Sets: Naive, Axiomatic and Applied - A Basic Compendium

In this review of Sets: Naive, Axiomatic and Applied: A Basic Compendium with Exercises, the bottom line is simple: this bilingual volume is best for mathematicians, teachers and students who want a compact, exercise-driven introduction to set theory without heavy logic prerequisites. The mixed English and Dutch presentation and clear organization make it a practical reference and classroom supplement, and the exercise sets reinforce concepts for working mathematicians and beginners alike. For readers seeking a focused, readable compendium, this book delivers accessible explanations and practice problems.

Key Features

• Bilingual text: English and Dutch presentation supports readers who prefer either language and aids translation or classroom use in multilingual settings.
• Exercise-focused: Each section includes exercises that reinforce definitions and theorems, helping readers shift from understanding to practical mastery.
• Clear scope: The compendium emphasizes basic set theory without deep logical formalism, making it approachable for non logicians and those in applied areas.
• Concise reference: The book compiles core notions and common techniques in a compact format suitable for quick consultation by working mathematicians.
• Teaching utility: The structure and examples make it straightforward to incorporate into introductory courses or seminar reading lists.

Who It's For

This edition is aimed at students beginning their study of set theory, mathematicians who need a quick refresher, and instructors looking for a compact set of exercises to assign. Its modest technical depth and practical problems suit those who want understanding and application without diving into formal logic.

Those who require exhaustive coverage of model theory, advanced axiomatic set theory, or a one-language scholarly monograph should look elsewhere. For multilingual classrooms and readers bridging English and Dutch, however, this compendium is especially useful.

Pros & Cons

Pros

• Concise, focused presentation makes it easy to follow core set theory topics without unnecessary formalism.
• Bilingual English and Dutch text increases accessibility for speakers of either language and supports translation use.
• Well chosen exercises give practical reinforcement and make the book suitable for classroom assignments.
• Compact format works well as a quick reference for working mathematicians and teachers.

Cons

• Not intended as a comprehensive, advanced treatise on axiomatic set theory, so specialists will need deeper texts for research-level topics.

Specifications

Title	Sets: Naive, Axiomatic and Applied: A Basic Compendium with Exercises
Authors / Brand	D. Van Dalen, H. C. Doets, H. De Swart, I. N. Sneddon
Languages	English, Dutch (translation)
Audience	Students, teaching mathematicians, working mathematicians
Scope	Introductory and applied set theory with exercises
Category hint	Books; Computers & Technology; Programming; Introductory & Beginning

Our Verdict

Sets: Naive, Axiomatic and Applied is a practical, value-minded compendium for anyone needing a clear, exercise-rich introduction to set theory without heavy logical apparatus. It is particularly worth buying for instructors and students who benefit from bilingual presentation and concise, focused treatment.

Frequently Asked Questions

Is this book suitable for beginners?
Yes. The compendium targets beginners and non logicians with clear explanations and exercises designed to build foundational skills.

Does it include exercises for classroom use?
Yes. Each section contains exercises intended for practice and use in teaching assignments or self-study.

What languages are in the book?
The book is presented in English with Dutch translation, making it useful in multilingual teaching contexts.