Course Structure

Lectures = 2 [HEC Recommended 3]        Labs = 0        Credit hours = 3

Prerequisite

1. Introduction to Computer Science        2. Algebra for Calculus        3. Trigonometry

Course Objectives

Cultivate clear thinking and creative problem solving. Thoroughly train in the construction and understanding of mathematical proofs. Exercise common mathematical arguments and proof strategies. Cultivate a sense of familiarity and ease in working with mathematical notation and common concepts in discrete mathematics.
Teach the basic results in number theory, logic, combinatorics, and graph theory. Thoroughly prepare for the mathematical aspects of other computer science courses. Specifically, it introduces the foundations of discrete mathematics as they apply to computer science, focusing on providing a solid theoretical foundation for further work. Furthermore, this course aims to develop understanding and appreciation of the finite nature inherent in most computer science problems and structures through study of combinatorial reasoning, abstract algebra, iterative procedures, predicate calculus, tree and graph structures. In this course more emphasis shall be given to statistical and probabilistic formulation with respect to computing aspects.

Course Outline

Introduction to logic and proofs: Direct proofs, Proof by contradiction, Sets, combinatorics, Sequences, Formal logic, prepositional and predicate calculus, method of proofs, mathematical induction and recursion, loop invariants, relations and functions, pigeonhole principle, trees and graphs, elementary number theory, optimization and matching; Fundamental Structures: Functions, relations (more specifically recursion), pigeonhole principle, cardinality and countability, probabilistic methods.

Class Time

Tuesdays 8:30 AM - 10:00 AM and Wednesdays 10:00 AM - 11:30 AM

Texts

Our Primary Source

Susanna S. Epp, Discrete Mathematics with Applications, PWS Publishing Company, Boston, MA, 1995.

Kenneth A. Ross and Charles R. B. Wright, Discrete Mathematics, Prentice Hall, New Jersey, 2003, (5th Edition).

Our Secondary Source

Seymour Lipschutz and Marc Lipson, Schaum's Outline of Theory and Problems of Discrete Mathematics, McGraw-Hill, 1997.

HEC Recommended Text Books/Reference Books:

Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th Edition, McGraw Hill, 2006.

Richard Johnsonbaugh, Discrete Mathematics, 7th Edition, Prentice Hall, 2008.

Kolman, Busby and Ross, Discrete Mathematical Structures, 4th Edition, Prentice Hall, 2000.

Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, Addison-Wesley, 1985.

Ethics

The Honor Code will be strictly enforced in the classroom. It is a violation to represent joint work as your own or to let others use your work; always acknowledge any assistance you received in preparing work that bears your name. You are expected to work independently unless explicitly permitted to collaborate on a particular assignment. It is not a violation to discuss approaches to problems with others; however, it is a violation to use wording or expressions in your assignments that have been written by others without acknowledging the source.

Tentative Schedule

Instructions/Lectures

Exams

Points Distribution

Grades

You can do it if you try!

If you wish to succeed in this course
If you wish to do better
If you wish to fail in this course