| Instructor - Robert Hochberg Office- STC C-121 Phone- 328-9685 Email- hochberg@cs.ecu.edu |
Text - Essential Discrete Mathematics for
Computer Science by Feil and Krone |
Office Hours Tuesday and Thursday 7-8am and 11am - 12:30pm And by appointment, of course |
| Tuesday December 8 |
Today's
Topics: Finish RSA example, and Introduction to Counting |
| Thursday December 3 |
Review of Exam 2 |
| Tuesday December 1 |
Exam
2 Sample Questions Covers chapters 3, 4 and 5, excluding the parts of chapter 5 concerning Euler's Theorem, Fast exponentiation and RSA. Also we did not do abstract Boolean algebras in Chapter 3, nor the Peano axioms in Chapter 4. |
| Thursday November 26 |
Thanksgiving No Class |
| Tuesday November 24 |
Topics
Covered Review for the exam |
| Thursday November 19 |
Topics
Covered Introduction to RSA |
| Tuesday Novermber 17 |
Topics
Covered Some theorems about the Euler phi function. |
| Thursday November 12 |
Topics
Covered Fermat's Little Theorem and techniques for computing exponentials mod a prime |
| Tuesday Novermber 10 |
Topics
Covered Introduction to modular arithmetic and some basic theorems |
| Thursday November 5 |
Topics
Covered The Euclidean algorithm and the "as + bt" theorem. This theorem says that if d is the gcd of a and b, then there exist s and t such that as + bt = d |
| Tuesday Novermber 3 |
Topics
Covered Introduction to number theory: prime numbers, divisibility, multiples, and some theorems about same. |
| Thursday October 29 |
Topics
Covered The difference between strong induction and regular induction. Note that what the text teaches is what we call "strong induction" |
| Tuesday October 27 |
Topics
Covered More proofs by induction |
| Thursday October 22 |
Topics
Covered Proof of the equivalence of PLNN and PMI. Lots of examples of proofs by induction. |
| Tuesday October 20 |
Topics
Covered Introduction to mathematical induction |
| Thursday October 15 |
Topics
Covered Commonalities between set systems, propositional logic and circuits. Simplifying boolean circuits, |
| Tuesday October 13 |
Fall Break No Class |
| Thursday October 8 |
Topics
Covered Switching circuits, their simplification, and some theorems of Boolean algebras in general. DNF. Homework #5, due Tuesday, October 20 Chapter 3 #2, 3, 7 (first part only), 9, 10, 13 (do the addition in binary), 14, 15, 45, 46, 48, 50, 51, 53, 54 |
| Tuesday October 6 |
Exam
1 This will cover Chapter 0 (excluding propositional logic and truth tables), Chapter 1 and Chapter 2. The best study guide for this exam are the first four homework assignments. You will be asked to prove things. |
| Thursday October 1 |
Topics
Covered Switching circuits and review for Exam 1 |
| Tuesday September 29 |
Topics
Covered Propositional logic from Chapter 0. Start of Chapter 3. Homework #4, due October 6 Chapter 2 #2, 8, 10, 12, 24, 26, 32. |
| Thursday September 24 |
Topics
Covered Properties of relations: transitive, symmetric, reflexive. Equivalence relations. |
| Tuesday September 22 |
Topics
Covered onto functions, invertible functions, logarithms, floor and ceiling functions, intro to relations |
| Thursday September 17 |
Topics
Covered Review of Sets homework. 1-1 functions, inverses. |
| Tuesday September 15 |
Topics
Covered Q&A on Homework 3, Cartesian products of sets, proof that if A and B are not empty, then AxB = BxA if and only if A = B. Start of Chapter 2 - Functions and Relations. |
| Thursday September 10 |
Topics
Covered Set relations subset and equality. Proofs that A is a subset of B and proofs that A equals B. The power set of a set, the empty set. |
| Thursday September 3 |
Topics
Covered Review of Homework 2 Definitions and examples of set operations: union, intersection, symmetric difference, minus and complement Homework #3 due September 17 Chapter 1 #2, 4, 6, 8, 9, 11, 13, 15, 18, 25, 30, 32, 36, 37, 44 |
| Tuesday September 1 |
Topics Covered Proof that sqrt(2) is irrational. This proof is in Chapter 0 of the text. Began work on Chapter 1, Sets. Homework due September 3 Read Chapter 1 of the text |
| Thursday August 27 |
Topics
Covered Implications, Direct Proofs, Indirect Proofs (Proofs by Contrapositive), Proofs by Contradiction Homework#2, due September 3 Chapter 0, Problems #6, 7, 14, 15, 16 And these problems: A. Prove that if a number's last digit is "8," then it is even B. For what values of n is the sum 1+2+3+ ... + n an even number? Prove your answer. |
| Tuesday August 25 |
Topics Covered Introduction to Proofs, definitions of odd and even, proof that the product of two odd numbers is odd proof that an A by B rectangle it tileable with 1x2 dominos if and only if at least one of A, B is even. Homework#1, due September 1 This worksheet Read Chapter 0 |