InnerPages - ICS 254: Discrete Structures II

Course Information

Class/Laboratory Schedule:

Class/Laboratory Schedule: Three 50 minutes lectures per week. No lab (3-0-3)

Designation:

Required Course

Course Level:

Undergraduate

Prerequisites

Prerequisite(s) by Topic:

Functions, Relations and Sets
Proof Techniques
Counting Techniques

Prerequisite Courses:

ICS 253: Discrete Structures I

Catalog Description:

Number Theory: Modular Arithmetic, Integer Representation, Fermat’s Little Theorem. Chinese Remainder Theorem, RSA., Applications from Number Theory; Recursive Definitions; Algorithm Correctness; Relations: Closures and Equivalence Relations, Partial Orderings and Lattices, Hasse Diagrams; Automata Theory: Finite State Machines, Regular Expressions, DFA, NFA and their equivalence, Grammars and Chomsky Hierarchy; Abstract Algebra: Groups, Homomorphism and Lagrange's Theorem, Applications.

Textbook(s):

K. H. Rosen, Discrete Mathematics and Its Applications, 6th Ed., McGraw-Hill, 2007.

Reference(s) and Other Material:

N. L. Biggs, Discrete Mathematics (revised edition), Clarendon Press, 1989.
Crisler, N., Fisher, P. and Froelich, Discrete Mathematics through Applications, 2nd Ed., W. H. Freeman Co., 2000.
R. P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, 4th Ed., Addison Wesley, 1998.

Course Outcomes:

Explain basic concepts in number theory and apply them in problem-solving.
Understand relations and their graphical representation
Understand foundational knowledge of group theory and automata theory

Topics Covered:

Number Theory
Induction & Recursion
Relations
Group Theory
Languages, Grammars and Finite State Machines

ICS

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ICS 254: Discrete Structures II

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