East Carolina University
Department of Computer Science

CSCI 2400
Discrete Structures I
Standard Syllabus

Catalog entry

P: MATH 1065. Application of basic concepts in discrete mathematics to solving problems in the computing discipline.

Course summary

Discrete Structures is arguably the most important course in the undergraduate computer science curriculum. It lays the foundation for several courses that you might probably take in future. The course objective is twofold. The first objective is to learn several basic topics in discrete mathematics and applications of them. The second and more important objective is to develop mathematical thinking. More specifically, you will learn to appreciate the need for proofs and mathematical rigor, write proofs formally and develop problem solving skills and algorithmic thinking.

Course topics

• Propositional Logic
• Predicate Logic
• Rules of Inference, Valid and Invalid Arguments.
• Proof Techniques
• Naive Set Theory
• Functions
• Elementary Number Theory
• Relations

Student learning outcomes

• Translate English Sentences into Propositional Logic and vice versa.
• Translate English Sentences into Predicate Logic and vice versa.
• Determine whether two given logical expressions are equivalent or not.
• Determine whether a given logical argument is valid or not.
• Determine whether a given mathematical proof is correct or not.
• Construct simple mathematical proofs using standard techniques.
• Model word problems using set theory and solve them.
• Identify whether a given mapping is a function and if so, is it one to one and onto.
• Compose functions and determine inverse functions when feasible.
• Perform Modular Arithmetic.
• Compute gcd and lcm.
• Solve Linear Congruence.
• Determine properties of a given relation
• Construct partitions corresponding to an equivalence relation and vice versa.
• Construct Hasse diagram corresponding to a partial order and vice versa.

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 Chapter 1 thoroughly and then a selection of topics from the chapters 2, 4, and 9. Please note that this is the first of a two course sequence on Discrete Structures. There is a good chance that the same book might (depends on the instructor) be used for the second course also and some of the remaining chapters will be covered in that course. Hence, you might want to retain the book even after you successfully complete this course.

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