## Search found 77 matches

Fri May 27, 2011 12:30 pm UTC
Forum: Mathematics
Topic: Interesting Problems?
Replies: 33
Views: 4779

### Re: Interesting Problems?

One of my favorite problems requires only a basic knowledge of geometric series and a bit of probabilistic reasoning to solve. Suppose that two people are playing tennis, and have reached a deuce. If the first player has probability p of winning a single point, you can use a geometric series to show...
Mon Feb 21, 2011 12:35 pm UTC
Forum: Mathematics
Topic: [Homework] Subgroups of U(n)
Replies: 3
Views: 678

### Re: [Homework] Subgroups of U(n)

The empty set is not a subgroup because every subgroup must contain the identity.

You have the definition of the subgroups U_k somewhat backwards though. Is 0 = 1 mod 1?
Sat Feb 05, 2011 6:19 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 283076

### Re: Math Books

I'll elaborate on forgetful functor's suggestions about functional analysis, because, well, I'm a functional analyst. While it's probably possible to learn functional analysis from Rudin's book, I feel like that's a tough route. Conway's book is a good suggestion; while I may not always love his wri...
Wed Feb 02, 2011 5:36 am UTC
Forum: Mathematics
Topic: Calculus issues
Replies: 5
Views: 1139

### Re: Calculus issues

try combining 1/sqrt(x)-1 into one fraction first.
Sun Jan 02, 2011 6:34 pm UTC
Forum: Mathematics
Topic: The Interesting Parts of Maths
Replies: 13
Views: 2915

### Re: The Interesting Parts of Maths

Ergodic theory is beautiful and accessible if you've had a reasonable amount of analysis and are willing to work hard to understand the measure theory.
Mon Oct 25, 2010 2:46 pm UTC
Forum: Mathematics
Topic: Disguised forms of 2
Replies: 114
Views: 13240

### Re: Disguised forms of 2

Using the Guass-Bonnet Theorem (one of my favorite theorems of all time, even though I'm not a geometer), we get the following representation of the number 2.

$2 = \frac{ 1 }{ 2 \pi } \int_M K\ dA,$

Here [imath]M[/imath] is any surface of genus zero (with no boundary) and [imath]K[/imath] is its Gauss curvature.
Mon Oct 25, 2010 2:34 pm UTC
Forum: Mathematics
Topic: Quintic Equations
Replies: 12
Views: 4445

### Re: Quintic Equations

Many posters above have given beautiful introductions to Galois theory. If you want a short (but not terribly illuminating) answer, it's that the alternating group on five elements is simple.
Mon Oct 11, 2010 1:54 pm UTC
Forum: Mathematics
Topic: Integrals over an infinite interval.
Replies: 8
Views: 1708

### Re: Integrals over an infinite interval.

Check out the wikipedia article on improper integrals.
Sun Oct 10, 2010 6:24 pm UTC
Forum: Mathematics
Topic: Giving slogans for mathematical disciplines
Replies: 13
Views: 2605

### Re: Giving slogans for mathematical disciplines

Functional analysis: infinite-dimensional convex geometry
Mon Oct 04, 2010 12:31 pm UTC
Forum: Mathematics
Topic: Finding an English translation of a math paper...
Replies: 7
Views: 1746

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

Here's a list of math vocabulary in French that has made its round of my department when we've been studying for our French language exam, which essentially consists of translating a few pages of a French textbook. Like you, my everyday French is excellent, and combined with this list, the exam was ...
Fri Oct 01, 2010 2:29 pm UTC
Forum: Mathematics
Topic: A math paper.
Replies: 6
Views: 1670

### Re: A math paper.

Or you could talk about the history of the prime number theorem; it's one of the crowning achievements of 19th century math, and it took almost a century to go from conjecture to proof, and the process involved some of the most influential mathematicians of the time (Legendre, Gauss, Chebyshev, Riem...
Mon Sep 13, 2010 2:27 pm UTC
Forum: Mathematics
Topic: Solving Compositing Permutations in Cyclic Notation
Replies: 2
Views: 1219

### Re: Solving Compositing Permutations in Cyclic Notation

Start with the leftmost number in the righthand permutation, in this case, a 1. In the righthand permutation, 1 gets mapped to 5, so we look for 5 in the lefthand permutation, and see that it gets mapped to 3, so in the composite perumtation, 1 gets mapped to 3. We now start with 3; it is fixed in t...
Fri Aug 20, 2010 5:56 pm UTC
Forum: Mathematics
Replies: 2
Views: 778

Also, you can do a lot of computations in basic probability theory by just knowing integration by parts. At one point, I used calculus to show my students that the deuce rules in tennis are significantly biased towards the better player (a player that has a 60% chance of winning any given point will...
Thu Aug 19, 2010 1:15 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 494831

### Re: Favorite math jokes

Best dirty math joke ever:

What's the square root of sixty-nine?

Eight someting.
Wed Aug 11, 2010 10:49 pm UTC
Forum: Mathematics
Topic: realtime latex?
Replies: 5
Views: 1289

### Re: realtime latex?

You definitely won't get realtime latex, but for something close, latexmk can be set up to automatically recompile the file any time one of the source files upon which it depends is modified and saved, and can automatically refresh your pdf viewer. Another nice feature is that it compiles the file a...
Sat Jul 24, 2010 4:09 pm UTC
Forum: School
Topic: Intellectual intimidation
Replies: 15
Views: 2905

### Re: Intellectual intimidation

Does anyone know the percentage of successful attempts at a PhD in theoretical mathematics? In my grad program, there's about a 50% attrition rate. That being said, the vast majority of people I know that have left have not done so for a lack of mathematical ability, but because they realized this ...
Mon Jul 19, 2010 11:27 pm UTC
Forum: General
Topic: Teach me math.
Replies: 38
Views: 9710

### Re: Teach me math.

Specificly, I have a bit of curiosity in non-euclidian geometry. At our uni, we do that as part of a 4th year Differential Geometry course. It has a minimum requirement of 3 years of calculus to even start it... Although differential geometry is a natural technical setting for the study of non-Eucl...
Wed Jun 23, 2010 3:02 am UTC
Forum: Mathematics
Topic: Differentials Hint Needed
Replies: 2
Views: 614

### Re: Differentials Hint Needed

Remember the Chain Rule!
Mon Jun 21, 2010 3:53 am UTC
Forum: Mathematics
Topic: Limit to infinity?
Replies: 18
Views: 2678

### Re: Limit to infinity?

mmmcannibalism wrote:limx->a f(x)=g'(x)/h'(x)

I think you also want a limit on the right hand side.
Mon Jun 21, 2010 3:00 am UTC
Forum: Mathematics
Topic: Limit to infinity?
Replies: 18
Views: 2678

### Re: Limit to infinity?

Unfortunately that requires knowledge and intuition of binomial expansions and infinite series Another way to do it is to look at y=(1+1/x)^x , take \ln y = x \ln ( 1 + 1/x ) , use L'Hopital's rule to show that \lim_{ x \to \infty } \ln y = 1 , and therefore \lim_{ x \to \infty } y ...
Mon Jun 14, 2010 11:22 am UTC
Forum: Mathematics
Topic: TI calculators
Replies: 10
Views: 2831

### Re: TI calculators

In the math classes I teach, not only would you not need a calculator, I would get somewhat angry if you brought one out. This is a math class though and the emphasis is on the mathematical ideas, not numbers (i try to make those as nice as possible)--I'm sure if you're going to do some sort of scie...
Fri Jun 04, 2010 11:56 pm UTC
Forum: Mathematics
Topic: I think I found something interesting in modular arithmetic
Replies: 58
Views: 5707

### Re: Um...hi.

So I've failed. It's a learning experience at least. You haven't failed at all. Any time to you any sort of research (at least mathematics research, of which I can speak from firsthand experience) you are wrong waaaaay more than you're right. It's the nature of problem solving that you struggle wit...
Fri Jun 04, 2010 11:11 pm UTC
Forum: Mathematics
Topic: I think I found something interesting in modular arithmetic
Replies: 58
Views: 5707

### Re: Um...hi.

Probably would be easier if you did tell us what you were thinking about. It's very hard to give the advice you want in a general context. I also think you'll find the people here pretty friendly--it is a distinct possbility that they may show that your work is not original, but I don't think anyone...
Sun May 30, 2010 4:43 pm UTC
Forum: Mathematics
Topic: Famous Math Quotes!
Replies: 32
Views: 8162

### Re: Famous Math Quotes!

If you know french...
"Allez en avant et la foi vous viendra"
Jean d'Alembert to students struggling with calculus
(Go forward and faith will come to you)
Sun May 30, 2010 3:27 am UTC
Forum: Mathematics
Topic: Most interesting mathematician?
Replies: 35
Views: 5261

### Re: Most interesting mathematician?

Galois..lived hard and died young.
Sat May 29, 2010 4:14 pm UTC
Forum: Mathematics
Topic: RIP Martin Gardner (1914-2010)
Replies: 5
Views: 1410

### Re: RIP Martin Gardner (1914-2010)

Apparently I also come here for my math news...I'm heartbroken about Rudin...his Real and Complex Analysis and Functional Analysis are never far away from where I'm working!
Sun May 16, 2010 9:16 pm UTC
Forum: Mathematics
Topic: A Small Calculus Question
Replies: 10
Views: 2039

### Re: A Small Calculus Question

You need to be very careful when you write \int (dx)^n . What set are you integrating over? In classicaly calculus, this expressions essentially makes no sense. Even if you're really reaching on the interpretation, like (dx)^2 = dx \wedge dx (in the sense of exterior algebra) this ex...
Thu May 13, 2010 11:50 pm UTC
Forum: General
Topic: Things to do in Nashville TN
Replies: 9
Views: 1681

### Things to do in Nashville TN

What to do in Nashville TN? I'm at Vandy for a conference and we have a day off tomorrow to accomodate graduation. We plan on seeing the Grand Old Opry...what else is good for two guys in their mid 20s to check out in Nashville? Bonus points for breweries or distilleries/and (or most likely) or near...
Sun Mar 21, 2010 1:16 pm UTC
Forum: Mathematics
Topic: Question about solving an exponential equation
Replies: 10
Views: 1683

### Re: Question about solving an exponential equation

hinchy34 wrote:I got...^[1/1.852]

Excellent...that's what I was angling you towards!
Sun Mar 21, 2010 1:25 am UTC
Forum: Mathematics
Topic: Question about solving an exponential equation
Replies: 10
Views: 1683

### Re: Question about solving an exponential equation

How would you solve it if the exponent were 2?
Fri Mar 12, 2010 3:13 pm UTC
Forum: Mathematics
Topic: Continuity of the Scalar Product
Replies: 10
Views: 2755

### Re: Continuity of the Scalar Product

As in a lot of analysis, the triangle inequality is your friend!
Wed Mar 10, 2010 3:47 pm UTC
Forum: Mathematics
Topic: Animating Geometry
Replies: 2
Views: 632

### Re: Animating Geometry

I have a friend around here that does a lot of somewhat heavy geometric visualization using Mathematica. I'm not involved in the research, so I'm hazy on the details, but you might consider that route. From what I understand its somewhat of an upfront investment to learn Mathematica's animation comm...
Fri Mar 05, 2010 11:34 pm UTC
Forum: General
Topic: What would you do with $10,000? Replies: 138 Views: 15965 ### Re: What would you do with$10,000?

Buy book, lots of books, and spend a long time reading all of them.
Wed Mar 03, 2010 3:04 am UTC
Forum: General
Topic: With passion...
Replies: 53
Views: 4613

### Re: With passion...

Skiing. My aunt took me regularly starting at 6 and I love it. I love my skis more than I love most people, unfortunately I'm in grad school in Illinois now--also known as the flattest place on Earth, but I take every opportunity I can to ski when visiting my family. In my mind nothing beats carving...
Tue Mar 02, 2010 2:23 pm UTC
Forum: School
Topic: Rejected
Replies: 10
Views: 2099

### Re: Rejected

I only got into two schools I applied to, out of a looooooooot more than that.
Thu Feb 25, 2010 4:41 pm UTC
Forum: School
Topic: University of Illinois Priority decisions
Replies: 9
Views: 1674

### Re: University of Illinois Priority decisions

Yup, around and still delicious.
Wed Feb 10, 2010 1:47 am UTC
Forum: School
Topic: Subjects you wish you were good at?
Replies: 87
Views: 11312

### Re: Subjects you wish you were good at?

French.
Wed Feb 10, 2010 1:43 am UTC
Forum: General
Topic: salaries of XKCD'ers with full time jobs?
Replies: 26
Views: 2350

### Re: salaries of XKCD'ers with full time jobs?

I decided grad student counts as full time...20 hr/week of teaching+research=a lot of hrs.
Wed Feb 03, 2010 12:24 am UTC
Forum: General
Topic: "What should you major in?" discussion
Replies: 19
Views: 2808

### Re: "What should you major in?" discussion

Fri Jan 15, 2010 12:27 am UTC
Forum: Mathematics
Topic: Real Analysis 1: What Topics Should Be Covered?
Replies: 9
Views: 1679

### Re: Real Analysis 1: What Topics Should Be Covered?

I think it depends on what kind of department that you take the course in. My undergrad school had a very applied math dept--what you said sounds like exactly what we covered in analysis I. If you wanted go to graduate school, it was strongly suggested you also take analysis II and learn about the m...