The Should I Become a Mathematician? Thread

 I'm sure you've heard this before, but my grades suffer from "dumb mistakes." I don't know how to stop making them, and I don't know if they are something that is eventually going to be ironed out or if I have to find another way to fix this. I really do take my time with everything, but they still seem to crop up.
I am a master at making dumb mistakes. That's part of why I did so much better when I got past high school math and lower division math. In the long run, it doesn't matter that much, as long as the mistakes are inadvertent ones. In "real world" situations (including research), you can check your work 20 times if you want to get it right.

 From childhood I was passionate about mathematics but I noticed I can not afford to become a mathematician.
Anyone can afford to be a mathematician to some extent. In America, all you have to do is do really well in high school and you can get a scholarship. Then, in grad school, you usually get paid. Even if you don't go to college, you can still teach yourself quite a bit on your own.

 Recognitions: Homework Help Science Advisor you might try becoming a mathematician who spends more time with her family. you could start a trend.

 Quote by mathwonk you might try becoming a mathematician who spends more time with her family. you could start a trend.
I recently started getting invited to gatherings with our math department, and it was funny to start finding out how many of the professors were married to each other. I had no idea, because most of the women kept their last names. So, I guess that's one way!

-Dave K

 Recognitions: Homework Help Science Advisor there are at least 5 couples in our department such that both spouses are either professors or instructors.
 Good to know. That was my intended course of action. (go outside the "syllabus" if I feel like it but then when there's exams, I focus on those) A lot of what motivated my initial question was that I had some ~12 exams within the span of 3-4 weeks and they were all exams that are much in the vein of the usual standardised testing... Does anyone here have any experience with the Jerry Shurman (at Reed College) notes on single variable calculus? I'm currently checking out Apostol and Spivak using the free previews available on Google Books and Amazon, before choosing which of the two to buy. Shurman says that he learned from them, Courant and Rudin. Mathwonk, I read on another post that you used Sternberg and Loomis after Spivak back in the day. What do you think about this course compared to the modern alternatives - Apostol's second volume, I guess? Would one be correct in assuming that the current MATH 55 course at Harvard assumes (equivalent?) knowledge of both that book and Spivak?

 Quote by Mariogs379 @mathwonk, Bit of a specific question but I thought you might be a good source of advice. Here's my background/question: Went to ivy undergrad, did some math and was planning on majoring in it but, long story short, family circumstances intervened and I had to spend significant time away from campus/not doing school-work. So I did philosophy but have taken the following classes: Calc II (A) Calc III (A) Linear Alg. (B+) ODE's (A) Decision Theory (pass) Intro to Logic (A-) Anyway, I did some mathy finance stuff for a year or so but realized it wasn't for me. I'm now going to take classes at Columbia in their post-bac program but wanted to get your advice on how best to approach this. They have two terms so I'm taking Real Analysis I in the first term and, depending on how that goes, Real Analysis II in the second term. I'm planning on taking classes in the fall semester as a non-degree student and was thinking of taking: Abstract Algebra Probability (some type of non-euclidean geometry) Anyway, here are my questions: 1) What do you think of my tentative course selection above? 2) How much do you think talent matters as far as being able to hack it if I ended up wanting to do grad school in math? 3) I'm also having a hard time figuring out whether math is a fit for me. By that, I just mean that I really like math, I'm reading Rudin / Herstein in my free time, but I've spoken with other kids from undergrad and it's clear that they're several cuts above both ability and interest-wise. Any thoughts on how to figure this out? Thanks in advance for your help, much appreciated, Mariogs
Thought I'd update. This 6 week real analysis class covers the first 6 chapters of Rudin. I'm finding the homework hard but we have a midterm on Monday; he showed us the one from last year and it looks *relatively* easy (definitely compared to the HW). Anyway, thinking I'm gonna take RA II, and some classes in the fall, decide about applying to grad school the following year.

In short, material's harder than I appreciated but also much more interesting. I think I'll enjoy it even more once I get more comfortable with some of the concepts (I feel like I spend a lot of time trying to understand Rudin's language/terminology/general technical writing even when he's conveying a *relatively* basic idea. A good example is his def. of convergence; easy now, but was a bit confusing at first. Tho I think once I'm able to get the ideas more easily, it'll be even more rewarding.

Thoughts?

 Quote by Mariogs379 Thought I'd update. This 6 week real analysis class covers the first 6 chapters of Rudin. I'm finding the homework hard but we have a midterm on Monday; he showed us the one from last year and it looks *relatively* easy (definitely compared to the HW). Anyway, thinking I'm gonna take RA II, and some classes in the fall, decide about applying to grad school the following year. In short, material's harder than I appreciated but also much more interesting. I think I'll enjoy it even more once I get more comfortable with some of the concepts (I feel like I spend a lot of time trying to understand Rudin's language/terminology/general technical writing even when he's conveying a *relatively* basic idea. A good example is his def. of convergence; easy now, but was a bit confusing at first. Tho I think once I'm able to get the ideas more easily, it'll be even more rewarding. Thoughts?
Wowza. Six chapters of Rudin in six weeks? How many times do you meet every week?

I'm not sure what you meant by thoughts?", I'll take it that you ask how to understand the material quickly. I don't think there's a tired and true method to expedite one's understanding other than practice in time. I'll also add that if you manage to understand the ideas in Rudin in 6 weeks, then you're doing fine. Also, this stuff takes a lot of time to understand. With that being said, try the following:

Write definitions, proofs, concepts, whatever you see fit really, in your own words. By explaining the ideas to yourself, you'll start figuring out how you understand things, and how to approach them. So next time you read a definitions or a proof, you'll be faster.

Get a few more books from your library. Sometimes Rudin is terse, and sometimes those proofs are hard. Other authors expand on the material more than Rudin. It'll be worth it to look some stuff up in those books. I recommend Charles Chapman Pugh's Real Mathematical Analysis. It has the same breadth and depth as Ruding, although sometimes the author does things with less generality.

Read about some of this stuff on Wikipedia. I tried to avoid Wikipedia for a long time, because I was afraid that I'll read an entry that was edited by some crank. All entries I've encountered were nicely written, explained the ideas in depth, and have a nice way of tying things together (how one theorem relates to another, why it's important, generalizations, etc.)

Good luck!

Especially if your first course in upper level math is with Analysis from Rudin. Rudin isn't a bad book, and in fact I like it quite a bit, however, it's a little hard for beginners

In fact, I think that practice and time will help you understand things more quickly

 Recognitions: Homework Help Science Advisor in my opinion loomis and sternberg is a show offy book (my book is harder than yours) and the two volumes of apostol or the two volumes of spivak, or of courant, are much better.

 Quote by Mépris ^ Sounds awesome! Post here to tell us how things pan out. What is "summer B" though? A summer class for business students? --- Does anyone have experience with the math departments at these colleges: - Berea College - Carleton College - Reed College - UChicago - Colorado College -Grinnell College - University of South Florida These are a few places I'm considering applying for next year. I don't know much about any of them except for what is found on their website and that a number of them are in cold, bleak places. And that they're quite selective...at least, for people who're non-US citizens requiring aid!
Just to let you know, it's MUCH harder to get into Berea, than Harvard. G'luck! Out of the "foreign students" pool of accepted students, only 30 aspiring applicants can be chosen, out of thousands. I'd still apply, if I were you. Just cross your fingers for good outcomes, from crazy probabilities. They usually prefer to accept "brilliant" foreign applicants who are living under crisis conditions, really deserve going to college, and/or wont ever have a chance at it; like that talented math-wiz living in Homs, Syria right now.

Either way, it's a great liberal arts school. In my opinion, you could get a great mathematics education there because it seems that their mathematics students graduate with a broad knowledge in mathematics, ranging from pure mathematics, applied mathematics, and statistics/probability; which is ideal, I think. Check out their mathematics courses! The only problem is, though, that they don't offer much variety in mathematics courses :b

And, have you considered, the best one of them all for math (in general), the University of Waterloo? It's in a town close to Toronto, Canada. I'd go there, if I didn't mind getting into debt; "Lulz."

By the way, unless you want to be chocking in debt after you graduate, then go to Colorado College! I'm infatuated with their block plan and great academic programs; and the MAGNIFICENT LOCATION; but it's totally not worth graduating with \$130,000+ in debt.

Lol

 Quote by grendle7 Just to let you know, it's MUCH harder to get into Berea, than Harvard. G'luck! Out of the "foreign students" pool of accepted students, only 30 aspiring applicants can be chosen, out of thousands.
Coincidence I came back to see this post. I read it before it was edited.

I think my grades may actually be just good enough to get me into Waterloo but it's really not worth the money...that I don't have. I don't know much about Colorado; it looked nice and has financial aid on offer, but it's very limited, as with most liberal arts colleges. I probably won't apply there. There's also the issue of limited coursework but few math/physics majors mean that one can try get some "independent study" thing going on. It doesn't mean grad-level courses, though.

Yeah, I read that about Berea. It's definitely going to be competitive but I believe it's free to apply, so I might as well give it a shot. There's also a list of those "free to apply to" colleges, somewhere on CollegeConfidential. It's easy to find - in case you can't find it, lemme know and I'll try dig it up.

Another thing about liberal arts colleges is that bar a few (Amherst and Williams, being one of those), there just isn't much money to give to international students, which makes the competition even fiercer. It makes more sense to apply to larger colleges. Casting too wide a net is also not a very good idea. Too many essays, too much money on application fees, etc but some people can manage that just fine. ;)

This looks interesting:
http://en.wikibooks.org/wiki/Ring_Th...rties_of_rings

 Quote by mathwonk in my opinion loomis and sternberg is a show offy book (my book is harder than yours) and the two volumes of apostol or the two volumes of spivak, or of courant, are much better.
It's the post below, on another thread, that made me ask the question. I had also, per chance, stumbled upon the book, which is available for free on Sternberg's website.

In spite of its "show offy" nature, is the book any good? As for Spivak, are you referring to "Calculus on Manifolds" or is there another text which comes after "Calculus"?

 Quote by mathwonk In the old days, the progression was roughly: rigorous one variable (Spivak) calculus, Abstract algebra (Birkhoff and Maclane), rigorous advanced calculus (Loomis and Sternberg), introductory real and complex analysis via metric spaces as in Mackey's complex analysis book, general analysis as in Royden, (big) Rudin, or Halmos and Ahlfors, algebra as in Lang, and algebraic topology as in Spanier. Then you specialize.