• The "top five" of December 2011 (“Mathematics and Strategies”)
• The "top five" of November 2011
• The "top five" of October 2011
• The "top five" of September 2011 ("Mathematical exhibitions")
• The "top five" of August 2011 (Weblogs)
• The "top five" of July 2011 ("Mathematical paper crafts")
• The "top five" of June 2011
• The "top five" of May 2011
• The "top five" of April 2011
• The "top five" of March 2011
• The "top five" of February 2011
• The "top five" of January 2011 These "top five" have been communicated by Thomas Bruss, Brussels. 
  
  The TOP5 Inpirations in Mathematics for December 2012 concern the common theme “Mathematics and Strategies”.  Strategies to win an election, strategies to select a best option under certain constraints, strategies to group people together for an optimal output , or strategies to look for new drugs ... all these problems seem to be quite different real-world problems. Nevertheless, the thinking behind it is mathematical rather than anything else, and 
  it is worth the effort to look out for common denominators. Here are a few selected suggestions.
  
  1. Mathematics and Politics 
  This is a sample from the book Mathematics and Politics by A.D. Taylor and A.M Pacelli to give the taste for the influence of Mathematics on strategic thinking. “ How come that the arms race often accelerates once negotiations to stop it have begun? How can one possibly be lead to offer $3.25 to obtain a prize of $1? 
  http://books.google.de/books?hl=de&lr=&id=jEL_cm-xOnEC&oi=fnd&pg=PR7&dq=Mathematics+and+Strategy&ots
  
  2. Shapley value (Shapley Wert; Valeur de Shapley) 
  Knowing what the “Shapley value” is and where it can be applied belongs to the general education of a mathematician. The simple by Wikipedia is among the best to get a quick grasp of its meaning. Here are the web addresses for versions in English, German and French:
  http://en.wikipedia.org/wiki/Shapley_value
  http://de.wikipedia.org/wiki/Shapley-Wert
  http://fr.wikipedia.org/wiki/Valeur_de_Shapley
  
  3. Election Campaigns and political cooperation 
  http://www.welt.de/wissenschaft/jahrdermathematik/article1659109/Strategische_Koalitionen.html
  http://www.welt.de/print-welt/article185290/Die_Mathematik_des_politisch_strategischen_Denkens.html
  (only in German available) 
  
  4. Mathematics of Optimal Stopping 
  Optimal stopping is that part of Mathematics which deals with optimal strategies for decision problems under online-constraints. The subject is subtle, but here are a few addresses for accessible introductions: 
  “The art of a right decision” 
  http://www.google.de/#sclient=psy ab&hl=de&source=hp&q=The+art+of+a+right+decision+EMS&pbx,http://www.americanscientist.org/issues/pub/knowing-when-to-stop. 
  
  5. Little “strategic” items and games 
  T.S. Ferguson's sample of unpublished items is an interesting source for strategies and games, also leading to further references: http://www.math.ucla.edu/~tom/papers/unpublished.html
  
  
   The "top five" of November 2011
  
  These "top five" have been communicated by Ehrhard Behrends, Berlin. 
  
  1. An interesting mathematical exhibition in Paris: http://fondation.cartier.com/files/press_file_2202_fr.pdf00
  2. An article (in German) on this exhibition: http://www.spiegel.de/kultur/gesellschaft/0,1518,792277,00.html
  3. Mathtrek - Mathematics can be found at many places:http://www.sciencenews.org/index/dispatches/activity/view/type/column/collection_id/2/title/Math_Trek
  4. Mathematics and art: http://mathart.eu/
  5. Recent book reviews for mathematicians: http://www.euro-math-soc.eu/bookreviewssearch.html
  
  
  
   The "top five" of October 2011
  
  These "top five" have been communicated by Karl Sigmund, Vienna. 
  
  1. An exhaustive list of significant references to mathematics in fiction: http://kasmana.people.cofc.edu/MATHFICT/
  
  2. An exhibiiton on Gödel  in Vienna: http://www.goedelexhibition.at/gallery/gallery.html
  
  3. A collection of visualizations of geometrical shapes by Herwig Hauser: http://homepage.univie.ac.at/herwig.hauser/index.html#Visualisierungen
  
  4. The Mandelbrot set explorer by Bob Devaney: http://math.bu.edu/DYSYS/explorer/mathematicla
  
  5. The virtual labs in evolutionary game theory: http://www.univie.ac.at/virtuallabs/
  
  
   The "top five" of September 2011
  
  These "top five" have been communicated by Ehrhard Behrends, Berlin. His theme is "Mathematical exhibitions". 
  
  1. A film on the Mathematical Museum in New York: http://www.youtube.com/museumofmathematics
  
  2. The "Mathematikum" in Gießen, Gemany: http://www.mathematikum.de/
  
  3. Il "Giardino di Archimede" in Florence: http://web.math.unifi.it/archimede/archimede/index.html
  
  4. The interactive mathematicla exhibition "Atractor" in Portugal: http://www.atractor.pt/index.html
  
  5. The permanent exhibition "Inspirata" in Leipzig, Germany: http://www.inspirata.de/
  
  
   The "top five" of August 2011
  
  These "top five" have been communicated by George Szpiro, Israel. 
  
  1. Timothy Gowers's weblog: http://gowers.wordpress.com/
  
  2. Terry Tao's weblog: http://terrytao.wordpress.com/
  
  3. Finding the fun in good math ...: http://scientopia.org/blogs/goodmath/
  
  4. Visualization of statistical data: http://flowingdata.com/
  
  5. Comics, not only mathematical ...: http://www.phdcomics.com/comics.php
  
  
   The "top five" of July 2011
  
  These "top five" have been communicated by Franka Miriam Brückler, Croatia. Her theme is "mathematical paper crafts".
  
  1. Origami Mathematics: http://mars.wnec.edu/~th297133/origamimath.html
  
  2. Paper Folding Geometry: http://www.cut-the-knot.org/pythagoras/PaperFolding/index.shtml
  
  3. Modular Origami Polyhedra: http://www.origami-resource-center.com/modular.html
  
  4. Basics of Flexagons: http://www.mathematische-basteleien.de/flexagons.htm
  
  5. The Flexagon Portal: http://www.flexagon.net

 The "top five" of December 2011

 The "top five" of June 2011

1. http://images.math.cnrs.fr/Poesie-spirales-et-battements-de.html
Poetic spirals. Communicated by Mireille Chaleyat-Maurel, France.

2. http://www.slu.edu/classes/maymk/banchoff/
Banchoff applets for single variable and multivariable calculus. Communicated by Martin Raussen, Denmark.

3. http://detexify.kirelabs.org/classify.html
From handwritten squiggles and doodles to exact LaTeX – for your paper or report. Communicated by Steen Markvorsen, Denmark.

4. http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html
Scale the Universe. Communicated by Steen Markvorsen, Denmark.

5. http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Flow/flow.html
Float your own domain in a vector field.Communicated by Steen Markvorsen, Denmark.


 The "top five" of May 2011 (communicated - mainly - by the student's team of the Freie Universität Berlin)

1. http://www.maa.org/devlin/devlin_03_10.html
The mathematics behind "Alice in Wonderland".

2. http://www.illusionworks.com/
Optical illusions: communicated by G. Bini.

3. http://www.youtube.com/watch?v=OmSbdvzbOzY
The dot and the line: a romance in lower mathematics.

4. http://www.youtube.com/watch?v=sRTKSzAOBr4
The Adventures of the Klein bottle.

5. http://plus.maths.org/content/maths-and-magic
Maths and magics ...


 The "top five" of April 2011 (communicated by the student's team of the Freie Universität Berlin)

1. http://www.mathpuzzle.com/
Martin Gardner celebrates math puzzles and Mathematical Recreations. This site aims to do the same.

2. http://ocw.mit.edu/courses/mathematics/
MIT OpenCourseWare is a free publication of MIT course materials that reflects almost all the undergraduate and graduate subjects taught at MIT.

3. http://www.kuro5hin.org/story/2003/5/23/134430/275
A Layman's Guide to the Banach-Tarski Paradox.

4. http://www.youtube.com/watch?v=DPHZyUAzFts
A video where Benford's law is explained (in German).

5. http://www.dfg-science-tv.de/de/projekte/diskrete-optimierer
Is mathematics dull? No! Visit the web page of Wiebke Höhn and Marco Lübbecke from the Mathematical Institute at the TU Berlin (in German).


 The "top five" of March 2011 (communicted by the student's team of the Freie Universität Berlin)

1. http://www.youtube.com/watch?v=1X-gtr4pEBU
From Wikipedia, the free encyclopedia:
Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complicated emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The universality of Langton's ant was proven in 2000. The idea has been generalized in several different ways, such as turmites which add more colors and more states.

2. http://www.youtube.com/watch?v=yaC7Xmc61hM
Another way how to multiply two numbers

3. http://www.youtube.com/watch?v=G_GBwuYuOOs
Fractals everywhere ... (see also http://www.heise.de/software/download/gnu_xaos/55162 in this connection)

4. Metamath - http://www.metamath.org
From their Webpage:
Metamath is a tiny language that can express theorems in abstract mathematics, accompanied by proofs that can be verified by a computer program. This site has a collection of web pages generated from those proofs and lets you see mathematics developed in complete detail from first principles, with absolute rigor. Hopefully it will amuse you, amaze you, and possibly enlighten you in its own special way.

5. http://9gag.com/gag/33554/
I Heart Math ...


 The "top five" of February 2011

1. http://greenfootgallery.org/about
   This site introduces a nice and simple platform for building ‘scenarios’ for games – and for learning. Including learning mathematics? Can you apply this or other similar environments for teaching and for learning? What do you think? Can you set up a game where the goal for the player is to learn how to solve quadratic equations? Or even better: Can you set up a game where the goal for the player is to construct such a game for himself or herself - using only the simplest possible programming tools – such as this green foot? Not to mention the prospect of learning Singular Value Decomposition in this way – or any other one of your favorite theorems. Please let us know if you have any experiences, ideas, or further examples on how to set up game based learning environments for mathematics. (Communicated by Steen Markvorsen, Denmark.)
2. http://en.wikipedia.org/wiki/Portal:Mathematics
   Happy birthday to Wikipedia! (Communicated by Steen Markvorsen, Denmark.)
3. http://www.matematita.it/materiale/?p=cat&sc=341,1014,1017,1020
   Möbius strips en masse. Which shapes would appear if they in each case were supposed to have the minimum possible bending energy? (Communicated by Ehrhard Behrends, Germany.)
4. http://vimeo.com/user798992/videos/page:1/sort:newest
   Beautiful architectural design, physics, and mathematics – mostly mathematics of course. Created by Daniel Piker, architectural student based in London. (Communicated by Steen Markvorsen, Denmark.)
5. http://www.atractor.pt/mat/puzzle-15/index.html
   A well known puzzle – with an interesting twist. (Communicated by Maria Dedo, Italy.)

 The "top five" of January 2011

1. http://www.youtube.com/watch?v=_A-ZVCjfWf8
   A couple of thought provoking quotes from this video, stated by two young students: “I will have 14 jobs before I am 38 years old. Most of those jobs do not exist today” – “Teach me to think, to create, to analyze, to evaluate, to apply.” Mathematics is clearly in demand – we must, we can, engage the students into mathematics and into the future.  
   (Communicated by Klaus Fink, Denmark.)
2. http://www.imaginary2008.de/
   Watch the imaginary lemon x^2 + z^2 = (1-y^3) y^3 on display – together with several other very well prepared mathematical sculptures.
   (Communicated by Martin Raussen, Denmark.)
3. http://vimeo.com/9953368
   A wonderful video about Fibonacci numbers and the golden ratio. These topics are common in many popularization activities, but here Voronoi tessellations and Delaunay triangulations are also introduced. All the information “behind” the video is given (in English and Spanish) at the following address: http://www.etereaestudios.com/docs_html/nbyn_htm/intro.htm
   (Communicated by Maria Dedo, Italy.)
4. http://republicofmath.files.wordpress.com/2009/12/collaboration.jpg
   Collaboration is important and needed – and makes the mathematics much more fun.
   (Communicated by Steen Markvorsen, Denmark.)
5. http://dmf.unicatt.it/~paolini/penrose/youtube.html
   Two fabulous animations with Roger Penrose’s darts and kites.
   (Communicated by Maria Dedo, Italy.)