## Search found 49 matches

- 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...

- 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...

- 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, ...

- 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...

- 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...

- 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.

- 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...

- 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

- 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...

- 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...

- 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,...

- 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!

Thanks!

- 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...

- 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 ...

- 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!

- 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 ...

- 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...

- 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!

- 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.

- 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...

- 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...

- 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.

- 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...

- 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 :/

That is what I need to know :/

- 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...

- 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...

- 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...

- 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...

- 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...

- 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-...

- 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...

- 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...

- 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"...

- 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 ...

- 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

- 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.

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.

- 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 ...

- 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.

- 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...

- 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 :~