Should I Become a Mathematician?

[pivoxa15]

he/she should love the subject and want to improve, and be willing to work hard to do so. that's about it. extreme persistence and some basic smarts takes care of the rest.

What about also starting at a managable level and getting the an extremely good grasp of the basics? An essential factor?

 

[yarp]

What if you have the knowledge, but you don't have the analytic thinking, problem solving skills, etc. Is it really something you can improve? It's hard for me to understand because I don't understand the more advanced questions. Even simple word problems are difficult.

 

[eastside00_99]

I kind of think that all you really need is the ability to be captivated by mathematics. I mean if you are at a university chances are you have the intelligence required to be a mathematician but the question is are you captivated enough by it to do the amount of hard work required? If you not really captivated by mathematics all that much, then I would delve into the history of mathematics (and science in general) a little bit. I think that is where most of my appreciation first came from. This is because when you do not know a lot of mathematics it is hard to be inspired by the beauty of it or have something to think about that interest you.

I would also say do not believe people when they say you have to have talent. Usually, those people are not very talented. Finally, there are all types of mathematicians. People who go around and just solve problems, people who build theories, people who make conjectures, people who apply theories, people who work out details, et cetera. Certainly every mathematician has a little bit of all these, but it does seem that people tend be more one than the other. Each type of mathematician takes a different kind of personality or character.

 

[mathwonk]

to second eastside, but less well, this question is reminiscent of people who wonder if they have a "math mind".

It aint so much what you've got, as the old walt disney record "so dear to my heart" said, "its what you do with what you've got."

you will never get anywhere if sit around wondering if you are cut out to be a fields medalist.

and even if you are potentially a genius, you still will not get anywhere unless you get to work.

As the lady in driving miss daisy said, more or less, i have seen many fairly stupid people who obtained phd's and even became somewhat well known. heck i are one myself.

 

[Werg22]

What virtues should a mathematician have? Aside from a fully updated knowledge of his/her field, what if (s)he misses the more important qualities like great creativity and problem solving skills? I mean, you can't go anywhere if you understand the books but not most of the problems, can you?

Haughtiness and obnoxiousness are strong assets.

 

[teleport]

Plz Werg, stop that! I see that since your last post in this thread your convictions of mathematicians haven't changed, and you maintain a position of being explicit about it, especially in this thread. This thread is in the voluntary business of helping people with mathematical interests. You are neither asking for it, nor providing it. Plz desist of adding stereotypes on anyone. I've seen many of your posts in other threads, and many of them seem to me very interesting. You obviously enjoy math and problem solving, and I am completely certain that (1): you check regularly into this thread, not for the reason that your posts imply, and (2): since you complain a group, even though it is in fact a much more tiny subgroup not representative of the master group, is obnoxious, then you might not belong to that subgroup, otherwise you would not pressumably notice they are obnoxious if you had the same level of obnoxiousness as everyone else in that subgroup, hence there is a perhaps greater possibility that you are not obnoxious, than you are, and hence you might have a lot more attractive things to tell than your posts in this thread imply. I am sure of it!

BTW, I have many examples of my profs refuting whatever correlations you may have concluded between erratic behavior described and profession. Q.E.D.

 

[muppet]

The three mathematics lecturers I have at the moment are all really very amiable people. Probably only one of them could do a passing imitation of what you might call normal , but there's no arrogance about them at all.

 

[proton]

whats a good proof-based math course to take after upper-div linear algebra? I'm thinking right now of either taking differential equations or systems of differential equations (both are upperdiv), since they are at least also useful for my undergrad physics. I want to take a challenging math class, but that is also applicable to physics

 

[PowerIso]

whats a good proof-based math course to take after upper-div linear algebra? I'm thinking right now of either taking differential equations or systems of differential equations (both are upperdiv), since they are at least also useful for my undergrad physics. I want to take a challenging math class, but that is also applicable to physics

Group theory wouldn't be a bad choice. Especially if you can figure out how to apply it.

 

[proton]

at my school, you have to take the 2nd quarter of abstract algebra to get to group theory. But I can take "algebra for applications", which is only 1 quarter to get group theory instead, but I don't think its that much proof-based. This is the book used for this class: https://www.amazon.com/dp/0387745270/?tag=pfamazon01-20

also, is it bad to wait to take real analysis and abstract algebra after just completing linear algebra? I want to take DE and PDEs courses before taking those.

how much is upperdiv DEs proof-based? the books used are:
https://www.amazon.com/dp/0738204536/?tag=pfamazon01-20

and
https://www.amazon.com/dp/0070575401/?tag=pfamazon01-20

 

[PowerIso]

Opps, I forgot to read after the linear algebra part! Well, I suggest Abstract Algebra, and then group theory.

It wouldn't be terrible if you waited to take real analysis and abstract algebra.

 

[jhgforth]

Well, i read through the posts...yup...all of them. Quite interesting/entertaining to me even as a non-mathemetician. Wanted to quote MW here: "of course it helps if the student tries to learn the concepts, and is not satisfied with merely gettting answers,... "

That right there sums up the point where i lost interest in math in high school and then early college reqs for math that i needed for a fine arts degree. the classes I had all wanted answers and didn't really push the learning of concepts. Memorization and regurgitation of the answers were more important than actually explaining the concepts. To be fair, concepts are always easier for me to learn by than techniques. I retain things much better and longer if i know the 'why' rather than the 'how' in most cases. Inquisitiveness is stifled in our education system a lot, primarily in elementary and secondary education. And somewhat relating to earlier posts, i feel like the few times i really understood things in math were using proofs as opposed to just working out answers...proofs have a process to them that is in my opinion, 'thinking out' on paper (or computer screen depending on the person in this day and age ;) ). This process is good for me, because as a visual artist (traditional figure drawing is my area, think charcoal and other like mediums) a lot of my process is also 'working things out on paper logically".

It makes me quite sad looking at history. It wasn't that long ago that art, math, philosophy and other sciences were much more intertwined in not only goals but in teaching. The early part of the past century, many founders of modern art were very well educated as both artists and many other fields such as math, science and philosophy. Today, however, it seems less and less common. The few math people that make art it is considered a 'hobby' and never taken very sincerely when in all reality math and art go hand in hand. Both disciplines study line, movement, value, shape, time, weight, beauty, life, interaction, etc and etc.

As far as the comments that mathematicians need to be stubborn and obnoxious, etc. People also think artists should be wild crazy drug heads. Neither is true for either field. The notorious ones may have those qualities, but the successful ones are such a variety of flavors of people that there is no point in trying to single out certain 'types'. That kind of limiting of people by behaviours is what causes many problems in society in general and leads to so many prejudices.

Well, this was much longer than I had anticipated and i wanted to say that I really enjoyed the forum and will be looking through many of the recommended books on math. Since i can do this on my terms it will be for the 'why' and not the 'how' and make me much happier with it.

--jhg

 

[sdobbers]

I haven't read this whole thread yet...74 pages is a lot (I've read a lot of it though!). I've been looking for some math books to buy lately, and I see that there have been a lot mentioned in this thread. My question is, can anyone make a comprehensive list so that we don't have to go searching through 74 pages to find the books?

 

[Dr1AB]

ummmm
im new here n i have to do a project
i found a project but have no idea wat it is
do n e of yous no
its on lissajous figures
please let me no
thanx

 

[Dr1AB]

btw i jst wanted 2 no wat math class u guyz r takin
please tell me
thanx

 

[whitay]

Learning English 101

 

[mathwonk]

"new" recommendations for good math books:

euclid (translation by heath, published by green lion press).

archimedes (trans. heath, publ. dover),

geometry, euclid and beyond: hartshorne;euler: Intro to analysis of the infinite (transl. J.B.Blanton);

(I just learned tonight his secret to calculating values of the zeta function at even arguments: he equates an infinite series for cosh with an infinite product for it, pages 137-140.)reietrate: calculus by courant (every time i read a new calculus book i see again the same things stolen from courant).

 

[The_Z_Factor]

Im in high school and I love math, so maybe being a mathematician would be ideal for me...But what should I start studying? The schools around here, like mentioned before, don't exactly teach you the stuff. They make you memorize it. Of course I can do an equation if its said the same way I was taught. I mean, the teachers, not only don't like what they teach and hate their job, but also don't teach you how to apply it to any kinds of problems outside of the particular problems they give you. If the book asks how soon you'll hear a siren from x miles away, and you're going s speed, they teach you how to solve that specific problem, not how to apply it to other problems. Of course, that's a simple problem and I could figure it out, but you get the idea. Anyways, what kinds of math should I study for the next few years? I asked my 'excellent' counsellor if I could take extra math courses, instead of the ridiculous courses she wants me to take, like marketing for sports and entertainment, and she won't let me. I go to my local library all the time though, and try to read books to enlighten myself, but its much harder reading books because sometimes they don't thoroughly explain it enough for me personally to learn. Maybe I am just not intelligent enough to understand it?

 

[mathwonk]

have you read the first 10 posts in this thread? they are aimed at you.

 

[mathwonk]

hard as it seems to believe, i have reread my advice here and there seems to be no advice on how to behave in college courses. just taking them is of no use if one does not take them seriously. perhaps readers of this thread have no need of this advice, but some may.

Here is the basic advice:
1) attend every class.
2) before every class, do the reading for that day, and prepare questions to ask in class.
3) after every class, the next period if possible, but certainly the same day, reread the lecture notes and prepare questions on matters not understood for next class.
4) do all the reading. while reading, work all examples out oneself, then compare to the solutions in the book. prepare questions on the reading for class.
5) work as many problems from the book as necessary, to master the concepts.
6) come to as many office hours as needed to settle all questions as early as possible.
7) make sample tests from selected problems in the book, and take them in a timed situation, to prepare for tests.
8) after every test, work out all problems completely, as if the same test will be given again, [ it may be].
9) read this advice again, it is serious, and not a joke. this is how good students behave. if no one you know does these things, your acquaintances are not good students. if they are successful at your school without studying this hard, your school is too easy.

 

[mathwonk]

I have handed out roughly the following advice every semester for 30 years. I have never had a class take it seriously. In fact most people seem not even to read it. I have even handed it out with "READ ME" at the top, and with the first sentence reading: "email me today with your email adress", and after 2 days not received but 2 emails. Then I tried projecting it on a screen and reading it to the class, but many people seemed to fall asleep and ignore me. I have had people come up after 14 weeks of a 15 week class and ask where my office is or when my office hours are. Don't be that person. Please peruse it for advice on how to succeed in a college calculus class.

EXPECTATIONS AND ADVICE:

1) LEARN ALL THE BASIC INFORMATION.
This means studying the book and the lectures until you know and understand all the definitions, theorems, formulas and procedures. This involves both memorizing and understanding. Thus you should be able to rattle off from memory the definition of a limit, derivative, continuous function, equation for a tangent line, etc... with perfect accuracy. You should also be able to explain clearly what each of these things means.

2) DEVELOP COMPUTATIONAL POWER.
This means learning to solve specific problems and to make detailed and accurate calculations. This can only be acquired by working large numbers of problems, not just the few that are to be handed in. You should spend as much time as you need to learn to work correctly as many problems in the book as possible. I will frequently choose problems from the book, or similar ones, to put on tests. Study the worked out examples, and get any troublesome points explained well before the test on that topic. I am never available for help on the day of a test.

3) PRACTICE LOGICAL REASONING.
One of the main benefits of a mathematics course is in learning to make logical arguments. (This can actually help you in arguing with a judge, or the IRS, or your boss, for example.) This means knowing why the procedures you have memorized actually work, and it means understanding the ideas of the course well enough to be able to adapt them to solve problems which we may not have explicitly treated in the lectures. It also means being able to make a clear statement and to prove it. Practice by understanding my proofs and the book's, and attempt some "prove" or "show" problems.

I will test you on your understanding of each topic, not just your ability to repeat computations exactly like ones worked on the board. You must be able to state general principles correctly, apply them to old and new situations, and write up your solutions in understandable, correct form, using words in complete sentences. It is important to keep up, and to study for the final, since past experience shows people who did not do well earlier, or who do not restudy for the final, do not do well on the final.

Ask lots of questions. I am glad to review anything at all from a previous course, but I can only do this if you ask me.

 

[tronter]

Another thing I would add: Pretend that you (the student) are a professor. Lecture on the topic (to yourself or to somebody else) and explain/do examples.

 

[eastside00_99]

Im in high school and I love math, so maybe being a mathematician would be ideal for me...But what should I start studying? The schools around here, like mentioned before, don't exactly teach you the stuff. They make you memorize it. Of course I can do an equation if its said the same way I was taught. I mean, the teachers, not only don't like what they teach and hate their job, but also don't teach you how to apply it to any kinds of problems outside of the particular problems they give you. If the book asks how soon you'll hear a siren from x miles away, and you're going s speed, they teach you how to solve that specific problem, not how to apply it to other problems. Of course, that's a simple problem and I could figure it out, but you get the idea. Anyways, what kinds of math should I study for the next few years? I asked my 'excellent' counsellor if I could take extra math courses, instead of the ridiculous courses she wants me to take, like marketing for sports and entertainment, and she won't let me. I go to my local library all the time though, and try to read books to enlighten myself, but its much harder reading books because sometimes they don't thoroughly explain it enough for me personally to learn. Maybe I am just not intelligent enough to understand it?

I would say you are at a fun stage in math though. I remember doing the exact same thing when I was younger. I would go to a library and get a book on linear algebra, diff eq, or abstract algebra and try and read them (now mind you I would always get these old dusty looking books which naturally did things in a difficult way). I could barely understood anything from those books but I read them worked out the problems I could. Maybe I got to the second or third chapter before giving up in despair. Everything was just so mysterious because there was very little motivation behind the subjects. It was fun and as I actually started learning the material for real, I started to remember these books and started to realize why the authors wrote in this or that way. That was a nice experience. Now, I still do this. I read things and try and work problems that I have no clue how to solve or what is going on when I have some time to kill and some inspiration. I know that one day that will pay off with at least a little bit of intuition. Anyway, one subject I would recommend is a soft introduction to linear algebra. In some ways linear algebra is the most basic subject for the undergrad (more than calculus) yet its breadth (or the amount of return you will get out of mastering a book in linear algebra) will open up a lot of doors into other areas of math. If you master linear algebra you will have the tools to study a lot of other areas of math at a high level (including applied subjects). But, linear algebra is also sort of easy in my opinion.

 

[mathwonk]

great advice! nothing like teaching to help learning. that's how i learned most of what i know.

 

[k3N70n]

thanks mathwonk
that's great advice. Hopefully I can apply it next semester!

 

[mathwonk]

Tronter, if you really want to behave like the teacher, I recall that when i started out teaching calculus from Thomas, I worked every problem at the end of every section before every class, so i could answer any question asked on them. Eventually I realized they were not all different and began to lighten up, but only when I really knew how to do them. I also volunteered to teach extra classes and to give seminars, so I could learn more. Thus in addition to my regular load I also taught a free extra section of Spivak style calculus since we did not offer one, and ran a seminar for faculty on the de Rham theorem using sheaf theory.

 

[tronter]

Thanks mathwonk.

I asked another mathematician if he followed those rules you gave. I was surprised when he said he generally never did any homework except for one course. Now I find that quite hard to believe. Perhaps he understood the concepts extremely well that he didn't need to do any problems?

 

[proton]

what kinds of jobs do pure mathematicians have (besides academia)? what are they like? do they involve a lot of computer programming? is it possible to for their work to involve physics too (like providing the mathematics for engineering)?

 

[mathwonk]

i also have difficulty believing your mathematician friend did not do hw. is he a real mathematician? i.e. does he do research, publish in good journals, and give invited talks at international meetings and bring in grant money? there are always a few exceptions to these rules, but they are very unusual. or is he a liar?

of course i also did not do hw, but i was unsuccessful until i did so.

 

[mathwonk]

if you read this lengthy thread you will see it mentioned that mathematicians do all kinds of jobs because they are able to learn to do anything after learning how to think and how to learn.

 

[tronter]

he is not a mathematician in academia, but he did get a PhD in math. Also what happens if you didn't know the answer to a question. If you don't have a solutions manual then that's good right? Then its a true test of your knowledge.

 

[mathwonk]

it sounds possible to me that your friends refusal to do his homework may have led to his not being able to continue his mathematical career.

 

[pivoxa15]

Thanks for your advice, if only I followed them during my undergrad years. It does explain why my grades are so poor but I'm willing to change myself. What extra advice would you give to students taking grad courses? I assume the lectures are more heavy going and less then undergrad courses so more condensed?

i also have difficulty believing your mathematician friend did not do hw. is he a real mathematician? i.e. does he do research, publish in good journals, and give invited talks at international meetings and bring in grant money? there are always a few exceptions to these rules, but they are very unusual. or is he a liar?

of course i also did not do hw, but i was unsuccessful until i did so.

I read that Ian Stewart said he didn't do much work in college nor did Stephan Hawkings, he did on average one hour a day but then again he didn't do that brilliantly getting a 2nd class honors I think in Oxford before moving to Cambridge for a Phd.

 

[proton]

I've skimmed through this whole thread, but I don't remember all the details. How difficult is it to find jobs after obtaining a phD in math (non-professor jobs)? is it similar to physics, where its extremely hard to unless you specialize in an area that has a lot of applications?

 

[J77]

I read that Ian Stewart said he didn't do much work in college nor did Stephan Hawkings, he did on average one hour a day but then again he didn't do that brilliantly getting a 2nd class honors I think in Oxford before moving to Cambridge for a Phd.

Regarding "homework"...

Back when I did my first degree, I can't remember doing too much homework: new university, new town, new friends -- there wasn't much time for work in the evenings.

However, I did attend nearly all lectures, and worked on assignments during the free periods between lectures.

I worked harder when doing my masters, but then the classes were a lot smaller and we all shared an office -- it felt a bit more grown-up

During my PhD, I think I did more homework, than in my UG, preparing for the teaching jobs we had to do

Now, doing research, it's of course necessary, and part of the job, to go out and seek things on your own -- you certainly don't have to recall everything you've been taught in the past. More, your level of maturity in dedicating yourself has to be there.

I guess that's the bottom-line, as you get older, you become more mature, I think you can see ideas from a higher perspective -- all which means you don't have to strain over a textbook trying to force yourself to understand something for, eg., an exam.

(I did go through the UK system though -- like the names you quote -- and it was a decade ago now. Times have moved on, maybe students are more dedicated to studying these days because they have to pay? I hope not, because uni should also be about enjoying yourself, not all study.)