# MAT016 Proofs from The Book (FS23)

Lecturer: Dr. Johannes Schmitt
Time and Place: Monday, 8:00-9:45, Room Y27H25
Further information can be found in the UZH Course Catalogue.

Content

"Proofs from THE BOOK" is a book written by Aigner and Ziegler that presents a collection of mathematical proofs, with a focus on trying to find the most instructive and elegant ways to derive various theorems.
The book is known for its clear proof presentations, which are often cited as models of good proof-writing. The book covers a wide range of mathematical topics, including geometry, number theory, and combinatorics. In addition to presenting the proofs themselves, the book also includes discussions of the background and motivation behind each proof, as well as tips on how to approach and understand the material.
In the seminar, each student will present content from one of the chapters of the book. Instead of building up one big theory, the chapters are independent, and the focus of the seminar is to aim at fully understanding the material and presenting it as clearly as possible.

List of talks

Here is the preliminary assignment of topics and dates:

Topic Date Student
Chapter 3: Binomial coefficients are (almost) never powers
Chapter 9: Four times $$\pi^2/6$$
06.03 Sibylle Schalbetter
Laura Depedrini
Chapter 36: Completing Latin squares
Chapter 2: Bertrand’s postulate
13.03 Annina Eggenschwiler
Keerthiga Rajakumar
Chapter 20: In praise of inequalities
Chapter 31: Shuffling cards
20.03 Andrin Schneeberger
Christian Farkas
Chapter 40: How to guard a museum
Chapter 21: The fundamental theorem of algebra
27.03 Jeremy Suter
Teodora Krstic
Chapter 15: The Borromean rings don’t exist 03.04 Irena Syla
Joel Zülle
Chapter 41: Turán’s graph theorem
Chapter 44: Of friends and politicians
17.04 Ira Griesshammer
Alicia Brockmöller
Chapter 19: Sets, functions, and the continuum hypothesis
Chapter 6: Every finite division ring is a field
24.04 Philine Schönenberger
Ida Krinn

Requirement for passing

In order to pass the seminar and get credit points, you have to:

• give a talk about one chapter from the book to the other participants
• hand in a written part towards the end of the semester; this should be written in LaTeX and can be a summary of the talk or solutions to exercises in the part of the script you are discussing
• attend (most of) the talks of the other participants
There is no grade for the seminar, so it is simply pass/fail.