The Complete 18cs36 | Discrete Mathematical Structures Notes

Description

Discrete Mathematical Structures (18CS35) | Vtu Notes

Course Code: 18CS33

Course Title: Discrete mathematical Structures

University: Visvesvaraya Technological University (VTU)

VTU 18CS36, also known as "Discrete Mathematical Structures," is a course offered by Visvesvaraya Technological University (VTU) that focuses on fundamental mathematical concepts and structures that are discrete in nature. This course is typically a part of computer science and engineering programs and serves as a foundation for various topics in computer science, including algorithms, data structures, and cryptography.

Key topics covered in VTU 18CS36 | Discrete Mathematical Structures typically include:

1. Sets and Relations: Students learn about the basic concepts of sets, set operations (union, intersection, complement), and relations (equivalence relations, partial orders). These concepts are fundamental in computer science for organizing and manipulating data.

2. Functions: This section explores functions, their properties, and classifications. Functions are vital for modeling relationships between elements in various computational scenarios.

3. Combinatorics: The course delves into combinatorial mathematics, covering permutations, combinations, and counting principles. Combinatorics is essential for analyzing algorithms and solving problems in computer science.

4. Graph Theory: Students study graph theory, including graph representation, types of graphs (trees, cycles, bipartite graphs), and basic graph algorithms. Graph theory has applications in network design, data structures, and optimization problems.

5. Lattices and Boolean Algebra: This part of the course introduces lattices, including partially ordered sets, and Boolean algebra, which is fundamental for digital logic design and computer architecture.

6. Propositional Logic and Predicate Logic: Students learn about propositional logic and predicate logic, which are essential for formal reasoning and programming language semantics.

7. Proof Techniques: This section covers various proof methods, such as mathematical induction, proof by contradiction, and proof by contrapositive. These techniques are crucial for establishing the correctness of algorithms and software.

8. Recurrence Relations: Students study recurrence relations, which are used to analyze the time complexity of recursive algorithms.

VTU 18CS36 provides a strong mathematical foundation for computer science students, enabling them to think logically, solve complex problems, and understand the theoretical underpinnings of various computational concepts. Mastery of these discrete mathematical structures is essential for success in advanced computer science courses and for a career in fields like software development, data analysis, and computer engineering.

What you will learn?

Module-1

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.

Module-2

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.

Module-3

Relations and Functions: Cartesian Products and Relations, Functions – Plain and One-to-One, 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.

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.

Module-5

Introduction to Graph Theory: Definitions and Examples, Subgraphs, Complements, and Graph Isomorphism, Trees: Definitions, Properties, and Examples, Routed Trees, Trees and Sorting, Weighted Trees and Prefix Codes