## 11 Películas con Matemáticas

Buscamos buenas historias donde la gente que la protagoniza sea matemática, es decir, gente cuya facilidad para comprender la abstracción de la naturaleza ha decidido sus caminos. Acá vamos a ver películas inspiradoras (como la del profesor de colegio), fuertes (como Straw Dogs), entretenidas (como la del muchacho que participa en la Olimpiada Internacional de Matemáticas), biográficas (como la de la matemática griega) y sobre todo, películas que nos hagan pensar en algo que va más allá que sólo mostrar símbolos matemáticos en la pantalla.

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## Woman arrested for stinking up bathroom and closing down restaurant

DAVE WEZL

CEDAR RAPIDS, IA – Police and fire-paramedics were called to a restaurant when it had to close its doors early on Tuesday evening after a woman spent 45 minutes in the bathroom causing ‘unbearable, inhuman stench’.

The 34 year old woman kicked open the restaurant doors, shouting “out of the way, I’m prairie-dogging!” and ran through the dining area, which was at capacity.

“We were so crowded, people were waiting up to two hours for a table,” says the hostess. “In comes this crazy woman, already smelling like she dumped her pants, running towards the bathroom.”

One customer adds, “I couldn’t breathe. I knew she was in there blasting fudge monkeys, but the smell was toxic. I had to take my son to the hospital, they thought he was exposed to sulphur. This woman is a monster, human beings are not capable of something so foul.”

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## Bing’s House

Cool diagrams

So there’s this example of a 2-complex that’s contractible, but not obviously so. Well actually, once you see it, it’s not too hard to see. Bing’s house with two rooms.

Blah. It’s not so apparent what’s going on. It’s a 2-complex, so let’s draw in the relevant 1-complex.

You can see two vertices and four edges. The surfaces of this 2-complex are all disks, and they make threefold incidences to the edges. The two loop edges bound disks, but they don’t show up since they’re the same translucent color as everything else. And all the corners can be somewhat misleading… Here’s a slicker picture with those two disks colored.

There has recently been a few words about it at MathOverflow where it’s pointed out that the contractiblity of Bing’s house is explained in Hatcher’s text and Cohen’s text. In this post, let’s see how this contraction works.

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## Trying out latex in WP v2.0

Found this blog

trying out some $\LaTeX$ in wordpress.

How did it come out? Please comment below.

## Topological maps or topographic maps?

While surfing the web the other day I read an article in which the author refers to a “topological map.” I think it is safe to say that he meant to write “topographic map.” This is an error I’ve seen many times before.

A topographic map is a map of a region that shows changes in elevation, usually with contour lines indicating different fixed elevations. This is a map that you would take on a hike.

A topological map is a continuous function between two topological spaces—not the same thing as a topographic map at all!

I thought for sure that there was no cartographic meaning for topological map. It turns out, however, that there is.

A topological map is a map that is only concerned with relative locations of features on the map, not on exact locations. A famous example is the graph that we use to…

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## Cayley-Menger determinants

Nice

Niccolo Fontana Tartaglia, whom you may recognise from having discovered Cardano’s solution to the general cubic equation, also discovered a generalisation of Heron’s formula to compute the volume of a tetrahedron:

As you may expect, this can be generalised to compute the volume of any n-simplex (n = 2 reducing to Heron’s formula for the area of a triangle). I wondered how one would go about proving this identity, and then realised it can be accomplished by elementary facts about determinants. Firstly, it is easy to show the following result:

• The volume of an n-simplex S with vertices at {, e_1, …, e_n} is equal to 1/n!, where e_i is the ith standard basis vector.

This can be proved, for instance, by subdividing a unit cube into n! simplices, each of which is congruent to S. Now…

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## Notes from Ring Theory

A list of notes, by date Nov 8 – Densidad…
Nov 15

• Pere Menal ($\cross\sim$ 1992) Ver si un módulo artiniano tiene $\End()$ semilocal. Rosa Camp & W. Ricki $\rightarrow$ Sí.
• Krull ’34 $\rightarrow$ Módulos Artinianos satisfacen el Teorema de Krull-Schmidt? No es difícil ver que si ${M_R}$ es artiniano ${\Rightarrow}$ \footnotesize(se forma una cadena descendiente)\normalsize ${M_R=N_1\oplus\cdots\oplus N_s}$, ${N_i}$ indescomponibles. Es la única descomposición bajo isomorfía y reordenación de los sumandos? (Teorema de Krull-Schmidt). Facchini, H Levy, Vamos ’96 ${\rightarrow}$ No.
• Un ${R}$-módulo ${M}$ generado por ${r}$ elementos – ${M}$ es imágen homomórfica de ${R^r}$

Ene 13

• Módulos proyectivos finitamente generados ${\leadsto}$ submonoides…
• “full affine”
• Monoids are tricky… why? No they’re not. They just have associativity and the presence of an identity
• Fundamental theorem of abelian groups ${\left(\math{N}^k\subseteq\math{Z}^k\right)}$
• ${P/PJ(R)}$ finitely generated ${\nRightarrow}$ ${P}$ finitely generated. Counterexample given by Geramnov, Sakhaev
• Fair-sized projective modules by Pavel (${A_5}$)
• The trace ideal is a bi-lateral ideal: ${Tr(P)=\sum_{f\in P^*}{f(P)}}$${(P\rightarrow R)\in P^*=\Hom_R(P,R)}$. Verify that ${\left[Tr(P)\right]^2=Tr(P)}$
• Whitehead, as cited in Pavel’s article: ${I}$ a bi-lateral idempotent ideal of ${R}$ such that ${_RI}$ is finitely generated ${\Rightarrow I=Tr(P_R)}$, with ${P_R}$ a projective ideal
• Hyman Bass ${\rightarrow}$ Big proyective ideals

\chapter{Features of the Standard LaTeX Report Class}

1. Section

Use the \verb”

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It holds \cite{KarelRektorys} the following

Theorem 1
(The Currant minimax principle.) Let ${T}$ be completely continuous
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arbitrary integer and let ${u_1,\ldots,u_{n-1}}$ be an arbitrary
system of ${n-1}$ linearly independent elements of ${H}$. Denote

$\displaystyle \max_{\substack{v\in H, v\neq 0\\(v,u_1)=0,\ldots,(v,u_n)=0}}\frac{(Tv,v)}{(v,v)}=m(u_1,\ldots, u_{n-1}) \ \ \ \ \ (1)$

Then the ${n}$-th eigenvalue of ${T}$ is equal to the minimum of these
maxima, when minimizing over all linearly independent systems
${u_1,\ldots u_{n-1}}$ in ${H}$,

$\displaystyle \mu_n = \min_{\substack{u_1,\ldots, u_{n-1}\in H}} m(u_1,\ldots, u_{n-1}) \ \ \ \ \ (2)$

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• Bunyip Mythical beast of Australian Aboriginal legends.6. Theorem-Like Environments

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\appendix

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{9}
\bibitem {KarelRektorys}Rektorys, K., Variational methods in Mathematics,
Science and Engineering
, D. Reidel Publishing Company,
Dordrecht-Hollanf/Boston-U.S.A., 2th edition, 1975

\bibitem {Bertoti97} \textsc{Bert\'{o}ti, E.}: On mixed variational formulation
of linear elasticity using nonsymmetric stresses and
displacements
, International Journal for Numerical Methods in
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\bibitem {Szeidl2001} \textsc{Szeidl, G.}: Boundary integral equations for
plane problems in terms of stress functions of order one
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\bibitem {Carlson67} \textsc{Carlson D. E.}: On G\”{u}nther’s stress functions
for couple stresses
, Quart. Appl. Math., 25, (1967),
139-146.

## The Fredholm Alternative

I came across this theorem while reading basic algebraic properties of Petri Nets and I wanted to know how many of you are acquainted with it. Please post in the comments!

One of the most useful theorems in applied mathematics is the Fredholm Alternative.  However, because the theorem has several parts and gets expressed in different ways, many people don’t know why it has “alternative” in the name.  For them, the theorem is a means of constructing solvability conditions for linear equations used in perturbation theory.

The Fredholm Alternative Theorem can be easily understood if you consider solutions to the matrix equation  $latex A v = b$, for a matrix $latex A$ and vectors $latex v$ and $latex b$.  Everything that applies to matrices can then be generalized to infinite dimensional linear operators that occur in differential or integral equations.  The theorem is:  Exactly one of the two following alternatives hold

1. $latex A v = b$ has one and only one solution
2. $latex A^* w = 0$ has a nontrivial solution

where $latex A^*$ is the transpose or adjoint of A. …

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## What riding my bike has taught me about white privilege

trending topic in the USA right now