Search found 49 matches

by afk2011
Sun Jun 03, 2012 6:32 pm UTC
Forum: Mathematics
Topic: Looking for uhhh... PenPals?
Replies: 0
Views: 1322

Looking for uhhh... PenPals?

Please excuse the abnormal topic, and accidental generalization of the capitalization in "PayPal": I am looking to find people who are excited about mathematics and interested in some dialog with a peer. I have read the forum rules and feel this is the best place for this post, at least if...
by afk2011
Tue Jan 31, 2012 11:10 pm UTC
Forum: Mathematics
Topic: Normal Subgroups of the Free Group
Replies: 4
Views: 3389

Re: Normal Subgroups of the Free Group

Thanks-- It slipped my mind that I was aware of that example (and should have mentioned that in my OP). The generalization is clear and makes sense, but let me ask you specifically then: what would be a generating set for a normal subgroup of index > 2? I'm not trying to trivially shift the question...
by afk2011
Tue Jan 31, 2012 9:44 pm UTC
Forum: Mathematics
Topic: Normal Subgroups of the Free Group
Replies: 4
Views: 3389

Normal Subgroups of the Free Group

Okay. Free group on n generators is residually finite, so there are normal subgroups of finite index, which are necessarily finitely generated (and free). My question is: can someone please just actually give me an explicit non-trivial normal subgroup? For the free group on 2 generators is a start, ...
by afk2011
Sat Apr 02, 2011 3:50 pm UTC
Forum: Science
Topic: Physics for a Mathematician...
Replies: 2
Views: 864

Physics for a Mathematician...

Hello, I am a 4th-year mathematics major, but recently I've decided I would really like to understand theoretical physics in much more depth. As is required by my curriculum, I have taken two semesters of basic physics. I was wondering if anyone could recommend resources for self-study in physics th...
by afk2011
Mon Mar 21, 2011 2:54 pm UTC
Forum: Mathematics
Topic: How many digits of Pi do you know?
Replies: 445
Views: 107164

Re: How many digits of Pi do you know?

Interestingly, I sat down in a bathroom at my school the other day and someone had written the digits of pi they had memorized on the wall, leading me to pen the following poetic protest (which may or may not cause most posters on this thread to dislike me immediately): On Memorizing Pi One day I sa...
by afk2011
Sun Feb 27, 2011 9:58 pm UTC
Forum: Mathematics
Topic: Presenting Abstract Algebra to High School Students
Replies: 7
Views: 4277

Re: Presenting Abstract Algebra to High School Students

It's great that you're introducing abstract algebra to your peers; I think it's a very beautiful field. If you can get people that understand some stuff about number theory, you can show some things about number theory using abstract algebra, like Fermat's Little Theorem or Wilson's Theorem.
by afk2011
Sun Feb 20, 2011 4:46 pm UTC
Forum: Mathematics
Topic: Simplicial Homology
Replies: 0
Views: 609

Simplicial Homology

Hey guys-- Again, I'm taking an algebraic topology course this semester, which I am LOVING but it is also pretty challenging. I am still having a somewhat hard time with simplicial homology. I understand how to triangulate certain spaces and my algebra is pretty strong, I guess I just am not underst...
by afk2011
Sat Feb 05, 2011 4:33 pm UTC
Forum: Mathematics
Topic: homology
Replies: 5
Views: 986

Re: homology

Thanks guys--- especially that long explanation. A couple of the ideas were presented in ways I hadn't thought of and I think it will help solidify my understanding :)
by afk2011
Thu Feb 03, 2011 7:38 pm UTC
Forum: Mathematics
Topic: homology
Replies: 5
Views: 986

Re: homology

I guess is this requirement that the composition of the consecutive deltas be the identity map related to the "simpler" construction of certain types of nice spaces, e.g., CW-Complexes? For example, in CW-Complexes n-cells are really only "attached" to n-1 cells and n+1 cells. Is...
by afk2011
Thu Feb 03, 2011 7:29 pm UTC
Forum: Mathematics
Topic: homology
Replies: 5
Views: 986

homology

I am taking algebraic topology this semester-- I am really loving it because it is challenging as an undergraduate, but I could use a little help understanding homology. Specifically, what I don't understand, is the significance of the boundary operators between the C_{n+1} and C_n chains. What exac...
by afk2011
Thu Feb 03, 2011 7:26 pm UTC
Forum: Mathematics
Topic: How should I get into 'higher' mathematics?
Replies: 11
Views: 1806

Re: How should I get into 'higher' mathematics?

Personally, if you are just interested and want to get into higher mathematics, at your age I would maybe consider reading some non-intensive but extremely interesting books that highlight some interesting mysteries/discoveries without boring you with rigorous math. For example, Godel, Escher, Bach,...
by afk2011
Thu Jan 27, 2011 3:10 pm UTC
Forum: Mathematics
Topic: Smash Product
Replies: 3
Views: 1688

Smash Product

Hey.... I am just trying to understand and visualize the smash product, but having some trouble. I know the definition very well at this point, but the idea of it is still not clear to me. Any insights from more experienced math enthusiasts would be appreciated.

Thanks!
by afk2011
Sat Jan 01, 2011 9:04 pm UTC
Forum: Mathematics
Topic: Math notation...
Replies: 2
Views: 571

Math notation...

Hey guys. This is something that you will definitely be able to help me with. I have some high-dimensional Eucliden space R^n. How can I denote the distance over just certain dimensions? e.g., if it is 4-dimensional and the points are of form (a, b, c, d), how can I denote the distance just with res...
by afk2011
Fri Dec 31, 2010 5:40 pm UTC
Forum: Mathematics
Topic: Number of graph isomorphism classes
Replies: 9
Views: 3491

Re: Number of graph isomorphism classes

Thanks. That sequence helps a little... I guess the answer to my question is that there is no known elegant solution. Yes, I did "Google it" before posting here, but I surprisingly couldn't find any results. Even the wikipedia page on "Graph Isomorphism" failed to mention at all ...
by afk2011
Thu Nov 18, 2010 6:37 pm UTC
Forum: Mathematics
Topic: What does it mean for a set to be "Ramsey"
Replies: 3
Views: 780

What does it mean for a set to be "Ramsey"

Looking for a simple explanation of what it means for a set to be "Ramsey". If anyone could enlighten me I would appreciate it!
by afk2011
Thu Nov 04, 2010 5:45 pm UTC
Forum: Mathematics
Topic: What kind of graphs are these?
Replies: 4
Views: 1032

What kind of graphs are these?

Quick question. Define a graph of n vertices with some set S in the following way. Label each of the vertices 1, 2, 3, ..., n. Then two vertices share an edge if and only if the absolute value of their difference mod n is in S. For example, if S={1} we have two vertices share an edge if and only if ...
by afk2011
Sun Oct 03, 2010 6:34 pm UTC
Forum: Mathematics
Topic: Number of graph isomorphism classes
Replies: 9
Views: 3491

Number of graph isomorphism classes

I've been rapt by graph theory this year so far and I still don't know the answer to this question (though it seems like something that I would be able to find on a wikipedia page (it's not)). How many different graphs are there (up to isomorphism) of any given number of vertices? For example, for 3...
by afk2011
Sun Oct 03, 2010 12:27 am UTC
Forum: Mathematics
Topic: Finding an English translation of a math paper...
Replies: 7
Views: 1717

Re: Finding an English translation of a math paper...

Ugh. I started translating it but then I found the version in English. The trick was just to find the correct translation of the title. Thanks for all the help!
by afk2011
Sat Oct 02, 2010 11:49 pm UTC
Forum: Mathematics
Topic: Finding an English translation of a math paper...
Replies: 7
Views: 1717

Re: Finding an English translation of a math paper...

I want to read it because it proves that a graph is planar if and only if it does not contain K(3,3) (bipartite graph) or a 5-clique, which I would like to understand in a thorough way before trying to learn more advanced results in this area of graph theory.
by afk2011
Sat Oct 02, 2010 4:12 pm UTC
Forum: Mathematics
Topic: Finding an English translation of a math paper...
Replies: 7
Views: 1717

Finding an English translation of a math paper...

Hey guys... just a general question about mathematics in the academic world. Are papers typically translated from their authors language into other languages? I think now the standard is probably to write math papers in English, but I need to read a paper from 1930 that is in French, and I do not kn...
by afk2011
Tue Sep 07, 2010 2:15 am UTC
Forum: Mathematics
Topic: quick algebra question (Group actions)...
Replies: 5
Views: 796

quick algebra question (Group actions)...

Let's say I have an infinite set X and an infinite group G that performs an action on X. Take x in X; a theorem is that the size of the orbit of x is equal to the index of its stabilizer. If the stabilizer of x is ISOMORPHIC to its group G, does that mean the orbit of x is all of X? I have a feeling...
by afk2011
Sat Aug 21, 2010 10:12 pm UTC
Forum: Mathematics
Topic: bounds on 3^a - 2^b
Replies: 8
Views: 1627

Re: bounds on 3^a - 2^b

Okay, I found a solution online. Problem solved.
by afk2011
Sat Aug 21, 2010 9:38 pm UTC
Forum: Mathematics
Topic: bounds on 3^a - 2^b
Replies: 8
Views: 1627

bounds on 3^a - 2^b

Hey guys.... This seems like something that should either be approachable with basic number or not at all, but I have failed to find my own solution. Basically, I am interested in how close the closest power of 2 is to any given power of 3. For example they can be only 1 away from each other at 3, 4...
by afk2011
Mon Aug 09, 2010 7:25 pm UTC
Forum: Mathematics
Topic: Simple question....
Replies: 6
Views: 758

Re: Simple question....

I am sure there is a simple way to say, starting with a, b, c, ... The set will have elements of form xn+y, where x and y are based on the initial a, b, c, ....

That is what I need to know :/
by afk2011
Mon Aug 09, 2010 6:48 pm UTC
Forum: Mathematics
Topic: Simple question....
Replies: 6
Views: 758

Re: Simple question....

It seems like it should have to do with the gcd, right? I, too, started by looking at the fact that there exists x and y such that ax+by=gcd(a, b). BUT, the way I've defined the operation is not equivalent to ALL linear combinations of them. Also, what would the identity element be if it were a grou...
by afk2011
Mon Aug 09, 2010 5:31 pm UTC
Forum: Mathematics
Topic: Simple question....
Replies: 6
Views: 758

Simple question....

Hey guys. This is the kind of question I should be able to figure out easily on my own, but alas, I don't know the right way to "prove" it. No, this is not for homework. Given some numbers a, b, c... set S has the following properties: a, b, and c are in S. If x, y, and z are in S, so is x...
by afk2011
Fri Jul 23, 2010 8:39 pm UTC
Forum: Mathematics
Topic: Intersection of Line Segments in a Circle
Replies: 32
Views: 4246

Re: Intersection of Line Segments in a Circle

2 line segments or 2 line segments of a given length? without any bounds on this, it seems to me that the probability approaches 0, since as you consider line segments shorter and shorter, the chance of them intersecting gets smaller and smaller, while there are more and more places that they can be...
by afk2011
Wed Jun 02, 2010 5:18 am UTC
Forum: Language/Linguistics
Topic: People that claim ethnicity but don't speak the language...
Replies: 47
Views: 8806

People that claim ethnicity but don't speak the language...

Hey guys. Just wondering if anyone else out there has had the experience of meeting someone who LOVES to talk about their "roots", how they are completely Italian or something, and how culturally strong they are, but then when you try to speak with them in that language that don't know any...
by afk2011
Sat May 01, 2010 5:50 pm UTC
Forum: Mathematics
Topic: Particular type of prime....
Replies: 11
Views: 1677

Re: Particular type of prime....

I understand your argument up to 7, because 3, 5 and 7 just have a difference of 2. But consider the next step: 11r = p+1, 2p+1, ..., 10p+1 Get rid of the even numbers. 11r = 2p+1, 4p+1, ..., 10p+1 We know 3r = 2p+1, 5r = 4p+1, 7r = 6p+1, but that STILL leave 11r = 10p+1 or 8p+1, and in the case th...
by afk2011
Sat May 01, 2010 4:53 pm UTC
Forum: Mathematics
Topic: Particular type of prime....
Replies: 11
Views: 1677

Re: Particular type of prime....

Let's say p is bigger than n 2 . Then the inverse modulo p of a prime between 1 and n has to be another prime, bigger than n. If r 3 is the inverse of 3, then we have 3r 3 = p+1, or 2p+1, or 3p+1. (Since at least one of those is a multiple of 3.) However, p+1 and 3p+1 are even, so 3r 3 = 2p+1 = 3p-...
by afk2011
Fri Apr 30, 2010 4:09 pm UTC
Forum: Mathematics
Topic: Particular type of prime....
Replies: 11
Views: 1677

Particular type of prime....

Just a question I've been thinking about concerning the multiplicative group Z*_p where p is prime. Does there exist a p where in Z*_p, the inverse of every prime is also a prime? Alternatively, if 2-being-even-ness turns out to some easy answer, do there exist p > 7 such that this holds for ODD pri...
by afk2011
Thu Apr 29, 2010 7:52 pm UTC
Forum: Mathematics
Topic: homomorphism attack!
Replies: 1
Views: 902

Re: homomorphism attack!

There a lot of different ways a cryptosystem can be secure; in this case, she mentions that it is not chosen ciphertext secure (CCA). The reason that she can't just straight up ask for the message she is looking for is semantic. In the definition of a CCA-secure system, the rule is that the adversar...
by afk2011
Fri Mar 26, 2010 8:18 pm UTC
Forum: Logic Puzzles
Topic: My Hobby: Simplifying Sentences
Replies: 16
Views: 7633

Re: My Hobby: Simplifying Sentences

"Owing to" is a given. So is "Straightforward". Something goes between "to" and "straightforward" that is a combination of the letters "owingts". It's obviously not going to be something like "swinging" "gowns" or "sting"...
by afk2011
Fri Mar 26, 2010 12:15 pm UTC
Forum: Logic Puzzles
Topic: My Hobby: Simplifying Sentences
Replies: 16
Views: 7633

Re: My Hobby: Simplifying Sentences

I think it would help if repeated and trailing spaces were preserved, which would tell you not only how many words, but how many words fall bewteen any two chosen words Yes, some sort of thing to indicate how many words or how many words of how many letters each would help reduce the lossy-ness of ...
by afk2011
Fri Mar 26, 2010 5:03 am UTC
Forum: Logic Puzzles
Topic: My Hobby: Simplifying Sentences
Replies: 16
Views: 7633

Re: My Hobby: Simplifying Sentences

Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern co mputers
by afk2011
Fri Mar 26, 2010 4:49 am UTC
Forum: Mathematics
Topic: I cant manage to solve this
Replies: 12
Views: 1753

Re: I cant manage to solve this

The probability of getting at least one triple number in 1000 throws is
1 - Q

Where Q is the probability of NOT getting a triple number at all in any throws. This should be enough to help you, since the probability of getting or not getting a triple number on a single throw is pretty trivial.
by afk2011
Mon Mar 15, 2010 9:34 pm UTC
Forum: Mathematics
Topic: Fill 100 spots using only sequences.
Replies: 11
Views: 1401

Re: Fill 100 spots using only sequences.

Sequences of coprime integers in ascending order (ie one sequence could be {4, 9, 25, 49}). (This is a very interesting question as finding the minimal case would seem like the tricky part of this question.) Well you need one sequence for every multiple of 2... and then put an odd number with each ...
by afk2011
Mon Feb 08, 2010 3:46 am UTC
Forum: Mathematics
Topic: question about lines and points and such...
Replies: 8
Views: 770

Re: question about lines and points and such...

Okay, I figured it out; for real this time. Thanks again.
by afk2011
Mon Feb 08, 2010 3:38 am UTC
Forum: Mathematics
Topic: question about lines and points and such...
Replies: 8
Views: 770

Re: question about lines and points and such...

This is hard without diagrams...but what you can do to get all three points is create a line going through the two points that are given to you. Now, recall that a line y=mx+b has a perpendicular line y=-\frac{1}{m}x+c . -\frac{1}{m} is easy to find. c can be found by some simple algebra. The third...
by afk2011
Mon Feb 08, 2010 1:24 am UTC
Forum: Mathematics
Topic: question about lines and points and such...
Replies: 8
Views: 770

Re: question about lines and points and such...

Nevermind, still having trouble... the equation for the slope of the hypotenuse is only a/b if it is on the axis :~

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