who wants to be a mathematician?

**PieceOfPi** · Oct2-09, 02:49 AM

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** · Oct2-09, 10:55 AM

This should be much better...

Originally Posted by lurflurf

^^
[Humor]In mathmatics 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...

Originally Posted by mrb

"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** · Oct2-09, 11:23 AM

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** · Oct2-09, 11:26 AM

Originally Posted by qspeechc

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 refering 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** · Oct5-09, 05:46 AM

Originally Posted by matt grime

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** · Nov3-09, 02:28 AM

Originally Posted by thrill3rnit3

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

Plus Magazine is written at a fairly low level, and I enjoy reading it. The AMS Notices are very good too, written at a slightly higher level, but still easily digested by an undergraduate. They're also avaibable online for free. In the current issue, the interview with Yuri Manin is interesting. A favorite of mine is Freeman Dyson's Birds and Frogs article.

**Jimmy84** · Nov3-09, 12:29 PM

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** · Nov3-09, 02:39 PM

Originally Posted by 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.

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** · Nov3-09, 06:31 PM

Originally Posted by martin_blckrs

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 im reading Apostol, and I would like to prepare for Differential Geometry. Im looking forward to head into that direction though and perhaps into applied math. Im still not sure in what im going to major though either math or physics. But for now im having some spare time and im 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. :-P

**qspeechc** · Nov4-09, 09:55 AM

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** · Nov4-09, 10:15 AM

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

**n!kofeyn** · Nov6-09, 12:42 AM

Originally Posted by Hurkyl

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 thread. 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 post 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 review 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** · Nov7-09, 11:12 AM

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** · Nov7-09, 12:47 PM

Originally Posted by 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

You should browse this sub-forum.

**tauon** · Nov7-09, 02:21 PM

Originally Posted by n!kofeyn

You should browse this sub-forum.

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

**Bourbaki1123** · Nov9-09, 07:32 PM

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.