11 Películas con Matemáticas

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— See this page in English – Sobre el Autor —

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

The Valley Report


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.”

The first responding firefighters had…

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Bing’s House

Cool diagrams

Sketches of Topology

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.

Picture 12

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

Picture 13

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.

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Topological maps or topographic maps?

Division by Zero

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


Complex Projective 4-Space

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”

2. Section

” command for major sections, and
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It holds \cite{KarelRektorys} the following

Theorem 1
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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
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{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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    \bibitem {Bertoti97} \textsc{Bert\'{o}ti, E.}: On mixed variational formulation
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    \bibitem {Szeidl2001} \textsc{Szeidl, G.}: Boundary integral equations for
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    \bibitem {Carlson67} \textsc{Carlson D. E.}: On G\”{u}nther’s stress functions
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    , Quart. Appl. Math., 25, (1967),

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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!

Scientific Clearing House

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


The phrase “white privilege” is one that rubs a lot of white people the wrong way. It can trigger something in them that shuts down conversation or at least makes them very defensive. (Especially those who grew up relatively less privileged than other folks around them). And I’ve seen more than once where this happens and the next move in the conversation is for the person who brought up white privilege to say, “The reason you’re getting defensive is because you’re feeling the discomfort of having your privilege exposed.”

I’m sure that’s true sometimes. And I’m sure there are a lot of people, white and otherwise, who can attest to a kind of a-ha moment or paradigm shift where they “got” what privilege means and they did realize they had been getting defensive because they were uncomfortable at having their privilege exposed. But I would guess that more often than…

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Alexander Grothendieck 1928–2014

Time to read a little bit about Grothendieck.

Gödel's Lost Letter and P=NP


Alexander Grothendieck, who signed his works in French “Alexandre” but otherwise kept the spelling of his German-Jewish heritage, passed away Thursday in southwestern France.

Today we mourn his passing, and try to describe some of his vision.

Part of the story of this amazing mathematician is that in 1970 he renounced his central position at the Institut des Hautes tudes Scientifiques (IHES) in Paris, and made himself so remote shortly after formally retiring from the University of Montpellier in 1988 that not even family and friends could track him. He boycotted his 1966 Fields Medal ceremony in Moscow to protest the Red Army’s presence in eastern Europe, and declined the Crafoord Prize in 1988.

As captured by this obituary, he had left to seek a society kinder and more just than the ones that killed his father at Auschwitz and convicted him in 1977 of violating a French law…

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