Should I Become a Mathematician?

[Bourbaki1123]

Real analysis is kinda the staple upper division math class, its absolutely necessary for grad school even if you focus in another area like set theory or algebra. Most of the programs I've seen expect you to have had analysis and topology/axiomatic geometry

 

[Les2.0]

How much do mathematicians get paid and in what way. Is it a fairly politics-free occuption

 

[MathematicalPhysicist]

Is it a fairly politics-free occuption

Every place where money is involved there's politics.

 

[DrJD]

Hey mathwonk,

I just had a question for you... Three pronged actually: First I am in medical school right now and have found that the more time I spend in the biological science the more I miss math! Anyway it has been quite a few years since I took Calculus in college and was trying to get back into it. I'm thinking of going through Apostol's slowly and really making sure I remember everything, what do you think?

Secondly, what would you suggest in terms of where to go after I get through Calculus? Linear Algebra? Does Apostol's Vol. II cover all the linear Algebra I would need? Just general advice would be great.

Finally, I was wondering if you know anyone personally who has come back to a math/physics career later in life and made significant contributions. For financial reasons at this point I need to see medicine through to the finish. (Loans!) I'm planning on going for a specialty with the most physics/math in it, but was just curious if I decided to go back to to get my PhD later in life if I would be laughed out of most departments.

Thanks a lot!

 

[uman]

Following Dr. Smith's advice to "read the masters, rather than their students", when I got to the sections on Lebesgue integration in my analysis book, before looking at them I decided to take a look at H.L. Lebesgue's original writings on the subject. Although I can read French, English would be more comfortable. Does anyone know if his "Intégrale, longueur, aire" has been translated?

 

[PhysicalAnomaly]

I just had my supervisor advise me to use Atiyah Macdonald's Introduction To Commutative Algebra for a first course (with a bit of Artin on the side). Can anyone tell me at what level the book is actually meant for? I had a look on Amazon and the first few pages seem like it's accessible (ie, had no problem understanding it). But I'm a bit intimidated by the fact that some of the chapters are 5 pages long.

 

[quasar987]

For a first course on what? On algebra or on commutative algebra? And if the latter, have you studied rings and modules before?

 

[PhysicalAnomaly]

A first course in algebra with some prior knowledge of groups and applied linear algebra. Obviously, I'll do some preliminary work on rings and modules with Artin. But I just wanted to know what kind of student the book is actually written for so that I can prepare myself.

 

[quasar987]

Well if it's for a first course on algebra, I doubt the material in Atiyah & Macdonald will have any relevance to what will be studied in the course! A first course on algebra usually talks about group while Atiyah & Macdonald is about commutative rings.

 

[PhysicalAnomaly]

I should have made it clear - it's not a first course... it's more like a first proper encounter. I'm actually doing a supervised reading course. Hence having a supervisor.

 

[Unknot]

I am not sure why you are not looking at something like Hungerford, Lang, Jacobson, or something like that, but if your advisor thinks Atiyah-Macdonald is appropriate then it probably is. Although it's really weird from your description because that's such an awkward choice for a first PROPER encounter with algebra. More like a course in commutative algebra that is. Actually, it WILL be a course in commutative algebra. But if you find it accessible - well let's see I have a copy here.

Hm I guess it's possible to learn from it things about rings and modules, but...

Maybe your advisor has a secret plan? Atiyah-Macdonald followed by Hartshorne is always mind-blowing, after all.

 

[PhysicalAnomaly]

Is that a good thing? What is this Hartshorne you speak of?

His specialty is in algebraic geometry if that helps...

 

[Unknot]

There we go. Commutative Algebra - Algebraic Geometry (Hartshorne) is the classic way to get into the subject.

He wants to teach you his specialty!

 

[cesc]

How come you have a reading course for a first course in algebra?

wouldn't you normally have just as part of coursework?

 

[eastside00_99]

I don't see anything wrong with starting with commutative algebra from the get go. I think it could make sense to talk about fields first. I mean geez these are the things that say an a lot of undergraduates work with if they study engineering and physics. I could see a course where you start like this fields -> matrices, vector spaces -> rings -> algebras and modules and then bam you are at the Cayley Hamilton theorem which is in Atiyah & Macdonald.

 

[PhysicalAnomaly]

I'm special. =P

Well, my uni doesn't have a very strong pure maths programme per se since very few people are actually interested in pure maths so it's all pretty easy. However, they do allow and encourage the capable and ambitious ones to do advanced studies.

 

[qspeechc]

That reminds me of my sorry state at uni.

 

[Bourbaki1123]

This is much like my school. There are only a handful of dedicated math students and even fewer students who want to go on to be mathematicians (probably less than 5? At least 2-3) so standard classes in upper level math beyond algebra and analysis are virtually non-existent(we have number theory, Discrete math, a graph theory course and PDE as well as a number of other classes but these don't run every year and sometimes not at all). However, since there are only a few strong math students, we have full reign over the professors who usually are happy to do an independent study/directed readings course.

I'm looking at Atiyah-Mcdonald and it looks like if follows directly from the Dummit and Foote material in chapter 9; it reviews ideals, maximal ideals, prime ideals nilpotent stuff, algebraic closure. I'm not sure how penetrable the material is without any background, however. It seems kind of odd to go right into a book which seems to presuppose a good deal of knowledge, however it will surely be manageable with the help of a professor.

What do you guys think of Eisenbud's book on commutative algebra?

 

[Unknot]

Matsumura I like better. But you need to look at both, Eisenbud's book shows that he is very interested in computation. Matsumura is more abstract.

 

[PhysicalAnomaly]

Well, I'm preparing myself with a few chapters from Artin. I'm hoping that'll make things easier to swallow.

Oh, and I'm confused... is homology a part of algebraic topology? Or is it it's own area? Would Munkres be a good place to learn algebraic topology or would a more specialised book be better?

 

[Unknot]

Homological algebra and homology (from algebraic topology) are similar.

For algebraic topology, I used Spanier but perhaps nowadays Bredon is much more reasonable choice. I never liked Munkres that much, too expensive.

 

[PhysicalAnomaly]

What about Massey?

Hmmm... I think I'll do algebraic topology in the second semester... best not to take on too much at one go.

 

[Unknot]

I have never read that book, so I am not sure. But Hatcher seems popular, just to give you another choice.

 

[alligatorman]

what happened to mathwonk?

 

[JasonRox]

I just realized today that I spent my whole undergraduate years thinking I was going into the topological field.

I'm doing my Master's in Number Theory.

 

[qspeechc]

Don't you find number theory problems are either quite simple, or devilishly difficult? I wouldn't know, I haven't done too much number theory, but that's how it seems.

How did you go from topology to number theory. Did the subject matter of topology lead you to number theory?
I'm still an undergrad, and I thought I was going into algebra, until I took a fun analysis course (my first analysis course was not a fun experience...), and a horrid algebra course. These things depend so much on the text used for me.

 

[JasonRox]

Problems in Number Theory can go from easy to mediocre to hard. Just like anything else.

I went from interests in topology to number theory simply because I didn't think I could do it. Then luckily for me the number theorists at my school asked me to work with him on my Master's. So, I took the offer.

Um... now I just work hard everyday. I'm working harder than I ever had before. With regards to course work.

 

[Werg22]

Mathwonk, I already asked this in another section but I'm interested in your answer particuliarly. Have you ever looked at Apostol's Mathematical Analysis? If so, have you looked at both the 1st and 2nd edition? Do you think the 1st is inferior to the 2nd and not worth getting?

 

[alligatorman]

Mathwonk hasn't been here in more than a month.

 

[JasonRox]

Mathwonk, I already asked this in another section but I'm interested in your answer particuliarly. Have you ever looked at Apostol's Mathematical Analysis? If so, have you looked at both the 1st and 2nd edition? Do you think the 1st is inferior to the 2nd and not worth getting?

2nd edition. It will correct errors from the 1st edition.

Why even ask such a question? Just buy it if you want to learn Analysis.

Second, Apostol isn't the only one either. If you are nervous about the quality, buy something else.

The best books are those that explore the subject and provide the perfect questions. I used to think Spivak was good, but now that I think about it, I don't think it is. I think it is good only if supplied by another textbook to give that nice, even easy exploration or by a really good professor that puts the time into his lectures.

I've never seen an Apostol textbook except his Number Theory book (same guy?), and looks like any other to me.

Note: I judged it, not by its cover, but its table of contents and preface. (Essentially a summary of what to expect.)