Other Should I Become a Mathematician?

[Phyisab****]

There is more of a continuum than a binary decision, either loving math or not. I have a love/hate relationship with math that would blow away (insert example that I can't think of a good example here).

 

[Deep water]

Until November 2009 I didn't think about becoming a mathematician. I was interested in Physics, Electronics and Computer science. However, I learned basics of Calculus, Analytical geometry, Mechanics, Discrete Math, Algebra, Trigonometry myself. I found learning Math does not actually depend on your motivation rather your attraction or dedication to it. I think one can be a mathematician if he/she wants to be one. examples are Banach, Poincare, Ramanujan

 

[uman]

Learning math certainly depends on your motivation...

 

[JYouker]

MATHEMATICAL NEUROSCIENCE

Math is what I like to do. My desire is to apply it to solve real-world problems, especially in neuroscience. It's too bad that I am just an average student, GPA-wise, so I may not stand out from the rest, when it comes time to find a job in this field. So, I am wondering what kind of opportunities there are, for me. My guess would be that the only positions in mathematical neuroscience are for the very successful students, because, it seems like a small and new field. Also, since a graduate degree will increase my chances of finding a job, is it possible to get accepted to a grad school with a GPA below 3.0? Lastly, are undergraduate courses in biology, physiology, and neuroscience required, or can I major in math/comp sci and pick up the biology, later? Alas, if someone can show me towards some more information (articles, websites, etc) in this field, that would help, too.

THanks,
-Joe

 

[TMM]

I know a guy who does statistical mechanics of the brain. Stat mech is a very mathematical branch of physics, you might find it interesting. Beyond that I don't know much.

 

[mrb]

Joe,

I don't know how many replies you will get here; it would make a lot more sense to start your own thread about this topic. Even then, I'm not sure anyone on this forum knows much about mathematical neuroscience specifically.

Here's what I can tell you:
* Often a PhD is more or less necessary to do real work in a math or science field. I imagine mathematical neuroscience is the same, so yes, you will probably need grad school.
* One often hears that 3.0 is the absolute cutoff for admission to grad schools (and really, they want much better than that. Anything under 3.5 is going to raise eyebrows. If you want to demonstrate you can handle grad school, why aren't you getting As in undergrad?). If you still have time, GET BETTER GRADES. If not, this may be a problem, and you may have to jump through some hoops to get where you want to go.
* Regarding if you need a bio background: I can only tell you what I know about Bioinformatics. In that field, I was told that it was highly desired that a student from a math/CS background had taken at least the intro course sequence in Bio, and preferably more. But even that wasn't necessary; this grad program would admit people with no bio background at all.
* Talk to a professor in the field. If your school has a program in this field, email a professor and ask if you can talk to him for a few minutes. This will get you a lot better answers than anyone here will probably be able to tell you.

 

[sudarshanabcd]

i think it is purely personal choice.
i personnaly prefer pure mathematics , though i am intersted in physics.
but the thing is that i tend to like logically learned things.
i hate differential equations as they are full of techniques,but calculus is beautiful
i think calculus , geometry and algebra should be taught in one stretch & not separately , as they are closely interrelated ,and help us solve problems more effectively

 

[mathwonk]

try arnold's ordinary differential equations book. it will change your opinion of diff eq. I promise. best wishes.

 

[sudarshanabcd]

is there any sight for free download of arnold's ordinary differential equations.?

 

[DrummingAtom]

Wait a second... mathwonk is back? Welcome back mathwonk, I enjoy your posts.

 

[andyroo]

I'm majoring in pure mathematics. Although I'll probably just complete course work for both applied and pure mathematics.

 

[thrill3rnit3]

try arnold's ordinary differential equations book. it will change your opinion of diff eq. I promise. best wishes.

mathwonk's back??

 

[Gib Z]

Mathwonk is back?

 

[quasar987]

Hi mathwonk, glad to hear from you!

 

[manlyman62]

Hello!
In regard to becoming a better mathematician, is there a good book I can read on proofs themselves? Or is proving mathematical theorems a skill you should pick up by simply doing it?

 

[thrill3rnit3]

^ How to Prove It by Velleman is a good book for proofs

 

[Chris11]

I want to be a mathematician. Math is the most exciting academic disipline possible.

 

[radou]

Although I don't have a degree in math, mathematics is one of my favorite hobbies. We had 4 math courses on our faculty of civil engineering (which consisted of a rough "section" through basic single and multi-variable calculus, linear algebra, and probability, along with some mathematical physics - all laid out in a pretty much non-rigorous manner, mostly without proofs etc.), and I took 2 linear algebra courses on the Mathematical department of our Faculty of natural sciences - sadly, I didn't have time for more, although I'm sure I would go and study math for real if I had the time and the money.

So, the only option is self-study, which I've been practicing for a long while, but it's a bigger challenge since you are forced to think your way through more intensively, and explore and try out a considerable number of textbooks and lecture notes (most found on-line), all written in their own style, and every one of them not necessary suitable for every one of us and for every level of "pre-knowledge".

Since I took linear algebra, I believe I have grasped some basic concepts related to this fundamental topic. On the other hand, I had to go through the basics of calculus on my own, and, although it may only be my impression, I find calculus a bit more difficult in general.

The last 2 months I am going through a set of lecture notes about metric spaces and topology - one found at the University of Dublin, and the other two found on the department of math of my university. I also downloaded problems to solve, since there is no sense in going through theory without solving problems. I find the subject interesting and challenging.

Also, I intend to go through some functional analysis.

To sum everything up, self-learning mathematics requires a lot of time and dedication, but if you really enjoy it, I believe it's worth the effort.

 

[Chris11]

Hey, there is a fairly old and REALLY CHEAP book out there on real AND functional analysis. It's published by dover. I have it, and it's pretty good, except for one of the exercises it asks you to prove that conjecture (unsolved to my knowlege) that there is no aleph number between aleph 0 and aleph 1. Anyways, it's worth the dime (about 12 Canadian). Good luck with your adventure! Also, for some inspiration, it's important to notice that some of the most significant mathematicians have been 'amatures,' with the most notable being piere fermat! So, I think that actual formal education is overrated--especialy if your self motivated and passionate about the subject.

 

[radou]

Hey, there is a fairly old and REALLY CHEAP book out there on real AND functional analysis. It's published by dover.

Could you point out the author and exact title?

 

[Chris11]

Absolutely. It is called "Introductory Real Analysis." It was written by A.N. Kolmogorov and S.V. Fomin. It's a translation.

 

[radou]

Thanks a lot, just looked at its preview of contents at Amazon, seems to cover a wide range of topics.

 

[radou]

Also, one thing I would like to point out - unfortunately, I started to practice this just recently - it seems tremendously useful to try to do proofs by yourself before going through them, since it develops your way of reasoning, and it automatically makes you review all the definitions/results you went through before and which you need for a certain proof. This is probably mentioned at some point before in this thread, but it's simply too huge to go through.

 

[Chris11]

Yeah, that's important. It's also important to make up problems for yourself to solve, although, sometimes, you end up 'making up' a well known and unsolved problem. I thought that the probability of what I now know to be called a (1,o) matrix to be invertible was an origanal problem. It wasen't, and people have been trying to solve it for a long time. Another good source for mathematical devolement are math contest-type problems. An exellent source of such problems is the art of problem solving website; google it and you'll find it.

 

[hunt_mat]

One topic that tends to be left out of maths degrees is integral equations. differential equations are done to death but integral equations tend to be used as example in functional analysis courses.

Mat

 

[MathematicalPhysicist]

One topic that tends to be left out of maths degrees is integral equations. differential equations are done to death but integral equations tend to be used as example in functional analysis courses.

Mat

In the FA courses which I have taken we mainly show that for an integral equation there exists a unique solution.

To find the solution you need to take derivatives anyhow.

 

[hunt_mat]

Not really, I bought a few books on integral equations and if that were the case then no one would even mention them. There are methods which don't take derivatives.

Mat

 

[sponsoredwalk]

I've browsed through a lot of the drama that is this interesting thread & I've gotten a bit of confidence from people but not an answer
to what was grating on my mind so I think it's better to ask/contribute

The ultimate aim of this post is to finish Rudin's Mathematical Analysis, it's a personal journey I'll be taking over the next few months
so bear with me as you read this, I'd really appreciate some in depth input from any thoughtful reader.

I've worked through Thomas calculus (exactly like Stewart calculus) up to chapter 12 having had to go elsewhere to learn every single concept
in those first 12 chapters anyway which is the smartest thing I've ever done in my life up until now so I quit the book &
went on amazon & found Wilfred Kaplan's Advanced Calculus which looked amazing.

I bought the book really cheap & got it like 3 weeks ago & am nearly in tears after wafting through the first chapter which is on linear algebra.
I've tried to learn linear algebra before & have quit those horrible computational style books as I absolutely despise memorizing stuff.
Admittedly Kaplan says that in his earlier single variable work he covered linear algebra more thoroughally but I have actually read the first 5 chapters
of that book, which is free online, & eventually just quit becuase of how bad it was.
I'm really stupid to have expected his advanced calc book would be any better but the allure of starting Fourier series,
functions of a complex variable & partial differential equations by the end of one single book was too strong

The thing is that I bought Serge Lang's Introduction to Linear Algebra with it as I know of Lang's reputation
& thought I'd give a slightly more theoretical book a shot.
Basically everything Lang writes is from the perspective of your inner mind & he knows how to get you to remember theorems & proofs well after you've read them.
Simple postulates have far reaching consequences!
Well, I have been toying with the idea of finishing Lang's linear algebra book then trying Kaplan's advanced calculus
post-chapter 1 but I bet the explanations will be terrible.

Because Lang's linear algebra book was making me so happy I decided to try his multivariable calculus book instead
so I went to my friends college library with him to find it.
We only got out the single variable calculus book & I've decided to go through it as a refresher then buy his multivariable book.
I'm going to sell the Kaplan book .
I've already read nearly 200 pages in 2 sittings (this is my second one ) & Lang is just brilliant.
The book isn't extremely taxing & he's clearing up so many concepts with basic ideas that are more theoretical than Thomas calc's ones for sure!
So, to close this section I would really like to hear any opinions on Lang's multivariable calculus book.
It doesn't cover as much ground as Kaplan's book but I get the feeling it will be deeper & longer lasting so I think it's a good trade off.
I've browsed PF forums & found very few multivariable calc book recommendations other than Apostol, Courant, Marsden or Stewart &
I have a plan of conquering Apostol a while after I finish Lang's book so I wonder, will Apostol be all I ever need in this field or
is the next step in multivariable calculus a solid analysis book on the topic? I really don't know


Now, I have to stress that Lang's single variable calculus book is not as difficult, by any means, as Spivak's calculus is.
I bought Spivak half a year ago when I could barely understand mathematics, being impatient, and am still shocked by it's subtlety.
I now see that it's conquerable but you need to be confident with logic, i.e. the logic of a proof, & I've never taken a course on dealing with that - but I have a plan!
I've ordered Steven R. Lay's Introduction to Analysis which takes it's first 10 chapters on this very topic!
I've tried to read some logic or proofing discussions but when they aren't applied to calculus it just doesn't click. I've looked in this book and he really shows you
how to apply logic to an analysis proof in the way that I've been looking for so I think I'll be able to pre-think actual proofs once I complete this book.

So, my idea as it stands is as follows. I'm going to finish Serge Lang's single variable calculus book in the next few days,
then as soon as I get his multivariable calculus book I'm going to work on doing that along with his linear algebra book.
Once I finish these I'm going to exclusively focus on Lay's analysis book to get used to proper proofs in a definite way.

(I may sound like I can't fathom a proof, I can but not in a sophisticated & systematic enough way to be confident,
I thought there was no theory to constructing a proof until I looked inside Lay's book so
the fact that it doesn't come out of thin air is a confidence booster)

Then, once I've really dealt with Lay's analysis book, which I know isn't that difficult from nearly every mention of the book online
I'm going to concurrently read both Spivak & Apostol and have confidence that I can answer the questions systematically.
Then I think I'll be able to deal with Rudin.

I'm afraid some people might say that this is overkill and it probably is but it's a personal quest & I think that if I can conquer these books then I could get anywhere in mathematics.
After failing math for nearly all 6 years of high school & having no understanding, I mean none! it's something I got to do.

Have you any tips for me, besides keeping the coffee boiled

 

[hunt_mat]

Have you tried "Engineering Mathematics" and "Further Engineering Mathematics" by K.A. Stroud et al?? It is the best textbook it has my fortune to read and understand.

 

[sponsoredwalk]

Have you tried "Engineering Mathematics" and "Further Engineering Mathematics" by K.A. Stroud et al?? It is the best textbook it has my fortune to read and understand.

I went through 2 engineering books to learn all of the precalculus I needed for thomas calculus (& some of the calculus) & there was so much left out of it that I can't really deal with an engineering book skipping the theory/motivation behind the concepts.
The book does look great on amazon though, I really could have used this one back then from the looks of it

I can't check it out but do the chapters on calculus give you a big sheet of all of the basic integrals and derivatives, their inverses & how to rederive all of them?
Does it explain least upper bounds and ε-δ limits & all that theoretically?
The first 350 pages look like they would have been useful to me but once you get past that I can't continue as it's just memorization.

The second Stroud volume looks pretty good but seeing as I don't know that much about the topics in it I'm potentially looking at repeating the past. You know what I mean, I'll go & do them but eventually just have to do it all over again because there's a wealth of material they're skipping for the sake of brevity/technique learning/memorization.

Thanks for the tip about this book though, I remember the cover from the shops & even looking in it quickly but ignoring it because another book (the one I bought) included a lot of stuf from the 2nd Stroud volume & that's why I bought it.
I can't get away with cramming anymore