Other Should I Become a Mathematician?

[mathwonk]

there is no difference at all mathematically in the french and english versions, so unless you enjoy the beauty of the french language i would read in the language that is easiest for you. for me that's english.

 

[mathwonk]

easier proofs of a result are usually ones that ignore all the information except the minimum amount needed to get ot the weakest version of the result. the harder proof usually proves more than necessary, and will hence sometimes indeed be useful for some other purpose as well.

 

[jostpuur]

Oh, btw:

who wants to be a mathematician?

o/ (jostpuur raises a hand)

I'm a student who found himself a little bit disappointed with physics, and who then became a student of mathematics. I hope I would be interested in mathematical physics, but I'm not really sure, because I don't think I know what it is, actually... Does this forum have university folks who do research in some mathematical physics group?

 

[eastside00_99]

Help!...

Hey, I am need some help actually with becoming a mathematician. I very worried about my graduate prospects. I feel as if the competition is very fierce (which I kind of like), but its so much that I feel as if my application my get looked over for undeserving reasons.

I am interested in Geometry (Possibly Algebraic Geometry or Arithmetic Geometry (They are hard so I am not completely sure it is the best choice even-though they attract me the most)). I also like Algebra, Combinatorics, and Global Analysis. I have hit a brick wall trying to understand schemes and am missing a lot of commutative algebra, so Analysis is starting to appeal to me an more (especially as I study more advanced Analysis). Nevertheless, I don't give up that easily. So I am still pursuing it.

Here is my raw data:
Senior NCSU
overall gpa 3.3
math gpa 3.5
gre v 530
gre q 710
gre math sub ... results pending


As you can see my overall gpa is somewhat low (maybe terribly low for most who apply to grad school in math). But, it really isn't a good indicator for my ability to get my Ph.D. I will have three solid recs. (one prof taught at two of the schools I am apply to). The greatest strength I have (and I consciously planned this), is that I will have 36 hours of grad credit when I graduate. These are the grad courses I have or will take:

Advanced Analysis
Functional Analysis (two courses)
general topology
algebraic topology
linear algebra (grad)
lie algebra
Abstract algebra (two courses, grad)
smooth manifolds
computational algebraic geometry
graph theory

I should mention I did independent study in Algebraic Curves all summer long also. I had, am, and will work very hard to do this, but it is worth it because my aim as an undergrad is to be prepared to pass the quals at whatever uni that accepts me with the minimum or no fuss (which will pretty much ensure that I get the Ph.D.--meaning most who drop out are those who can't pass the quals).

I don't know; I just feel very prepared to do grad work because I have been doing it. I have gotten use to the level of work that is required for the first or second year of grad school. But, I am worried that this will not really show up in the application because of silly factors like overall gpa. Anyway, here is the list of schools I am applying to (they are listed in order of preference based on overall rep, strength in algebraic geometry, and location):

1) brown
2) berkeley
3) Rice
4) Duke
5) U of Washington
6) Washington U
7) Cuny
8) U of Ill (urbana)
9) unc (chapel hill)
10) georgia

Now, I actually think that schools like georgia, ill, and unc are better than Rice and Duke and maybe Cuny, but the location or overall rep forces to put them in this order. I may turn out to decline an acceptance from say Duke over something lower on the list. I don't really know at this point. I do know that these are all really good schools and that I would be very happy at any of them (brown and berkeley are completely out of reach but I am applying just for fun). Now, what do you think my chances are for getting accepted to any of these schools? Do you think I am prepared and/or are desirable to any of these programs?

I do have the ultimate fall back; I can do a masters at NCSU in a year or a masters at wake forest in a year if I want to. I think I will apply to these things so that I have such a fall back (I can get support for doing this). The reason I am kind of afraid of my chances is the people I keep running into really have stellar marks (albeit I have not ran into a single person who has completed the level of course work I have) but they balance that out quite nicely with 4.0s or being from a very nice school. For instance, I was talking to an undergrad who is at one of the top schools (but not in math) and he said that I will probably not get into any of these schools. Although he said Georgia is feasible. He probably doesn't know what he is talking about because I kind of think if none of these schools accept me then georgia will not either. He said that my overall gpa and quant score is too low and that I should aim much lower (whatever that means). But, this does confirm my thinking that I am in a very stiff competition here and that others although not as well prepared as me will have much better looking applications. This infuriates me a little; but, it is how it goes.

Anyway, what advice do you guys have? What are my chances? Do you think some of these schools will see that I am prepared and ignore the annoying average overall gpa as well as gre scores? If they don't, I have to admit I will be little bit angry. I mean as much work as I have put into this and everything and then getting rejected I know would be a miserable experience as well as probably effect my confidence in my own future. Regardless, I am happy with doing the grad work when I could have just taken easier math courses and gotten all A's. I feel challenged and stimulated. Mathematics is great at any level; and I have gotten four years to spend as much time on math as I have wanted. Finally, the prof I worked with over the summer doesn't seem very concerned. He gives me the impression I will not have very much trouble getting into some of these schools. He knows my work and my grades, but maybe he doesn't see the competition I see. Anyway, please respond with your comments and suggestions on whether or not my choices are viable.

 

[cristo]

Now, what do you think my chances are for getting accepted to any of these schools? Do you think I am prepared and/or are desirable to any of these programs?

You appear to be prepared, and it seems somewhat apparent from your post that grad school is something you want to do. I don't know much about the US education system, but I can't imagine that universities will accept people on solely their GPA.

(Incidentally, mathwonk is a professor at uga, so may have something to say!)

The reason I am kind of afraid of my chances is the people I keep running into really have stellar marks (albeit I have not ran into a single person who has completed the level of course work I have) but they balance that out quite nicely with 4.0s or being from a very nice school.

I presume that your GPA is calculated from an average over your the grad classes as well as the undergrad classes you've taken? If so, it's pretty obvious that it's easier to get a higher score on less advanced classes! I imagine if you send in your transcript (list of marks in specific modules) then this will be looked at, and probably won't matter half as much as you are worrying about!

For instance, I was talking to an undergrad who is at one of the top schools (but not in math) and he said that I will probably not get into any of these schools.

Would you take your car to a doctor to get fixed? I wouldn't pay much attention to what someone who isn't studying maths has to say, especially as he appears to be just discouraging you!

Anyway, what advice do you guys have?

Just keep working hard, and stay enthusiastic. I imagine if you get an interview then it'll be easy to show your enthusiasm; the hard part os getting an interview (that's even if they interview in the US; I imagine they would, but not 100% sure!) Either way, make sure your application letter and CV (if needed) are good-- i.e. don't write them the day before your application is due!

Good luck!

 

[PowerIso]

For instance, I was talking to an undergrad who is at one of the top schools (but not in math) and he said that I will probably not get into any of these schools.

There will always be people who will want to hold you back and make you afraid. Just shrug it off. I say you probably will have a good chance to get into these schools depending one how good your recommendations are, and what activities you have done. It's really hard to tell though, grad school admins are a crazy bunch.

 

[J77]

and i also recommend as the greatest geometry book of all time, the one by euclid.

I've just received this edition -- what a great book!

I've never read any Euclid before, but having read the first few propositions, it's brought back to me what I first enjoyed during elementary school.

The simplicity of the proofs is the real winner here.

I've seen mentioned a few times that the simplest proofs are the best, and these writings prove this. I think I mentioned that a couple of weeks ago I fell asleep in my office reading a proof. If only all current mathematicians wrote in the same style as Euclid (translation assumed) did, the world would be a much brighter place

 

[eastside00_99]

Thanks cirsto and poweriso. I had a long talk with one of my professors and he said that I should be able to get in, but he said that my score on the math subject is going to be very important because of my GPA. He said that the university is going to want to know that I took the graduate courses because I really understand the basics and the GRE subject will indicate that. He said a 700 should be good enough and that anything above 750 is very strong. He also said that if I get below 650 I should take it again. So, we will see what my score is. I will know this in a couple of weeks.

To mathwonk, any information about how I compare to other students applying to UGA would be very appreciated. I am sure you get all kinds of people: people with stellar grade, great GREs, and people with a lot of grad credit. Do you think a 700 hundred with my gpa and the grad credit will make very strong application to UGA?

 

[morphism]

I have a question. How well did you do on the graduate courses?

 

[eastside00_99]

Some As some Bs.

 

[morphism]

Then, personally, I don't see why your overall GPA will be a hindrance.

 

[Werg22]

Mathwonk, would you happen to have introductory lecture notes on commutative rings the arithmetic of their elements?

 

[mathwonk]

look at my web notes in algebra.

as to your grad application, these are the things in your post that appeal to me:

I feel as if the competition is very fierce (which I kind of like) ...[this is good]....Nevertheless, I don't give up that easily. [this is good.]

"Here is my raw data:
Senior NCSU
overall gpa 3.3
math gpa 3.5
gre v 530
gre q 710
gre math sub ... results pending "

this means nothing without knowing the school, the average grade, the other students, the profesors opinion of you etc... but the gre is kind of low."These are the grad courses I have or will take:

Advanced Analysis
Functional Analysis (two courses)
general topology
algebraic topology
linear algebra (grad)
lie algebra
Abstract algebra (two courses, grad)
smooth manifolds
computational algebraic geometry
graph theory"

[this means also nothing unless i know how you did in these courses, just taking courses means nothing.]

I should mention I did independent study in Algebraic Curves all summer long also.

[this is good since it shows interest.]

I had, am, and will work very hard to do this [this is good, as evidence of motivation.]

"my aim as an undergrad is to be prepared to pass the quals at whatever uni that accepts me with the minimum or no fuss (which will pretty much ensure that I get the Ph.D.--meaning most who drop out are those who can't pass the quals)."

[this is bad, as it indicates a desire to take the low road.]1) brown
2) berkeley
3) Rice
4) Duke
5) U of Washington
6) Washington U
7) Cuny
8) U of Ill (urbana)
9) unc (chapel hill)
10) georgia

[this is a good list of schools.]

Now, what do you think my chances are for getting accepted to any of these schools? Do you think I am prepared and/or are desirable to any of these programs?

[without your letters of evaluation from your profs it is impossible to guess at your chance of acceptance at these schools. even at georgia your gre is low. without more data i would myself not vote to admit someone with those scores. with all those grad courses it is hard to understand why you would not score 780 or more on gre. i hope this helps.]

 

[eastside00_99]

I guess I could take the general again. I don't know why I didn't get a perfect score on the quant section. I guess I made some mistakes. I have to admit that I always envisioned the gre general as something grad schools do not care terribly about (in regards to math). Maybe, this is a mistake. I had the impression that the GRE general was something for the overall graduate school that one has to get a minimum score in order to get support. I am sure if I take it again I will do better; I will wait for my GRE subject test scores to come in before I decide to do this.

Anyway, thanks for your comments mathwonk. Yeah, I didn't mean that I don't want to work hard my first or second year to pass quals. It is just that I had a friend at the time who was a grad student at U Penn who said that in order to prepare for grad school in math, it is best for me to try and get as much exposure as possible to the level of work expected for the quals. Maybe that was misguided in that I could have taken a lot more general math courses at the undergrad level. Truly, I have heard mixed things about this, and I am not sure what is the best path. But, at a certain point in undergrad math -- it was probably during my junior year taking my first real analysis course and a general topology course -- I noticed this huge difference in the instruction of these two classes. Real analysis was basically about how to write rigirous proofs; but topology (while that was of course a part of it) was about having a good idea or two. Truthfully, topology was a very hard class (and I had even studied general topology before I took it); the test were difficult and completing them in 50 minutes was quite a frantic time. But, man, when you had that geniune good idea, and you solved this "tough" problem under pressure; that was a good feeling. I never got that from any of my undergrad classes (although they served another purpose which was to learn about some of the basics of modern mathematics and to be able to write proofs). Maybe, it was a bad idea to skip a few undergrad classes, but I haven't been able to help myself.
This is enough raving. I guess you recommend I consider taking the GREs again (or else balance that out with something else). That is understandible. My Recs should be pretty good; and hopefully the GRE subject could sooth doubts about my ability to think quickly about basic material.

Anyway, back to the orginal discussion I guess.

Here is a good website for some writtings of Alexander Grothendieck:

http://www.grothendieckcircle.org/

Its really amazing to read his letters to Serre to see how casually he talks about really abstract mathematics, how he offers advice on possible future research, and just a good mixture of formal and informal mathematical writing.

I personally want to read the something by Galois. He is sort of the person the young adolecent future mathematician can relate to.

 

[mathwonk]

if you really care about doing math, you have nothing to worry about. you will find a school where you can progress.

 

[eastside00_99]

Yes. This is true. I have a place I can go and there is no need to worry a terrible amount.

I can't force a school to accept me. If these schools feel as if I am not qualified, then that is what happens. I pretty confident in my abilities but there may be something to such a thing happenning to me in that it may be a good idea to stay a year and study some more. I am a little concerned that if this happens, it would be somewhat of a waste of time in respect to getting the Ph.D. But, that doesn't mean some good will not come out of it. Maybe, I will be able to get into a very good school after such a time and also be more prepared for the competition at this school. I guess I feel as if I want to be "great" and very attractive to the schools I apply to, but right now I feel as if I am in a position of just squeeking into admissions which is kind of a downer. It definitely hurts that my GPA was a 3.7 just a year ago but that I got one very low grade in a statistics course (the abosolute minimimum that will count toward my degree) and a C in a basic computer programming course because of the lack of time I spent on the course. I envisioned graduating with a very high GPA and a lot of grad credit. I actually transferred to the university I am at and these are really the only "bad" grades I have gotten. I fumbled the ball a little and I am paying for it without a doubt.

 

[mathwonk]

i did not say you were not qualified, or did not appear qualified. i said much of the data you present is not that useful in deciding. the best data is the letters from the professors.

i had a 1.2 gpa my first three semesters in college, out of 4, and still got into a good grad school. then i flailed around for 5 years without finishing, doing essentially nothing the last 2 years. i still was recruited by one of the professors from that grad school as a student at the next school he went to, with a top fellowship. it all depends on what they see in you. that is hard to discern from a list of courses.

 

[eastside00_99]

ah, yes, I see. Ok. Thanks for your help.

 

[mathwonk]

a vote for possibly my favorite physicist: bill amend, the cartoonist who writes the foxtrot comic strip, recently retired from the dailies. i always thought physicists were more creative than mathematicians, who ever heard of a funny mathematician?

 

[mjmetro]

complex analysis

as an undergraduate junior, I'm considering taking a graduate complex analysis course next semester (apparently, this is the most commonly taken graduate course by undergrads in the math major at my school). I've taken 2 courses in algebra (abstract), real analysis, 2 courses in linear algebra and the basic undergrad complex variables course. how much does taking graduate courses as an undergrad factor into grad school admissions and in the most general sense, is it generally a good idea? i realize that this is a tough question since anyone answering it knows nothing about my mathematical ability. another question: what is the main difference between a graduate math course and the corresponding undergrad one?

thanks for any help.

edit: by the way, I'm at suny stony brook, if that helps at all.

 

[eastside00_99]

I am going to try and respond to this; but of course, I am not exactly sure.

The grad courses do help in grad school admissions. They will look at the courses you have taking and grades. My question is if a lot of courses actually helps that much. I mean I have made good grades but not all As. I probably could have done much better if I had taken just undergrad courses and concentrated on spreading them out as well as giving myself time to concentrate on my non-major classes. But, I felt at the time as if I would be wasteing some time.

I have not taken a complex analysis course and a good solid complex analysis course is the first thing I will sign up for in grad school. I kind of think that one good idea is to take as much analysis as possible but the same could be said for taking as much abstract algebra as necessary I guess. The reason I say take as much analysis as possible though is that it is much more concrete than say a topology course or an abstract algebra course (in that respect it can be sometimes harder). That is just an idea you can think about. Really, I think you should just take whatever really interest you at the time including at least a graduate course or two so that you can see what the level of work is like.

The difference between a graduate math course and undergrad really depends on the school. Your second course in abstract algebra was probably pretty close to the what a graduate course at your school would be like. The difference that I noticed is that you idea generation, intuition, and wrestling with homework problems was at a higher level. I am not sure I ever felt that these things where appart of undergrad courses.

I think it is a good idea.

 

[mathwonk]

eastside please be very careful in answering questions like this, since as an undergraduate, you have no expertise at all in this area. i.e,. this should be answered by professors not students. having said that i admit your answer is very good and compliment you on your insight.

the grad course is a good idea, if you have already taken all the relevant undergrad courses. as eastside said correctly it does factor into admissions considerations, at least if you do well in comparison to your graduate student competition.

complex analysis is often a relatively easy course, hence is the favorite choice of undergrads taking graduate courses.

play the game carefully, take courses that are valuable to you, and also take a few that count in your favor in admissions. make sure you understand advanced calculus and linear algebra. then take what you want.

 

[proton]

how do you guys study for your upperdiv math classes? I'm currently taking upper-div linear algebra using the book by friedberg. sec 1.6, bases and dimension, alone has 4 theorems and 3 corollaries, including the Replacement Theorem.
If I look at the proof given in the book, I'm able to understand it. But when I look at the thm/corollary after a few hours or so, and try to prove it in my head, often I get lost and forget the process of proving it. Am I taking the right approach by constantly looking at the thms/corollaries and then proving it in my head?
I'm trying this same process for my HW probs that are proofs as well

in other words, what's the best method for studying upperdiv math?also, speaking of complex analysis, how difficult is the undergrad one when one hasnt had any prior upperdiv math, let alone real analysis? (I'm concurrently taking lin alg and complex analysis for applications, which I heard real analysis helps for)

 

[ekrim]

how do you guys study for your upperdiv math classes? I'm currently taking upper-div linear algebra using the book by friedberg. sec 1.6, bases and dimension, alone has 4 theorems and 3 corollaries, including the Replacement Theorem.
If I look at the proof given in the book, I'm able to understand it. But when I look at the thm/corollary after a few hours or so, and try to prove it in my head, often I get lost and forget the process of proving it. Am I taking the right approach by constantly looking at the thms/corollaries and then proving it in my head?
I'm trying this same process for my HW probs that are proofs as well

in other words, what's the best method for studying upperdiv math?


also, speaking of complex analysis, how difficult is the undergrad one when one hasnt had any prior upperdiv math, let alone real analysis? (I'm concurrently taking lin alg and complex analysis for applications, which I heard real analysis helps for)

I took complex as my first upper division course. It was a gentle starter, but the teacher was probably the best teacher I've had in college so far. I came in not having even basic proof knowledge. ask around to get the reputation of the course at your school

 

[Diffy]

Hi,

I am 4 years out of college, with a BS in mathematics. Ever since graduating I have dreamt and thought (almost daily) about mathematics. I love it. At work when someone mentions a number, I think about whether or not it is a perfect number, a square, a cube, what the prime factorization is. I constantly re-read My Abstract Algebra College book and try problems in my spare time. I have a strong desire to learn more about math. I have purchased books since graduating, and have tried to get through them on my own. Unfortunately, I often find that on my own, learning is very time consuming. I believe with help and guidance though, I am fully capable to take my understanding to the next level. I may not be the best test taker, but I CAN work extremely hard. I have a strong desire to learn more, but there are several barriers that stand in my way.

I have a full time job. It is not conceivable that I will go back to school full time. My lifestyle demands the income of a full time job. I am young, but I do have others who depend on me. I have a family. Time with them is not negotiable, they need me, and that’s that.

Part time may be possible. Two hours at night for classes, I can manage a few times a week. I can study and do course work at home. (Who needs sleep? That’s what coffee is for, right?)

At my current job, I am an analyst. I get to study trends, and deal with large quantities of numbers. I don’t get to apply much pure math, but certainly High School Algebra, and sometimes Calculus. Perhaps I am mathematician already… But I don’t think so, not when there is so much more I can learn in Graduate level classes.

I am not sure if I am looking for advice, or encouragement or what. But please comment.

I've been dying for someone to comment. Mathwonk told me to talk to Huryl, but he has not responded. I sent him a Private Message to respond but he must have not checked his inbox for the past couple weeks. Anyone want to respond?

 

[mathwonk]

well, you sound like someone who loves mathematics, and i can only encourage that. but you seem not to be that fascinated with it, i.e. yoiu seem rather to be seeking some human feedback here than spending your time doing math.

it is hard for us to respond since you ask no mathematical questions. perhaps you have not yet found the right books to really spark your interest, and speak clearly to you. it will be easier to get in the swing of a conversation herre if you actually plunge into your studies enough to have some specific questions.

good luck.

 

[Phred101.2]

I never got past complex planes at Uni, because I did an IT qual, but minored in Phys. and Chem. I've since been fairly intensely interested in cosmology and quantum mechanics. I have followed the development of some of the new theories, and I find that, although I can't understand all the symbology, it doesn't matter all that much because I know what the paper is about, I know that it's all terminology and just mapping, just functions and numbers and you can learn it.
I also play piano and can see parallels between learning the shorthand of Math and learning how to read music (and play at the same time).

 

[Droner]

Hello guys, I was wondering if anybody had some thoughts on how best to efficiently study Maths on a degree, because I feel that I am missing something. (Note: I am studying in the UK) For my different modules I have a large number of different textbooks of varying difficulty (including four for Analysis), printed lecture notes produced by the lecturers, and my own notes that I have taken during the lectures. Now, I find that it is physically difficult for me to have enough time to do everything. I've tried to incorporate notes from all the books and lecture notes into one large set of notes, but I fear that, in the large number and variety of material available, I will lose sight of the importance of theorems/proofs that I will actually be examined on. Also, the more that I spend on my notes, the less time that I have to do any exercises on the topics. What do you think is roughly a good proportion to have for theory/problems?

Lots of the books cover very similar topics, and it is difficult for me to convince myself to skip lots of chapters in a book and get to topics that are relevant for that week's work, but that might be something I just need to get over. So really, my problems are a) I feel swamped with the amount of theory available (although not the amount covered in lectures) and fear that missing something is going to compromise my understanding b) Covering too much theory means I get very few problems done beyond work that is given out for credit c) I'm not sure whether to try and read ahead, or instead do huge amounts of work/re-work on the present topics, or to focus on just what is given in lectures, or to get the basic theory understood and spend the great majority of my time on problems; and so on...

Does anybody have any thoughts or advice?

 

[eastside00_99]

How many classes are you taking like this? I say this because taking four classes with four books for each class is way too much. To be expected to read and understand everything in one book for a class may actually be too much.

I really do not know how the UK system works in terms of the test you have at the end of the year. I know it is difficult to get the highest marks but that is about it. If it is your teacher who gives the test then the best bet is to understand pretty much everything in his notes in class, anything he ask you to read on your own explicitly, and any problems he assigns or suggests. But, if it is a test that covers all the material in the books then I don't really have any good advice on that.

I would say working problems is more important than reading a bunch of books and that you could probably work problems in such a way that you highlight some of the theory behind the course.

Also, if it is an oral exam, then just being able to state some of the basics about some theoritical aspects that you do not know in detail will still be impressive. Sometimes just saying that you have seen the proof of a theorem but cannot recall how it goes is worth while in a oral exam.

I would ask your teacher what they consider to be the five to ten most important theorems in the course and then make sure you understand the theory and the proof of the theorems. It may also be beneficial to work with other students--say get four of you guys together each in charge of a different book. Then get together weekly to discuss how the authors discuss things, prove theorems, and material in one book that is not in another. That sounds like the only way to read four books in one semester in an effective a sensible way (unless you are only required to read four books the entire semester and that is it--i.e., you have no other classes).

What I have posted is just my ideas and I am an undergraduate in America who is only in charge of reading one book per course and not required to read all the material in one book. So take this at face value (these are just some ideas you can work with). My personal technique is to do as many problems in each course as possible and to understand and prove as many of the theorems as possible that I am responsible for. I hope this helps.

 

[Droner]

Thanks for the advice.

How many classes are you taking like this?

The four books was a bit of an anomaly. I am taking five courses and have four books for Analysis, one book for each of DE / Algebra / Vectors&Matrices, and no book for Relativity. (But add on the lecture's notes to each of those)

I really do not know how the UK system works in terms of the test you have at the end of the year. I know it is difficult to get the highest marks but that is about it. If it is your teacher who gives the test then the best bet is to understand pretty much everything in his notes in class, anything he ask you to read on your own explicitly, and any problems he assigns or suggests.

Yes, the lecturer for the course writes the test.

I would ask your teacher what they consider to be the five to ten most important theorems in the course and then make sure you understand the theory and the proof of the theorems.

I asked this but he wouldn't say which theorems in the notes were the most important! :p:

 

[J77]

The way I'd proceed is:

1. Make sure you take full notes in lectures.
2. Rewrite those notes outside of lectures -- ie. at home.
3. Do your assignments.
4. Reread the last lecture before going into the next one.

Only then, if you want, try to read other textbooks.

The danger is that by reading other textbooks, you may drift from the lecturers style. This can be dangerous, eg. if your work's being marked by grad students with a marking scheme, they could easily mark stuff wrong if an alternative method is used.

(btw. I did maths in the UK.)

 

[DavidSmith]

Dammit this thread pisses me off because we are treating mathematics like it is a chore. All these people cramming away, trying to learn how to integrate. Trying to differentiate, but then what? Nothing. They can't do anything afterwards because they don't truly understand the math nor can they appreciate it.

It isn't. And unless you have talent and stop treating like a chore you won't get very far.

 

[mathwonk]

well we answer whatever questions people have, perhaps you could ask a better question, or maybe it is time to strangle the thread. 60,000 hits is a lot.

 

[ekrim]

Anyone have any advice for preparing for the Putnam?

I've bought Larson's Problem Solving Through Problems, have been practicing geometric proofs, and reviewing the math I've forgotten.

 

[eastside00_99]

Don't learn any math just memorize math and tricks. Then work 2,000 problems. Hehe, I am taking a class on this for some reason. This is what they suggest.

 

[J77]

Dammit this thread pisses me off because we are treating mathematics like it is a chore. All these people cramming away, trying to learn how to integrate. Trying to differentiate, but then what? Nothing. They can't do anything afterwards because they don't truly understand the math nor can they appreciate it.

It isn't. And unless you have talent and stop treating like a chore you won't get very far.

If you were reacting to my post, that's what I'd suggest to someone taking a course.

Of course, maths shouldn't be a chore but going through the basics is necessary to get a degree which is necessary to go futher.

Obviously, you don't have to have a degree and PhD, you can just read and understand in your own time, but if you want to be paid as a mathematician, there's really no other way.

On your last note, perhaps this is more what you're getting at: that you need some natural ability. If so, I usually think this way too; you should have some natural ability over doing exercies. However, exercises are needed to get your degrees/pieces of paper, and proceed further.

 

[leon1127]

Dammit this thread pisses me off because we are treating mathematics like it is a chore. All these people cramming away, trying to learn how to integrate. Trying to differentiate, but then what? Nothing. They can't do anything afterwards because they don't truly understand the math nor can they appreciate it.

It isn't. And unless you have talent and stop treating like a chore you won't get very far.

Student having a hard time to do basic calculus because their prior education did not lay a concrete foundation. This is neither student nor teacher's fault. Moreover, the responsibility of an instructor is not just to teach someone who likes mathematics, we have to teach the one who will NEED mathematics in their life.

 

[MathematicalPhysicist]

and the one that likes maths doesn't need it?

 

[Cyborg31]

So what kind of jobs can you get as a major in Mathematics?

The only job I can think of is a teacher/instructor in mathematics.

 

[J77]

So what kind of jobs can you get as a major in Mathematics?

The only job I can think of is a teacher/instructor in mathematics.

I'm sure this is answered in the first few pages, but I can't think of a more flexible degree than a maths degree.

However, I guess the main jobs are financial -- loads of my friends went into accountancy, a lot went to work for investment banks, only a very few go into academia.

(The other obvious job is in the defence industry.)

 

[Cyborg31]

But aren't those jobs more into business major?

And by math major, I mean stuff like number theory, etc. When does a mathematician apply the higher level math they learn into real-life jobs?

I mean scientists are constantly researching and learning more but they're contributing to newer technology and developments.

 

[J77]

But aren't those jobs more into business major?

And by math major, I mean stuff like number theory, etc. When does a mathematician apply the higher level math they learn into real-life jobs?

I mean scientists are constantly researching and learning more but they're contributing to newer technology and developments.

Nah -- afaic, it's best to have the core degree below your belt before you decide on your career path; eg. you can take an MBA as your next degree.

For the "real-life jobs" -- it's not about necessarily employing specific skills, more about your employer knowing that you have the qualities neceesary to have understood such complex ideas in the first place.

Although, and I'm sure I posted this before, an example of jobs for pure mathematicians, it's corny, but: http://www.gchq.gov.uk/recruitment/careers/math_videosmall.html

(see also eg: http://www.he.courses-careers.com/mathematics.htm http://www.math-jobs.com/uk/)

 

[mathwonk]

my friends who have gone into industry, emphasized that it is not the mathematical facts that were useful, but the mental training.

I.e. after taking a maths degree where they were required to master difficult and exacting material and ideas, they were able to learn other things faster and more effectively than their peers with other training.

Since in every job, most of the useful learning occurs on the job, the person who can learn fastest has an advantage. Maths apparently teaches you how to learn and how to think in a way few other degrees do, except maybe physics.

thus as we have said before, there are fields where recruiters have learned from experience that math and physics students make more successful candidates than do others. this includes medicine.

to keep it simple, math, done properly, teaches people to think, and that is useful in every field.

of course it helps if the student tries to learn the concepts, and is not satisfied with merely gettting answers, or worse yet getting someone else's answers from an answer book or online. i.e. also in math there are students so clueless that they actively try to miss out on the prime benefit of a math degree, as many reveal here by their comments.

 

[leon1127]

But aren't those jobs more into business major?

And by math major, I mean stuff like number theory, etc. When does a mathematician apply the higher level math they learn into real-life jobs?

I mean scientists are constantly researching and learning more but they're contributing to newer technology and developments.

Look up what QUANT is...

 

[sepowens]

Actually, math and physics majors are now THE studs of the financial world. Look up the basic salary for a quantitative analyst. They pull down £250k/$500k per year in London and about the same in any of the other financial capitals of the world and their bonsus can double that. Risk management is another big earner in finance and basicly combines being able to write memos that tell the rest of the guys playing with people's pension funds to gamble carefully while crunching numbers to show just how safe the worlds largest casino is. Ito calculus or probability theory anyone?

 

[mathwonk]

there is a former pure mathematician named simons, who made about a billion dollars last year with a math model for hedge funds i believe. that's his share not his company's.

 

[symbolipoint]

But aren't those jobs more into business major?

And by math major, I mean stuff like number theory, etc. When does a mathematician apply the higher level math they learn into real-life jobs?

I mean scientists are constantly researching and learning more but they're contributing to newer technology and developments.

The mathematics major students must choose among other sets of related courses, generally classified as "cognates". These are courses outside of the Mathematics curriculums which rely on various kinds and various levels of Mathematics. The mathematics majors will use their skills for a few other subjects; this directly gives some realistic real-world type experience.

 

[mathwonk]

we could always shoot for 100,000 hits, but it is my opinion this thread is losing its zing. Opinions?

i would hate to trash the good advice, but the sheer length of it now makes it hard for someone to find the useful stuff.

or maybe people like having a sort of chat room for any kind of remarks about math, work, and life?[edit much later: for some reason this thread went on another 15 years and reached over a million hits.]

 

[DeadWolfe]

If you're concerned about the length and difficulty of sorting out advice maybe you could condense the thread into a FAQ on your webpage?

 

[kaotak]

Question:

I have just started an independent study of algebra using the same textbook that my uni's algebra class uses (which I have already bought). I would be taking this class in a year or two. If I were to use this book a great deal, would I be in danger of being "ruled out" for the algebra class, since I'd have an advantage due to my experience with the textbook (mainly in having solved a portion of its problems)? I would be following the curriculum of a different university that uses this same textbook and posts its problem sets online.

Oh, and if you don't know from another thread I made, it's Dummit's book.