Should I Become a Mathematician?

[proton]

i thought the pikachu was the patron saint of mathematicians. Is it not so?But to be honest, from the limited choices of avatars here I first tried "the punisher", as a cool comic book character, and then I felt it might scare off students with questions, so I then chose a less threatening looking icon I had never seen before. It seems to be a pikachu, whatever that is.

so the idea was that a guy with rude answers should pretend to be nice at least in his icon.

thats my story and I am sticking to it.

wow, that's pretty funny. I've always wondered why you liked pikachu. i thought it just had to do something with him being cute

 

[mathwonk]

yes, I've been at my school since 1977, and became a full prof about 1989. in those days we had no procedure for automatically bringing people up for consideration for promotion, and so it just happened whenever someone thought of it.

thus you could linger unnoticed for a while unless you complained or inquired as to what was going on. consequently a lot of people were left unpromoted for longer than they should have been. we have remedied that now, and everyone is given timely consideration, or at least the ability to remind us and demand it, every year.

by the way, so pikachu is just one character, like bilbo? not a whole race, like hobbits?

 

[mathwonk]

ok i found out they are not as harmless as appearance suggests, able to store electricity in their cheeks, and make lightning attacks. well that seems about right.

so they are not exactly schmoos, if you know what that is.

 

[Doctoress SD]

Hey, I am doing a Major in Physics, but since I got here I have been excited about Maths, like wow, I discovered Topology and I was hooked. I didn't know Topology, it is a huge area. I would also like to finish reading my book by Penrose.

I would have done a Maths minor, but my University doesn't offer Maths, it specialises in Chemistry and Maths was dropped due to the increase in "Micky Mouse Subjects".

So I just have to be happy with my own background reading.

SD

 

[Doctoress SD]

...

by the way, so pikachu is just one character, like bilbo? not a whole race, like hobbits?

You don't know that, yet you have Pikachu as your avatar? There are more than one Pikachu's by the way. But Ash's Pikachu is the most well known and famous. It kind of like having dogs which are animals, then you have breeds of Dogs, well you have Pokemon and Pikachu is a breed of a certain group of pokemon. Like you have rock, fire, electricity and water. Kinda like sets, Pikachu is a subset of electricity which is a subset of pokemon.
Only Ash's Pikachu is a subset of all the pikachu's.

I am a bit worried as to why I know this. They annoyed me so much, my little brother was obsessed with them.

 

[ValenceE]

guess you might have a closer relationship with your brother than you thought...



VE

 

[mathwonk]

wait, I am confused, fire, water, electricity, ash, pikachu,...

im lost, this is so much more complex than the singularity theory of the discriminant locus of principally polarized abelian varieties.and i cannot handle the idea of a university that dropped MATH because it was becoming so mickey mouse.i mean just WHAT is wrong with mickey mouse?>? if not for my comic book reading, (see mystery of man eater mountain), i would never have developed the creativity needed to do pure math research.

back me up here zapper.

 

[The|M|onster]

I will be taking my first course in Abstract Algebra this fall. The textbook that we will be using is:

Contemporary Abstract Algebra (6th ed) by Joseph Gallian

Does anyone have any experience with this text? Also, can anyone recommend a good text to use as a supplement?

 

[uman]

I have been reading Algebra by Michael Artin. I like it a lot although I haven't looked at any other algebra texts (except Dummit and Foote, which I wasn't prepared for) so I don't have much to compare it too, but I find he makes the material interesting and there are a lot of good exercises.

I'm only about halfway through the second chapter, so take my advice with a grain of salt, but from what I've seen so far it's a solid book. Try checking it out from the library.

 

[mathwonk]

good algebra books include:

birkhoff and maclane, shifrin, artin, dummitt and foote, jacobson, van der waerden, lang, hungerford.

some people like herstein, but i found it deceptively slick, but the problems are useful.

oh yes, and i wrote several which are free on my website, and also james milne has several free ones on his website, and also lee lady, and many other people.

http://us.geocities.com/alex_stef/mylist.html

 

[Doctoress SD]

I am learning Programming from scratch over summer. I will be using Tordran or something like that. And C and Python.

I have tried downloading compilers but they don't want to work. I think I am having most difficulty knowing what to do with the blank screan in which I am expected to write codes.

 

[DavidWhitbeck]

I am learning Programming from scratch over summer. I will be using Tordran or something like that. And C and Python.

I have tried downloading compilers but they don't want to work. I think I am having most difficulty knowing what to do with the blank screan in which I am expected to write codes.

Have you tried gcc (GNU C Compiler)? Regardless of your platform it should work. As for the blank sheet thing-- try hello world first. That is see if you can write a program that just prints out the line "Hello World!", that's the classic first program. Actually if you get a self study focused programming book it should have plenty of exercises for you to do.

 

[Quincy]

wait, I am confused, fire, water, electricity, ash, pikachu,...

im lost, this is so much more complex than the singularity theory of the discriminant locus of principally polarized abelian varieties.

I've always wanted to explain pokemon to a mathematician! (sarcasm intended)

In a fictional world, there are creatures called "pokemon," a lot like animals in the real world. Each of these "pokemon" have a certain "type." Three of these types are fire, water, and electricity. People in this fictional world collect pokemon and some have their pokemon battle other people's pokemon (cruel, yes i know, but the pokemon don't mind). They battle by having the pokemon use certain attacks against the opposing pokemon; all these attacks have names and there are hundreds of them. I won't go into the other battling mechanics, as they are too complicated, and involve math by the way.
Pikachu is one of these pokemon; it is of the electric type. In the animated show called Pokemon (english-dubbed from the japanese and original version of the animated show), the main character's name is Ash. He has a pikachu, making it the most famous pikachu, though there are indeed many other pikachus in the fictional pokemon world. Pokemon is in the top 5 of the longest running animated shows in the U.S.A. (9 years) and has the most episodes of any other animated show (509 episodes). Presumptively directed towards children, many pokemon episodes have been censored due to sexual, violent, and mature content.

 

[mathwonk]

this does remind me in a perverse way, of schmoos, conceived by al capp, no doubt well before your time. schmoos were bowling pin shaped animals which were extremely delicious when prepared in any of a wide variety of ways, and which enjoyed presenting themselves to hungry humans as pork chops, bacon, or any other variety of meat chops, all ready sliced for eating. check them out on google and see if their history survives.

yes in fact they have their own wikipedia article.

 

[mathwonk]

if you are asking yourself what schmoos and pikachu have to do with becoming a mathematician, remember my dictum that math is all about rampant creativity, at least before the hard technical part begins.

 

[The|M|onster]

I have been reading Algebra by Michael Artin. I like it a lot although I haven't looked at any other algebra texts (except Dummit and Foote, which I wasn't prepared for) so I don't have much to compare it too, but I find he makes the material interesting and there are a lot of good exercises.

I'm only about halfway through the second chapter, so take my advice with a grain of salt, but from what I've seen so far it's a solid book. Try checking it out from the library.

good algebra books include:

birkhoff and maclane, shifrin, artin, dummitt and foote, jacobson, van der waerden, lang, hungerford.

some people like herstein, but i found it deceptively slick, but the problems are useful.

oh yes, and i wrote several which are free on my website, and also james milne has several free ones on his website, and also lee lady, and many other people.

http://us.geocities.com/alex_stef/mylist.html

Thanks, guys. I checked out a copy of Artin from the library and started going through those links. There's some good stuff on that geocities page, Mathwonk.

 

[d1ff30m0rf1zm]

Mathwonk,

What book do you recommend for a basic course in Lebesgue integration? Currently I am using Lebesgue Integration on Euclidean Space by Frank Jones. Also, can you tell me what a course using this book [or your preferred book] would look like, i.e., topics by week? The syllabus outlined here: h ttp:// w ww.maths.no tt.ac.uk /personal/jff/G1CMIN/ seems to be roughly equivalent to the first 3 or 4 chapters of LIoES.

Thanks.

 

[mathwonk]

i'm sorry but that is one of the many topics i know next to nothing about, another being lie groups.

but do not despair, as i have many friends who are experts in analysis, and i will forward their recommendations.

one recent favorite text for that course is by wheeden and zygmund, zygmund being the famous classical analyst in that pairing.

another favorite for a long time is a text by royden, which i myself did not greatly like, but the first couple of chapters seem excellent, since he tries to take a hands on concrete approach, with simple, clear maxims for beginners. i would get it from the library and copy the first couple chapters, as to me the rest is abstract crapola. but who am i to judge?

of course all experts, but few students, like rudin. if you must choose rudin, and again i recommend going to the library for this, i suggest big rudin not baby rudin, since big rudin is a good book, with stuff you do not get everywhere, but little rudin has stuff you do get elsewhere, only it is harder to read it in baby rudin.

all books by george simmons are readable. i also like calculus of several vbls by wendell fleming, which includes lebesgue integration, a wonderful book.

i and experts seem to agree, that the book by riesz and nagy is excellent, but very old fashioned.

if you only want one recommendation, and you want MINE, knowing i am not an expert, i recommend fleming.

 

[mathwonk]

forgive me, i do not answer your second question as i have not taught it since 1968, when i used lang, analysis II, a very abstract book I do not recommend for a first course. i.e. i even taught the course but did not learn a lot myself.

of course 40 years later, after hearing an introductory talk by an expert i realized what lang was trying to tell me, and did appreciate it, so of course you always learn something, but it is hard to wait 40 years to find out what it was!

 

[d1ff30m0rf1zm]

i'm sorry but that is one of the many topics i know next to squat about, another being lie groups.

but do not despair, as i have many friends who are experts in analysis, and i will forward their recommendations.

one recent favorite text for that course is by wheeden and zygmund, zygmund being the famous classical analyst in that pairing.

another favorite for a long time is a text by royden, which i myself did not greatly like, but the first couple of chapters seem excellent, since he tries to take a hands on concrete approach, with simple, clear maxims for beginners. i would get it from the library and copy the first couple chapters, as to me the rest is abstract crapola. but who am i to judge?

of course all experts, but few students, like rudin. if you must choose rudin, and again i recommend going to the library for this, i suggest big rudin not baby rudin, since big rudin is a good book, with stuff you do not get everywhere, but little rudin has stuff you do get elsewhere, only it is harder to read it in baby rudin.

all books by george simmons are readable. i also like calculus of several vbls by wendell fleming, which includes lebesgue integration, a wonderful book.

i and experts seem to agree, that the book by riesz and nagy is excellent, but very old fashioned.

if you only want one recommendation, and you want MINE, knowing i am not an expert, i recommend fleming.

I remember reading Ch. 3 and some of Ch. 4 of Royden some time ago, but I didn't spend enough time on it to remember it well. I know the basics of measures from W. W. L. Chen's lecture notes. I should be able to summon Daddy Rudin, Royden, and Fleming using my dark magic without much difficulty [but it might be overkill to get all three]. I've been reading The Elements of Integration by Robert Bartle and I have really enjoyed it very much.

forgive me, i do not answer your second question as i have not taught it since 1968, when i used lang, analysis II, a very abstract book I do not recommend for a first course. i.e. i even taught the course but did not learn a lot myself.

of course 40 years later, after hearing an introductory talk by an expert i realized what lang was trying to tell me, and did appreciate it, so of course you always learn something, but it is hard to wait 40 years to find out what it was!

I see. That's fine.

I have another question. At the moment I am considering attending the HCSSiM program. However, a friend who attended tells me that it might end up being a waste of my time since a lot of the material there will be review for me [but I haven't studied graph theory]. She said its more of an introduction to proofs. Furthermore, its about $2300 [though there is financial aid] and six weeks long; that money can be used for my classes.

The dilemma is that my main goal in the next few months is to prepare for my classes at the university in the Fall. To that end I am spending, and must spend, quite a lot of time reviewing and preparing myself. HCSSiM only leaves 5 hours after classes, which isn't enough to prepare for 3 [maybe 4] rigorous classes. Another friend who has experience with such things suggests that going to a place like HCSSiM will give some kind of verification for my self-studying, and it'll set me up for getting in touch with professors. However, I have been lucky enough to have to been able to do that on my own. My uncle has been able to get me in touch with the head of the mathematics department at a very respectable university. I talked with him recently -- he was impressed, and he said he would talk to his colleagues and friends at Princeton [on the topic of mentors -- i.e., someone to verify my self-studying and serve as a mentor for [possibly] research in the future].

Do you think it would be beneficial to attend?

Thanks for your advice.

 

[mathwonk]

contact with smart people who are currently engaged in research is often very helpful. in the beginning of ones career, it is often advised.

 

[d1ff30m0rf1zm]

Indeed. So classes start in two months. Should I attend HCSSiM?

 

[mathwonk]

i cannot say, but if you attend, make sure you listen well.

 

[Doctoress SD]

Have you tried gcc (GNU C Compiler)? Regardless of your platform it should work. As for the blank sheet thing-- try hello world first. That is see if you can write a program that just prints out the line "Hello World!", that's the classic first program. Actually if you get a self study focused programming book it should have plenty of exercises for you to do.

No, I am pretty new to this. I don't have a clue, and how I am supposed to be able to make a fractal using programming, I don't know.

 

[Werg22]

I am disappointed in the way my undergrad education is going. I have the impression that people who want to dig deeper and get a more satisfactory understanding of things are not the ones favored in the academic system. Rather, it's people who don't ask questions and focus on the "how's" rather than the "why's" who succeed. I get satisfaction from math because I find in it completeness, clarity and conviction. This is why I always feel the need to dig deeper and deeper still. I want to look at mathematics from the confident logician's and even philosopher's point of view. How can someone truly be confident in his understanding of mathematics if he/she does not study logic, deductive reasoning and the mathematical method? I don't understand why so little emphasis is put on the foundations nowadays. Students (in mathematics) learn how to integrate in several variables and yet they won't even know what a mathematical structure is if you asked them. I feel that if I just content myself to course material, I'll never be intellectually satisfied with the depth (or lack thereof) of my understanding. What do people in this thread think of this?.

 

[ekrim]

I am disappointed in the way my undergrad education is going. I have the impression that people who want to dig deeper and get a more satisfactory understanding of things are not the ones favored in the academic system. Rather, it's people who don't ask questions and focus on the "how's" rather than the "why's" who succeed. I get satisfaction from math because I find in it completeness, clarity and conviction. This is why I always feel the need to dig deeper and deeper still. I want to look at mathematics from the confident logician's and even philosopher's point of view. How can someone truly be confident in his understanding of mathematics if he/she does not study logic, deductive reasoning and the mathematical method? I don't understand why so little emphasis is put on the foundations nowadays. Students (in mathematics) learn how to integrate in several variables and yet they won't even know what a mathematical structure is if you asked them. I feel that if I just content myself to course material, I'll never be intellectually satisfied with the depth (or lack thereof) of my understanding. What do people in this thread think of this?.

The system often rewards those who can predict the test questions based on the material that has to be covered, and after that it's just a matter of memorizing the steps to a solution. Some teachers take the step to design problems which their students have never seen, and only a truly prepared mind can solve them.

Though you should employ some patience and focus on the given material, even if it is not satisfying. Depth will come later.

 

[mathwonk]

i think your observations are directly opposite to mine. what is your definition of "succeed"? i think those who seek deep understanding are the ones who succeed in the sense of gaining understanding and obtaining jobs in the field and good recommendations from professors.

or are you deceiving yourself and thinking that you have a deep understanding even though your scores on tests are low?

 

[SCV]

I am disappointed in the way my undergrad education is going. I have the impression that people who want to dig deeper and get a more satisfactory understanding of things are not the ones favored in the academic system. Rather, it's people who don't ask questions and focus on the "how's" rather than the "why's" who succeed. I get satisfaction from math because I find in it completeness, clarity and conviction. This is why I always feel the need to dig deeper and deeper still. I want to look at mathematics from the confident logician's and even philosopher's point of view. How can someone truly be confident in his understanding of mathematics if he/she does not study logic, deductive reasoning and the mathematical method? I don't understand why so little emphasis is put on the foundations nowadays. Students (in mathematics) learn how to integrate in several variables and yet they won't even know what a mathematical structure is if you asked them. I feel that if I just content myself to course material, I'll never be intellectually satisfied with the depth (or lack thereof) of my understanding. What do people in this thread think of this?.

My experience was completely the opposite to yours. While I can imagine a situation that would make you feel this way, I was wondering if you could give some examples as to how your undergrad education is going that is making you feel this way. I know that there are things I could have done differently, mainly in the classes I took, that would have given me an experience similar to the one I imagine you are having. However at my school, I had the opportunity to take many honors classes and graduate classes and definitely the academic system favored people such as you describe yourself.

 

[Werg22]

i think your observations are directly opposite to mine. what is your definition of "succeed"? i think those who seek deep understanding are the ones who succeed in the sense of gaining understanding and obtaining jobs in the field and good recommendations from professors.

or are you deceiving yourself and thinking that you have a deep understanding even though your scores on tests are low?

I don't get low marks on tests, and I really don't think I have a deep understanding. But from what I can say, I might be in a very small minority that actually tries to gain a deep understanding. I'm still a freshman, and if my education isn't going to give me what I'm looking for, I better do thing on my own, because, frankly, I don't think that at the pace it's going I'll have anything more than a superficial understanding of mathematics.

 

[mathwonk]

werg, it sounds as if possibly your courses stink. are you in a crummy school? or are you in crummy classes? either way, switching is in your hands.

but it could be your attitude, since a good student can usually find something to enjoy in any class.

 

[symbolipoint]

Werg22, just in case we (or I) are missing something, are you enrolled in this course for the summer session? Quality or effectiveness of courses taught during a summer session may become flawed for various reasons. Which course is this?

 

[Werg22]

Totally unrelated to what I've just been saying, but Mathwonk, how do you find the style of modern math books in comparison to older ones? Maybe it's a wrong impression, but I think the today everything is written more concisely. Reading books from the 50's, then the 70's, and then from recent years come off to me as different experiences. Whereas the older books tend to have prolonged discussions about the material, the others prefer to express as much symbolically and as little in words. Personally, I prefer the latter style because it's always nice to have the authoritative voice of a good author to guide you.

 

[mathwonk]

well i guess there is a wide variety of modern books. maybe we need to be more specific. the modern books i see are more verbose than the older ones and greatly dumbed down, and less deep and less challenging.

compare a book like apostol from the 60's to stewart or finney and thomas from the 90's.

or compare goursat from 100 years ago or dieudonne from the 60's to almost anything from today.

compare spivaks little classic advanced calc book of only 140 pages from the 60's to any advanced calc book today.

it is true some very old books were quite conversational in tone. i found that charming, such as courant's calc book from the 30's.

but traditional calc books that we use in most courses today are very verbose and dumbed down compared to those from the 60's at least. they may not be as wordy as books from the 1910's (e.g. hardy) but are more dumbed down than those.

very old books did math deeply and in detail. then in the 60's the math books got more abstract and more succinct in some cases, but some books like apostol and kitchen were both detailed and deep. then in the 90's books got more shallow and more verbose, as if aimed at morons. indeed titles like "advanced calculus for compleat idiots" actually became popular in the US.

compare a detailed but well written and no nonsense linear algebra book from the 60's like hoffman and kunze, to a verbose and relatively shallow current one, like friedberg, insel, and spence.

the latter book proves most of the same stuff, but brags about omitting the main ideas, like making the presentation easier by omitting "polynomials". since the main idea in classifying linear maps is determining what polynomials they satisfy, i find this ridiculous and frustrating in the extreme. and this is a relatively good book. but they are consciously dumbing it down as if that were a virtue.

 

[alligatorman]

Dr. Mathwonk,

What are your thoughts on attending a graduate school in mathematics that is not in the so-called "top 25"?

The more I read about getting a Ph.D in mathematics, the more I think that, with the way things are going these days, if I go to a "tier 2" graduate school, I won't have any decent offers, in either academia or industry. I keep reading that going to a top graduate school is pretty much necessary in order to get a position at a university or as a mathematician outside academia.

I did poorly in a few major courses (Abstract Algebra and Analysis), and though I am taking graduate level algebra and modern analysis in my last year, I fear my application will remain scarred by my two C's. (Everything else has been B+ or higher)

Some background: my school of choice is Univ. of Illinois at Urbana-Champagne. I currently go to the University of Florida. I think I could get into the UF program, but it's not a very recognized math dept (despite one Fields Medalist in the faculty).

Any opinions? Convince me that going to UF (or any other average school) for graduate school isn't closing doors?

I know job seeking after graduate school is tough these days, regardless of school attended, but I don't want to make it any worse than it already is.

Thank you.

 

[eastside00_99]

Dr. Mathwonk,

I keep reading that going to a top graduate school is pretty much necessary in order to get a position at a university or as a mathematician outside academia.

I did poorly in a few major courses (Abstract Algebra and Analysis), and though I am taking graduate level algebra and modern analysis in my last year, I fear my application will remain scarred by my two C's. (Everything else has been B+ or higher)

Some background: my school of choice is Univ. of Illinois at Urbana-Champagne. I currently go to the University of Florida. I think I could get into the UF program, but it's not a very recognized math dept (despite one Fields Medalist in the faculty).

Any opinions? Convince me that going to UF (or any other average school) for graduate school isn't closing doors?

I know job seeking after graduate school is tough these days, regardless of school attended, but I don't want to make it any worse than it already is.

Thank you.

Where did you read that you can't get a job as a mathematician if you don't go to a top school for grad school? Qualifiers are important when discussing a topic other than pure deductive logic. It may be *less likely* that you will get a job as a mathematician if you go to a school ranked as second tier but not completely impossible. Just because you go to a top tier school doesn't mean you are going to have an all star career as a mathematician either. Your focus should really be on going to a school that has a couple of people who are experts in the field you are interested in. If you don't know what field, but you know something like you are most interested in algebra, geometry, analysis, or something else, then you might want to find the schools that have good programs in that. There are so many universities out there that the real trick will be trying to actually figure out why you would like to go to one school over another when you get past brand name type of stuff. I went to NC State as an undergrad. The grad program is second tier, if you follow the rankings you can get on the internet, but everyone of the recent Ph.D. grads have university jobs. Now, no one is going to do a postdoc at yale, but they all have jobs that revolve around doing mathematics on a daily basis.