Discrete Mathematics

 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

General Notes
• Each chapter should be read in advance of the classes on that chapter.
• Remember that any time you read a technical book, you should have pencil and paper nearby
• It is important to do the transcript as you go.  Please don't do it all at once at the end.
• Link to the GraphCalc program

Homework Assignments

 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