Fall 2009
CS131 Combinatorial Structures
Homework 2
Homework 2, due Sept 22
You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check ex
Discrete Mathematics
Dr. Fred Phelps
Lecture 1
Counting and
Set Theory
Announcements
Please register for discrete math on the
site http:/dl.iitu.kz. The main textbook is
on that site.
The syllabus is
Discrete Mathematics
Dr. Fred Phelps
Lecture 2
More Counting:
Permutations and
Combinations
Announcements
Please register for discrete math on the
site http:/dl.iitu.kz. The main textbook is
on that s
Discrete Mathematics
Dr. Fred Phelps
Lecture 3
Induction and
Stirlings
Formula
LVP 2.1 Mathematical
Induction n
A tool to prove formulae for every .
What is the sum of the first n odd numbers,
n
i.e.
Discrete Mathematics
Dr. Fred Phelps
Lecture 4
The Pigeonhole
Principle
& The Binomial
Theorem
LVP 2.4 Pigeonhole Principle
If we have n boxes and we
place more than n objects
into them, then there wi
Discrete Mathematics
Dr. Fred Phelps
Lecture 5
The InclusionExclusion Principle
& More Counting
Problems
LPV 2.3 & Chen 13 The
Inclusion-Exclusion Principle
1.
This is covered in LPV 2.3 but the lectu
Discrete Mathematics
Dr. Fred Phelps
Lecture 6
Pascals
Triangle and the
Normal
LPV 3.5 Pascals Triangle
nth row consists
n n n n
, ,.
, .
0 1 n 1 n
LPV 3.6 Pascals Triangle identities
Recall the i
Combinatorial Structures
Freely using the textbook by Lovsz-Pelikn-Vesztergombi
Pter Gcs
Computer Science Department
Boston University
Fall 2009
Pter Gcs (Boston University)
CS 131
Fall 09
1 / 176
Int
Week Five Problems Recurrence Relations
Name 1_
Name 2_
Name 3_
Group_
Work in groups of three (or two if necessary). Please write the solutions nicely on the back of this
paper and continue on more p
Week One Solutions
1) Consider a group of five men and four women with the following hand shaking rules and
calculate how many possible handshakes there are:
Only men shake hands with each other. How
Week One SSWT Assignment
1) Consider a group of five men and four women with the following hand shaking rules and
calculate how many possible handshakes there are:
Only men shake hands with each othe
Fall 2009
CS131 Combinatorial Structures
Self-test questions
Self-test questions
These questions are provided for additional self-testing, on material for which the book does not have enough self-test
Fall 2009
CS131 Combinatorial Structures
Midterm exam 2
Midterm exam 2
Only a single hand-written crib sheet can be used, no books or notes. Even if I ask
for just a yes/no answer, you must always giv
Fall 2009
CS131 Combinatorial Structures
Homework 3
Homework 3, due Sept 29
You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check ex
Fall 2009
CS131 Combinatorial Structures
Homework 1
Homework 1, due Sept 15
You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check ex
Fall 2009
CS131 Combinatorial Structures
Homework 4
Homework 4, due Oct 15
You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check exe
Fall 2009
CS131 Combinatorial Structures
Homework 5
Homework 5, due Oct 20
You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check exe
Fall 2009
CS131 Combinatorial Structures
Homework 6
Homework 6, due Oct 27
You must prove your answer to every question.
Do not rely only on the homework for exercise: there are several self-check exe
Fall 2009
CS131 Combinatorial Structures
Homework 7
Homework 7, due Nov 3
You must prove your answer to every question.
Do not rely only on the homework for exercise: there are several self-check exer
Fall 2009
CS131 Combinatorial Structures
Homework 8
Homework 8, due Nov 17
You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check exe
Fall 2009
CS131 Combinatorial Structures
Homework 9
Homework 9, due Nov 24
You must prove your answer to every question. Do not rely only on the homework for exercise: there are several self-check exe
Fall 2009
CS131 Combinatorial Structures
Homework 10
Homework 10, due Dec 8
You must prove your answer to every question.
Do not rely only on the homework for exercise: there are several self-check ex
Fall 2009
CS131 Combinatorial Structures
Midterm exam 1
Midterm exam 1
Only a single hand-written crib sheet can be used, no books or notes. Even if I ask for just a yes/no answer, you must always giv
Second Week Practice Assignment
Counting Review:
1.8.27 Alice has 10 balls (all different). First, she splits them into two piles; then she picks one of
the piles with at least two elements, and split