Course Outline MTH 256 Discrete Mathematics General Education ...

Course OutlineMTH 256 Discrete MathematicsMay 2011Department: MathematicsCredit Hours: 3Prerequisite: MTH 156General Education: #9 Quantitative CompetenceLearning Outcomes: II D________________________________________________________________________I. Course Description: Introduces the basic topics and techniques of discrete mathematics, includinglogic, set theory, counting techniques, recurrence relations, and topics from graph theory.II. Purpose of the Course: This course is designed to introduce students to the techniques,algorithms, and reasoning processes involved in the study of discrete mathematical structures.Students will be introduced to set theory, inductive reasoning, elementary and advanced countingtechniques, equivalence relations, recurrence relations, graphs, and trees. Through their study ofthese topics students will develop a greater understanding of the breadth of mathematics and willacquire a familiarity with concepts, structures and algorithms that are essential to the field ofcomputer science and applied mathematics.III. Learning Outcomes and Objectives:II Intellectual and Practical SkillsD Students can use mathematical or formal reasoning to answer questions or to achievedesired goals.IV. Course Objectives:1. Students should be able to distinguish between the notion of discrete and continuousmathematical structures.2. Students should be able to demonstrate an understanding of the basic concepts of set theory.3. Students should be able to apply fundamental counting algorithms to solve applied problems,particularly those found in the area of computer science.4. Students should be able to prove mathematical statements by means of inductive reasoning.5.Students should be able to demonstrate an understanding of the principle of recursion and apply it tothe study of sequences and sets.6. Students should be able to demonstrate an understanding of the basic concept of an algorithmand apply appropriate algorithms to solve problems in combinatorial mathematics.7. Students should be able to identify the basic properties of graphs and trees and use theseconcepts to model simple applications.8. Students should be able to communicate mathematical ideas in both written and oral form fora variety of audiences.9. Students should be able to understand and critically analyze the mathematical writings ofothers

V. Topical Outline:A. Introduction to Logic1. Basic definitions and notation2. Appropriate use of quantifiers3. Tautologies and contradictionsB. Sets1. Notation, operations and relations2. Finite and infinite sets3. Principle of Inclusion & ExclusionC. Relations and Functions1. Basic definitions and properties2. Binary relations3. Equivalence relations and partitionsD. Mathematical Induction1. The Well Ordering Principle2. Proof by mathematical inductionE. Recursion1. Recursively defined sequences2. Linear recurrence relations with constant coefficientsF. Algorithms1. Basic concept of algorithms2. Analysis of algorithms3. Euclidean algorithm4. Searching and sorting algorithmsG. Counting Techniques1. Fundamental counting techniques2. Permutations and combinations3. The Pigeonhole Principle4. Binomial coefficients and Pascal’s Triangle5. Introduction to generating functionsH. Graph Theory1. Fundamental concepts of graphs and subgraphs2. Weighted graphs3. Paths and circuits4. Euler and Hamiltonian paths and circuits5. Planar graphs6. Graph coloringI. Trees1. Basic definitions and properties of trees2. Spanning trees3. Weighted trees