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 ICS 253: Discrete Structures I

Course Information

Class/Laboratory Schedule: 

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

Designation:   Required Course

Course Level:   Undergraduate

Prerequisites

Prerequisite(s) by Topic: 

  • Introduction to Computing.
  • Algorithms and problem solving

Prerequisite Courses: 


Catalog Description:
 
Propositional Logic, Propositional Equivalence, Predicates and Quantifiers, Nested Quantifiers, Rules of Inference, Introduction to Proofs; Sets, Set Operations, Functions, Sequences and Summations; Mathematical Induction, Strong Induction, Recursive Definitions and Structural Induction; The Basics of Counting, The Pigeonhole Principle, Permutations and Combinations, Binomial Coefficients, Generalized Permutations and Combinations; Discrete Probability, Probability Theory; Recurrence Relations, Solving Linear Recurrence Relations, Generating Functions, Inclusion-Exclusion; Graphs and graph Models, Graph Terminology and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Planar Graphs, Graph Coloring; Introduction to Trees, Applications of Trees, Spanning Trees.

Textbook(s): 

  • Rosen, Kenneth H. Discrete Mathematics and Its Applications, 6th Edition. New Your, McGraw Hill, 2007.
  • Course Outcomes: 
  • Formulate and derive propositional/predicate logic expressions, and apply proving methods.
  • Apply counting techniques to solve combinatorial problems.
  • Comprehend graphs and trees and their mathematical properties.

Topics Covered: 

  • Functions, relations, and sets
  • Basic logic
  • Proof techniques
  • Basics of counting
  • Graphs and Trees​