Video: Some important themes in geometry

Saturday, January 30th, 2010 | Author:

In the series "Mathematics for non-mathematicians", I recommend a talk by Dan Freed, titled "The Hodge Conjecture" - but you don't need to be interested in the Hodge Conjecture to benefit from this video!
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Math 2.0

Thursday, January 28th, 2010 | Author:

The term Web 2.0 was coined by Darcy DiNucci in 1999 and popularised by Tim O'Reilly in a 2004 conference named Web 2.0. In the beginning, it wasn't totally clear what Web 2.0 really meant for the ordinary web consumer. Then it crystallised out that users associate with the term Web 2.0 an interactive internet. During that time, the first large collaborative dynamic websites were seen, such as Wikipedia and YouTube. Web 1.0 are static HTML pages that don't allow interaction.

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Problematic elections

Sunday, January 24th, 2010 | Author:

Since I recently finished reading Donald G. Saari's wonderful book "Chaotic Elections - A Mathematician Looks at Voting" (published by the American Mathematical Society), I decided to give a short example of what goes wrong in elections, so you'll know how voting paradoxes influence our lives and why you should know something about it. This is about Germany, but I tried to design the example such that you don't have to know anything about Germany to understand it.
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Found nice introductory paper on cryptography & complexity

Tuesday, November 17th, 2009 | Author:

I just found this very nice paper on cryptography & complexity theory on the arXiv:

Jörg Rothe: "Some Facets of Complexity Theory and Cryptography: A Five-Lectures Tutorial"
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Some nice introductory/expository papers

Thursday, October 29th, 2009 | Author:

On Math Overflow, someone asked for "A single paper everyone should read?"
and some answers were particularly nice to read for me, so I repeat it for you, ordered by how much math is needed (from none up to little):

  • Paul Lockhart: "A Mathematician's Lament" shares my opinion about the math eduction disaster in schools. I think you should read this if you disliked your math classes in school or if you will ever have children (who will have to take a math class, then).
  • Terry Tao: "What is good mathematics?" which is a short (10 pages) paper about the benefit we have from mathematicians different tastes and approaches. I recommend to every scientist reading the first 3 pages (the other 7 pages are only understandable with some background in mathematics).
  • Freeman Dyson: "Birds and Frogs" which is a must-read for anyone interested in history and/or progress of mathematics.
  • Misha Gromov: "Spaces and Questions" which is readable with almost no background, although might be funnier if you know basic differential geometry. It tells a dense story of geometric ideas and their development in history. And it doesn't take much time to read/skim it.
  • Timothy Chow: A beginner's guide to forcing is a really gentle introduction to forcing.

Math Overflow is a new community website where mathematicians can discuss research problems. It is based on Stack Exchange, the software powering Stack Overflow, which does the same for computer science.

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Mathe für Nichtmathematiker

Wednesday, July 29th, 2009 | Author:

Kürzlich habe ich mal versucht NichtmathematikerInnen zu erklären, was ich da eigentlich so mache (in meinem Mathematikstudium).

Da ich algebraische Geometrie benutze, wollte ich versuchen die Intuition zu vermitteln, was ein Schema ist oder wieso man in diese Richtung denkt. Das versuche ich jetzt also einmal in geschriebener Form:

Stell dir einen Kreis mit Radius r vor, also die Menge aller Punkte, die vom Mittelpunkt des Kreises genau den Abstand r haben. In der x,y-Ebene lässt sich ein Kreis, dessen Mittelpunkt der Ursprung 0 ist, leicht beschreiben, denn der Abstand vom Nullpunkt ist für einen Punkt (x,y) gegeben durch die Formel \sqrt{x^2+y^2}. Der Kreis wird dann beschrieben durch die Menge K = \{(x,y) \in \mathbb{R}^2 \ |\ \sqrt{x^2+y^2}=r\}, dabei bedeutet (x,y) \in \mathbb{R}^2 ganz einfach, dass (x,y) ein Punkt in der Ebene ist, dessen Koordinaten x und y reelle Zahlen sind, also z.B. 1,2,3, 4.5, 7.777777... oder auch \pi, \frac{12}{7} usw. Jetzt schreibe ich die Menge K noch ein kleines bisschen anders:
K = \{(x,y)\in\mathbb{R}^2\ |\ x^2+y^2-r^2=0\}, man überzeuge sich davon, dass dies die selbe Menge von Punkten in der Ebene \mathbb{R}^2 ist.

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