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Discrete Structures

Indian Institute of Technology, Kharagpur , NPTEL via Swayam

Description

ABOUT THE COURSE:This course builds the mathematical foundation of computer science. It introduces the elements of mathematics like sets, functions, relations that form the basics of almost the entirety of computer science. It gives a clear understanding about the formal statements and their proofs and the counting techniques. The course develops the concept of algebraic structures and how they are used in defining mathematical applications. All the topics are illustrated with a handful of problems to make the course interesting as well as easy to understand.INTENDED AUDIENCE:Computer Science, MathematicsPREREQUISITES:Knowledge of Class 12 Mathematics and basics Computer ProgrammingINDUSTRY SUPPORT:All companies that work on research problems

Abstract Algebra

Syllabus

Week 1: Introduction to Propositional Logic
Week 2: Predicate Logic
Week 3: Methods of Proofs and Induction
Week 4: Sets and Functions
Week 5: Relations and their Properties
Week 6: Recursion
Week 7: Recurrence Relations
Week 8: Counting Techniques and Pigeonhole Principle
Week 9: Combinatorics
Week 10: Algebraic Structures
Week 11: Rings and Modular Arithmetic
Week 12: Finite Fields and Applications