Search found 31 matches

by bobdylan
Thu Dec 16, 2010 3:53 pm UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

if they ask you to give them a step by step solution to something really do want just that Yes, and if your 5-year-old kid asks for cake instead of vegetables, they really do want just that. Doesn't mean you should give it to them, though... Read the whole sentence or flame? Up to you mate. You're ...
by bobdylan
Thu Dec 16, 2010 2:57 pm UTC
Forum: Mathematics
Topic: Very specific Risk question.
Replies: 11
Views: 1821

Re: Very specific Risk question.

Are you playing with mission cards? Here's what will happen: Yellow guy in Europe throws all his units at Greenland until he has nothing left. Blue guy in Africa wipes out yellow guy in Europe. Wins game. That was his mission.
by bobdylan
Thu Dec 16, 2010 2:52 pm UTC
Forum: Mathematics
Topic: Very specific Risk question.
Replies: 11
Views: 1821

Re: Very specific Risk question.

I can pretty much guarantee that they will not get any other territories without a serious attack, because they control all of the territory. If I were advising them, I'd have them trade off attacking a territory so they can keep getting the cards (the number of armies for the cards increases rapid...
by bobdylan
Thu Dec 16, 2010 2:47 pm UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

PS, I just read the rules. They don't actually say anything about what help to offer with homework. They just say "don't expect us to be very helpful" (whoever "we" may be).

So... I dunno. Maybe you should add that in, if that's the way you prefer it.
by bobdylan
Thu Dec 16, 2010 2:40 pm UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

Maybe saying "what IS a geometric series?" will help. Maybe not. If the student thinks, as in this case, that a geometric series "is" a series in which the n-th term is given by ar^n then it's possible the student has been really, really badly taught. Maybe the student just need...
by bobdylan
Thu Dec 16, 2010 1:19 pm UTC
Forum: Mathematics
Topic: Useless Math
Replies: 60
Views: 10089

Re: Useless Math

I think a way to approach this sort of question without bringing up physics at all is to ask whether there are "coincidences" in math. Some properties of the number 4, for example, might be considered to be coincidences due to the law of small numbers. Maybe? But what about pi? Feynman wo...
by bobdylan
Thu Dec 16, 2010 1:04 pm UTC
Forum: Mathematics
Topic: A simple puzzle (hopefully)
Replies: 6
Views: 1727

Re: A simple puzzle (hopefully)

Why not try it for small numbers, and take them out of hex? It might make it easier to spot a pattern!
by bobdylan
Thu Dec 16, 2010 12:59 pm UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

PS you may consider me chastised, I won't do it again :mrgreen:
by bobdylan
Thu Dec 16, 2010 12:59 pm UTC
Forum: Mathematics
Topic: I don't get quaternions
Replies: 22
Views: 2547

Re: I don't get quaternions

I was under the impression that heavy duty algebraic topology was only needed to prove the (obviously related) Radon-Hurwitz formula for the number of linearly independent non-vanishing vector fields on S n . The topological result that's quoted is the non-existence of a map S^{2n+1}\to S^{n} of Ho...
by bobdylan
Thu Dec 16, 2010 12:51 pm UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

I like to try to teach people how to think about the problems so they can solve similar ones. In my experience of being and knowing undergraduates, professors like to twerk problems to see if you did NOT just have someone show you how to do number one and memorize how to solve that type of problem,...
by bobdylan
Thu Dec 16, 2010 12:43 pm UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

Teaching someone how to do a question by doing it for them is great if your goal is to teach the person how to do the question. In some courses, that is the goal. An engineering mathematics course that covers finding eigenvalues might actually be about finding eigenvalues. The goal might be to teac...
by bobdylan
Wed Dec 15, 2010 3:17 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 279309

Re: Mathematics Texts?

I'm hoping to enroll into a four-year college next fall with the intention of pursuing a mathmatics major. I have always loved mathematics, and when in high school the books I would typically read would be mathematics books and computer science books. In the mean time, I'm wondering if anyone has a...
by bobdylan
Wed Dec 15, 2010 3:05 pm UTC
Forum: Mathematics
Topic: I don't get quaternions
Replies: 22
Views: 2547

Re: I don't get quaternions

I was under the impression that heavy duty algebraic topology was only needed to prove the (obviously related) Radon-Hurwitz formula for the number of linearly independent non-vanishing vector fields on S n . The topological result that's quoted is the non-existence of a map S^{2n+1}\to S^{n} of Ho...
by bobdylan
Wed Dec 15, 2010 10:47 am UTC
Forum: Mathematics
Topic: Homework: Eigenvalues
Replies: 18
Views: 3003

Re: Homework: Eigenvalues

Depending on who the grader is, this might be too nitpicky to worry much about, but note that somewhere in there, you are using the fact that matrix times scalar times vector = scalar times matrix times vector. This is a course on linear algebra; I'm pretty sure you can stop saying "by the def...
by bobdylan
Wed Dec 15, 2010 10:42 am UTC
Forum: Mathematics
Topic: Homework: Eigenvalues
Replies: 18
Views: 3003

Re: Homework: Eigenvalues

Plus, diagonalizing a linear transformation is a bit harder if the space you are talking about is not finite in dimension. The result, meanwhile, holds even if the space is not finite in dimension. True, although that typically is not covered in an Intro to LinAlg course. Well, again, I suppose tha...
by bobdylan
Wed Dec 15, 2010 10:35 am UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

It's a series where the ratio of successive terms is always the same. Yes. Which is what I wanted the OP to realize on their own by thinking about the questions z4lis and I asked... You have high hopes :D From my experience teaching undergraduates, they like you to basically do question one for the...
by bobdylan
Wed Dec 15, 2010 10:33 am UTC
Forum: Mathematics
Topic: Useless Math
Replies: 60
Views: 10089

Re: Useless Math

I think Non-Euclidian metrics and Lorentz manifolds and whatnot had been studied in depth long before Relativity stepped in and made them useful for real-world applications... Non-Euclidean geometry is a great example, as it essentially arose from the quest to prove the parallel postulate from the ...
by bobdylan
Wed Dec 15, 2010 10:25 am UTC
Forum: Mathematics
Topic: Useless Math
Replies: 60
Views: 10089

Re: Useless Math

How about the classification of finite simple groups? Some of the larger exceptional groups have no obvious relevance in the real world. Where in nature do you see an action of the Baby Monster? Nowhere that I know. Vertex algebras and conformal field theories. Topology is very abstract too. In a t...
by bobdylan
Wed Dec 15, 2010 10:15 am UTC
Forum: Mathematics
Topic: Cantor Diagonalization Formula
Replies: 11
Views: 2848

Re: Cantor Diagonalization Formula

Hmm. Yes, the lexicographic ordering is useless here. The way I've always seen this particular trick done is to step through NxN by first running through pairs (x,y) with x+y=2, then through pairs with x+y=3, and so on. It's usually drawn like a snake, going backwards and forwards up the diagonals, ...
by bobdylan
Wed Dec 15, 2010 10:06 am UTC
Forum: Mathematics
Topic: Topology Resources
Replies: 30
Views: 3588

Re: Topology Resources

I really enjoyed Fraleigh's "A First Course in Abstract Algebra", which goes all the way from the definition of a group to field extensions and Galois theory. The old edition I had and sadly lost also had a short section on simplicial homology, which is what first got me interested in alge...
by bobdylan
Wed Dec 15, 2010 9:57 am UTC
Forum: Mathematics
Topic: I don't get quaternions
Replies: 22
Views: 2547

Re: I don't get quaternions

bobdylan wrote: Why are we limited to only 4 real division algebras? "Algebraic Topology" by Hatcher contains a simple (if you know algebraic topology!) proof that any division algebra over R must have dimension a power of two. The fact that only 1, 2, 4 and 8 are possible is somewhat tri...
by bobdylan
Tue Dec 14, 2010 6:43 pm UTC
Forum: Mathematics
Topic: Geo. and Arith. Seq. (and some induction!)
Replies: 23
Views: 2514

Re: Geo. and Arith. Seq. (and some induction!)

Find x so that the three numbers x, x + 1, x + 2 form a geometric progression


Forget the equation. What IS a geometric series? It's a series where the ratio of successive terms is always the same.

So (x+1)/x = (x+2)/(x+1).
by bobdylan
Tue Dec 14, 2010 6:41 pm UTC
Forum: Mathematics
Topic: Homework: Eigenvalues
Replies: 18
Views: 3003

Re: Homework: Eigenvalues

People who want this done in terms of Eigenvalue decomposition - you realise that this is the homework for a first course in linear algebra, right? Ok, so the second part is easy because A is diagonalisable. But in the first part A may not be diagonalisable. So are you suggesting the OP use Jordan N...
by bobdylan
Tue Dec 14, 2010 6:29 pm UTC
Forum: Mathematics
Topic: Ln(-1)...?
Replies: 10
Views: 2816

Re: Ln(-1)...?

Wait till you learn about Riemann surfaces. They're awesome. For example, you can't give a continuous inverse to the squaring map z\mapsto z^2 from C to C. But you CAN do it if you replace the second C with a new surface that projects onto C. So instead of the squaring map wrapping C around C itself...
by bobdylan
Tue Dec 14, 2010 6:24 pm UTC
Forum: Mathematics
Topic: Cantor Diagonalization Formula
Replies: 11
Views: 2848

Re: Cantor Diagonalization Formula

One "standard" ordering of NxN is the lexicographic ordering. (a,b)<(c,d) if a<c or (a=c and b<d).
by bobdylan
Tue Dec 14, 2010 6:21 pm UTC
Forum: Mathematics
Topic: inflection points of x^(1/x)
Replies: 13
Views: 2519

Re: inflection points of x^(1/x)

It depends what you mean by "solve". As Blatm says, it's very likely the solutions can't be expressed in a "nice" form at all, never mind finding such an expression. It's similar to the insolubility of the general quintic. In general the solutions of ax^5+bx^4+cx^3+dx^2+ex+f=0 ca...
by bobdylan
Tue Dec 14, 2010 6:08 pm UTC
Forum: Mathematics
Topic: Intersection between a plane and a straight line
Replies: 5
Views: 923

Re: Intersection between a plane and a straight line

If you start with some equations, and deduce that 0\lambda=\lambda , you have deduced nothing. If you suspect that the whole line lies in the plane, plug the coordinates of the line into the equation of the plane and check that it is true for all \lambda . As you know, this is NOT the same as deduci...
by bobdylan
Tue Dec 14, 2010 6:05 pm UTC
Forum: Mathematics
Topic: Imaginary Numbers
Replies: 14
Views: 2323

Re: Imaginary Numbers

You're gonna have to do some geometry. Multiply J(w) by iw. Now draw a picture and work out what the argument of iwJ(w) is.
by bobdylan
Tue Dec 14, 2010 5:57 pm UTC
Forum: Mathematics
Topic: Useless Math
Replies: 60
Views: 10089

Re: Useless Math

How about the classification of finite simple groups? Some of the larger exceptional groups have no obvious relevance in the real world. Where in nature do you see an action of the Baby Monster? Nowhere that I know. Topology is very abstract too. In a three dimensional universe (OK, maybe eleven dim...
by bobdylan
Tue Dec 14, 2010 5:51 pm UTC
Forum: Mathematics
Topic: Topology Resources
Replies: 30
Views: 3588

Re: Topology Resources

If you didn't know what a group was, you're probably not ready for Algebraic Topology by Hatcher. It is, however, cheap and/or available free online. It's quickly becoming the standard graduate textbook
by bobdylan
Tue Dec 14, 2010 5:48 pm UTC
Forum: Mathematics
Topic: I don't get quaternions
Replies: 22
Views: 2547

Re: I don't get quaternions

How do they relate to other numbers? Here's something quite neat. You know how the real numbers are a subset of the complex numbers? Well, the complex numbers can be embedded in the quaternions in LOADS of ways. Specifically, take v=ai+bj+ck for any real numbers a, b and c such that a^2+b^2+c^2=1 ....

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