Illinois Institute of Technology
Department of Computer Science
Lectures 1011: February 1823, 2015
CS 330 Discrete Structures
Spring Semester, 2015
I think youre begging the question, said Haydock, and I can see looming ahead one of
those terrible exercis
Illinois Institute of Technology
Department of Computer Science
Homework Assignment 3
CS 330 Discrete Structures
Spring Semester, 2015
Due: Friday, February 27, 2015
1. The Mayan Tzolkin calendar combines a cycle of twenty day names with a second cycle of
HW2 Solution, CS330 Discrete Structures, Spring 2015
Instructor: Professor Edward M. Reingold
TA: Taeho Jung
January 28, 2015
1
Page.398 #70
For each variable, we have 2 possible cases: T, F, therefore we have to have 2n lines in one truth table.
Then, fo
Illinois Institute of Technology
Department of Computer Science
Lecture 9: February 16, 2015
CS 330 Discrete Structures
Spring Semester, 2015
Polynomial evaluation: how complexity depends on the method
As part of the development of a polynomial approximat
HW1 Solution, CS330 Discrete Structures, Spring 2015
Instructor: Professor Edward M. Reingold
TA: Taeho Jung
January 25, 2015
1
1.1
Page.15 #32
(b)
p p
p
T
F
1.2
p
F
T
p p
F
F
(d)
(p q) (p q)
p
T
T
F
F
2
q
T
F
T
F
pq
T
F
F
F
pq
T
T
T
F
(p q) (p q)
T
T
T
T
Illinois Institute of Technology
Department of Computer Science
First Examination
CS 330 Discrete Mathematics
Spring, 2015
11:25am12:40pm, Wednesday, February 11, 2015
113 Stuart Building
Print your name and student ID, neatly in the space provided below;
Illinois Institute of Technology
Department of Computer Science
Solutions to First Examination
CS 330 Discrete Structures
Spring Semester, 2015
Exam Statistics
47 students took the exam. The range of scores was 1986, with a mean of 54.87, a median of 56,
Illinois Institute of Technology
Department of Computer Science
Lectures 78: February 49, 2015
CS 330 Discrete Structures
Spring Semester, 2015
Another combinatorial identity
Let us examine the identity
n k
n nr
=
(1)
k
r
r
kr
An algebraic proof is simple
Illinois Institute of Technology
Department of Computer Science
Lecture 1: January 12, 2015
CS 330 Discrete Structures
Spring Semester, 2015
1
Why Study Mathematics and Theoretical Computer Science?
This question is best answered by an example. Consider y
Illinois Institute of Technology
Department of Computer Science
Homework Assignment 2
CS 330 Discrete Structures
Spring Semester, 2015
Due: Friday, February 6, 2015
1. Page 398, problem 70
2. Page 414, problem 28
3. Page 421, problem 20; also, explain the
Illinois Institute of Technology
Department of Computer Science
Homework Assignment 1
CS 330 Discrete Structures
Spring Semester, 2015
Due: Friday, January 23
1. Page 15, problems 32 (b) and (d)
2. Page 155, problem 74 (c)
3. Given an input sequence v1 ,
Illinois Institute of Technology
Department of Computer Science
Lecture 5: January 28, 2015
CS 330 Discrete Structures
Spring Semester, 2015
1
How big is n!?
In the preceding material we have seen that n! occurs in many contexts when counting arrangements
Illinois Institute of Technology
Department of Computer Science
Solutions to First Examination
CS 330 Discrete Structures
Fall Semester, 2013
Fifty three students took the exam; the statistics were:
Minimum
13
Maximum
88
Median
43
Average
45.85
Std Dev
17
Illinois Institute of Technology
Department of Computer Science
First Examination
CS 330 Discrete Mathematics
Fall, 2013
11:25am12:40pm, Wednesday, September 18, 2013
IT 6C7-1 (sixth oor of IIT Tower, 35th & State)
Print your name and student ID, neatly i
Illinois Institute of Technology
Department of Computer Science
Lecture 2: January 14, 2015
CS 330 Discrete Structures
Spring Semester, 2015
1
Proof by contradiction
We will now look at an important but easily misunderstood proof technique. The essence of
Illinois Institute of Technology
Department of Computer Science
Lecture 3: January 21, 2015
CS 330 Discrete Structures
Spring Semester, 2015
Three Applications of Induction
Crossing the desert
The same idea as in the book-stacking example leads to the fol
Illinois Institute of Technology
Department of Computer Science
Lecture 6: February 2, 2015
CS 330 Discrete Structures
Spring Semester, 2015
1
Combinations
We have examined the question of how many ways there are to arrange (permute) n dierent items. Supp
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