CS 23022-001 Discrete Structures for Computer Science
Fall 2006
MSB - Room 115
Mondays and Wednesdays 9:15 AM - 10:30 AM
MSB - Room 115
Mondays and Wednesdays 9:15 AM - 10:30 AM
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| Lecture | Date | Comment | Material | Reading Assignment |
| 1 | M-Aug. 28 | Warm-up questions, Ceiling/Floor functions and Syllabus. | Sec. 1.1, Office Hours 1.2 (page 15), To the Student Especially (Part of Preface, page xv). | |
| 2 | W-Aug. 30 | Continue warm-up questions. The ideas and notation of divisors and primes with examples. | Sec. 1.2 | |
| 3 | W-Sept. 06 | Detail study of Divisibility, gcd, lcm, and quotient-remainder theorem with example. Detail studies of functions and properties of functions (into, onto, inverse, etc) with examples. | Sec. 1.2 and; Sec. 1.5 and Sec. 1.7 (pretty standard stuff!); and lecture consists of some proofs. | |
| 4 | M-Sept. 11 | Pretty light lecture | sets, sequences and introduction to formal language/grammar. Pay especial attention to notation P(S) and ∑*. | Sec. 1.3, Sec. 1.4, & Sec. 1.6 |
| 5 | W-Sept. 13 | Pretty interesting lecture | Propositional Logic (Calculus), Introduction to logical terms and symbols, implication, equivalence, talked about "How to start the proof." | Sec. 2.1, Sec. 2.2, Sec. 2.3, & Sec. 2.4 |
| 6 | M-Sept. 18 | Pretty tough lecture | Predicate Logic (Calculus), Introduction to quantifiers, negation of universal and existential quantifiers, work on logic of proofs. | Sec. 2.1 (this time concentrate on quantifiers), Sec. 2.5, and Sec. 2.6. |
| 7 | W-Sept. 20 | Pretty long lecture | Introduce the concept of Relation with example, detail study of Reflexivity, Symmetry, and Transitivity with example. Suggests that pictures may be helpful. Equivalence Relations and Partitions: Gives the whole story on equivalence relations, which we view as another way of thinking about partition. | Sec. 3.1 & Sec. 3.4 |
| 8 | M-Sept. 25 | Anti-reflexivity/Anti-symmetry, very basic definition of graph theory (graphs and digraphs), Reachable and Adjacency relations: Matrices (pretty standard stuff). | Sec. 3.2 & Sec. 3.3 | |
| 9 | W-Sept. 27 | Pretty important lecture | Detail introduction of the principle of mathematical Induction with everyday example (abolish penny) and worked on example (sum of first n integers) in depth concentrating on the fundamental technique of mathematical induction. | Sec. 4.2 |
| 10 | M-Oct. 02 | Pretty tough and important lecture | Loop Invariants and Big-Oh Notation | Sec. 4.1 & Sec. 4.3 |
| 11 | W-Oct. 04 | Revision | Chapter 1 | Chapter 1 |
| 12 | M-Oct. 09 | Revision | Chapter 2 and Homework problems (Chapter 1 and Chapter 2) | Chapter 1 & Chapter 2 |
| 13 | W-Oct. 11 | Midterm I | Chapter 1 and Chapter 2 (Sections 2.1, 2.2 and 2.3) | |
| 14 | M-Oct. 16 | Revision | Worked on two "relation" problems | Sec. 3.1 |
| 15 | W-Oct. 18 | Revision | Chapter 3 |
Lecture Notes
Floor and
Ceiling Functions
Divisibility
Introduction to Set Theory
Fundamentals of
Functions
Sequences
(Definition)
Introduction
to Propositional Logic
Logical
Equivalence
Conditional Statements
Valid and
Invalid Arguments
Valid
Argument Forms
Fallacies
Introduction
to Predicate Logic
Relation on
Sets
Relations and Functions
Inverse
Relation
Reflexivity, Symmetry and Transitivity
Congruence
Relations
Equivalence Class
of an Equivalence Relation
Exams| Midterm I | Chapters 1 and 2 | Wednesday, Oct. 11 |
| Midterm II | Chapters 3 and 4 | Wednesday, Nov. 15 |
| Final |
Chapter 1 |
Thursday, Dec. 14 10:15 - 12:30 p.m. |
Home
Works| Assigned: Sept. 6 | Homework 1 | Due: Sept. 20 | Solution 1 |
| Assigned: Sept. 20 | Homework 2 | Due: Oct. 04 | Solution 2 |
Quizzes| Quiz 1 | Sept. 13 |
| Quiz 2 | Sept. 20 |
| Quiz 3 | Sept. 25 |
| Quiz 4 | Sept. 27 |
| Quiz 5 | Oct. 31 |
| Quiz 6 | Nov. 02 |
Grades
You can do it if you try!
Resources
