Set Theory for Beginners

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Book Description

Level up your Logical Reasoning and Mathematical Understanding through Set Theory Fundamentals!

Dive into “Set Theory for Beginners” by Subhomoy Haldar and discover how mastering the fundamentals of Set Theory can revolutionise your approach to problem-solving in mathematics, computer science, and beyond. This comprehensive guide makes complex concepts accessible and engaging, ensuring you gain both the “why” and the “how” behind the theory.

Why Read This Book?

• Build Strong Foundations: Grasp the essential building blocks of modern mathematics.
• Level Up Your Skills: Apply set theory to write better algorithms and make informed technical decisions.
• See Real Applications: Connect theoretical concepts directly to software development, relational databases, and general problem-solving.

What You’ll Learn:

• Organizing Information Better: Discover how sets help manage and structure data efficiently.
• Avoiding Duplicates: Utilise set properties to streamline data processing and ensure uniqueness.
• Combining and Filtering Data: Master set operations to merge and refine datasets effectively.
• Making Decisions: Leverage set theory for strategic decision-making and problem-solving.
• Step-by-Step Problem-Solving: Break down complex problems into manageable parts using set theory principles.

What’s Included:

• Detailed Explanations: Clear and concise descriptions of set theory concepts.
• Illustrative Examples: Numerous examples and illustrations to aid understanding.
• Practical Implementations: Code snippets and unit tests for a simple set data structure in the Go Programming Language.
• Advanced Topics: Explore beyond naïve set theory with resources for further reading.

Why Does This Book Exist?

• Bridging the Gap: Most resources either focus purely on theory or jump straight to implementation. This book connects both worlds.
• Industry Experience: Written by a practicing software developer who uses these concepts daily.
• Accessible Introduction: Designed for beginners, this book is an affordable, comprehensive learning resource. The type we wish we had when we were starting out.

Transform your software development proficiency and start your mathematical journey with “Set Theory for Beginners” today!

Check the full table of contents below.

Subhomoy Haldar is a Software Developer at Component Sense, Visiting Researcher at the University of Manchester. He has an MSc in Computing Science with Distinction from the University of Glasgow. Learn more about the publisher Coders’ Compass Publishing at coderscompass.org and the author at hungrybluedev.in.

More Information

• ISBN:
  • eBook: 978-1-0685741-0-8
  • Paperback: 978-1-0685741-1-5
• Publisher: Coders’ Compass Publishing
• Publication Date:
  • eBook: 2025-01-22
  • Paperback: 2025-07-22
• Language: English
• File Format (eBook): ePub, Mobi (other formats available on request post purchase)
• Page Count (Paperback): 226
• Source Code Repository: GitHub - set
• Errata: Set Theory for Beginners - Errata
• Current Version: 1.2

Errata

All reported errata for the book are published here. If you have found an error in the book, please contact us with the details.

Signed Copy Validation

If you have a signed copy of “Set Theory for Beginners” and wish to validate it, please follow the instructions on the Validate Your Signed Copy page. We will confirm the validity of your signed copy and provide proof via email.

Set Package in Go

An open-source set package in Go is available for demonstration purposes. The package provides a simple set data structure in Go, with a generic set interface and an in-memory hash set implementation that uses a map as the underlying data structure.

Learn more about the Set Package in Go.

Table of Contents

Explore what's inside Set Theory for Beginners. Click on chapters to see their sections.

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Front Matter (3 chapters)

1. Dedication and Acknowledgements p. 1

   1. Dedication p. 1
   2. Acknowledgements p. 1
2. How to Read this Book p. 3

   1. Elevated Difficulty p. 3
   2. Reading Order p. 3
   3. Work Through the Examples p. 3
   4. Hands-on Approach p. 4
3. Prologue p. 5

Content (9 chapters)

1. What Are Sets? p. 7

   1. Introduction p. 7
   2. Definition p. 8
   3. Why Should We Care About Sets? p. 13
   4. Chapter Summary p. 19
2. *On Mathematical Terms p. 21

   1. Introduction p. 21
   2. Comparison p. 21
   3. Logical Operations p. 23
   4. Quantifiers p. 28
   5. Relations, Functions, and Maps p. 30
   6. Chapter Summary p. 42
3. Representation of Sets p. 43

   1. Introduction p. 43
   2. Roster and Descriptive Notations p. 43
   3. Set Builder Notation p. 44
   4. Venn Diagrams p. 46
   5. Chapter Summary p. 48
4. Special and Common Sets p. 49

   1. Introduction p. 49
   2. Universal Set p. 49
   3. Empty Set p. 50
   4. Singleton Set p. 50
   5. *Pure and Impure Sets p. 51
   6. Number Sets p. 52
   7. Chapter Summary p. 69
5. Operations on Sets p. 71

   1. Introduction p. 71
   2. Membership p. 71
   3. Subset, Superset, and Equality p. 73
   4. Unordered Equality p. 77
   5. Cardinality p. 77
   6. Union and Intersection p. 85
   7. Complement p. 92
   8. Differences: Regular and Symmetric p. 100
   9. Cartesian Product p. 106
   10. Power Set p. 117
   11. Chapter Summary p. 124
6. Our Own Set Data Structure p. 127

   1. Introduction p. 127
   2. Why Go? p. 127
   3. Source Code p. 128
   4. Preparation p. 128
   5. The Set Interface p. 128
   6. Implementing a Set using a Map p. 129
   7. Testing the Hash Set p. 132
   8. The Comparison and Basic Operations p. 136
   9. Cartesian Product and Power Set p. 142
   10. Using the Set Package p. 146
   11. Conclusion p. 148
7. Relational Algebra and Set Theory p. 151

   1. Introduction p. 151
   2. Relations are Tables p. 151
   3. Projection and Selection p. 156
   4. Union, Intersection, and Difference p. 161
   5. Renaming Columns p. 167
   6. Aggregation p. 167
   7. Joining Tables p. 171
   8. Practical Advice p. 182
8. *Going Beyond Naive Set Theory p. 187

   1. Introduction p. 187
   2. Partitions p. 187
   3. What if the membership condition is not binary? - Fuzzy Sets p. 192
   4. Is there a set of all sets? - Russell's Paradox p. 194
   5. So, What Now? p. 195
   6. Chapter Summary p. 197
9. Conclusion: Wrapping Up p. 199

   1. Our Journey Through Set Theory p. 199
   2. Where to Go From Here p. 200
   3. Final Thoughts p. 202

Appendix (1 chapter)

1. Catalogue of Tables, Figures, and Listings p. 203

   1. List of Tables p. 203
   2. List of Figures p. 204
   3. List of Source Listings p. 209
   4. List of External Links p. 210

Back Matter (1 chapter)

1. About the Author p. 215

* = elevated difficulty