## Search found 159 matches

Wed Jul 22, 2009 8:00 am UTC
Forum: Mathematics
Topic: (ln -1)/i = pi?
Replies: 16
Views: 15026

### Re: (ln -1)/i = pi?

To give the negative values a meaning, you're switching to the complex logarithm function. The normal logarithm and the complex logarithm agree for positive, real numbers, but the complex logarithm has a larger domain. It also doesn't have the nice arithmetic properties that you are using in your ar...
Mon Jul 20, 2009 8:11 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 279896

### Re: Math Books

I would not use that as an introduction to abstract algebra. It assumes you are very comfortable with rings and modules. It could be helpful when you are learning the Nullstellensatz, but you should probably wait awhile. It's an excellent book with very enlightening exercises and extremely concise a...
Sun Jul 19, 2009 7:45 pm UTC
Forum: Mathematics
Topic: Academic Papers & Their Authors
Replies: 2
Views: 744

### Re: Academic Papers & Their Authors

I think it's standard in math to list authors alphabetically (this is known as the Hardy-Littlewood rule). It is not this way in other fields though, but in math it shouldn't matter.
Wed Jul 15, 2009 6:28 pm UTC
Forum: Mathematics
Topic: Graph Theory (Bollobás) Discussion
Replies: 21
Views: 2323

### Re: Graph Theory (Bollobás) Discussion

Yeah, I can't make the same guarantee either, but I will try to participate as well.
Tue Jul 14, 2009 4:00 am UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

The prerequisites for Calculus on Manifolds are probably just some solid single-variable real analysis. For the differential geometry book, you're gonna need the material from Calculus on Manifolds, point-set topology, linear algebra, and probably a little exposure to abstract algebra and manifolds ...
Tue Jul 14, 2009 3:49 am UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

A question, though: what sort of keywords would I look for to identify books that work on "multivariable" (and vector) analysis, by analogy to multivariable/vector calculus? I'd really like to see the theory behind gradients, Green's theorem, multiple integrals, partial derivatives, etc. ...
Tue Jul 14, 2009 3:08 am UTC
Forum: Mathematics
Topic: Hints for Exercises
Replies: 9
Views: 927

### Re: Hints for Exercises

In any good, upper-level text, the hints are usually given because you need them. Some disagree, but I think it would be much more productive to just use hints and get more done faster than spend days working on something that you may never get. In fact, if you can't get something, I think a better ...
Mon Jul 13, 2009 9:53 pm UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

From the reviews on Amazon that I read, it seems like that book doesn't really prove much. So you guys shouldn't have a problem finding exercises to do; just prove everything that they state without proof. Anyways, I'll try to grab a copy if I can get my lazy ass to the library before its ridiculous...
Mon Jul 13, 2009 12:46 am UTC
Forum: Mathematics
Replies: 53
Views: 9592

### Re: Post your interesting/challenging/fun integrals

If you're going to study pure math, get into the habit of using log for base-e. Almost every textbook will use this without noting what it means, as well as pretty much every single lecturer.
Sat Jul 11, 2009 8:12 pm UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

If there is anyone interested in some slightly more advanced reading, I would be interested in "An Introduction to Graph Theory" from Dover, "Algebraic Topology from a Homotopical Viewpoint" (which is £50 unfortunately) or something on Category Theory. The first two I have had a...
Fri Jul 10, 2009 5:50 pm UTC
Forum: Mathematics
Topic: What should I learn.
Replies: 47
Views: 4173

### Re: What should I learn.

Politely correcting a professor's mistake is fine, as it benefits everyone's understanding. But why be a smartass? It just makes everyone hate you. There's a place that was created so you can be a smartass without any consequences, and it's called the internet.
Fri Jul 10, 2009 5:13 pm UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

It's only \$25 on Amazon. Maybe buying textbooks has me jaded, but that's extremely cheap by my standards. Does this book have much depth at all? I know I could at least suggest problems for a few of those subjects (either from past exams, problem sets, textbooks, memory, etc.).
Fri Jul 10, 2009 4:02 am UTC
Forum: Mathematics
Topic: Commutative Algebra Questions
Replies: 9
Views: 1527

### Re: Commutative Algebra Questions

Someone else here could give you a lot better description and explanation, but just as a preliminary, I've heard it said that the tensor product is the first object we learn where the universal property is key to understanding it. So you might want to think more about the universal property and what...
Fri Jul 10, 2009 3:17 am UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

[I read through some of a book on category theory without having any formal education on topology or algebra and did well enough just looking at things on Wikipedia. Category theory is definitely a "high-level" topic that doesn't require too many prerequisites at first. The reason it's ta...
Fri Jul 10, 2009 12:39 am UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

i was thinking we would choose well known, well written textbooks, that were slim and easy to access, like dover or springer. I will selfishly suggest Atiyah and MacDonald's Commutative Algebra, as I'm supposed to read as much as possible over the summer. Maybe it's too high of a level.... but it's...
Thu Jul 09, 2009 6:47 pm UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4475

### Re: math book club

What kind of books? Popular, easy-reading math books, or serious textbooks?
Sun Jun 28, 2009 7:17 am UTC
Forum: Mathematics
Topic: Commutative Algebra Questions
Replies: 9
Views: 1527

### Re: Atiyah-Macdonald Intro to Commutative Algebra typo?

Yeah, unless I'm missing something obvious, that would have to be the case. The next step says, "Taking N to be M", and f to be the identity mapping, it follows that vu=0...", which you could only deduce from fvu=0 not vuf=0 (errr, I think that's right).
Sun Jun 28, 2009 3:31 am UTC
Forum: Mathematics
Topic: What should I learn.
Replies: 47
Views: 4173

### Re: What should I learn.

I like examples and lots of em, but the ones in Dummit and Foote all seemed not to be helpful in figuring out the concepts, just examples of some routines to go through. Yeah, I would agree with that. That's why they should have cut down on them a little. And Rudin? Awesome, algebra for people who'...
Sun Jun 28, 2009 3:18 am UTC
Forum: Mathematics
Topic: What should I learn.
Replies: 47
Views: 4173

### Re: What should I learn.

Why would anyone use Lang except under coercion? If this is just for fun, choose a pleasant little text like Gallian. Lang is completely useless for a first look, and Dummit and Foote probably only mostly useless. Gallian could be a fun one. I really liked Artin, but maybe because it is an algebra ...
Sat Jun 27, 2009 10:02 pm UTC
Forum: Mathematics
Topic: What should I learn.
Replies: 47
Views: 4173

### Re: What should I learn.

Buttons wrote:Why would anyone use Lang except under coercion?

To prove their manliness, obviously.
Tue Jun 23, 2009 6:51 pm UTC
Forum: Mathematics
Topic: What should I learn.
Replies: 47
Views: 4173

### Re: What should I learn.

If you are really serious about doing pure mathematics (which you might not be, which is fine), definitely start with some set theory. In hindsight, if I were in your position, I would start learning point-set topology and abstract algebra as soon as possible. This might not be as immediately reward...
Tue Jun 23, 2009 7:49 am UTC
Forum: Mathematics
Topic: Strange definitions of flaws and mathematical rigour
Replies: 114
Views: 8063

### Re: Strange definitions of flaws and mathematical rigour

Successful troll is successful. Assuming that you aren't just getting a good laugh out of all of this, why do you even care? You have stated that you are not a mathematician, and it certainly seems that your mathematical knowledge is very elementary, so why is this something that you care so much ab...
Tue Jun 23, 2009 1:13 am UTC
Forum: Mathematics
Topic: Erdos Conjecture
Replies: 17
Views: 6037

### Re: Erdos Conjecture

well Paul Erdos came up with a system of, titles for mathematicians and what not. Paul Erdos himself had the title of Erdos 0. From there, anyone who worked directly with him, would have the title Erdos 1 (very respected in the math world). Then people who worked with people who worked with Erdos w...
Mon Jun 22, 2009 6:10 pm UTC
Forum: Mathematics
Topic: Analysis Help!
Replies: 16
Views: 1348

### Re: Analysis Help!

Torn Apart By Dingos wrote:If the property is satisfied for the interval [a,b], it's satisfied for all subintervals [a',b'] with a<a'<b'<b. So [imath]f(b')-f(a') \geq 0[/imath] for all a'<b'.

Ahh yes, thank you. It's amazing how much one can forget a week after school is over.
Mon Jun 22, 2009 8:21 am UTC
Forum: Mathematics
Topic: Analysis Help!
Replies: 16
Views: 1348

### Re: Analysis Help!

Prove that f(b)-f(a) \geq 0 . My issue is that this would in turn imply that f is non-decreasing on the interval and so is differentiable almost everywhere. I need to sleep so maybe I'm missing something obvious, but how does f(b)-f(a) \geq 0 imply nondecreasing? Cou...
Sun Jun 21, 2009 6:08 pm UTC
Forum: Mathematics
Topic: Greater achievement - Perelman's or Wile's proof?
Replies: 23
Views: 3443

### Re: Greater achievement - Perelman's or Wile's proof?

I find the latter case much more descriptive, after all, it's called 'The prime number theorem' and 'The main theorem of arithmetic', neither are named after Euclid which proved them. The infinitude of primes is actually called Euclid's Theorem (check Wikipedia if you don't believe me). As has been...
Sun Jun 21, 2009 8:10 am UTC
Forum: Mathematics
Topic: Greater achievement - Perelman's or Wile's proof?
Replies: 23
Views: 3443

### Re: Greater achievement - Perelman's or Wile's proof?

That theorems and laws are named after people is also really just a sign of human lust for glory and popularity. How do you figure? Wouldn't it make more sense that we are just trying to honor people that we respect? People do not (usually) name theorems and definitions after themselves. Edit: Plus...
Sun Jun 21, 2009 8:07 am UTC
Forum: Mathematics
Topic: Part-time math hobbyist, I just took ODE. Any applications?
Replies: 30
Views: 3308

### Re: Part-time math hobbyist, I just took ODE. Any applications?

Yes and no, yes because it often does happen no because you don't hear from it if it doesn't happen of course. There have been countless pure maths results which no one really knows of except the most esoteric of mathematicians because they never found a function. You just hear from them if they do...
Sun Jun 21, 2009 7:33 am UTC
Forum: Mathematics
Topic: Part-time math hobbyist, I just took ODE. Any applications?
Replies: 30
Views: 3308

### Re: Part-time math hobbyist, I just took ODE. Any applications?

Doesn't pure mathematics drifts farther and farther away from real life applications and reaches into a realm beyond usefulness but only for the satisfaction of its own author or people who are reading them? I have never been properly introduced into pure mathematics, thus so far I haven't found an...
Sun Jun 21, 2009 5:16 am UTC
Forum: Mathematics
Replies: 6
Views: 1337

### Re: Who taught your professors?

I'm not sure it's fair to say that Euler and Gauss "taught" your professors, any more than they have taught all of us. :P I think what's more fun is hearing stories about the mathematicians your professors were taught by when they were students. To quote one professor I know, "I'm goi...
Sun Jun 21, 2009 5:06 am UTC
Forum: Mathematics
Topic: Greater achievement - Perelman's or Wile's proof?
Replies: 23
Views: 3443

### Re: Greater achievement - Perelman's or Wile's proof?

I just hate Wiles because he did it for the glory with his working in secrecy business, serves him right that he erred on the first go. Also, I share Perelman's idea that it should be about the results and not about the people. Also, every mathematical theorem proven is essentially built upon other...
Sun Jun 21, 2009 2:58 am UTC
Forum: Mathematics
Topic: Greater achievement - Perelman's or Wile's proof?
Replies: 23
Views: 3443

### Re: Greater achievement - Perelman's or Wile's proof?

I would guess that a grad in math, maybe a PHD, would probably be able to do it, but maybe you're right. Where would I be able to find a place with people who have such mastery of modern mathematics as you think are needed to weigh this question? There might be some professors out there, but I thin...
Thu Jun 18, 2009 4:32 am UTC
Forum: Mathematics
Topic: question regarding simple multiplication
Replies: 5
Views: 553

### Re: question regarding simple multiplication

So basically you want to factorize c into two factors? First of all, I don't see what this would have to do with d+e=c, unless you want some sort of relation between them and a,b. Second, factorizing it to just two numbers will not be unique in general (unless c is prime of course). I don't see what...
Mon Jun 15, 2009 4:11 am UTC
Forum: Mathematics
Topic: Necessary condition for goldbach
Replies: 42
Views: 4419

### Re: Necessary condition for goldbach

I have just started giving a try at some of the major open problems in maths . What's your background like? I would suggest that your time would be better spent learning a LOT of math. If you are serious about wanting to try to make progress towards something big like Goldbach, I would suggest you ...
Thu Jun 11, 2009 8:47 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 279896

### Re: Math Books

Any suggestions for Algebraic Number Theory? Is the standard reference Lang? My professor suggested I look into Lang or Ribenboim. Any help would be appreciated.
Thu Jun 11, 2009 2:38 pm UTC
Forum: Mathematics
Topic: What do you think the "tree of math" is, pedagogically?
Replies: 8
Views: 1807

### Re: What do you think the "tree of math" is, pedagogically?

For instance, as much as topology can be involved in analysis, you wouldn't be well-served by studying it before you study calculus, which is where studies in non-trivial mathematics traditionally begins. Actually, you'd be very well-served indeed. Whether one could get very far with it is a differ...
Sat Jun 06, 2009 3:10 am UTC
Forum: Mathematics
Topic: Supremum and infimum over C
Replies: 12
Views: 1565

### Re: Supremum and infimum over C

I would say that the ordering used is definitely ambiguous. Unless I'm mistaken, there's no "canonical" ordering of C.
Wed Jun 03, 2009 12:17 am UTC
Forum: Mathematics
Topic: how do I pronounce the cartesian product
Replies: 14
Views: 2228

### Re: how do I pronounce the cartesian product

Yeah I think both "cross" and "times" work just fine, but thinking about it now, I more often say "cross".
Tue Jun 02, 2009 2:54 am UTC
Forum: Mathematics
Topic: Can imaniary numbers and real numbers be related?
Replies: 10
Views: 1986

### Re: Can imaniary numbers and real numbers be related?

Kurushimi wrote:If not complex, what about just imaginary. Can numbers i, 2i, 3i...be placed into an ordered field?

Well they wouldn't be a field, because multiplying two of them together will give you a real number, and a field must be closed under multiplication.
Mon Jun 01, 2009 1:31 am UTC
Forum: Mathematics
Topic: Real-world examples of -x * -y = +z
Replies: 66
Views: 8263

### Re: Real-world examples of -x * -y = +z

Two wrongs make a right.