Discrete Mathematics for Computer Science

Discrete Mathematics PPT

Click on the blue colored links to download the lectures.

Course description

The purpose of this course is to understand and use (abstract) discrete structures that are backbones of computer science. In particular, this class is meant to introduce logic, proofs, sets, relations, functions, counting, and probability, with an emphasis on applications in computer science.

Prerequisites: 2 years of high school algebra.

Syllabus

Textbook:

Kenneth Rosen. Discrete Mathematics and Its Applications, 6th Edition , McGraw Hill Publishing Co., 2007.

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Tentative Syllabus

• Logic: propositional logic, logical equivalence, predicates & quantifiers, and logical reasoning.
• Sets: basics, set operations
• Functions: one-to-one, onto, inverse, composition, graphs
• Integers: greatest common divisor, Euclidean algorithm.
• Sequences and Summations
• Mathematical reasoning: Proof strategies, Mathematical Induction, Recursive definitions, Structural Induction
• Relations: properties, Combining relations, Closures, Equivalence, partial ordering
• Counting: basic rules, Pigeon hall principle, Permutations and combinations, Binomial coefficients and Pascal triangle.
• Probability: Discrete probability. Expected values and variance.

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Lectures

Lectures	Topic(s)		Readings		Assignments
September 1	Administrivia. Propositional logic.		Section 1.1.		.
September 3	Propositional logic		Section 1.1-2.		Homework assignment 1
September 8	Propositional logic:Equivalences. Predicate logic.		Section 1.2-3.