 and work through absolutely everything?

 

[mathwonk]

well start wherever you like. its all very helpful. if you start on page 1, and get bogged down, just skip ahead.

 

[mathwonk]

after talking with recent members of the graduate program, it is still hard to give a completely precise description of how to get into our grad program.

Basically we are looking for candidates who will succeed in our program, and we take everything we can find out about them academically, into account. There is a committee making recommendations, so different people look at different things.

This means everything matters to some extent, recommendation letters, grades, gre scores, extra activities, and also a consistent picture should be revealed by all of these taken together.

The most substantive data is perhaps a record of success in substantial courses over time, but letters from professors giving a personal opinion are also important.

Personal qualities can also matter, as there are a few people whose records show gaps or flaws, but who persevere and improve, and eventually come out on top. These cases are harder to recognize but do exist.

A candidate with a strong record of challenging courses and high grades in most or all of them, combined with high gre's and letters that identify the student as outstanding among all those over a number of years, even at a small college, should stand very well in our competition, but not all successful candidates have these qualifications.

Our current stipends range from 24K - 25K for 5 or more top qualifiers, and those are not for every year, but roughly every other year, to the average stipends of 14-15K. And we apparently do manage to support most students also in the summer. A few students are sometimes admitted without support I believe, provisionally, based on demonstrating success, but this is not the norm.

We are one of only a dozen departments in the US whose VIGRE grant has been renewed, which is testimony to our success and commitment to helping our admitted candidates graduate.

Specifically, our vigre program is considered innovative and effective at "fostering graduate student research at an early stage".

One area in which we excel, outside the usual pure and applied mathematical areas, is in education of mathematics teachers from primary school through high school. This is a collaboration between our excellent mathematics education department and members of the mathematics department.

A recent nationwide study identified UGA as having one of only a very few exemplary programs in math education in the nation. In particular some books for this purpose authored by Professor Beckmann in the math dept. were recognized as outstanding. Candidates interested primarily in preparing to teach mathematics would do well to look over the programs here in math and math ed.

For sincerely interested and qualified students we can usually help provide some assistance to visit campus this spring, in late February 2009.

 

[PowerIso]

1) presence of researchers working in a subject of interest.?
This was the most important factor for me. A strong research group had to be present with well known people in the field.
2) supportive grad program
This was also key. I wanted to feel that the program was behind me and that I would fit in nicely with the group of people there.
3) availability of adequate/generous student stipends.
Also played a role. Adequate was all I was looking for, generous was just a bonus.
4) appealing community/social life.
Not so much for me, I came to grad school to learn math. Good community and social life is a plus, but I also figured if I am there with other people who are interested in the same thing I am, i'll probably have a good social life regardless.
5) prestigious name/reputation of university.
Minor factor, not as important as number one on the list.
6) congenial geographic location.
Not important to me at all.
7) large diverse grad program (to maximize choice of specialty)
I didn't really think about to, maybe I should have. Thinking about it now, this probably should've carried more weight.
8) other?
One other aspect was the number of PhD that graduated from their program that had jobs five years after graduation.
Report Post Reply With Quote

 

[Vid]

The VIGRE grants are pretty great. LSU got their first one this year, and already this Spring there are 5 research classes that mix undergraduates and graduates.

https://www.math.lsu.edu/dept/vigre/crews

 

[Bourbaki1123]

How much weight would solving some problems in undergrad journals such as Crux Mathematicorum and having your solutions displayed hold in admission considerations?

 

[mathwonk]

well it would be another plus, maybe a small one, but it shows ability and interest. Of course if the problems are really hard and the solutions are brilliant, it counts more.

 

[Epsilon36819]

Mathwonk,

I have a question for you. There is this graduate class given next term which is a second course in topology. The first class was given this term and I unfortunately couldn't take it, as it overlapped a core course for my degree. This first course covered the basic of topology and the fundamental group, covering spaces, simplicial complexes, singular and simplicial homology, among other things.

Now I am very tempted to take this second course without the prerequisite. I do know the basics of topology and I am willing to put lots of time and work (as well as take a lighter courseload) to make up on my own for what I don't know yet. The thing is I am really, REALLY interested in the material and the course is given by one of the best teachers in the department. I also know without a doubt that I will improve by taking this class. And I don't care what grade I get (as long as I pass, I guess...)

However, my advisor objects to this idea, saying that courses must be followed in the right order to ensure that we are properly ready.

Of course, I am not asking you what to do (you don't know me nor the course) but I would like to know, as a general rule, if you would encourage interested students to skip a few steps and put themselves in a situation where the level of difficulty is much higher for them than for anyone else in the classroom. Or would you instead suggest taking time to lay down a proper foundation, at a slower pace, risking perhaps to not be as challenged as one would like to.

Thanks in advance!

 

[mathwonk]

the general question usually has answer no. but your specific question may have answer yes. The reason is that fundamental group and so on is not really a necessary prereqisite for many later topology courses.

so the person to ask is the professor offering the spring semester course. He/she will know whether you will really be overwhelmed by not knowing the previous material. you also have the option of spending the xmas break reading a book on fundamental groups, and covering spaces, like that by massey.

 

[Epsilon36819]

Thanks mathwonk, I'll have a look at this book.

 

[mathwonk]

try this:

Algebraic Topology: An Introduction.
Massey, William S.

[30 Day Returns Policy]
Bookseller:
J. HOOD, BOOKSELLERS, ABAA/ILAB
(Baldwin City, KS, U.S.A.)
Bookseller Rating: Book Price:
US$ 15.00

 

[Vid]

I've been reading Introduction to Algebraic Topology by Wallace, and I really like it. It contains all the point set topology required.

 

[mathwonk]

great suggestion. is this about the fundamental group? i think this was the first book i read as senior that really made me understand algebraic topology for the first time! if so, it is really clear and thorough for beginners just trying to grasp the concept of homotopy.

 

[PhysicalAnomaly]

What's the difference between an undergrad journal and the typical kind? I was under the impression that the usual journals also published undergrad research.

What are living costs like in the USA? I live in aussie and 14K doesn't really sound like it's enough to live like a pauper but that's compared to our currency and living costs. Do students get much more from teaching?

 

[Vid]

Undergrad journals publish expository articles on a topic rather than just new research.

 

[mathwonk]

14K is not very much. But in Athens, Georgia life is cheaper than in many places.

Our problem is our average stipends are low, but our good stipends are high.

So I would suggest applying for our best stipends, and deciding what to do if you only get the average one.

 

[PhysicalAnomaly]

I have just been made aware that many universities require one to be able to read maths texts in German/Russian/French to do a PhD. I don't know either. *panics*

 

[SticksandStones]

Mathwonk: do you know what the current state of research into Topology is? I mean, is there still a lot of interest in the topic?

 

[mathwonk]

well with perelman's fairly recent solution of the poincare conjecture, yes, i would say topology is one of the hottest subjects.

 

[Bourbaki1123]

Mathwonk,

You seem to give quite a bit of praise to Michael Artin's book on algebra. What do you think of his father Emil's book on the subject?

 

[mathwonk]

the only books i know of by the father are "galois theory" notes from notre dame lectures, and "geometric algebra". these books are great classics, but they are not as easy to read as mike's book. mike wrote his book for sophomore students whereas emil seemed to write his books for eternity. i.e. whoever can read them is welcome, and not one word is wasted.

i myself never could really learn from e. artin's galois theory book as it was too condensed for me. he also has some algebraic geometry notes from nyu but those also leave much to be desired from my viewpoint for learning ease. But it is almost sacrilegious to criticize anything written by e. artin, who is regarded with great awe by many people.

but i regard mike's books as much more user friendly.

but as i meant to imply, i am not aware of any books by e. artin strictly on abstract algebra. of course the great book by van der waerden is based on lectures of e. artin and e. noether. Is that what you mean by e. artin's book? I like it quite well and learned a lot from it as a student.

If that is representative of e. artin's lecture style then he was a very fine teacher. Indeed I have read in his own works that he always tried to write more than usual on the board when lecturing so that the student who was not following could recover the lecture from his notes. this struck me as admirable and i long followed this practice in my own lecturing.

 

[SticksandStones]

well with perelman's fairly recent solution of the poincare conjecture, yes, i would say topology is one of the hottest subjects.

That's good to hear. I started reading Cairne's "Introductory Topology" and so far I've found it pretty fascinating. I can't wait to be able to take a class on it.

 

[mathwonk]

topology is the most fundamental branch of geometry. as such i believe it will always be one of the most fundamentally important topics.

the ideas developed in topology of ways to understand different types of connectivity, are absolutely crucial in all areas of mathematics.

the tool of cohomology, which is present in algebra, geometry, and analysis, received its greatest development within topology. Sometimes I think the greatest ideas in mathematics grew there.

that is probably unfair to analysis, but anyway.

 

[SticksandStones]

Your post went a bit over my head. :)

I really liked Abstract Algebra when I took it. It looks like group theory plays a roll in Topology, from skimming some things. Am I right in assuming this?

 

[mathwonk]

i am just saying that the ideas that were developed in the 30's, 40's and 50's within topology, like bundles, characteristic classes, and sheaves, and cohomology, grew outward and illuminated complex analysis and algebraic geometry in the 60's and 70's and are universally used now.

you are currently at the beginning, studying point set topology, but later when you study algebraic topology this will be meaningful.

 

[nomaris]

Mathwonk,

In the first page of the thread you said that a high school student should explore probability, linear algebra, calculus after having a thorough grasp of geometry and algebra. What constitutes knowing Euclidian geometry and algebra well?

 

[mathwonk]

i would say mastering harold jacobs' books on those topics are a minimum for a high schooler. if more ambitious you might search out smsg books from the 60's. say arent there numerous such recommendations in that thread? have you only read page 1?

 

[PhysicalAnomaly]

Do they really expect PhD students to learn 2 foreign languages in 3 years?

 

[Wretchosoft]

Do they really expect PhD students to learn 2 foreign languages in 3 years?

I don't see why this requirement would be intimidating. Two semesters in college is enough to teach the average student the basics of a language; with the generally higher capabilities of PhD students, I would imagine this time could be shortened. From there, it's just practice.

 

[alligatorman]

From what I've heard, the language exam is usually just to translate a mathematical paper from the language into English. I can't imagine that it's too difficult.