About Myself
Discrete Mathematics
Recitation Course 1
2011.03.10
AN-CHE CHENG
1-1 Ex.10
Let p, q, an r be the propositions
P: You get an A on the final exam.
q: You do every exercise in this book.
r: You get A in this class.
d) You get an A on the fi

Department of Electronics Engineering
National Chiao Tung University
Discrete Mathematics, Spring 2011
March 10, 2011
Iris Hui-Ru Jiang
Name: _ ID: _
Sample Solutions to Quiz #1 (March 10, 2011)
Instructions: This is a closed book test. Please write down

Department of Electronics Engineering
National Chiao Tung University
Discrete Mathematics, Spring 2011
March 15, 2011
Iris Hui-Ru Jiang
Name: _ ID: _
Quiz #2 (March 24, 2011)
Instructions: This is a closed book test. Please write down your solution on thi

Department of Electronics Engineering
National Chiao Tung University
Discrete Mathematics, Spring 2011
April 11, 2011
Iris Hui-Ru Jiang
Name: _ ID: _
Sample Solutions to Quiz #3 (April 14, 2011)
Instructions: This is a closed book test. Please write down

2011/5/7
The Well-Ordering Property
IRIS H.-R. JIANG
19
Well-ordering: a strict total order
Let S be a set. We say S is well-ordered if there is a relation <
set. We say
well
if there is relation
defined over S such that
For any a, b S, either a=b, a < b

Department of Electronics Engineering
National Chiao Tung University
Discrete Mathematics, Spring 2011
April 29, 2011
Iris Hui-Ru Jiang
Name: _ ID: _
Quiz #5 (May 5, 2011)
Instructions: This is a closed book test. Please write down your solution on this s

EDA Courses in NCTUEE
IRIS H.-R. JIANG
2
Undergraduate
Graduate
Foundation
Data structures
Discrete mathematics
Algorithms
Foundation
Advanced algorithms
Advanced
Introduction to EDA
Advanced
Special topics in CAD
logic synthesis &
verification
Ph

Outline
IRIS H.-R. JIANG
2
CHAPTER 1
THE FOUNDATIONS:
LOGIC AND PROOFS
Iris Hui-Ru Jiang
Spring 2011
Logic and proof
Propositional Logic
A proposition is a declarative sentence that is either true (T) or
false (F), but not both.
E.g.,
Propositions
Not p

Outline
IRIS H.-R. JIANG
2
Content
Sets
Set Operations
Functions
Sequences and Summations
Reading
Chapter 2
CHAPTER 2
BASIC STRUCTURES:
SETS AND FUNCTIONS
Iris Hui-Ru Jiang
Spring 2011
Sets and functions
Most of the following slides are by courtesy o

Outline
IRIS H.-R. JIANG
2
CHAPTER 3
THE FUNDAMENTALS:
ALGORITHMS, THE INTEGERS
AND MATRICES
Iris Hui-Ru Jiang
Spring 2011
Algorithms and integers
Algorithms
An algorithm is a finite set of precise instructions for
performing a computation or for solving

CHAPTER 5
COUNTING
Outline
IRIS H.-R. JIANG
2
Content
The basics of counting
The pigeonhole principle
Reading
Chapter 5
Counting
Most of the following slides are by courtesy of Prof.
J.-D. Huang and Prof. M.P. Frank
Combinatorics
IRIS H.-R. JIANG
3
Com

CHAPTER 3
THE FUNDAMENTALS:
ALGORITHMS, THE INTEGERS
AND MATRICES
Outline
IRIS H.-R. JIANG
2
Content
Algorithms
The Growth of Functions
Complexity of Algorithms
The Integers and Division
Primes and Greatest Common Divisors
Integers and Algorithms
A

CHAPTER 2
BASIC STRUCTURES:
SETS AND FUNCTIONS
Outline
IRIS H.-R. JIANG
2
Content
Sets
Set Operations
Functions
Sequences and Summations
Reading
Chapter 2
Sets and functions
Most of the following slides are by courtesy of Prof.
J.-D. Huang, Prof. H.-

Department of Electronics Engineering
National Chiao Tung University
Discrete Mathematics, Spring 2011
June 15, 2011
Iris Hui-Ru Jiang
Name: _ ID: _
Quiz #6 (June 16, 2011)
Instructions: This is a closed book test. Please write down your solution on this

Department of Electronics Engineering
National Chiao Tung University
Discrete Mathematics, Spring 2011
April 29, 2011
Iris Hui-Ru Jiang
Name: _ ID: _
Quiz #5 (May 5, 2011)
Instructions: This is a closed book test. Please write down your solution on this s

Outline
IRIS H.-R. JIANG
2
CHAPTER 9
GRAPHS
Iris Hui-Ru Jiang
Spring 2011
Graphs
Graphs
Define a graph G = (V, E) where V is a nonempty set of vertices
(or nodes) and E a set of edges. Each edge has one or two
vertices associated with it, called its endpo

Proof Methods Review
Prove pq
Discrete Mathematics
Recitation Course 2
2011.03.17
AN-CHE CHENG
Direct Proof
1. The first step: Assume p is true
2. rules of inference
3. The final step: q must also be true
Proof by Contraposition
Prove -q -p
Proof

2-3 Ex.6
Find the domain and range of these functions
b) the function that assigns to each positive integer its
largest decimal digit
c) the function that assigns to a bit string the number if
ones minus the number of zeros in the string
e) the functi

Discrete Mathematics
Recitation Course 8
2011.5.12
AN-CHE CHENG
5-2 Ex.16
How many numbers must be selected from
the set cfw_1, 3, 5, 7, 9, 11, 13, 15 to guarantee
that at least one pair of these numbers add up
to 16?
4 groups: cfw_1, 15, cfw_3, 13, cfw

Discrete Mathematics
Recitation Course 12
2011.6.16
AN-CHE CHENG
9-1 Ex.12
9-2 Ex.20
9-2 Ex.26
9-3 Ex.34-44
Determine whether the given pair of graphs is
isomorphic
38)
40)
9-4 Ex.12
Determine whether each of these graphs is
strongly connected and if

About Myself
Discrete Mathematics
Recitation Course 4
2011.03.31
AN-CHE CHENG
Name : Jason
Chinese Name :
e-mail:[email protected]
Lab: ED413
Ext:54226
1-2 Ex.61
SAT Application
Explain how an algorithm for determining
whether a compound propositi

Department of Electronics Engineering
National Chiao Tung University
Discrete Mathematics, Spring 2011
March 10, 2011
Iris Hui-Ru Jiang
Name: _ ID: _
Quiz #1 (March 11, 2011)
Instructions: This is a closed book test. Please write down your solution on thi