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Discrete Mathematics for Computer Science

by zowardkandle (Author)
File Type: Zoward Edition (Zip File)
Category: eBooks

About This Item

In the fast-evolving world of computer science, mathematical thinking is the invisible engine driving algorithms, logic, and computational efficiency. Discrete Mathematics for Computer Science equips learners with the mathematical tools and logical reasoning necessary to excel in areas such as programming, software development, data science, cybersecurity, and theoretical computing.

This textbook (available in several editions) emphasizes precision, problem-solving, and the bridge between abstract concepts and practical applications. Written with students of computer science in mind, it covers a wide range of topics foundational to computing and algorithmic design.


🔸 Core Topics Covered

1. Propositional and Predicate Logic

This section introduces formal logic, which is the foundation of programming and reasoning in computer science:

  • Logical operators, truth tables, tautologies.

  • Predicate logic and quantifiers (universal ∀, existential ∃).

  • Logical equivalences, implications, and proofs.

  • Applications in software verification, logic circuits, and AI.

2. Proof Techniques

Understanding how to construct proofs is essential in algorithms and complexity theory.

  • Direct proof

  • Proof by contradiction

  • Mathematical induction and strong induction

  • Applications in recurrence relations and loop invariants

3. Set Theory

Sets are the language of data structures:

  • Basic operations: union, intersection, complement

  • Power sets and Cartesian products

  • Venn diagrams and applications in relational databases

4. Functions and Relations

The concepts of functions and mappings are fundamental in programming:

  • Injective, surjective, bijective functions

  • Inverse functions and function composition

  • Binary relations, equivalence relations, and partial orders

  • Applications in modeling state machines and program behavior

5. Number Theory and Modular Arithmetic

Critical in computer security, hashing, and coding theory:

  • Divisibility and prime numbers

  • GCD, LCM, Euclidean Algorithm

  • Congruences and modular systems

  • Cryptography applications (e.g., RSA encryption)

6. Counting and Combinatorics

Counting principles allow for performance estimation and problem modeling:

  • Permutations, combinations

  • Pigeonhole Principle

  • Binomial Theorem and Pascal’s Triangle

  • Inclusion-Exclusion Principle

  • Discrete probability and expected values

7. Recurrence Relations and Mathematical Induction

Vital in analyzing recursive algorithms:

  • Defining and solving linear recurrence relations

  • Applications in Fibonacci numbers, binary search trees, and divide-and-conquer algorithms

  • Using induction to prove properties of recursive programs

8. Graph Theory

A critical component in networks, AI, and data organization:

  • Graph types (directed, undirected, weighted)

  • Paths, circuits, connectivity

  • Breadth-First and Depth-First Search (BFS, DFS)

  • Minimum spanning trees, Dijkstra’s algorithm

  • Applications in social networks, maps, and routing

9. Trees

Used extensively in hierarchical data storage and search:

  • Binary Trees, Binary Search Trees (BST), AVL Trees

  • Tree traversals: Preorder, Inorder, Postorder

  • Applications in parsing, file systems, and decision-making processes

10. Boolean Algebra and Logic Gates

The mathematical backbone of digital electronics and computer logic:

  • Boolean expressions and truth tables

  • Simplification using identities and Karnaugh maps

  • AND, OR, NOT, NAND, NOR gates

  • Applications in computer architecture and digital design

11. Algorithms and Complexity (in many editions)

  • Introduction to algorithmic thinking

  • Time and space complexity

  • Big-O notation

  • Basic sorting and searching algorithms


🔸 Special Features of the Book

  • Clarity and Structure: Each topic is introduced with motivation, definitions, examples, and guided exercises.

  • Computer Science Integration: Every mathematical idea is linked directly to computing—through algorithms, logic, or programming paradigms.

  • Problem Sets: Hundreds of exercises ranging from basic to challenge-level questions.

  • Real-World Applications: Discrete math is tied to cybersecurity, networks, artificial intelligence, databases, and more.

  • Visual Learning: Concepts like graphs, trees, and Venn diagrams are illustrated visually for intuitive understanding.


🔸 Why This Book Matters for Computer Science

Discrete math provides the vocabulary and logic for computer science. Just as grammar is essential to language, discrete math is essential to computational thinking. It builds the capacity to:

  • Write correct and efficient algorithms.

  • Analyze problems systematically.

  • Understand theoretical limits of computation.

  • Develop secure systems and protocols.

Whether you're studying data structures, writing a compiler, or training an AI model, the principles in Discrete Mathematics for Computer Science are your intellectual toolkit.


🔸 Who Should Use This Book?

  • Undergraduate Computer Science Students: Often a required course in 1st or 2nd year.

  • Software Developers and Engineers: To strengthen your problem-solving and algorithm design.

  • Exam Candidates: Ideal for GATE, GRE CS, UGC-NET, and coding competitions.

  • Instructors and Educators: A solid teaching resource with built-in exercises.

  • Self-learners and Enthusiasts: Perfect for building foundational knowledge for a CS career.


🔸 Variants and Editions

Some popular editions/titles include:

  • Discrete Mathematics for Computer Science by Ken Bogart, R. Kent Dymond, and Cliff Stein

  • Discrete Mathematics with Applications by Susanna Epp

  • Discrete Mathematics and Its Applications by Kenneth Rosen (widely used)

  • Discrete Structures for Computer Science by Judith Gersting

All cover core concepts but may differ in emphasis or style (theoretical vs. practical).

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In the fast-evolving world of computer science, mathematical thinking is the invisible engine driving algorithms, logic, and computational efficiency. Discrete Mathematics for Computer Science equips learners with the mathematical tools and logical reasoning necessary to excel in areas such as programming, software development, data science, cybersecurity, and theoretical computing.

This textbook (available in several editions) emphasizes precision, problem-solving, and the bridge between abstract concepts and practical applications. Written with students of computer science in mind, it covers a wide range of topics foundational to computing and algorithmic design.


🔸 Core Topics Covered

1. Propositional and Predicate Logic

This section introduces formal logic, which is the foundation of programming and reasoning in computer science:

  • Logical operators, truth tables, tautologies.

  • Predicate logic and quantifiers (universal ∀, existential ∃).

  • Logical equivalences, implications, and proofs.

  • Applications in software verification, logic circuits, and AI.

2. Proof Techniques

Understanding how to construct proofs is essential in algorithms and complexity theory.

  • Direct proof

  • Proof by contradiction

  • Mathematical induction and strong induction

  • Applications in recurrence relations and loop invariants

3. Set Theory

Sets are the language of data structures:

  • Basic operations: union, intersection, complement

  • Power sets and Cartesian products

  • Venn diagrams and applications in relational databases

4. Functions and Relations

The concepts of functions and mappings are fundamental in programming:

  • Injective, surjective, bijective functions

  • Inverse functions and function composition

  • Binary relations, equivalence relations, and partial orders

  • Applications in modeling state machines and program behavior

5. Number Theory and Modular Arithmetic

Critical in computer security, hashing, and coding theory:

  • Divisibility and prime numbers

  • GCD, LCM, Euclidean Algorithm

  • Congruences and modular systems

  • Cryptography applications (e.g., RSA encryption)

6. Counting and Combinatorics

Counting principles allow for performance estimation and problem modeling:

  • Permutations, combinations

  • Pigeonhole Principle

  • Binomial Theorem and Pascal’s Triangle

  • Inclusion-Exclusion Principle

  • Discrete probability and expected values

7. Recurrence Relations and Mathematical Induction

Vital in analyzing recursive algorithms:

  • Defining and solving linear recurrence relations

  • Applications in Fibonacci numbers, binary search trees, and divide-and-conquer algorithms

  • Using induction to prove properties of recursive programs

8. Graph Theory

A critical component in networks, AI, and data organization:

  • Graph types (directed, undirected, weighted)

  • Paths, circuits, connectivity

  • Breadth-First and Depth-First Search (BFS, DFS)

  • Minimum spanning trees, Dijkstra’s algorithm

  • Applications in social networks, maps, and routing

9. Trees

Used extensively in hierarchical data storage and search:

  • Binary Trees, Binary Search Trees (BST), AVL Trees

  • Tree traversals: Preorder, Inorder, Postorder

  • Applications in parsing, file systems, and decision-making processes

10. Boolean Algebra and Logic Gates

The mathematical backbone of digital electronics and computer logic:

  • Boolean expressions and truth tables

  • Simplification using identities and Karnaugh maps

  • AND, OR, NOT, NAND, NOR gates

  • Applications in computer architecture and digital design

11. Algorithms and Complexity (in many editions)

  • Introduction to algorithmic thinking

  • Time and space complexity

  • Big-O notation

  • Basic sorting and searching algorithms


🔸 Special Features of the Book

  • Clarity and Structure: Each topic is introduced with motivation, definitions, examples, and guided exercises.

  • Computer Science Integration: Every mathematical idea is linked directly to computing—through algorithms, logic, or programming paradigms.

  • Problem Sets: Hundreds of exercises ranging from basic to challenge-level questions.

  • Real-World Applications: Discrete math is tied to cybersecurity, networks, artificial intelligence, databases, and more.

  • Visual Learning: Concepts like graphs, trees, and Venn diagrams are illustrated visually for intuitive understanding.


🔸 Why This Book Matters for Computer Science

Discrete math provides the vocabulary and logic for computer science. Just as grammar is essential to language, discrete math is essential to computational thinking. It builds the capacity to:

  • Write correct and efficient algorithms.

  • Analyze problems systematically.

  • Understand theoretical limits of computation.

  • Develop secure systems and protocols.

Whether you're studying data structures, writing a compiler, or training an AI model, the principles in Discrete Mathematics for Computer Science are your intellectual toolkit.


🔸 Who Should Use This Book?

  • Undergraduate Computer Science Students: Often a required course in 1st or 2nd year.

  • Software Developers and Engineers: To strengthen your problem-solving and algorithm design.

  • Exam Candidates: Ideal for GATE, GRE CS, UGC-NET, and coding competitions.

  • Instructors and Educators: A solid teaching resource with built-in exercises.

  • Self-learners and Enthusiasts: Perfect for building foundational knowledge for a CS career.


🔸 Variants and Editions

Some popular editions/titles include:

  • Discrete Mathematics for Computer Science by Ken Bogart, R. Kent Dymond, and Cliff Stein

  • Discrete Mathematics with Applications by Susanna Epp

  • Discrete Mathematics and Its Applications by Kenneth Rosen (widely used)

  • Discrete Structures for Computer Science by Judith Gersting

All cover core concepts but may differ in emphasis or style (theoretical vs. practical).

Technical Details
File Size: 5.4 MB
Format: Zip File
Last Updated: Aug 02, 2025
Version: 1.0
Compatibility: All modern browsers
Requirements: None

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