"Proofs from the BOOK" seminar, TCD 2018/19
This seminar will discuss selected parts from "Proofs from the BOOK" by Martin Aigner and Günter M. Ziegler. It also will have a problem-solving component, with problems usually related to the weekly topic(s) of the seminar.Speakers are assigned two weeks prior to the seminar, and reporters are assigned one week prior to the seminar.
LaTeX template for reports is here; you may also want to use the BiBTeX file stored here.
Materials:
| Seminar | Topics covered | Reports | Homeworks/Solutions |
|---|---|---|---|
| 1 (12/09) | Organisational meeting. Model presentation. "Pigeonhole principle and double counting": speaker Pedro Tamaroff, reporter Vincent Gélinas. | Report 1-1 [PDF] | HW1 [PDF] |
| 2 (19/09) | "Six proofs of infinity of primes": speaker Ronan O'Gorman, reporter Alden Mathieu. "The fundamental theorem of algebra", speaker Peter Phelan, reporter David Glynn. "Tiling rectangles", speaker Daniel Mulcahy, reporter Oisín Flynn-Connolly. | Report 2-1 [PDF] Report 2-2 [PDF] Report 2-3 [PDF] | HW2 [PDF] |
| 3 (26/09) | "Some irrational numbers": speaker Cathal Ó Cléirigh, reporter Jonathan Keogh. | Report 3-1 [PDF] | HW3 [PDF] |
| 4 (3/10) | "The law of quadratic reciprocity": speaker Oisín Flynn-Connolly, reporter Ronan O'Gorman. "The Borromean rings don't exist": speaker Alden Mathieu, reporter Daniel Matthews. "Every finite division ring is a field" (part 1): speaker Daniel Matthews, reporter Peter Phelan. | Report 4-1 [PDF] Report 4-2 [PDF] | HW4 [PDF] |
| 5 (10/10) | "Every finite division ring is a field" (part 2): speaker Daniel Matthews, reporter Peter Phelan. "Sets, functions, and the continuum hypothesis": speaker Jonathan Keogh, reporter Cathal Ó Cléirigh. | Report 5-1 [PDF] Report 5-2 [PDF] | HW5 [PDF] |
| 6 (17/10) | "A theorem of Pólya on polynomials": speaker David Glynn, reporter Alden Mathieu. "One square and an odd number of triangles": speaker Ronan O'Gorman, reporter Oisín Flynn-Connolly. | Report 6-1 [PDF] Report 6-2 [PDF] | HW6 [PDF] |
| 7 (31/10) | "How to guard a museum": speaker Daniel Mulcahy, reporter Daniel Matthews. "Three famous theorems on finite sets": speaker Alden Mathieu, reporter Daniel Mulcahy. "Buffon's needle problem": speaker Peter Phelan, reporter Ronan O'Gorman. | Report 7-1 [PDF] Report 7-2 [PDF] Report 7-3 [PDF] | HW7 [PDF] |
| 8 (7/11) | "Lattice paths and determinants": speaker Oisín Flynn-Connolly, reporter Daniel Mulcahy. "Five-coloring plane graphs": speaker Daniel Matthews, reporter David Glynn. | Report 8-1 [PDF] Report 8-2 [PDF] | HW8 [PDF] |
| 9 (14/11) | "Of friends and politicians": speaker Cathal Ó Cléirigh, reporter Ronan O'Gorman. "The Dinitz problem": speaker David Glynn, reporter Alden Mathieu. | Report 9-1 [PDF] Report 9-2 [PDF] | HW9 [PDF] |
| 10 (21/11) | "On a lemma of Littlewood and Offord": speaker Daniel Matthews, reporter Peter Phelan. "Binomial coefficients are (almost) never powers": speaker Daniel Mulcahy, reporter Jonathan Keogh. "Three applications of Euler's formula" (part 1): speaker Peter Phelan, reporter Matthew Curran. |
Report 10-1 [PDF]
Report 10-2 [PDF] |
HW10 [PDF] |
| 11 (28/11) | "Three applications of Euler's formula" (part 2): speaker Peter Phelan, reporter Matthew Curran. "Three times π2/6": speaker Jonathan Keogh, reporter Matthew Curran. | Report 11-1 [PDF] |
Marking scheme:
- 10% attendance
- 20% weekly homeworks (10 homeworks during the teaching term, for which at most 5 marks can be earned by each student; full solutions for any single homework are worth one mark, group work is permitted but then the one mark is divided between the group; please indicate on your homework if it is done in collaboration with someone)
- 25% presentation(s) in class, 1-1.5 hours in total, 1 or 2 presentations
- 45% report on someone else's presentation(s), covering 1-1.5 hours in total (usually 1-2 presentations), usually more detailed, at least 10 pages PDF in total (usually 1-2 presentations) typeset in LaTeX (each report submitted within two weeks after the presentation happens)