Discrete Mathematical Structures Syllabus for VTU BE/B.Tech Computer Science Engineering & Information Science Engineering third sem complete syllabus covered here. This will help you understand complete curriculum along with details such as exam marks and duration. The details are as follows.
| Subject Code | 15CS36 | IA Marks | 20 |
|---|---|---|---|
| Number of Lecture Hours/Week | 4 | Exam Marks | 80 |
| Total Number of Lecture Hours | 50 | Exam Hours | 3 |
CREDITS – 04
Course Objectives:
This course will enable students to:
- Prepare for a background in abstraction, notation, and critical thinking for the mathematics most directly related to computer science.
- Understand and apply logic, relations, functions, basic set theory, countability and counting arguments, proof techniques,
- Understand and apply mathematical induction, combinatorics, discrete probability, recursion, sequence and recurrence, elementary number theory
- Understand and apply graph theory and mathematical proof techniques.
| Modules | Teaching Hour | Text book |
|---|---|---|
| Module -1 | _ | |
| Fundamentals of Logic: Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic, Logical Implication – Rules of Inference. The Use of Quantifiers, Quantifiers, Definitions and the Proofs of Theorems, | 10 Hours | Textbook 1: Ch 2 |
| Module -2 | _ | |
| 10 Hours | Textbook 1: Ch 4: 4.1, 4.2 Ch 1. | |
| Module -3 | _ | |
| Relations and Functions: Cartesian Products and Relations, Functions – Plain and One-toOne, Onto Functions. The Pigeon-hole Principle, Function Composition and Inverse Functions. Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial Orders – Hasse Diagrams, Equivalence Relations and Partitions. | 10 Hours | Textbook 1: Ch 5:5.1 to 5.3, 5.5, 5.6, Ch 7:7.1 to 7.4 |
| Module -4 | _ | |
| 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. | 0 Hours | Textbook 1: Ch 8: 8.1 to 8.4, Ch 10:10.1 to 10.2 |
| Module -5 | _ | |
| Introduction to Graph Theory: Definitions and Examples, Sub graphs, Complements, and Graph Isomorphism, Vertex Degree, Euler Trails and Circuits , Trees: Definitions, Properties, and Examples, Routed Trees, Trees and Sorting, Weighted Trees and Prefix Codes. | 10 Hours | Textbook 1: Ch 11: 11.1 to 11.3, Ch 12: 12.1 to 12.4 |
Course outcomes: After studying this course, students will be able to:
- Verify the correctness of an argument using propositional and predicate logic and truth tables.
- Demonstrate the ability to solve problems using counting techniques and combinatorics in the context of discrete probability.
- Solve problems involving recurrence relations and generating functions.
- Construct proofs using direct proof, proof by contraposition, proof by contradiction, proof by cases, and mathematical induction.
- Explain and differentiate graphs and trees
Graduate Attributes (as per NBA)
- Engineering Knowledge
- Problem Analysis
- Conduct Investigations of Complex Problems
Question paper pattern:
- The question paper will have ten questions.
- There will be 2 questions from each module.
- Each question will have questions covering all the topics under a module.
- The students will have to answer 5 full questions, selecting one full question from each module.
Text Books:
- Ralph P. Grimaldi: Discrete and Combinatorial Mathematics, , 5th Edition, Pearson Education. 2004.
Reference Books:
- Basavaraj S Anami and Venakanna S Madalli: Discrete Mathematics – A Concept based approach, Universities Press, 2016
- Kenneth H. Rosen: Discrete Mathematics and its Applications, 6th Edition, McGraw Hill, 2007.
- Jayant Ganguly: A Treatise on Discrete Mathematical Structures, Sanguine-Pearson, 2010.
- D.S. Malik and M.K. Sen: Discrete Mathematical Structures: Theory and Applications, Thomson, 2004.
- Thomas Koshy: Discrete Mathematics with Applications, Elsevier, 2005, Reprint 2008.
For all other BE/B.Tech 3rd Sem Subject syllabus do follow VTU 3rd Sem BE / B.Tech Syllabus CBCS (2015-16) Scheme for Computer Science & Engineering/Information Science & Engineering Group.
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