1. CS 245 Introduction to Discrete Structures Instructor: Dr Eric Anson
Background – CSc 245 v1.1 (McCann) – p. 1

2. CS 245 – Fall 15 Instructor: Dr. Eric Anson eason@email.arizona.edu
GS 823
Office Hours: Mon, Wed, Fri 9:30-10:30
Or by Appointment
SLs:
Nicholas DeJaco
William Forma
Helen Jones
David Porfirio
Dori Steinbach
Alexa Zarbock
Websites:
Background – CSc 245 v1.1 (McCann) – p. 1

3. Who is this guy and where’s Dr McCann?
Dr. Eric Anson
VERY recent addition to Computer Science Faculty
BS Math/Comp Sci – Pepperdine University – 1985
MS Mathematics – University of Arizona – 1993
PhD Comp Sci – University of Arizona – 2000
Worked all throughout industry and government from the Feds to the County and from biotech to Raytheon
Taught 14 math classes while a TA in mathematics

4. Syllabus Highlights Sign Up For Piazza!!!!
Required Text Discrete Mathematics and its Applications (Rosen), 7th ed
Remember the goal ALWAYS is for you to learn the material!

5. ------------------------------------------------------- Total: 100%
Grading
Section Attendance: 5%
Homework + Quizzes 36%
3 Midterms (13% each) 39%
Comprehensive Final 20%
Total: %

6. Final Grades A 90-100% B 80-89% C 70-79% D 60-69% E 0-50%
I might lower the total required for a grade, but I will NEVER raise it.
The Goal is for everyone to get an A

7. Homework I will shoot for 1 homework assignment a week.
Most, if not all, homework should written or printed on paper.
Please write legibly, and include your name and section clearly on the top of the page.
The homework is given purely so you will learn the material, so seek help if you need it to understand, but do your own work.
If there are programming homework I will give more detailed instructions when they are assigned.

8. Cheating - (Summary: Don’t Do It)
Cheating is turning in work that is not your own or providing your work for someone else to turn in.
Your integrity is worth more than a score on an assignment/test or even grade in a course
Eventually it will catch up with you. If you don’t do the homework, you will not do well on the tests. If you don’t know the material from this class you will not make it through the classes that follow.
The department takes cheating VERY seriously and if you get caught the consequences are grim.

9. Classroom Behaivor Don’t Disturb Other Students!
Electronics are OK, but nothing that makes noise.
Attendance of lectures is STRONGLY encouraged, but roll will not be taken.
Attendance of Sections is REQUIRED. Roll will be taken.
Be kind to and respectful of fellow students.

10. What Is Discrete Math? Not to be confused with: discreet adjective
careful and circumspect in one's speech or actions, especially in order to avoid causing offense or to gain an advantage.

11. What Is Discrete Math? Instead: discrete adjective
individually separate and distinct..

12. What Is Discrete Math? Definition: Discrete Mathematics
Discrete Mathematics is the study of collections of distinct objects.
Contrast this with ‘the calculus,’ which was developed by Newton and Leibniz to study objects in motion. As a result:
‘The Calculus’ tends to focus on real values
Discrete Mathematics tends to focus on integer values

13. Sample Discrete Math Topics
Topics that fall under the umbrella of discrete math include:
Functions and Relations
Matrix Operations and Representations
Sets
Sequences and Summations
Discrete Probability
Counting (Permutations/Combinations, Recurrence Relations)
To understand those, you also need:
First-Order Logic
Logical Arguments
Proof Techniques
. . . and a fair amount of pre-calculus mathematics

14. “But Why Do I Have To Take Discrete Math?”
Discrete Structures is an ACM/IEEE core curriculum topic
See:
DM topics underlie much of Computer Science, including:
Logic → Knowledge Representation, Reasoning,
Natural Language Processing, Computer Architecture
Proof Techniques → Algorithm Design, Code Verification
Relations → Database Systems
Functions → Hashing, Programming Languages
Recurrence Relations → Recursive Algorithm Analysis
Probability → Algorithm Design, Simulation

15. Other Reasons You are studying to become computer SCIENTISTS
It’s like taking your brain to the gym
You need to know this for other classes, in particular, csc345
It’s FUN (or can be with the right attitude)

16. Topics You May Need To Review
Mathematical concepts, including, but not limited to:
Fractions
Rational Numbers
Basics of Sets
Associative, Commutative, Distributive, and Transitive Laws
Properties of Inequalities
Summation and Product Notation
Integer Division (Modulo, Divides, and Congruences)
Even and Odd Integers
Logarithms and Exponents
Working with Quadratic Equations
Positional Number Systems
Please read the Math Review appendix (available from the class d2l web page) to review these topics.
How to program with basic data structures in Java
We trust that you can review this on your own!

17. Notations for Sets of Valuesℤ
{. . . , −2, −1, 0, 1, 2, . . .}
{1, 2, 3, . . .}
{0, 1, 2, 3, . . .}
{. . . , −4, −2, 0, 2, 4, . . .}
{. . . , −3, −1, 1, 3, . . .}
All integers
+ +
ℤ , ℕ
All positive integers ∗
ℤ , N0 The non–negative integers
Zeven
ℤodd Q
Even integers
Odd integers a
/ b,
a, b∈Z, b!=0
Rational numbers
Q ℝ
{i |i ∈/ ℚ}
{Q ∪ Q}
Irrational Numbers
The real values
Note: Avoid the term “natural numbers” and the plain ℕ.

18. Remember! Study your notes from section this week, and
All of the math review topics are fair game for quizzes and exams (including the final!).
If you are not confident in your knowledge of them:
Work the sample Math Review exercises from the class web page,
Study your notes from section this week, and
Review the topics on your own!