Other Should I Become a Mathematician?

[mrb]

In mathematics we do not care about motivation or background.

"It is impossible to understand an unmotivated definition."
- VI Arnold

Who should we believe, lurflurf from an online forum, or VI Arnold? Somebody did not write down the definition of topological space out of the blue one day and start proving theorems. Instead, the definition was developed and refined over years with the specific purpose of coming up with a good generalization of concepts from analysis. If there weren't this connection, nobody would ever have been interested in topological spaces... except, apparently, lurflurf. The sad thing is that it seems people adopt this attitude so they can sound smart and condescending, but of course they just look foolish. (And nobody anywhere has ever learned calculus out of baby Rudin... learning Calculus BEFORE college, then taking a baby Rudin course early on is a very different thing.)

 

[PieceOfPi]

Thanks for your comments again

I agree baby Rudin is not a great text.

The good news is, I'm starting to like this book. When I read this book last year, I thought it was really difficult to read. I thought that there were so many theorems and definitions that I felt like I could never memorize. However, after taking a few more math classes, I finally realized you don't memorize definitions and theorems... rather, you try to understand why they are important. And it turned out that they are actually important in proving the big theorem at the end. For example, Rudin presents many definitions/theorems so that it gives me the important results like Heine-Borel and Weierstrass.

And mrb, I got to agree with VI Arnold for this one.

I will go to the lectures one more time tomorrow. So far, I'm leaning toward taking analysis and algebra, and take topology in my senior year. But then again, topology sure does sound interesting as well...

 

[PieceOfPi]

The another alternative is to take two of those courses this term, and start taking complex analysis (or functions of complex variables) that is offered in winter-spring quarters.

 

[lurflurf]

This should be much better...

^^
[Humor]In mathematics we do not care about motivation or background. [/Humor]

I can see how a lover of fallicies would hate mathematics.
Wow lots of fallicies in there...

"It is impossible to understand an unmotivated definition."
- VI Arnold

Who should we believe, lurflurf from an online forum, or VI Arnold? Somebody did not write down the definition of topological space out of the blue one day and start proving theorems. Instead, the definition was developed and refined over years with the specific purpose of coming up with a good generalization of concepts from analysis. If there weren't this connection, nobody would ever have been interested in topological spaces... except, apparently, lurflurf. The sad thing is that it seems people adopt this attitude so they can sound smart and condescending, but of course they just look foolish. (And nobody anywhere has ever learned calculus out of baby Rudin... learning Calculus BEFORE college, then taking a baby Rudin course early on is a very different thing.)

So we hare argumentum ad verecundiam, an argument stands on its own. A faulty argument by Andrew Wiles is still faulty. That Arnold quote is very silly, I will assume that is because it has been removed from its context, ironic.
Argumentum ad populum, popularity of a belief does not make it valid.
The part about you trying to sound smart, but looking foolish is spot on.
Multiple fallacies of Relevance and straw man. If people are not reading baby Ruding to learn calculus why are they reading it? Many people have used it with success as a primary source, though no one here suggested that, if such a person had difficulties, the causes would be having one source and that one source being poorly written. What you were trying to say with that bit I have no clue. My point being Munkres and Rudin could be read in either order or at the same time. Symbolically 0<[Munkres,Rudin]<epsilon if you like. Though one wanting to learn what those cover could choose better sources, they were presented as so called course books. Which one who enjoys motivation or background should agree with, Rudin in my view motivates the topology he introduces very poorly.

 

[mrb]

Yes, because every point made in an informal discussion in an online forum must be a rigorous proof. I completely forgot about that. If your earlier post was supposed to be humorous, then so be it, but I certainly didn't perceive it that way.

I tend to agree with you that the questioner probably has sufficient background now to take topology, if that's your point.

 

[lurflurf]

For the rest of us mere mortals, it's more usual to go:
Calculus(Stewart or Spivak) --> Analysis (baby Rudin) --> Topology (Munkres)
The only "topology" needed for baby Rudin is metric spaces. The 95% I was referring to was that it is the most common course to take real analysis before topology, and for good reasons; like I said the motivation and background for topology out of a book like Munkres is from real analysis, real analysis also gives you maturity.

As for your statement that mathematicians don't need motivation or background, I suggest you read the preface to Needham's Visual Complex analysis, even Munkres' preface talks of the need for motivation. All mathematicians need intuition, motivation and background, they're bluffing if they say they don't.

The motivation this was a fuuny joke. The reader should bring some motivation of their own though. The topology books with 150 pages of streched out deformed giraffe show how easy it is to overdo that sort of thing.

You are almost making my point for me. Baby blue Rudin has about twenty pages of topology, reading say a hundred pages about topology (while not stricktly necessary) would provide background and motivation. Do not try make topology a slum of analysis, topology is a slum of combinatorics.[another joke] Courses in knots, combinatorics, differential geometry, or algebra would be at least as useful as preludes to topology as analysis "light". Even if your 95% is close it says nothing about which group (5% or 95%) is better off. One might say the 5% shows that topology first is a valid option. There are many courses that tend to procede others for no good reason.
Why take calculus before linear algebra?
The goals motivation and background are served by learning things as they are needed, not by learning lots of random things with the hope that they will become helpful in the future.

 

[economist13]

Hell no. Maths and economics majors know jack about maths either pure or applied. Economists struggle to add up, never mind do maths properly (including applied maths).

If you really think that is the case I suggest you look at modern economics again...in particular I might suggest Microeconomic Theory by Mas-Colell...or maybe
Recursive Methods in Economic Dynamics by Stokey, Lucas, Prescott

both standard PhD Micro/Macro books...

 

[n!kofeyn]

What are good mathematics publications/magazines? I guess something that a high school student can appreciate...

http://plus.maths.org/" article.

 

[Jimmy84]

I was wondering how good is the book Real and Complex Analysis by Rudin?

It has 424 pages it seems tempting to learn both real and complex analysis in such a short amount of pages. I was wondering how rigurous the book might be? Is the book a good preparation to start with differential geometry?

Im considering to do

Calculus, Apostol
Advanced Calculus, Loomis Sternberg
Real /Complex Analysis, Rudin (complementing with some other books on the subject)


Also searching on the net for Differential geometry books I found:

Differential Geometry, Analysis and Physics by Jeffrey M. Lee . I was wondering if someone knows about it and could recommend it?

The index is amazing, it seems to cover everything on the subject.

 

[martin_blckrs]

I was wondering how good is the book Real and Complex Analysis by Rudin?

It has 424 pages it seems tempting to learn both real and complex analysis in such a short amount of pages. I was wondering how rigurous the book might be? Is the book a good preparation to start with differential geometry?

Im considering to do

Calculus, Apostol
Advanced Calculus, Loomis Sternberg
Real /Complex Analysis, Rudin (complementing with some other books on the subject)Also searching on the net for Differential geometry books I found:

Differential Geometry, Analysis and Physics by Jeffrey M. Lee . I was wondering if someone knows about it and could recommend it?

The index is amazing, it seems to cover everything on the subject.

So what exactly do you want to study? Are you just starting with calculus and want to prepare for Differential Geometry?

Rudin's Real and Complex Analysis is an advanced book treating subjects like Measure Theory, Integration, some basics of Functional Analysis and quite a deal of Complex Analysis. If you just started with Calculus this is NOT the book you want to consider. This book will also tell you little of what you can use in Differential Geometry later on.

The book by Rudin is of course very rigorous (actually I think Rudin is a synonym for "rigorous" :-)) and you would generally consider the book, if you've already had a decent course on analysis (like Rudin's "Principles of Mathematical Analysis") and are considering going further in the field of Analysis.

If you've just started with calculus and want to prepare for DG, then Apostol and Loomis&Sternberg are a good preparation. You might also consider Spivak's "Calculus" and then also his "Calculus on Manifolds". Also Rudin's "Principles of Mathematical Analysis" is a great text as well as Munkres "Analysis on Manifolds".

For DG, I think there's no cannonical text, but there are some good books. A good introductory text is John M. Lee "Introduction to Smooth Manifolds". It's not really my taste (mainly because of lengthy and not so elegant proofs), but it covers a lot of topics and explains everything in detail (which becomes sometimes also its disadventage). Another good text is Warner's "Foundations of Differentiable Manifolds and Lie Groups" (less topics, more advanced). For more intuitive treatment and exercises there's a book by Fecko "Differential Geometry and Lie Groups for Physicists" ("for Physicists" says everything :-D).

 

[Jimmy84]

So what exactly do you want to study? Are you just starting with calculus and want to prepare for Differential Geometry?

Rudin's Real and Complex Analysis is an advanced book treating subjects like Measure Theory, Integration, some basics of Functional Analysis and quite a deal of Complex Analysis. If you just started with Calculus this is NOT the book you want to consider. This book will also tell you little of what you can use in Differential Geometry later on.

The book by Rudin is of course very rigorous (actually I think Rudin is a synonym for "rigorous" :-)) and you would generally consider the book, if you've already had a decent course on analysis (like Rudin's "Principles of Mathematical Analysis") and are considering going further in the field of Analysis.

If you've just started with calculus and want to prepare for DG, then Apostol and Loomis&Sternberg are a good preparation. You might also consider Spivak's "Calculus" and then also his "Calculus on Manifolds". Also Rudin's "Principles of Mathematical Analysis" is a great text as well as Munkres "Analysis on Manifolds".

For DG, I think there's no cannonical text, but there are some good books. A good introductory text is John M. Lee "Introduction to Smooth Manifolds". It's not really my taste (mainly because of lengthy and not so elegant proofs), but it covers a lot of topics and explains everything in detail (which becomes sometimes also its disadventage). Another good text is Warner's "Foundations of Differentiable Manifolds and Lie Groups" (less topics, more advanced). For more intuitive treatment and exercises there's a book by Fecko "Differential Geometry and Lie Groups for Physicists" ("for Physicists" says everything :-D).

Yea I finished my calculus high school book now I am reading Apostol, and I would like to prepare for Differential Geometry. I am looking forward to head into that direction though and perhaps into applied math. I am still not sure in what I am going to major though either math or physics. But for now I am having some spare time and I am studying on my own.

Im going to check Rudin's "Principles of Mathematical Analysis" Does it has a good complex analysis content?

thanks a lot for the recommendations.

 

[qspeechc]

Here's an article written by U. Dudley on calculus books. I thought some people might find it interesting. He talks about, among other things, how calculus books are too long, have silly apllications, not enough geometry and so on. I agree with most of what he says. He read 85 (!) calculus textbooks before making this review!

http://www.jstor.org/stable/2322923

 

[qspeechc]

Btw, I came across that article on this cool website:
http://mathdl.maa.org/

 

[n!kofeyn]

We have a politics forum to cater to those times when people want to talk about politics; the academic guidance forum is not the place for it. (And mathwonk's comment completely derailed the thread before it could even get started)

I don't doubt this. It's never good for Physics Forums to lose a member this way, but I personally found mathwonk's posts (not in the thread in question though) often very distracting. For instance this https://www.physicsforums.com/showthread.php?t=67268". Tom Mattson had found a version of David Bachman's book, A Geometric Approach to Differential Forms, on arxiv. Tom wanted to get a group discussion going where they would work through the book, but mathwonk almost immediately took over. In my opinion, he wasn't even participating in the discussion (and certainly not in the way Tom had hope for) and just rambled with very large posts, one after the other.

Tom even invited David Bachman, the author of the textbook and professional mathematician, to the thread, to which he accepted and started posting. Although, it wasn't long before mathwonk was basically insulting the author by constantly providing corrections or ways the material should have been presented, even in the face of statements by the author and Tom that the text was for undergraduates and that rigor was intentionally sacrificed for readability.

On top of that, mathwonk's self-indulging comments took over the thread and basically made it impossible for it to operate, which was very rude given Tom Mattson's original plan for the thread. In the end, mathwonk definitely seemed to irritate Bachman as seen in post 82, and you can easily see mathwonk's arrogance and complete disregard for the original purpose of the thread in https://www.physicsforums.com/showthread.php?t=67268&page=5#83". Just take a look at the thread, and you'll see near entire pages of the thread were just mathwonk posts.

I found this thread when I became interested in differential forms and found it completely useless due to mathwonk's meddling. I remember this frustrating me highly and even considered to quit coming here, even though I had basically just joined. mathwonk cost Physics Forums a possible member who is a professional mathematician and basically ran him off, as Bachman doesn't participate in the thread after the above mentioned posts.

All this is to say, mathwonk probably needed an infraction before this incident, and I find it a little frustrating he wasn't. I've seen other threads where this behavior of his took place as well. This has been bothering me because I've seen interesting threads shut completely down because they violated rules, in the case I'm referring to the post was deemed fringe science and not welcome. This is after just ONE post and a legitimate question in my opinion. The other point is that mathwonk's pinky up approach and condescending tone (see his winetasting https://www.amazon.com/review/R3RD2ULNTR37EU/ref=cm_cr_rdp_perm"&tag=pfamazon01-20 on Amazon :) is replicated somewhat by other PF members as well, which I think takes away from PF's ability to attract worthwhile members.

 

[tauon]

I'll be blunt and short: I'm a first year student reading mathematics and I was wondering if anyone here can recommend me some good textbooks...

I'm taking algebra, mathematical analysis, geometry and mathematical logic courses (which are mandatory) as well as an optional course in topology.

help? :P

 

[n!kofeyn]

I'll be blunt and short: I'm a first year student reading mathematics and I was wondering if anyone here can recommend me some good textbooks...

I'm taking algebra, mathematical analysis, geometry and mathematical logic courses (which are mandatory) as well as an optional course in topology.

help? :P

You should browse this https://www.physicsforums.com/forumdisplay.php?f=21".

 

[tauon]

You should browse this https://www.physicsforums.com/forumdisplay.php?f=21".

oh, I will. thanks for the tip. I don't know how I missed it. :)

 

[Bourbaki1123]

What is the probability of becoming a professor at some point after your PHD in mathematics? Also, to what extent does area of expertise affect this likelihood?

E.g. Suppose candidate X wrote his thesis on something in Automatic Theorem Proving candidate V wrote Something in Topos Theory, Candidate Y wrote his on something in Algebraic Geometry and candidate Z wrote his in some area of Analysis. Do these specializations affect qualification for an assistant professorship? I ask this because I wonder if being in a less popular area means less funding for research or if being in a more popular area means more competition or (more likely) some combination of both.

I'm talking about overall chances, so don't assume flagship school or state U, include southeastern state college X also.

 

[Chewy0087]

What is the probability of becoming a professor at some point after your PHD in mathematics? Also, to what extent does area of expertise affect this likelihood?

E.g. Suppose candidate X wrote his thesis on something in Automatic Theorem Proving candidate V wrote Something in Topos Theory, Candidate Y wrote his on something in Algebraic Geometry and candidate Z wrote his in some area of Analysis. Do these specializations affect qualification for an assistant professorship? I ask this because I wonder if being in a less popular area means less funding for research or if being in a more popular area means more competition or (more likely) some combination of both.

I'm talking about overall chances, so don't assume flagship school or state U, include southeastern state college X also.

this is the wrong section, you need to post this in the homework support - maths section, i'd consider a binomial approximated to a normal distribution.

 

[huenikad]

Hello,

I am a Gr. 12 Canadian student and I am deciding between math or engineering now for university. I was wanting to look into some math work to get a better idea of what I want to do. I've always found math at school to be ridiculously easy and have always enjoyed it but just get bored of the repetitivity. I have done math contests etc. over the years but haven't done too much further research into math yet. Sort of realizing how much I actually enjoy it now.

I am planning on looking at Courant and Robbins "What is mathematics", as well as Principles of Mathematics, by Carl Allendoerfer and Cletus Oakley. I was wondering if I should take a look at a specific calculus book or look for some more linear algebra type of stuff.

Any other books that I should take a look at that may pique the interest of a future mathematician?
Any books focused particularly on proofs would also be helpful.

 

[Landau]

I think Spivak's Calculus will certainly be of interest to you. It's a pleasure to read, but has also very challenging exercises. Take a look for yourself: click.

Of course, this is a 'serious' mathematics book. If you want to read a book about mathematics (instead of a mathematics book), I think Courant and Robbins may be a good choice.

 

[Bourbaki1123]

this is the wrong section, you need to post this in the homework support - maths section, i'd consider a binomial approximated to a normal distribution.

I guess that's an attempt at humor? Seriously though, if anyone has any actual insight into the process of becoming a professor (in mathematics) and what factors play into it and to what degree, I would appreciate it. I'm aware that it's highly competitive as far as getting a position and I want to know how to raise my chances aside from the obvious: pumping out tons good of research.

 

[rootofunity]

Hi, I am new here. I have my masters in Math and would like to renew my independent study of physics. The question is where to start. I have an older version of University Physics by Hugh D. Young, Roger A. Freedman, which is undergraduate calc based physics. But since math wise my understanding of math is a bit more advanced should I start at a higher level? And if so where? Sorry for jumping into an ongoing conversation. Still getting the hang of things.

 

[JasonRox]

forgive me if i am over sensitive, but the following message was so insulting to me i decided to leave the forum:

from russ_watters:


russ_watters is Online:
Posts: 13,297
You have received an infraction at Physics Forums
Dear mathwonk,

You have received an infraction at Physics Forums.

Reason: General Warning
-------
That's not a forum for editorializing or challenging people's motives. If you don't have anything useful to contribute, stay out.
-------

This infraction is worth 1 point(s) and may result in restricted access until it expires. Serious infractions will never expire.

Original Post:
https://www.physicsforums.com/showthread.php?p=2019454
creating bombs to kill people is cool? please think about your options. there might be something out there with a better impact on the world.


to be honest, you don't need me. this forum is going extremely well. best wishes!

I'd definitely rather see russ_watters gone

I was making a "come back" to PF, but to see mathwonk gone and matt_grime gone (haven't seen him) then I'm out too.

Cheers!

 

[Bourbaki1123]

Darn. We're losing our math community one at a time...What happened to matt grime?

 

[rootofunity]

Although I am not a Phd in math I am a newer user with a solid math background :D

 

[Cod]

How important is it to be part of a professional organization (AMS, MAA, etc.)? Does membership provide any benefits when pursing graduate study and/or a career in a mathematics-related field?

 

[mrb]

Since mathwonk is no longer here, it might be better for people to ask questions in their own thread; there's no point in stuffing more posts in this thread.

 

[fabletls]

Hell no. Maths and economics majors know jack about maths either pure or applied. Economists struggle to add up, never mind do maths properly (including applied maths).

If you're going to be a good applied mathematician then you'll be able to do Apostol and the purer stuff: you might not see the utility of it a great deal at times, but you will be able to do it, and it might well come in useful later.

Economists struggle to add up what? I realize this is 4 years over due, but this is just ignorant and non nonsensical. If they're math , in addition to econ, majors, how is it that they 'know jack' about maths? Aren't mathematicians supposed to have sense than to make vapid generalizations like this?

There are plenty of math and econ majors who take rigorous math courses in line with those math majors would take. And there are plenty of economists with solid math backgrounds who are more than capable of 'adding up and doing maths properly.' Good thing most mathematicians don't possesses such unwarranted disdain towards economists.

 

[Deep water]

Euler, Abel, Gauss, Galois, Weierstrass, Eisenstein, Riemann, Dirichlet, Roch, Hilbert, Klein, Ramanujan, Erdos, Serre, Milnor, Wiles, Thurston and all other greats were born as human like us. I believe they are never bored in Math. That's why they are great. I think their love for Math made them great. One of my teacher said (about me), "You can not learn Math as you do not love Math. If you love, go to library and read any book to start learning"

 

[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?