Introduction
Margaret M. Fleck 23 August 2010
This lecture does a brief introduction to the course and reviews administrative matters.
1
Introductions
This course is Computer Science 173, Discrete Structures. Introduce myself and any other teaching sta wh
Number Theory: Factors and Primes
9/1/2016
http:/www.brooksdesignps.net/Reginald_Brooks/
Code/Html/pin2.htm
Discrete Structures (CS 173)
Gul Agha
Slides based on Derek Hoiem, University of Illinois
1
Goals of this lecture
Understand basic concepts of num
CS 173, Spring 17
Examlet 7, Part B
1
Name:
NetID:
Lecture:
Discussion:
Thursday
Friday
10
11
12
A
1
B
2
3
4
5
6
1. (11 points) Lets define two sets as follows:
A = cfw_(x, y) R2 : y = 3x + 7
B = cfw_(2, 1) + (1 )(1, 10) : R
Prove that A = B by proving tw
CS 173, Spring 17
Examlet 7, Part A
1
Name:
NetID:
Lecture:
Discussion:
Thursday
Friday
10
11
12
A
1
2
B
3
4
5
6
Use (strong) induction to prove the following claim:
Claim:
Pn
2
p=1 p2 +2p
=
3
2
1
(n+1)
1
(n+2)
Solution: Proof by induction on n.
Base case
CS 173, Spring 17
Examlet 7, Part A
1
Name:
NetID:
Lecture:
Discussion:
Thursday
Friday
10
11
12
A
1
Use (strong) induction to prove the following claim:
Claim:
Pn
2
p=1 p2 +2p
=
3
2
1
(n+1)
1
(n+2)
Proof by induction on n.
Base case(s):
Inductive Hypothe
CS 173, Spring 17
Examlet 7, Part B
1
Name:
NetID:
Discussion:
Lecture:
Thursday
Friday
10
11
12
A
1
2
B
3
4
5
6
1. (11 points) Lets define two sets as follows:
A = cfw_(x, y) R2 : y = 3x + 7
B = cfw_(2, 1) + (1 )(1, 10) : R
Prove that A = B by proving tw
Appendix B
Acknowledgements and
Supplementary Readings
Most of the basic ideas and examples in this book date back many years and
their original source is almost impossible to trace. Ive consulted so many
books and worked with so many helpful teachers, st
Appendix C
Where did it go?
When teaching the first few chapters of this book, you may be disconcerted to
find some important topics apparently missing or breezed through absurdly
fast. In many cases, whats happening is that the missing topics are covered
Boolean Algebra and Its Rela1on to Gates
An Introduc+on to CS233
1
233 in one slide!
!
The class consists roughly of 4 quarters:
1.
2.
3.
4.
!
You will build a simple computer processor
You will learn how highlevel language code
BuildinganALU(Part2):
1
Todayslecture
Wellfinishthe32bitALUtoday!
32bitALUspecification
Complete1bitALU
Assemblingthemtomake32bitALU
Handlingflags:
zero,negative,overflow
2
3
Building32bitALU
control
out =
0
undefined
1
undefined
2
A + B
3
A B
4
A AND
Congruence and Sets
Dali  The Persistence of Memory
Discrete Structures (CS 173) Lecture 5
Gul Agha
University of Illinois at UrbanaChampaign
Based on lecture notes by Derek Hoiem
1
Review of Last Class
A composite integer can be factored into smaller
Strategies for Proofs
La Clairvoyance'  Ren Magritte
Discrete Structures (CS 173) Lecture 3
Gul Agha
Slides based on Derek Hoiem, University of Illinois
Logistics
Moodle Activity tonight. Due Wednesday
HW 1 to be released today
Remember your discussio
CS 173: Discrete Structures, Fall 2011
Homework 1
This homework contains 1 problem worth 15 points.
1. [15 points] Summations
(a) (2 points) Rewrite r =1 log(12+4) as a new summation with an index variable
k
k
named n which runs from 3 to r 4. The terms
CS 173: Discrete Structures, Fall 2011
Homework 1 Solutions
This homework contains 1 problem worth 15 points.
1. [15 points] Summations
(a) (2 points) Rewrite r =1 log(12+4) as a new summation with an index variable
k
k
named n which runs from 3 to r 4.
CS 173: Discrete Structures, Fall 2011
Homework 2
This homework contains 5 problems worth a total of 47 points. It is due on Friday, September 9th at 4pm. As usual, put your homework into the appropriate dropbox in the basement of Siebel.
1. [9 points] Tr
CS 173: Discrete Structures, Fall 2011
Homework 3
This homework contains 4 problems worth a total of 40 points. It is due on Friday, September
16th at 4pm.
When writing your proofs, be sure to use the denitions of key concepts (e.g. divisible) as
presente
CS 173: Discrete Structures, Fall 2011
Homework 3  Solution
This homework contains 4 problems worth a total of 40 points. It is due on Friday, September
16th at 4pm.
When writing your proofs, be sure to use the denitions of key concepts (e.g. divisible)
CS 173: Discrete Structures, Fall 2011
Homework 2 Solutions
This homework contains 5 problems worth a total of 47 points.
1. [9 points] Truth tables
(a) (3 points) Give the truth table corresponding to the following expression:
(p q ) r
Include a column f
CS173 Lecture 2: Propositional Logic
Gul Agha
Presented by Karl Palmskog
August 25, 2016
CS173 Announcements
If you arent registered for the class:
Please write your name on the list at front!
CS173 Announcements
Lecture B website now up:
https:/courses.e
Functions
Discrete Structures (CS 173)
Gul Agha
Magritte
Slides based on Derek Hoiem, University of Illinois
1
REMARKS ON PREVIOUS LECTURES
2
Example Inverse
Definition: is the inverse of in ( ) iff
1 ( )
number
0
1
2
3
4
5
inverse

1



5
 inverse
Relations and Functions
Discrete Structures (CS 173)
Gul Agha
Magritte
Slides based on Derek Hoiem, University of Illinois
1
Remarks on previous lectures
Definition of divisibility:
a  b if b = a * n for some integer n
provided a 0
2
Tautology
A tautol
State: From Latches to Flip Flops
1
Todays lecture
!
!
Storing State
! SR Latch
Synchronous Design
! Clocks
! D Flip Flops
3
Propoga;on Delay
!
!
Real gates dont switch instantaneously
! There is a latency between when the input c