Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Discrete Mathematics
CS204
Lecture #7
September 18, 2009
at KAIST
1
What is a function?
The Blackbox Analogy  The mechanism that assigns to each input an output is ignored.  Two blackboxes are equivalent as functions if they produce identical outputs fr
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Discrete Mathematics
CS204
Lecture #5
September 14, 2009
at KAIST
1
Review
Recall that  Proof by examples does not count as a proof unless the examples are exhaustive.  Among methods of direct proofs, there are
Constructing a counterexample for negatio
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Discrete Mathematics
CS204
Lecture #4
September 11, 2009
at KAIST
1
Review
Recall that  A proof is a sequence of purely logical arguments from hypotheses to a conclusion.  A long but nonexhaustive list of veried examples or cases does not count as a pr
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Discrete Mathematics
CS204
Lecture #3
September 9, 2009
at KAIST
1
Some Terminology from the last class
Suppose a conditional proposition
pq
is true. Then  we may use q as a criterion to test the truth value of p, and  we may use also p as a criterion t
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Homework #1
[was just due]
Show all your work in your homework.
Sets and Logic
Chapter 1 (1.4 Arguments and Rules of Inference 1.5 Quantifiers) September 7, 2009
Section 1.1 Exercises (p.12~13)
#50~54 #87~90 #94
Section 1.2 Exercises (p.20~21)
#49~54 #6
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Homework #1
[due: 9/7 11AM]
Show all your work in your homework.
Sets and Logic
Chapter 1 (1.2~1.3 Propositions) September 4, 2009 2009
Section 1.1 Exercises (p.12~13) (p
#50~54 #87~90 #94
Section 1.2 Exercises (p.20~21)
#49~54 #68,69,71,72
Section 1
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Sets
Sets and Logic
Chapter 1 (1.1 Sets) September 2, 2009
A set is a collection of objects, order is not taken into account. Objects = elements, members elements members How to describe it?
By listing all members: A = cfw_1,2,3,4 listing all members: c
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Recurrence Relations
Recurrence Relations
Chapter 7
(7.2 Solving Recurrence Relations)
A recurrence relation for the sequence a0, a1, is an equation that relates equation that relates an to certain of its predecessors certain of its predecessors a0, a1,
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
End Note Questions
Functions, Sequences, & Relations Relations
Chapter 3 (3.4 Equivalence Relations) September 23, 2009 23 2009
Any specific topic for me to review from 1.6~3.2?
Strong form of induction (6 students) Mathematical Induction related (3 stu
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
For the past two weeks
Finished Chapter 1: Sets and Logic Learn Chapter 2: Proof Chapter 2: Proof Started Chapter 3: Functions and Sequences Questions? direct to Prof.Song: [email protected] Homework #1 graded
Average= 84.5 (Max= 100, Min= 51)
Functions, S
Korea Advanced Institute of Science and Technology
Discrete Math
COMPUTER S Cs206

Spring 2008
Discrete Mathematics
CS204
Lecture #6
September 16, 2009
at KAIST
1
Review
Recall that  Mathematical induction, as a method of proof, is based on the following property of the set of positive integers. For n
Z+ ,
S (1) (n S (n) S (n + 1) n S (n)
where S