## 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.### News

- no new news

### Previous announcements

- Kick-off meeting on July 31 (Tuesday) at 14:30 in room 03.12.020B (outside of the M5 hallway). You should have received an email about that.
- First seminar session on Tuesday, October 23, at 14:15 in seminar room 03.10.011

### Learning goals

- Acquire a mathematical topic on your own, including literature research
- Give a presentation that is understandable to your peers; present in English

### Requirements, Format of the Presentations

- Read through the literature provided (separate email to each participant). This should be the starting point for you to find other resources or explanations on your own (books, internet, etc.). Prepare your presentation well in advance.
- It is required that you schedule a meeting with your assigned supervisor at least one week prior to your seminar presentation, in order to show your presentation and get feedback for improvement.
- Presentation duration: approx. 75 minutes, plus approx. 15 minutes for questions/discussion
- Medium: blackboard, possibly Powerpoint (but then need to go slowly), or a balanced mix of the two.
- Language: English
- At the beginning of your presentation you should perform the magic trick of which you are going to explain to underlying mathematical structure. So, please practice it well.
- Nevertheless, your presentation has to focus mainly on the mathematics behind the tricks, explaining it in a general way. Applications and side directions can be mentioned at the end.
- One week after your presentation, we require a brief 1-2 page summary sheet to be handed to all participants, listing the resources you found most useful for your presentation and containing the main points of your presentation. (For xeroxing, you can see us.)
- If we feel that some parts of your presentation were not well-explained, we may require you to write these parts up.
- In case of questions, contact us (your assigned supervisor)

### Tips for your presentation

- The
**main goal**of your presentation is to make the audience understand your topic and connections within it. - During your preparation you should become familiar with the all the details of your topic. However, please consider that it will not be possible to cover all those details in your talk in an understandable way.
- Nevertheless, the main proofs (or main derivations) have be shown to the audience. In other places,
**intuitive**and**understandable**explanations may be appropriate. In longer proofs and explanations, always make the**crux of the argument**clear. -
**Practice**your talk under real-world conditions (blackboard, ...). This will help you adjust the timing, and may help with the language (English). - When giving your presentation, always be aware that the material is new to your audience.
**Do not assume**that your audience knows more about the topic than you did before your preparation. - Sometimes it is helpful to state important points/facts/definitions/etc
**more than once**, before the audience will understand the importance. -
**Before**doing something or explaining something or starting a proof, always say**what**your are going to do or explain or prove next (and maybe why). Constantly make the**structure**clear. - Manfred Lehn: Wie halte ich einen Seminarvortrag
^{}(in German)

### 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: 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)