Summer 2003 `B' Term-- Proofs from the Book -- MAT 5932-24

Meets MTWRF 9:30-10:50 112 MCH
Instructor Steve Bellenot (bellenot at math.fsu.edu) 850.644.7189
OFFICE HOURS MTWR 11:00-11:30am
Text: Proofs From the Book, by Martin Aigner and Gunter Ziegler
Amazon link to the book.


The course Syllabus.
The on-line gradebook
Links, Quizzes and Exercises. Here are some old Activities.

Chapters spoken for include ch 5 -- Goce; and ch20 -- Fazhe;

Tentative order of topics for the five week. (Jun 9-13, 2003)

  1. chap 4 Representing numbers as the sums of two squares
  2. chap 8 Lines in the plane and decompositions of graphs
  3. chap 18 On a lemma of Littlewood and Offord
  4. chap 29 Turan's graph theorem

Tentative order of topics for the fourth week. (Jun 2-6, 2003)

  1. chap 13 Every large set has an obtuse angle
  2. chap 32 Probability makes counting (sometimes) easy.
  3. chap 24 Caylay's formula for the number of trees
  4. chap 17 A Theorem of Polya on polynomials

Tentative order of topics for the third week. (May 27-30, 2003)

  1. chap 22 Three famous theorems on finite sets.
  2. chap 19 Cotangent and the Herglotz trick
  3. chap 2 Bertrands postulate (there is always a prime between n and 2n).
  4. chap 13 Every large set has an obtuse angle -- but it is a short week so perhaps we will not get this far.

Tentative order of topics for the second week. (May 19-23, 2003)

  1. chap 15 Sets, functions, and the continuum hypothesis
  2. chap 6 Some irrational numbers
  3. chap 7 Hilbert's third problem: decomposing polyhedra
  4. chap 27 Five-coloring plane graphs

Tentative order of topics for the first week. (May 12-16, 2003)

  1. 6 proofs of the infinity of primes (chap 1 part of Number Theory)
  2. How to guard a museum (chap 28 from Graph theory)
  3. Sperners's Lemma (sec 6 of chap 21 (Pigeon-hole and double counting) part of Combinatorics) and an application, the Brouwer fixed point theorem of topology.
  4. In praise of inequalites (chap 16 part of Analysis) --Omitted
  5. Three applications of Euler's formula (chap 10 part of Geometry)

Outline of the course

The class "ad"

The great mathematican Paul Erdos said God maintains perfect mathematical proofs in ``The Book''. Aigner and Ziegler (with many suggestions from Erdos) have collected a number of candidates for such ``perfect proofs'', those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems in number theory, geometry, analysis, combinatorics and graph theory. The book was to be a tribute to Erdos on his 85th birthday.

While there are results in all fields, most are inspired by the wide ranging interests of Paul Erdos. Proofs are chosen because of their simplicity and elegance.