Angel "Java" Lopez en Blog

Publicado el 25 de Agosto, 2012, 11:26

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Luego de teoría de grupos, topología debe haber sido el primer tema "serio" que encontré en mi estudio de las matemáticas. Llegué a ella seguramente en los ochenta, y a la rama de topología general primero, y topología algebraica después. Estoy escribiendo sobre la primera en mi serie de posts.

Leo en la Wikipedia:

http://en.wikipedia.org/wiki/Topology

Topology (from the Greek τόπος, "place", and λόγος, "study") is a major area of mathematicsconcerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing, although the notion of stretching employed in mathematics is not quite the everyday notion: see below and the definition of homeomorphism for details of the mathematical notion. Topology emerged through the development of concepts fromgeometry and set theory, such as space, dimension, and transformation.

Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, which was referred to in Latin as the geometria situs("geometry of place") or analysis situs (Greek-Latin for "picking apart of place"). This later acquired the modern name of topology. By the middle of the 20th century, topology had become an important area of study within mathematics.

Vengo hoy esta primera entrega de enlaces:

Fürstenberg's proof of the infinitude of primes
http://en.wikipedia.org/wiki/F%C3%BCrstenberg%27s_proof_of_the_infinitude_of_primes
On Furstenberg"s Proof of the Infinitude of Primes
http://www.idmercer.com/monthly355-356-mercer.pdf

The Birkhoff-Kakutani theorem
http://terrytao.wordpress.com/2011/05/17/the-birkhoff-kakutani-theorem/

Physics - Weyl electrons kiss
http://physics.aps.org/articles/v4/36
Topology, the mathematical description of the robustness of form, appears throughout physics, and provides strong constraints on many physical systems.

Milnor wins 2011 Abel Prize « Gowers's Weblog
http://gowers.wordpress.com/2011/03/23/milnor-wins-2011-abel-prize/

YouTube - Cutting a Bagel
http://www.youtube.com/watch?v=hYXnZ8-ux80

Mathematically Correct Breakfast -- Mobius Sliced Linked Bagel
http://georgehart.com/bagel/bagel.html

Manifolds « The Unapologetic Mathematician
http://unapologetic.wordpress.com/2011/02/22/manifolds/

Actualización de Entanglement, juego de cuerdas y nudos | Gaussianos
http://gaussianos.com/actualizacion-de-entanglement-juego-de-cuerdas-y-nudos/

Nathaniel Johnston » The Maximum Score in the Game "Entanglement" is 9080
http://www.nathanieljohnston.com/2011/01/the-maximum-score-in-the-game-entanglement-is-9080/

El Topo Lógico: El Omegón y todo eso... (Parte 18)
http://eltopologico.blogspot.com/2011/01/el-omegon-y-todo-eso-parte-18.html

Los topólogos predicen una nueva forma de la materia
http://www.cienciakanija.com/2011/01/03/los-topologos-predicen-una-nueva-forma-de-la-materia

Doodling in Math Class
http://golem.ph.utexas.edu/category/2010/12/doodling_in_math_class.html

Topology and Electromagnetism
http://www.emph.com.ua/18/pdf/barrett.pdf

I Hate Math! (Not After This, You Won't) : Krulwich Wonders… : NPR
http://www.npr.org/blogs/krulwich/2010/12/16/132050207/this-is-for-the-i-hate-math-crowd-not-after-this-you-won-t?ps=cprs

Physics of a Parallel Universe "Exerting a Ghostly Grip on Our Universe"
http://www.dailygalaxy.com/my_weblog/2010/12/news-flash-new-form-of-matter-exerting-a-ghostly-grip-on-our-universe.html

Hilorama de E8 « Juegos topológicos
http://topologia.wordpress.com/2010/10/10/e8-con-hilo-tensado/

A Concise Course in Algebraic Topology
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf

Mike on Topological Quantum Computing, at Georgia
http://sbseminar.wordpress.com/2009/05/18/mike-on-topological-quantum-computing-at-georgia/

Icosien | GEEKY juegos
http://geekyjuegos.com.ar/2010/06/icosien/

Motive-ating the Weil Conjecture Proof
http://sbseminar.wordpress.com/2010/06/10/motive-ating-the-weil-conjecture-proof/
Algebraic topology, cohomology theories, and my idol, Grothendieck
"Leverage the level of abstraction" with steroids ;-)
Inside Grothendieck mind:
http://www.jmilne.org/math/xnotes/mot.html

Mathematical Problem Solved After More Than 50 Years: Chern Numbers Of Algebraic Varieties
http://www.sciencedaily.com/releases/2009/06/090610124858.htm

Poincaré Project
http://jtauber.com/poincare_project/
Working through the mathematics required to understand the Poincaré Conjecture and the possible solution recently proposed.

The Poincaré Conjecture
http://www.claymath.org/poincare/

on Topology
http://ontopo.wordpress.com/

What is computational topology ?
http://geomblog.blogspot.com/2009/11/what-is-computational-topology.html

Nonstandard analogues of energy and density increment arguments
http://terrytao.wordpress.com/2009/11/16/nonstandard-analogues-of-energy-and-density-increment-arguments/

Convexity Using Metric Balls « on Topology
http://ontopo.wordpress.com/2009/03/23/convexity-using-metric-balls/

The Topology of Higher-Dimensional Real Spaces « The Unapologetic Mathematician
http://unapologetic.wordpress.com/2009/09/15/the-topology-of-higher-dimensional-real-spaces/

Solution of the Poincaré conjecture
http://en.wikipedia.org/wiki/Hamilton%E2%80%93Perelman_solution_of_the_Poincar%C3%A9_conjecture

Open problems in algebraic topology
http://claude.math.wesleyan.edu/~mhovey/problems/index.html

Algebraic Topology and Distributed Computing
http://www.cs.brown.edu/~mph/topology.html
 
Mis posts:
Topología, Física y Solzhenitsyn
http://ajlopez.zoomblog.com/archivo/2011/04/15/topologia-Fisica-y-Solzhenitsyn.html
Motivado por este fragmento: http://www.maths.ed.ac.uk/~aar/surgery/first.pdf
Vean que Solzhenitsyn estaba equivocado: la topología en física es hoy un tópico "caliente" en ciencia.
Poincaré y la topología
http://ajlopez.zoomblog.com/archivo/2007/02/01/poincare-y-la-topologia.html
Felix Hausdorff por Laurence Young
http://ajlopez.zoomblog.com/archivo/2011/05/05/felix-Hausdorff-por-Laurence-Young.html
Abstracción y Definición en Matemáticas
http://ajlopez.zoomblog.com/archivo/2011/05/02/abstraccion-y-Definicion-en-Matematica.html

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez