DISCRETE STRUCTURE

Discrete Structure

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic– do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term "discrete mathematics."

Course Objectives

This course focuses on the mathematics needed for success in computer science. As such, the course will address a variety of topics, including propositional and predicate logic, proof techniques (including mathematical induction), the algebra of sets (including relations and functions), elements of the theory of directed and undirected graphs, and the application of these topics to various areas of computer science.

The objectives of this course include, but are not limited to, the following:

• Learning formal logic.
• Learning proofs, recursion, and analysis of algorithms.
• Learning sets, relations, and functions.
• Learning graphs and graph algorithms.
• Applying these concepts to various areas of computer science.

Textbook

• "Discrete Mathematics and its Application" by Kenneth H Rosen [ TMH]
• Trembly J.P and Manohar R, “Discrete Mathematical Structures with Applications to Computer Science”, Tata McGraw–Hill Pub. Co. Ltd, New Delhi,
• Seymour Lipschutz and Mark Lipson, ”Discrete Mathematics”, Schaum’s Outlines,Tata McGraw-Hill Pub. Co. Ltd., New Delhi, Second edition.

Attendance