User las3rjock - MathOverflow

Answer by las3rjock for Something like mathoverflow in other sciences

2009-11-07T13:13:44Z

Here is a brief list of science-related sites that run on the same platform as Math Overflow:

A complete list of these sites is available here.

The one thing that I personally feel is missing is a lower-level mathematics site (a Math Underflow, if you will). I understand the desire to keep Math Overflow relevant and interesting for professional mathematicians, but there is currently no equivalent site for amateurs and students.

Update: (Sept 2010)A math site for university level mathematics exists now.

There are also sites for theoretical computer science and for statistics.

(April 2011) There is a TEX Q/A site!

(September 2011) Area 51: science contains new proposed stackexchange sites related to science. We can mention especially proposals for Theoretical physics (and mathematical physics) (closed), economics (closed), research economics, game theory, computational sciences, philosophy (the site is running), numerical models and simulations, Mathematica, mathematics in german.

Answer by las3rjock for Math Vs Social Science

2009-11-14T20:53:21Z

Here's a relevant book, written by a mathematics professor at Cambridge: Naive Decision Making: Mathematics Applied to the Social World

Answer by las3rjock for Definition of elementary number theory

2009-11-07T01:50:52Z

Wikipedia has a definition of elementary number theory, but I don't know how well accepted it is.

Answer by las3rjock for Learning LaTeX properly

2009-10-27T16:39:30Z

I'm surprised that no one has mentioned the American Mathematical Society's Short Math Guide for LaTeX.

Answer by las3rjock for Do good math jokes exist?

2009-10-19T00:13:36Z

An excerpt from H. Petard, "A contribution to the mathematical theory of big game hunting," The American Mathematical Monthly, vol. 45, no. 7, pp. 446-447, 1938:

The Hilbert, or axiomatic, method. We place a locked cage at a given point of the desert. We then introduce the following logical system.

Axiom I. The class of lions in the Sahara Desert is non-void.

Axiom II. If there is a lion in the Sahara Desert, there is a lion in the cage.

Rule of Procedure. If p is a theorem, and "p implies q" is a theorem, then q is a theorem.

Theorem I. There is a lion in the cage.

The method of inversive geometry. We place a spherical cage in the desert, enter it, and lock it. We perform an inversion with respect to the cage. The lion is then in the interior of the cage, and we are outside.

The method of projective geometry. Without loss of generality, we may regard the Sahara Desert as a plane. Project the plane into a line, and then project the line into an interior point of the cage. The lion is projected into the same point.

The Bolzano-Weierstrass method. Bisect the desert by a line running N-S. The lion is either in the E portion or in the W portion; let us suppose him to be in the W portion. Bisect this portion by a line running E-W. The lion is either in the N portion or in the S portion; let us suppose him to be in the N portion. We continue this process indefinitely, constructing a sufficiently strong fence about the chosen portion at each step. The diameter of the chosen portions approaches zero, so that the lion is ultimately surrounded by a fence of arbitrarily small perimeter.

Answer by las3rjock for Do good math jokes exist?

2009-10-19T00:29:09Z

"Finite Simple Group (of Order Two)" by the Klein Four a cappella group at Northwestern University (lyrics by Matt Salomone):

The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true

But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two

I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two

Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense

I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two

I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")

I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.

Answer by las3rjock for How to approximate a solution to a matrix equation?

2009-10-04T01:52:56Z

As Anon mentions, linear least squares is the standard method for solving this problem. It involves solving the system of linear equations

A^TAx = A^Tb

which are known as the normal equations. If the system is small enough to solve by hand, one can apply Gaussian elimination or calculate the Moore-Penrose pseudoinverse (A^TA)^-1A^T (assuming A^TA is invertible), but the standard computer algorithms for solving linear least squares problems use either Cholesky factorization, QR factorization, or singular value decomposition.

Answer by las3rjock for LaTeX based document editors

2009-10-02T02:49:17Z

Since it sounds like you're using Windows, I think TeXnicCenter is probably your best free option. (Anton and Montecristo seem to have covered the non-free options like WinEdt and BaKoMa TeX pretty well.)

Comment by las3rjock

2009-11-07T15:49:40Z

@Gerald: I'm not sure omission of Cramer's Rule is such a big deal. Cramer's Rule is helpful for solving small linear systems (2 or 3 unknowns) since there are useful heuristics for calculating the determinants of 2x2 and 3x3 matrices, but Gaussian elimination is a more powerful and general algorithm for solving linear systems.

Comment by las3rjock

2009-11-07T15:33:01Z

Not really, there's definitely room for a StackExchange site for the freshman-calculus-type questions that get closed so quickly on this site.

Comment by las3rjock

2009-10-19T19:37:25Z

Yeah, the method of inversive geometry is one of my favorites.

Comment by las3rjock

2009-10-19T01:09:08Z

I have replaced the JSTOR link with Michael's link.

Comment by las3rjock

2009-10-06T01:04:19Z

I mentioned the Moore-Penrose pseudoinverse because I was describing the situation (small m,n) where it should be fairly easy to determine whether or not (A^T A) is invertible. I agree that the notation is sloppy, but it's fairly common in science and engineering literature (which tends to be sloppy about assumptions and notation).

Comment by las3rjock

2009-10-05T11:02:34Z

I realized that was probably one of the things your script did after I had posted my answer, but I think it's still worth posting how to do this explicitly in the Markdown editor.