The Should I Become a Mathematician? Thread

reenmachine

thanks

I have another dumb question (and I understand the answer is likely to vary quite a bit depending which mathematician we're talking about) , but how long does it take to produce a ''work''? Do you publish or make public on the net any single advance you do on your work or do you wait for your work to be completed before sharing? How many work is an average mathematician likely to produce in a decade for example? (approximative number)

mathwonk

Better work takes longer of course, but unfortunately the frequency of publications is often influenced greatly by the deadline for renewing your grant or for promotion. I.e. people are forced to publish works in time for those events to occur. Since most grants are for 3 years or less, it is very hard, if not impossible to work on a project taking longer than that, except for very well established or secure people.

In some departments it is expected to publish at least one paper a year, and in some areas many more than that is usual.

My first project took about 5 years, but i was young and naive and even so was having to fend off people telling me that I was not publishing fast enough. Everyone I know who has done a big 5 year project has had the same problems.

Ideally one wants to complete some significant piece of work before publishing it, but there may be a race with someone else working on a similar project to be first. If on waits too long priority may be lost. Ideally one does not care about this and just tries to do the best science possible, but the support for pure science is not so great. A good journal will often reject a paper that has only partial results on a given problem, even decent partial results.

Sometimes the people receiving the most recognition in the form of promotions, grants, etc, are publishing large numbers of minor works. There are department chairmen who evaluate their personnel merely by counting the number of papers published. But this is perhaps within a restricted setting. Worldwide, top recognition usually follows the best work.


One should try not to be guided too much by these mundane considerations, insofar as one can avoid it, but you have to pay your bills, in order to be able to work.

dkotschessaa

I was wondering about that. Seemed to come with the forum upgrade.

reenmachine

I see , this is where the ''publish or perish'' expression comes from.

Suppose you are working on something very hard , something that will probably require 5+ years to complete or at least advanced to a significant degree , do you still have the time to work a something more trivial that you can publish just in order to satisfy people that are pressuring you to publish?Mostly uninteresting work but just good enough to publish it.

About publishing , suppose you're in some decent math department , how do the publishing process works exactly? Does being published = who you know/who knows you or is it guaranteed you are going to get published if you have a job in a math department? If your work doesn't get published where is your work going?

In the same vein , suppose you pretend to have proven a theorem but you aren't a big name and your proof ends up unpublished or at least people aren't taking the time to review it , if your proof was indeed correct , does that mean somebody could actually re-prove it in 10 years , get more attention and take all the credit despite the fact you proved it first?

sorry for these dumb questions I'm just trying to built a clearer picture on the whole process and I have to ask the dumb questions before asking better questions in the future :)

thansk for taking the time

cheers

mathwonk

it is smart to have several smaller works to publish while working on a bigger one, but it takes a bit of savvy to manage that.

If you have done something significant it will get published, but unimportant work will not be published just because you have a job in a math dept.

your correct and significant work will not be denied recognition just because you are unknown. it will be reviewed with respect.

horror stories like galois' work being lost by cauchy are extremely rare.

epenguin

If I may make a modest suggestion for mathematicians with this in mind, if you keep wide interests and contacts from the start you might see applications for your competences in other sciences, or if they know you they know someone to come to or reccommend for their problems, which may even seem trivial to you. (For example Hardy must be far more widely known for the Hardy-Weinberg theorem in genetics that biology students struggle to do excercises in, and which is nothing but the binomial theorem for n=2 (!) , than he is for anything else.) But you have to understand something of their sciences as they frame it or there are fantastic misunderstandings. Beyond the well-worn higher physics-maths connection problems are thrown up in medicine, biology, earth sciences, materials sciences,... for a sideline and the odd publication or so for you.

Or possibly a Nobel Prize - by accident I came across; "John Pople...Cambridge University and was awarded his doctorate degree in mathematics in 1951. ... Pople considered himself more of a mathematician than a chemist, but theoretical chemists consider him one of the most important of their number..."

dkotschessaa

I'm going to be taking Elementary Abstract Algebra in the Summer (6 week course) despite swearing I'd never take a summer math course again. But if I don't, it will put a lot of other courses on hold (and it's already taking me too long to get through my degree.)

We use this book: Modern Algebra: An Introduction by John R. Durbin

I'd like to pre-study for this class, which thankfully is in the *second* summer session and gives me a bit of time to prepare. Two approaches - I cold get the book itself and try to get a head start - or I could find another smaller book and perhaps have it completed.

I started to work with a professor on this book:
Abel's Theorem in Problems and Solutions: Based on the lectures of Professor V.I. Arnold by V.B. Alekseev

In an informal independent study last summer, but we got side tracked, and I didn't quite have enough background for it. (Despite the introduction saying it should be readable by high school students - they meant *Russian* high school students. It seems to touch on a lot of the same material as Elem Abstract Algebra.

Or is there another book that might give me a good crash course? Or should I just get the textbook itself?

The reason I ask is that - I've found that "Studying ahead" for a class in a textbook is nice - but only works as far as you've gotten. Once you get to where you've studies ahead, you can get just as behind again as anyone. Advice?

mathwonk

As to how many publications is normal, look at some mathematicians' vitas, available on their web pages.

Here is the publication list for the first 10 years of an absolute star, Lenny Ng. He has about 2 a year for the first 10 years. And bear in mind he spent most of that time as a fellow at research institutes such as MSRTI, IAS, and AIM. And he is brilliant, so is much more productive than average.

http://www.math.duke.edu/~ng/math/professional/pub.pdf


I myself, in 33 years, published 33 papers (of varying significance), gave about 60 invited talks and courses, mostly conference and seminar talks, and taught some 150 college courses, (about 40 different titles).

reenmachine

thanks a lot again for the quick , precise and good quality answers!

Being isolated from the mathematical world for the moment , this forum is a gold mine for me.If I one day become a mathematician in many years , I promise to contribute to it to give back.

mathwonk

here is my summary vita.

Attached Files

2012 summary vita.pdf (44.5 KB, 64 views)

reenmachine

very impressive !!! Despite finishing your ph.d in your 30s , you had a long and productive career.And you're still doing math today so it's not over!

It is an inspiration for guys like me who would finish their ph.d around the same age if they go for it (mid to late-30s).

dkotschessaa

Any thoughts on my above post? Don't mean to be a bother, and I know you are answering a lot of people's questions. (Anyone feel free to contribute as well).

Sankaku

I would suggest asking your question in the textbook forum. This thread has become too big and unfocused for most people to want to keep reading it.

mathwonk

absolutely! hear hear! what else could possibly be learned here? popularity is its own curse. If we let this thread go to a million views it may never die!

But on the general principle that it is better to actually answer a question than to make smart alecky remarks, I recommend the OP go to my web page where there are several free algebra books posted for download.

http://www.math.uga.edu/~roy/

by all means read as much as possible. you can only do so much but whatever you do helps.

dkotschessaa

hehe. Thanks mathwonk. As far as I'm concerned, this thread is 90% of PF. I actually don't have much luck when posting to other subforums here anyway.

Thanks!

Dave K

RJinkies

AndrewKG: Hello I saw it in an earlier post o. Here, but does anyone know if the humongous book of calculus problems is a good book to start calculus with. Or does anyone have any other good texts. Also if possible not a 1200 page book.

Well, I'd say it's in the top 50 for an approachable book.
It is still 500-600

I'll summarize it this way:


The Humongous Book of Calculus Problems: For People Who Don't Speak Math - W. Michael Kelley - Alpha 2007 - 576 pages

[W. Michael Kelley is a former award-winning calculus teacher and author of The Complete Idiot’s Guide to Calculus, The Complete Idiot’s Guide to Precalculus, and The Complete Idiot’s Guide to Algebra. He is also the founder and editor of calculus-help.com, which helps thousands of students conquer their math anxiety every month.]
[why aren't more books like this one?]
[Back to the Basics]

[I bought the book for my daugther. I went through it. It was clear and simple to review. I gave it to my daugther (she is taking Calculus in High School). She went over a few chapters; then she shared her thoughts with the teacher. Her final evaluation "This book makes Calculus look so simple. I love it [the book] Mom."]
[I have always wanted to be a mathematician, and have decided to do it. I need to learn Calculus well (Calc I-III), so that I can go on for a masters in math program. This book covers Calc I and II. Of course before you open to page 1, you must know algebra and trig well. So take a few weeks to do that. Then, you should get this authors Idiots Guide to Calc, and go thru it. If you are good with your alg and trig, you can get thru that book. Then, the next step is this "Humongous" Book. I am now half way through it. Ive taken it slow so that I can process everything. I feel pretty good about it, but now I am going back through the first half all over to solidify. Then its on to the second half over the winter, and by Spring I will have a good foundation in Calc I and II, and be ready to move on to III. Calc in and of itself is not hard - its the algebra and trig you have to know well. This brings me to my final point - Michael Kelley does a great job of stripping away the gobbledygook and delivering you the nuts and bolts of calculus ON PAR with the "hardcore texts". There are many of those "hardcore" books, and they just dont teach well. What this author has done is to teach you how to solve the problems as well as the underlying logic. Believe me, this book is great. If you see it, open it up and read the introduction - if you buy it and work it, you will be saying its a home run too.]

[This book covers what you need before actually delving into the arena of calculus. This book assumes that you have at least a rusty knowledge of algebra and trigonometry.]

[By far the most entertaining and comprehensive coverage of calculus 1 and 2 I have ever seen. Very clear presentation of material that makes the entire topic of calculus much less intimidating.Exquisitely written making it ideal for either self study or quick review.]

[This book really deserves all the praise it receives. Go through this, then get a supplemental text such as Schaum's to work more problems.]

[liked by Cargal]


----

Now calculus can be something where one book, might be your style, and not someone elses.

a few of the books worth peeking at:


How to Ace Calculus/How to Ace the Rest of Calculus - Adams
Schaum's Outlines
Silvanus P. Thompson - Calculus Made Easy - 1914
JE Thompson - Calculus for the common man - 1931
Engineering Mathematics - Stroud and Booth - Programmed Instruction Series [dozen books in the series]
Calculus Without Limits - Sparks
Calculus - Gootman
Sherman Stein - Calculus and Analytic Geometry 1973
[1968 first edition was called Calculus in the First Three Dimensions]
Kleppner - Quick Calculus [famous for his physics book on Intermediate Mechanics similar to Symon's book]
Essential Calculus with Applications - Richard A. Silverman - Dover 1989 - 304 pages [dense - no trig]
Morris Kline - Calculus [liked by some, disliked by some]
The Calculus Lifesaver - Banner
Calculus: The Elements - Michael Comenetz
The calculus: A college course guide - William Leonard Schaaf [Very easy read; very accessible] - early 60s
What Is Calculus About? (New Mathematical Library) - W. W. Sawyer
The Humongous Book of Calculus Problems - Kelley
The Calculus - Louis Leithhold [ i think it's in the 7th edition now called TC7]
Prof. E McSquared's Calculus Primer: Expanded Intergalactic Version - Howard Swann and Johnson
A First Course in Calculus - Serge Lang - 1964
Understanding Calculus - H. S. Bear
Calculus and Pizza: A Cookbook for the Hungry Mind - Clifford A. Pickover - Wiley 2003 - 208 pages
[useful book for pushing at 15 year olds - but only does 5% of what Calculus Made Simple teaches]



[similar stuff with a lot more depth, was discussed between reenmachine and I a few weeks ago, and that slightly messy thing is up on my blog here]


Anyways, it's hoped that people keep asking about books, and there's a fast and furious exchange of opinions about books, especially about introductory math books.

It's much more than a book list, but a living breathing exchange of opinions, where the people who don't know calculus or a lot of algebra should interact with the higher ups as much as possible!


if i was building a library for calculus I'd probably run out and get:
Sylvanius Thompson - JE Thompson - Kleppner - Sawyer - Stein
Gootman - Kelley - Calculus/Schaums - Advanced Calculus/Schaums - REA Problem Solver Calculus
and Spivak [for one deep book to compare and browse to the easier books]

and any ton of crappy old 20s 30s 40s 50s 60s 70s 80s math texts for a dollar in a used book store - good or bad, stale or interesting, you just might find one could be an okay reference, and if you think it's a stinker, at least you can compare your good books with it! At least if a book is stale or difficult or mind-numbing, there are always cool examples rarely seen or wacky problems. [some crappy math books for reading, may have interesting problems]

Sankaku

I am sorry you saw it as a "smart alecky remark." It was intended as useful advice. Asking for textbook information in a textbook forum seems like a logical step, no?