Fundamentals of Logic:
Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic, Logical Implication – Rules of Inference. Fundamentals of Logic contd.: The Use of Quantifiers, Quantifiers, Definitions and the Proofs of Theorems.
Text book 1: Chapter2
RBT: L1, L2, L3
Properties of the Integers:
The Well Ordering Principle – Mathematical Induction,
Fundamental Principles of Counting:
The Rules of Sum and Product, Permutations, Combinations – The Binomial Theorem, Combinations with Repetition.
Text book 1: Chapter4 – 4.1, Chapter1
RBT: L1, L2, L3
Relations and Functions:
Cartesian Products and Relations, Functions – Plain and One-toOne, Onto Functions. The Pigeon-hole Principle, Function Composition and Inverse Functions.
Relations:
Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial Orders – Hasse Diagrams, Equivalence Relations and Partitions.
Text book 1: Chapter5 , Chapter7 – 7.1 to 7.4
RBT: L1, L2, L3
The Principle of Inclusion and Exclusion:
The Principle of Inclusion and Exclusion, Generalizations of the Principle, Derangements – Nothing is in its Right Place, Rook Polynomials.
Recurrence Relations:
First Order Linear Recurrence Relation, The Second Order Linear Homogeneous Recurrence Relation with Constant Coefficients.
Text book 1: Chapter8 – 8.1 to 8.4, Chapter10 – 10.1, 10.2 RBT: L1, L2, L3
Introduction to Graph Theory:
Definitions and Examples, Sub graphs, Complements, and Graph Isomorphism,
Trees:
Definitions, Properties, and Examples, Routed Trees, Trees and Sorting, Weighted Trees and Prefix Codes
Text book1: Chapter11 – 11.1 to 11.2 Chapter12 – 12.1 to 12.4 RBT: L1, L2, L3
Course Outcomes:
The student will be able to :
• Use propositional and predicate logic in knowledge representation and truth verification.
• Demonstrate the application of discrete structures in different fields of computer science.
• Solve problems using recurrence relations and generating functions.
• Application of different mathematical proofs techniques in proving theorems in the courses.
• Compare graphs, trees and their applications.
Question Paper Pattern:
• The question paper will have ten questions.
• Each full Question consisting of 20 marks
• There will be 2 full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub questions covering all the topics under a module.
• The students will have to answer 5 full questions, selecting one full question from each module.
Textbooks:
1. Ralph P. Grimaldi: Discrete and Combinatorial Mathematics, 5th Edition, Pearson Education. 2004.
Reference Books:
1. Basavaraj S Anami and Venakanna S Madalli: Discrete Mathematics – A Concept based approach, Universities Press, 2016
2. Kenneth H. Rosen: Discrete Mathematics and its Applications, 6th Edition, McGraw Hill, 2007.
3. Jayant Ganguly: A Treatise on Discrete Mathematical Structures, Sanguine-Pearson, 2010.
4. D.S. Malik and M.K. Sen: Discrete Mathematical Structures: Theory and Applications, Thomson, 2004.
5. Thomas Koshy: Discrete Mathematics with Applications, Elsevier, 2005, Reprint 2008.