# CIS 2210 Discrete Structures

### Basic Information

• Instructor: Prof. Neng-Fa Zhou
• Class hours: 12:50-02:05PM Monday and Wednesday (room New Ingersoll 238)
• Office hours: 5:00-6:00 Monday (room Ingersoll 1161)
• Textbook: Discrete Mathematics, 5th ed., by - K. Ross & C. Wright, Prentice-Hall.
• Homework
• There will be one homework assignment each week. Unless notified otherwise, each homework is due in one week after it is assigned. Please email your homework to cisc2210 (AT) picat-lang.org. Please write your name, student ID, and the number of the assignment in the Subject of the email. Sample answers to the homework questions will be given and selected questions will be reviewed in class. There will be a one-point deduction for each missing homework or late submitted homework. The total deduction will not exceed 10 points.
• Exams
• There will be two tests and one final exam, all closed-book. Each test acounts for 30% and the final exam 40%.
• How to do well in this class?
• Read the message "To the Student Especially" in the textbook. In short, to do well you need to read ahead, attend classes and participate in class discussions, review notes after class, and study for tests.
• Fun Math Problems

### Course Outline and Homework Assignments

1. Weeks 1 & 2: Sets, Sequences, and Functions (Set Operations; Functions; Inverses of Functions; Sequences)
• H.W. - Chapter 1:
• 1.3 - 1, 3, 5, 8, 9, 11, 13 (Special Sets)
• 1.4 - 1, 3, 5, 7, 8, 11, 13 (Set Operations)
• 1.5 - 1, 3, 5, 7, 8, 13 (Functions)
• 1.6 - 1, 3, 5, 7, 8, 9 (Sequences)
• 1.7 - 1, 3, 5, 7, 8, 11 (Properties of Functions)
2. Weeks 3 & 4: Elementary Logic (Propositional Calculus; Methods of Proof; Analysis of Arguments)
• H.W. - Chapter 2:
• 2.1 - 1, 8, 9, 15 (Introduction)
• 2.2 - 1, 3, 5, 7, 8, 9, 19 (Propositional Calculus)
• 2.3 - 5, 7, 8, 9, 13 ((Proofs)
• 2.4 - 1, 3 8 (Methods of Proofs)
• 2.5 - 1, 3, 7, 8, 9, 17 (Logic in Proofs)
• 2.6 - 1, 5, 8, 9a,c, 13 (Analysis of Arguments)
3. Test #1: ( Sample )
4. Weeks 5 & 6: Relations (Relations; Digraphs and Graphs; Matrices; Equivalence Relations and Partitions)
• H.W. - Chapter 3:
• 3.1 - 1, 3, 8, 9, 11, 13 (Relations)
• 3.2 - 1, 3, 8, 9, 10, 11, 15 (Digraohs and Graphs)
• 3.3 - 3, 5, 8, 11, 15 (Matrices)
• 3.4 - 1, 5, 7, 8, 13, 15 (Equivalence Relations and Partitions)
• 3.5 - 1, 3, 5, 8, 15 (The Division Algorithm and integers Mod p)
5. Weeks 7 & 8: Induction and Recursion (Loop Invariants; Mathematical Induction; Recursive Definitions; Recurrence Relations)
• H.W. - Chapter 4:
• 4.1 - 8, 9, 11, 17, 19, 21 (Loop Invariants)
• 4.2 - 1, 5, 7, 8, 13, 17, 19 (Mathematical Induction)
• 4.4 - 1, 3, 7, 8, 9, 17 (Recursive Definitions)
• 4.5 - 1, 3, 7, 8, 11, 15 (Recurrence Relations)
• 4.6 - 1, 7, 8, 11, 13 (More Induction)
6. Test #2:( Sample )
7. Weeks 9 & 10: Counting (Basic Counting Techniques; Elementary Probability; Inclusion-Exclusion Principle; Binomial Methods; Counting and Partitions; Independence; Bayes Formula)
• H.W. - Chapter 5
• 5.1 - 1, 3, 7, 8, 9, 11, 15 (Basic Counting Techniques)
• 5.2 - 1, 3, 5, 7, 8, 9, 15, 19 (Elementary Probability)
• 5.3 - 1, 3, 7, 8, 9, 15, 17 (Inclusion-Exclusion and Binomial Methods)
• 5.4 - 1, 3, 5, 8, 9, 11 (Counting and Partitions)
• 9.1 - 1, 3, 7, 8, 9, 13, 17, 19 (Independence in Probability and Bayes Formula)
8. Weeks 11 & 12: Boolean Algebra (Boolean Algebras; Boolean Expressions; Logic Networks; Karnaugh Maps: Isomorphism)
• H.W. - Chapter 10:
• 10.1 - 5, 7, 8 (Boolean Algebra)
• 10.2 - 1, 3, 7, 8 (Boolean Expressions)
• 10.3 - 1, 3, 8 (Logic Networks)
• 10.4 - 1, 5, 7, 8, 9 (Karnaugh Maps)
• 10.5 - 1, 3, 5, 8 (Isomorphism)
9. Weeks 13 & 14: Introduction to Graphs and Trees (Graphs; Edge Traversal Problems; Trees; Rooted Trees; Vertex Traversal Problems; Minimum Spanning Trees)
10. Final Exam 5/22/2017 1:00 PM - 3:00 PM 238 IA/NE, ( Sample )