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Mathematics and Magic [MA6001]

Wintersemester 2012/2013

Prof. Michael M. Wolf, Dr. David Reeb, Dr. Daniel Reitzner

Place and time: Tuesdays, 14:15-15:45, seminar room 03.10.011
Dates: 23.10., 30.10., 6.11., 13.11., 20.11., 4.12., 11.12., 18.12.
Literature: has been provided (sent in separate emails to each participant)
Language: English
Prerequisites: Analysis 1 & 2, Linear Algebra 1 & 2
Participation: In each seminar session your participation is compulsory

Contents

A good magician is an honest liar — s/he says s/he is going to decieve you and then s/he does! S/he relies on good abilities of sleight of hand, the power of influence and suggestion and of course on abilities to perform. But sometimes a good trick contains something more — mathematics is a founding stone in many tricks. We will learn about such magic tricks which have an interesting underlying mathematical structure. The mathematics ranges from combinatorics over knot theory to differential equations. The corresponding 'magic' involves card tricks as well as invisibility cloaks.

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Requirements, Format of the Presentations

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Schedule and Presentation Topics


We will talk about the requirements and the setup of our seminar, and will distribute/assign the presentation topics. Please have a look at the topics beforehand. If, for urgent reasons, you cannot attend this meeting, then please reply via email with your preference of presentation topics.


Card trick: Prepare to be awed and puzzled by the skills of mind-reading. Does the presenter really possess the power of extrasensory perception?
(supervised by D. Reitzner) | (handout)


Card trick: Does one need to be a proficient shuffler to be able to prepare a deck so that after shuffling he can still get a good hand?
(supervised by D. Reitzner) | (handout doc, odt)


Card trick: How can one find a chosen card within a shuffled deck? Is it magic? Is it deception? Or just some good ole’ math?
(supervised by D. Reitzner) | (handout)


Card trick: Previously we had shuffles that did not allow one to decide how to shuffle, but here we will see, that even if you have a word into the way how one shuffles, the result may be surprising.
(supervised by D. Reitzner)


Games and probability: Probability is a concept we encounter every day in our lives. Yet it can have many strange and counterintuitive consequences.
(supervised by D. Reitzner) | (handout)


Loops and homotopy: Knots seem simple enough for the majority of people to believe they understand them - we all tie shoe-laces and some of us even ties. Loops are one of the simple knots, yet if one knows how, one can fool a lot of people.
(supervised by D. Reeb) | (handout)


Invisibility cloaking: 'How to Make Statue of the Liberty Disappear'. David Copperfield once made the statue of Liberty disappear. Hiding of physical objects was for a long time an arena for illusionists or for science fiction. A recent boom in studies of invisibility shows, that reality might not be so far.
Note: This topic should be covered by a student with a physics background, so if you are a physics minor or major, please consider volunteering here. Some basic knowledge in geometrical optics (refractive index) and/or classical mechanics is helpful.
(supervised by D. Reeb) | (handout docx, pdf)


Paradoxes in set theory and axiomatics: How to free many prisoners if they have a choice function from a large collection of sets (infinite hatted queue paradox), and how to divide a sphere into a few parts and to rearrange the parts in order to get two spheres of the same size (Banach-Tarski paradox).
(supervised by D. Reeb) | (handout)