# Discrete Mathematics Notes Pdf – DM Notes | Free Lecture Notes Download 2024-SW

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Here you can download the Free lecture Notes of Discrete Mathematics Notes – DM notes pdf materials with multiple file links to download. The Discrete Mathematics Notes pdf – DM notes pdf book starts with the topics covering Logic and proof, strong induction,pigeon hole principle, isolated vertex, directed graph, Alebric structers, lattices and boolean algebra, Etc.

## Discrete Mathematics pdf notes – DM notes pdf file

Complete Notes

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Note :- These notes are according to the R09 Syllabus book of JNTU. In R13 and R15,8-units of R09 syllabus are combined into 5-units in R13 and R15 syllabus. If you have any doubts please refer to the JNTU Syllabus Book.

### Discrete Mathematics | PDF, Syllabus, Books | B Tech (2024)

Discrete Mathematics is a fundamental subject in computer science and engineering that deals with countable, distinct, and separable mathematical structures. It focuses primarily on finite collections of discrete objects, making it essential for understanding computer algorithms, data structures, cryptography, and network theory. As the digital world continues to expand, the importance of discrete mathematics has grown significantly, making it an indispensable component of modern computer science and engineering education.

These lecture notes are aligned with the Jawaharlal Nehru Technological University (JNTU) syllabus, providing students with accurate and comprehensive resources for their B.Tech course. The notes are designed to facilitate effective learning and thorough understanding, making them essential for students aiming to excel in their academic pursuits.

### Overview of DM Notes Pdf

The DM Notes Pdf is structured into five units, each focusing on a distinct area of discrete mathematics. The notes cover the following topics in detail:

1. Unit 1: Logic and Proof
• Propositions and connectives
• Truth tables and basic logical operations
• Laws of logic, including De Morgan’s laws and the idempotent law
• Concepts of tautology, contradiction, and contingency
2. Unit 2: Combinatorics
• Strong induction and the pigeonhole principle
• Permutations and combinations
• Recurrence relations and the principle of inclusion and exclusion
3. Unit 3: Graph Theory
• Types of graphs, including simple, directed, undirected, and multigraphs
• Graph properties, such as degree, path, cycle, and connectivity
• Euler paths, Euler circuits, Hamiltonian paths, and Hamiltonian cycles
4. Unit 4: Algebraic Structures
• Properties of algebraic structures, including closure, commutativity, and associativity
• Groups, subgroups, rings, and fields
• Lagrange’s theorem and homomorphisms
5. Unit 5: Lattices and Boolean Algebra
• Properties of lattices, including reflexivity, symmetry, and transitivity
• Boolean algebra and its applications
• Laws of Boolean algebra, including the commutative and associative laws

### The Following Topics Are Covered in Discrete Mathematics Handwritten Notes:

• Logic and Proof:
Logic and proof are foundational to discrete mathematics, enabling students to construct valid arguments and verify mathematical statements. The notes cover propositions, logical connectives, truth tables, and essential laws of logic, providing a solid foundation for further study.
• Combinatorics:
Combinatorics involves the study of counting and arrangement, which is crucial for understanding complex algorithms and data structures. The notes cover permutations, combinations, the pigeonhole principle, and recurrence relations, offering students a comprehensive understanding of combinatorial techniques.
• Graph Theory:
Graph theory is a key area of discrete mathematics, used extensively in computer science for modeling networks and solving problems related to connectivity and traversal. The notes cover various types of graphs, their properties, and fundamental concepts like Euler and Hamiltonian paths.
• Algebraic Structures:
Algebraic structures provide a framework for understanding complex mathematical systems. The notes cover groups, rings, fields, and related properties, equipping students with the tools needed to analyze and manipulate algebraic systems.
• Lattices and Boolean Algebra:
Lattices and Boolean algebra are essential for understanding logical operations and decision-making processes in computing. The notes cover the properties of lattices and the laws of Boolean algebra, providing students with a strong foundation for further study.

Access the comprehensive notes for each unit by following the links below:

These notes are meticulously structured to provide students with a deep understanding of discrete mathematics, enabling them to prepare effectively for their examinations.

Students can download the DM Notes Pdf and study materials for free. These resources are designed to provide a thorough understanding of the subject and support students in their academic endeavors. The notes are available in PDF format, making them easily accessible for study on any device.

### Topics Covered in This DM Notes Pdf

#### Unit-1: Logic and Proof

• Propositions and Connectives:
• Understanding propositions and statement logic
• Connectives and truth tables
• Laws of Logic:
• Basic logical operations: And, Disjunction, Conditional, Biconditional
• Tautology, contradiction, fallacy, and contingency
• Logical Equivalences:
• Idempotent, associative, commutative, De Morgan’s laws

#### Unit-2: Combinatorics

• Strong Induction and Pigeonhole Principle:
• Principles of strong induction
• Applications of the pigeonhole principle
• Permutations and Combinations:
• Understanding permutations and combinations
• Solving problems using recurrence relations
• Principle of Inclusion and Exclusion:
• Applications in counting and arrangement

#### Unit-3: Graph Theory

• Types of Graphs:
• Simple, directed, undirected, and mixed graphs
• Properties: degree, path, cycle, connectivity
• Graph Isomorphism and Matrices:
• Path matrices and graph isomorphism
• Euler and Hamiltonian Concepts:
• Euler paths and circuits
• Hamiltonian paths and cycles

#### Unit-4: Algebraic Structures

• Properties of Algebraic Structures:
• Closure, commutativity, associativity, identity, inverse
• Groups and Subgroups:
• Understanding groups and subgroups
• Homomorphisms and isomorphisms
• Rings and Fields:
• Introduction to rings and fields
• Lagrange’s theorem and its applications

#### Unit-5: Lattices and Boolean Algebra

• Properties of Lattices:
• Reflexivity, symmetry, transitivity, antisymmetry
• Boolean Algebra:
• Applications in computing
• Laws of Boolean algebra

### DM Notes Pdf from JNTU

The DM Notes Pdf are specifically tailored to the JNTU syllabus, providing students with relevant and accurate study materials. These notes are compiled by experienced faculty and experts in the field of mathematics and computer science, ensuring that students receive high-quality resources for their studies.

Smartzworld is a reliable platform for accessing educational resources. By choosing Smartzworld, students can be assured of receiving up-to-date and accurate study materials tailored to their academic needs. The platform offers free downloads of lecture notes, making it an ideal choice for students seeking reliable study resources.

### Benefits of FREE DM Handwritten Notes PDF

• Comprehensive Coverage: The notes cover all essential topics in discrete mathematics, providing a thorough understanding of each concept.
• Easy to Understand: The notes are written in a clear and concise manner, making them easy to comprehend and follow.
• Structured for Exam Preparation: The notes are organized to facilitate quick revision and effective exam preparation, helping students achieve their academic goals.
• Aligned with JNTU Syllabus: The notes are tailored to the latest JNTU syllabus, ensuring that students receive relevant and up-to-date content.

### FAQs

You can download the notes from the provided links for each unit or the complete set from Smartzworld.

Click on the respective links provided for each unit to download the DM notes in PDF format.

Q3. How many modules are covered in DM Notes Pdf?
The notes cover five comprehensive units, each focusing on different aspects of discrete mathematics.

Q4. Topics Covered in DM Notes Pdf?
Refer to the list of topics outlined for each unit above.

Q5. Where can I get the complete DM Handwritten Notes pdf FREE Download?

### Conclusion

Discrete Mathematics is a vital subject for computer science and engineering students, providing them with essential mathematical tools to solve complex problems. The comprehensive notes provided here cover all key topics, offering students an invaluable resource for their studies. By downloading the DM Notes Pdf from Smartzworld, students can ensure they are well-prepared for their examinations and equipped with the knowledge needed to excel in their academic and professional careers.

The detailed coverage of logic, combinatorics, graph theory, algebraic structures, and Boolean algebra offers students a complete understanding of discrete mathematics, enabling them to apply these concepts in real-world scenarios and excel in their academic pursuits.

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