Fri April 1: Pages 1-15
Mon April 4: Pages 20-26
Wds April 6: Pages 63-68 (Methods of proving theorems) and Pages 71-73 (Mistakes in Proofs)
Fri April 8: Pages 77-85
Mon April 13: Pages 86-94. Also see the Wikipedia articles on
Russell's paradox and the barber's paradox.
Wds April 15: Pages 30-38 and 44-50
Fri April 17: Pages 68-70. We discussed the non-constructive proof that the first player has a strategy to win or tie in tic-tac-toe
Mon April 18: Pages 153-158, and the
Sieve of Eratosthenes. Be sure to check out the interactive
animation link at the bottom of the page. Here are
lecture notes on the proof we used.
Wds April 20: QUIZ (on material from 4/1-4/17), and Pages 159-161.
Fri April 22: Pages 144-152.
Mon April 25: Page 131-142.
Wds April 27: Continued.
Fri April 29: Improved analysis of the Sieve of Eratosthenes. The Nth harmonic number.
Mon May 2: Introduction to proof by induction. Pages 238-249.
Wds May 4: More examples of induction. Well-Ordering Property and a formal proof for induction, pages 251-253.
Fri May 6: Strong induction, and examples. Sums proved by induction.
Mon May 9: MIDTERM, in class. One page of notes allowed.
Wds May 11: Recursive algorithms and proofs by induction. Pages 274-283.
Fri May 13: Recursively defined objects: trees and the Fibonacci numbers. Pages 256-270. See also the Wikipedia page on the golden ratio.
Mon May 16: Counting problems. Pages 302-309, and the Wikipedia page on the
IEEE floating point standard.
Wds May 18: Bit-strings and subsets, tree diagrams, pidgeon-hole principle and applications. Pages 313-319.
Fri May 20: Permuations, binomial coefficients. Pages 321-330.
Mon May 23: Pascal's triangle, theorems about binomial coefficeints,
applications in probability. Pages 331-333, and the Wikipedia article on the
Wds May 25: Introduction to graphs, QUIZ on counting.
Fri May 27: Directed graphs, bipartite graphs, and relations. Connectivity.
Mon May 30: Holiday.
Wds June 1: Equvalence relations.
Fri June 3: Guest lecture: Patrice Koehl. Planar graphs.
Mon June 6: Guest lecture: Boris Mederos. Eulerian and Hamiltonian paths.
Wds June 8: Guest lecture: Boris Mederos. Eulerian and Hamiltoian paths, cont.
Wds June 15: 8:00-10:00 AM FINAL EXAM