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Assignment of topics was on: We, 06.07., 12:30 hrs., HS 2

Dates of presentation: 3 presentations will be given on 16. November (09.00 - 12.45), 5 presentations on 01. December (09.45 - 17.00), 2 presentations on 19. December (17.00 - 19.30) and 2 presentations on 23. December (09.00 - 11.30).

Language: 3 presentations will be given in English (01. December afternoon), the other in German.

I got the idea for this topic from my diploma advisor Martin Aigner who co-authored with Günter Ziegler the renowned mathematics book "Proofs from THE BOOK". They got the idea from the uncomparable mathematician of the century Paul Erdös who dedicated his whole life to mathematical problems and their proofs and claimed the thesis that God kept for each mathematical problem an elegant proof in THE BOOK, and it were the task of every mathematician to discover such proofs. Aigner and Ziegler tried to detect such proofs and dedicated their book to the memory of Erdös.

The topics below come from different areas and do not require more knowledge than taught at FH Wedel. For most topics one mathematical course is sufficient where Discrete Mathematics would suit best because of its general foundations of mathematical concepts. Some topics even deepen topics explicitly covered in Discrete Mathematics.

Interested students may also apply for other proofs from THE BOOK. It is sufficient that you tell at the issuing date, but an advance consultation of myself would be advisable.

Most topics may be held on the level of a bachelor programme as well as of a master programme while both levels are treated different by requirement and grading. Some topics are only suited for bachelor students.

Each participant should not only present the problem and its proof as stated in the book, but also should also look for further material to the problem and illustrate the problem with examples before the hard proof is shown.

Each participant must discuss his topic far before the date of presentation, but only after the issuing date. However, you may immediately consult me in any issued of the seminar.

In our library you find:

Martin Aigner / Günter Ziegler: Proofs from THE BOOK, Springer 2010 (4. edition), ISBN 978-3-642-00855-9

German translation: Das BUCH der Beweise, Springer 2004 (2. edition), ISBN 3-540-40185-7

You may also use newer editions.

The use of more references is explicitly welcome.

1) 4 proofs for the infinity of primes (in German) (ch. 1, Kap. 1)
The book contains even more proofs.

presented by: Lukas Raschke
16. November 2016, 09.00 hrs., HS 5

2) Each finite division ring is a field (in German) (ch. 6, Kap. 5)

presented by: Lene Judika Stampa
16. November 2016, 10.15 hrs., HS 5

3) How to prove that a number is irrational (in German) (ch. 7, Kap. 6)

presented by: Arif Özütemiz
16. November 2016, 11.30 hrs. HS 5

4) A cotangent formula (in German) (ch. 23, Kap. 20)

presented by: Annrieke Wulf
01. December 2016, 09.45 hrs., HS 5

5) Decomposing a square into an odd number of equal triangles (in German) (ch. 20)

presented by: Timm Hoffmann
01. December 2016, 11.00 hrs., HS 5

6) Function and decryption of Enigma

presented by: Torben Tietgen (in English)
01. December 2016, 13:15 hrs., HS 5

7) Buffon's needle problem (ch. 24, Kap. 153)

presented by: Aschot Petrosjan (in English)
01. December 2016, 14.30 hrs., HS 5

8) 5-coloring of maps (ch. 34, Kap. 30)

presented by: Maryam Roustaei (in English)
01. December 2016, 15.45 hrs., HS 5

9) 4 applications of the pidgeon-hole principle (in German) (ch. 25)

presented by: Jonatan Spincke
19. December 2016, 17.00 hrs., HS 6

10) Completing Latin squares (in German) (ch. 32, Kap. 27)

presented by: Sylvia Reißmann
19. December 2016, 18.15 hrs., HS 6

11) Completing colors in squares (in German) (ch. 33, Kap. 28)

presented by: Mirco Krohn
23. December 2016, 09.00 hrs., HS 5

12) Minimum number of guards in polygons (in German) (ch. 35, Kap. 31)

presented by: Christoph Altrock
23. December 2016, 10.15 hrs., HS 5