East Carolina University
Department of Computer Science

CSCI 2405
Discrete Structures II
Standard Syllabus

Catalog entry

P: CSCI 2400. Continuation of CSCI 2400. Application of advanced concepts in discrete mathematics to solve computational problems.

Course summary

Please note that this is the second of a two course sequence on Discrete Structures and hence should be thought of as a continuation of the first course. In this course, you will learn more advanced proof techniques such as mathematical induction and more advanced discrete structures such a graphs and trees. You will also learn some aspects of combinatorics in this course.

Course topics

• Mathematical Induction Basic Mathematical Induction, Strong Induction, Structural Induction.
• Elementary Combinatorics Basic Principles of Counting, Permutations and Combinations, Binomial Coefficients and Identities, Generalized Permutations and Combinations, Pigeonhole Principle, Inclusion-Exclusion principles.
• Advanced Combinatorics Recurrence Relations, Different Techniques for solving them, Generating Functions.
• Essential Graph Theory Different Types of Graphs, Representing Graphs, Graph Isomorphism, Connectivity, Euler and Hamiltonian Paths, Planarity, Graph Coloring, Shortest Paths.
• Trees Different Types of Trees, Properties of Trees, Applications of Trees such as Decision Trees and Game Trees, Different Traversals of Trees, Depth First and Breadth First Searches, Spanning Trees and Minimum Spanning Trees.

Student learning outcomes

• Prove theorems using the technique of Mathematical Induction (basic, strong and structural).
• Given a description of arrangements (ordered or unordered) of objects, determine the number of such arrangements without explicitly enumerating them.
• Use Recurrence Relations to Model Counting Problems.
• Solve Linear Homogeneous and Non-Homogenous Recurrence Relations.
• Use Generating Functions to Solve Counting Problems, Solve Recurrence Relations and to Prove Identities.
• Prove Simple Properties of Trees and graphs.
• Traverse trees in different ways.
• Use Graphs and Trees to Model Real Life Problems.

Textbook

Discrete Mathematics and Its Applications by Kenneth H. Rosen, McGraw-Hill Inc., Seventh Edition, 2012.

This is an excellent text book written in a lucid style and at the same time without loss of mathematical rigor. We would be covering a selection of topics from chapters 5, 6, 8, 10 and 11.

Other required material

All students will be required to have an account in McGraw Hill's Connect System. This system will be used for web based assignments

Grading

Your grade in this course will be based on your performance in assignments and examinations. The examinations will count for two third of your grade and the assignments will count for one third of your grade.

Assignments must be taken seriously and must be submitted in time. There will not be any programming assignments in this course. Most of the assignments will be done using the web based ``McGraw-Hill's Connect System'' (that will be auto-graded) and the remaining assignments will be traditional paper based assignments (homework) that are graded manually.

There will be two regular examinations during the semester and a final comprehensive examination at the end of the semester.

Grade meanings