Class/Laboratory Schedule: Three 50 minutes lectures per week. No lab (3-0-3)
Designation: Required Course
Course Level: Undergraduate
Prerequisite(s) by Topic:
- Functions, Relations and Sets
- Proof Techniques
- Counting Techniques
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.
- 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.
- 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
- Group Theory
- Languages, Grammars and Finite State Machines