Other Should I Become a Mathematician?

[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.