REU 2007 Apprentice Class Lecture 8
Instructor: Laszlo Babai
Scribe: Ian Shipman
July 5, 2007. Revised by instructor.
Last updated July 5, 5:15 p.m.
A8.1
The Cayley-Hamilton Theorem
Recall that for a
REU 2007 Apprentice Program Lecture 5
Instructor: Laszlo Babai
Scribe: Ian Shipman
June 29, 2007. NOT PROOFREAD by instructor.
Last updated June 29, 3 p.m.
A5.1
Vector space review
Let V be a vector s
REU 2007 Discrete Math Lecture 4
Instructor: Laszlo Babai
Scribe: Shawn Drenning
June 21, 2007.
Last updated June 28, 12:45 a.m.
PARTIALLY REVISED BY INSTRUCTOR. Look for further updates.
4.1
Puzzle p
REU 2007 Apprentice Class Lecture 12
Instructor: Laszlo Babai
Scribes: Courtney Morris and Gabriel Kerr
July 11, 2007. Revised by instructor.
Last updated July 11, 9:30 p.m.
A12.1
Rational roots of po
REU 2007 Apprentice Program Lecture 1
Instructor: Laszlo Babai
Scribe: Michael Broshi
June 25, 2007.
Last updated June 26, 3:30 p.m.
Proofread by the instructor.
A1.1
The Determinant of an n n matrix
REU 2007 Discrete Mathematics Lecture 10
Instructor: Laszlo Babai
Scribe: Damir Dzhafarov
July 10, 2007. Partially revised by instructor.
Last updated July 10, 9:00 PM
10.1
Review: Inequalities and Me
BABAI DISCRETE MATHEMATICS REU 2008
EXERCISES FROM LECTURE 12, TUESDAY JULY 29
SCRIBE: JOSHUA A. GROCHOW
Exercise 1 (Reminder of a previous exercise). If a rectangle is the union
of smaller rectangles
REU 2007 Apprentice Program Lecture 6
Instructor: Laszlo Babai
Scribe: Michael Broshi
July 2, 2007. Revised by instructor.
Last updated July 2, 8 p.m.
A6.1
Convexity
Definition A6.1.1. The line segmen
BABAI DISCRETE MATHEMATICS REU 2008
EXERCISES FROM LECTURE 11, THURSDAY JULY 24
SCRIBE: MATTHEW STROM BORMAN
Theorem. If N = A1 Ak is the union of k 2 disjoint arithmetic
progressions, then not all of
REU 2007 Transfinite Combinatorics Lecture 7
Instructor: Laszlo Babai
Scribe: Travis Schedler
August 6, 2007. NOT revised by instructor.
Last updated August 6, 5:30 PM
7.1
Matchings
(with all edges h
REU 2007 Discrete Math Lecture 6
Instructor: Laszlo Babai
Scribe: Shawn Drenning
June 26, 2007.
Last updated June 26, 11:59 p.m.
Revised by the instructor.
6.1
Finite Probability Spaces
For an introdu
REU 2007 Apprentice Class Lecture 9
Instructor: Laszlo Babai
Scribe: Courtney Morris
July 6, 2007. Revised by instructor.
Last updated July 8, 12:50 a.m.
A9.1
Circulant Matrices
Recall that a circulan
REU 2007 Transfinite Combinatorics Lecture 2
Instructor: Laszlo Babai
Scribe: Damir Dzhafarov
July 23, 2007. NOT revised by instructor.
Last updated July 27, 6:00 AM
2.1
More Problems and Examples in
REU 2007 Transfinite Combinatorics Lecture 9
Instructor: Laszlo Babai
Scribe: Travis Schedler
August 10, 2007. Revised by instructor.
Last updated August 11, 3:40pm
Note: All (0, 1)-measures will be a
REU 2007 Discrete Math Lecture 2
Instructor: Laszlo Babai
Scribe: Shawn Drenning
June 19, 2007. Proofread by instructor.
Last updated June 20, 1 a.m.
Exercise 2.0.1. Let G be an abelian group and A G
REU Apprentice
First Friday
Instructor: Laszlo Babai
Scribe: Benjamin McKenna
2
Second class: Friday, June 27
2.1
Abelian groups, vector spaces: axioms
Recall: If v1 , . . . , vk V for V a vector spac
REU 2007 Discrete Mathematics Lecture 9
Instructor: Laszlo Babai
Scribe: Damir Dzhafarov
July 6, 2007. Revised by instructor.
Last updated July 8, 3am
9.1
General and Special Linear Groups
Recall that
REU 2007 Apprentice Program Lecture 3
Instructor: Laszlo Babai
Scribe: Gabriel Kerr
June 27, 2007. Revised by instructor.
Last updated June 27, 10 p.m.
For basic definitions and facts about graphs and
BABAI DISCRETE MATHEMATICS REU 2008
EXERCISES FROM LECTURE 3, THURSDAY, JUNE 26
SCRIBE: MATTHEW J. THIBAULT
Exercise 1 (Clearing the Corner.). A game is played on a grid in the first
quadrant of the p
REU 2007 Apprentice Class Lecture 2
Instructor: Laszlo Babai
Scribe: Michael Geline
June 26, 2007.
COMPLETE notes. Revised by instructor. Last updated June 28, 1:30 a.m.
A2.1
A Determinant Calculation
REU 2007 Discrete Math Lecture 3
Instructor: Laszlo Babai
Scribe: Aaron Marcus
June 20, 2007.
Last updated June 20, 8:30 p.m. Revised by instructor.
3.1
Orders of group elements
Let G be a group, and
REU 2007 Transfinite Combinatorics Lecture 5
Instructor: Laszlo Babai
Scribe: Aaron Marcus
August 1, 2007. Revised by instructor.
Last updated August 2, 5:05 PM
5.1
The Continuum Hypothesis
Recal that
REU Apprentice
Fourth Wednesday
Benjamin McKenna
10
10.1
Tenth Class: Wed. 7/16/14
First session: Graph isomorphisms, graph colorings, girth, regularity
Recall: A graph G = (V, E) is composed of a set
BABAI DISCRETE MATHEMATICS REU 2008
EXERCISES FROM LECTURE 6, THU JULY 3
SCRIBE: JOSHUA A. GROCHOW
Throughout these exercies, G = (V, E) denotes a graph, V its vertex set,
and E its edge set.
Exercise