CS 171 Lecture Outline
January 13, 2011
Example.
Prove that for all positive integers n, n is even 7n + 4 is even
Solution. Let n be a particular but arbitrarily chosen integer. Proof for n is even 7n + 4 is even. Since n is even, n = 2k for some integer
Data Structures and Algorithms Solutions to Homework 1
January 25, 2011
1.
Answer each of the following questions. You dont need to show your work.
Questions a-e are based on the scenario that a president, treasurer, and secretary, all dierent, are to be
Data Structures and Algorithms Homework Assignment 1
Given: January 13, 2011 Due: January 20, 2011
This assignment is due by the end of the class on the due date. Unless all problems carry equal weight, the point value of each problem is shown in [ ]. To
Gender Equitable
development Projects
APMASS & WAP, AIT: Vietnam
Phng Th Vn Anh
Gender Trainer/ Consultant
Centre for Community
Empowerment (CECEM)
GENDER & DEVELOPMENT
BASIC CONCEPTS
Sex
Sex indicates biological characteristics of man and
woman .
Peopl
Advanced Algorithms Lecture Outline
January 05, 2011
Counting
Counting is a part of combinatorics, an area of mathematics which is concerned with the arrangement of objects of a set into patterns that satisfy certain constraints. We will mainly be interes
Advanced Algorithms Lecture Outline
January 05, 2011
Counting
Counting is a part of combinatorics, an area of mathematics which is concerned with the arrangement of objects of a set into patterns that satisfy certain constraints. We will mainly be interes
Mathematical Foundations of Computer Science Lecture Outline
January 08, 2011
Permutations of Selected Elements.
We looked at permutations of n elements out of the available n elements. Now we will consider permutations of r elements out of the available
Mathematical Foundations of Computer Science Lecture Outline
January 08, 2011
Permutations of Selected Elements.
We looked at permutations of n elements out of the available n elements. Now we will consider permutations of r elements out of the available
Advanced Algorithms Lecture Outline
January 10, 2011
Example.
Prove that n n n n + . . . + (1)n 0 1 2 n =0
Solution. One way to solve this problem is by substituting x = 1 in the previous example. When x = 1 the above equation becomes
n
0n = 0 =
k =0
n (1
Advanced Algorithms Lecture Outline
January 10, 2011
Example.
Prove that n n n n + . . . + (1)n 0 1 2 n =0
Solution. One way to solve this problem is by substituting x = 1 in the previous example. When x = 1 the above equation becomes
n
0n = 0 =
k =0
n (1
Proof by Contradiction
Math 235 Fall 2000
Proof by contradiction is perhaps the strangest method of proof, since you start by assuming that what you want to prove is false, and then show that something ridiculous happens thus your original assumption must
UIUC Putnam Training Sessions
Fall 2010
Putnam Training Session 6: Number Theory
Primes and Composite Numbers: An integer n 2 is called prime if its only positive divisors are 1 and n; and is called composite otherwise. Equivalently, an integer n 2 is pr
V. Adamchik
21-127: Concepts of Mathematics
Mathematical Induction
Victor Adamchik Fall of 2005
Lecture 1 (out of three)
Plan
1. The Principle of Mathematical Induction 2. Induction Examples
The Principle of Mathematical Induction
Suppose we have some sta
AwesomeMath 2007
Track 4 Modulo Arithmetic
Week 2
Lecture 6 : Divisibility and the Euclidean Algorithm
Yufei Zhao July 24, 2007 1. If a and b are relatively prime integers, show that ab and a + b are also relatively prime. 2. (a) If 2n + 1 is prime for so
Veermata Jijabai Technological Institute
VEERMATA JIJABAI TECHNOLOGICAL INSTITUTE
[ Autonomous Institute affiliated to University of Mumbai ]
SYLLABUS
FOR
S.Y. B. TECH.
(Computer Engineering)
VEERMATA JIJABAI TECHNOLOGICAL INSTITUTE, [V.J.T.I.] MATUNGA, M
Solution Week 80 (3/22/04)
Nine divisible by 9 First, consider the following simpler problem: Problem: Given any ve integers, show that there is at least one subset of three integers whose sum is divisible by 3. Solution: Let us try to nd a set of ve inte