# Blog Profile / The Art of Problem Solving

URL : http://community.livejournal.com/mathematics/ Academics / Mathematics 156 0.3 March 17, 2008

## Blog Post Archive

For an example for some research I'm working on, I need to think of a problem - it can be anything, but a simple (possibly geometric) problem would be ideal - where the problem can be formulated as a number of inputs, say I_1,..., I_n,...Show More Summary

### Find total execution time of the program ??

A CPU has a five-stage pipeline and runs at 1 GHz frequency. Instruction fetch happens in the first stage of the pipeline. A conditional branch instruction computes the target address and evaluates the condition in the third stage of the pipeline. Show More Summary

### ???????? ??? ??????? ?????????? ?? ????????? "?????? ???????????" ????, ??? ? ??? ?? ?????

???????? ???? ? matholimp ? ???????? ??? ??????? ?????????? ?? ????????? "?????? ???????????" ????, ??? ? ??? ?? ????? ?????? ?????, ? ???? ????????????? olenenyok, tiina, al_med, vasily_sergeev, urfin1657 ? ?????? ??????, ?????? ?????? ?? ??? ???? http://matholimp.livejournal.com/1162423.html, ?-??? ?? ??????, ? ??????? ?? ??? ????????. Show More Summary

### Result related to Brauer-Fowler theorem?

Let G be a finite group with involution x such that the centralizer of x coincides with the subgroup generated by x. Then |G:G'|=2.I think this has something to do with Brauer-Fowler, but I don't see how the derived subgroup comes u...

### Journal question

Kind of a dumb question perhaps, but how do Proceedings of the AMS and Bulletin of the LMS compare in terms of prestige? They seem to serve the same purposes (national journals for short papers) so I'm finding it hard to see which is 'better'. Are they more or less equal in prestige?

### MathOlymp 2013 Belarus

Dear community members! I would to like to notify you of the International Student Mathematical Olympiad, which is scheduled to be held in Belarus on February 20-22, 2013. Please feel free to contact me, if you have any further questions or concerns. Yours faithfully, Vitaly.

### Logic/Induction

Problem: 1000 perfect logicians are imprisoned. 500 have blue eyes, 499 people have brown eyes, and one has green eyes. They can see each other's eyes but not their own, and cannot communicate eye colors to each other. At the end of every day, those who have deduced their own eye color are freed. Show More Summary

For an example for some research I'm working on, I need to think of a problem - it can be anything, but a simple (possibly geometric) problem would be ideal - where the problem can be formulated as a number of inputs, say I_1,..., I_n,...Show More Summary

I often hear people reference the conjugate gradient algorithm as though it can be used as a general algorithm for minimizing any continuous function, though one may have to assume that it is Lipschitz or convex.When I try to understand...Show More Summary

### The Axiom of Infinity

What am I missing here? These definitions are taken from Smullyan's Set Theory and the Continuum Hypothesis.A class W is called inductive if(f) ? is an element of W and for any set x in W, x ? {x} is also an element of W. We call a set...Show More Summary

### Harmonic functions

Let G in C be an open set and take a in G. Suppose that u(z) is harmonic in G-{a} such that lim_{z-> a} u(z) exists and equals A. Show that U:G-->R given by U(z)=u(z) for z=/=a and U(a)=A is harmonic in G.Somehow this relates to the Dirichlet problem, but I only know how to solve it for a disk and can't figure out quite how it applies to this problem. Any help is appreciated!

### The Lottery

1) What are your thoughts on lotteries in general,2) When the expected winnings are greater than the cost of the ticket (as in tonight's Mega Millions game, $640 million jackpot at odds of 1 in ~176 million;$1 to play), would that make you substantially more likely to buy a ticket?Note: It is not physically feasible to buy one of each combination. Show More Summary

### Breech of Contract Incentives

The question is this: If a Client has a certain amount of capital (let’s assume 100) and wants to to pay someone (the Agent) to complete a task, how much should the Client offer up front and how much should be left for after the completion...Show More Summary

### Finite fields, vector spaces, and linear dependence

Hey all.I'm working on a proof for a theorem that I know to be true, and I'm hoping to derive an easy, elegant proof for the theorem. It relies on vector spaces over finite fields, which isn't a strong area of mine, so I was hoping someone...Show More Summary

### Number of functions

Assuming the generalized continuum hypothesis, how many functions are there from R^n to R?Is it correct that there are |R|^{|R^n|}=|R|^{|R|}= \aleph_2?

### Arg Sup vs Arg Max

Let X be the space of functions from R -> R.Let f be a function from X->RIs arg max_{x \in X} f(x) = arg sup_{x \in X} f(x)?I think this is true because, if the supremum exists, but the maximum doesn't, then there is no x that creates the supremum's value, so the "arg supremum" does not exist. I'm well outside of my comfort zone though, so I wanted to check with you guys.

### Conformal mappings

I have two questions:1. Find a bijective conformal mapping from G={z in C : |z| 1} onto the open unit disc D.I'm not really sure where to begin. This set G is more complicated than any of the examples we have of this sort of process; all of our examples have been simply connected.2. Show More Summary

### Convolution

Trying to teach myself the black art, I attempted to convolute (convolve?) t 2 and e t.I get 2e t - t 2 - 2t - 2.Have I got it right, or do I need to go bash my head against the brick walls of algebra and integration-by-parts again?

### Long proofs in beamer

Anyone know how to put long proofs in Beamer onto two or more frames (since it won't fit onto one)? allowframebreaks along with \framebreak or \break doesn't seem to work, and I can't find anything online to help.

### math terminology in Spanish

This semester I have several students whose first language is Spanish, and one has obviously taken some calculus before. Today we started talking about limits, and he used the terminology "the limit as x equals a of f(x)" and said that was the terminology used in Spanish. Can someone comment on the Spanish terminology for this, and how it translates/transliterates into English?

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