A Concise Introduction to Pure Mathematics, 4th Edition
By: Martin Liebeck
About This Book
In addition to the Introduction to Analysis chapters contained in previous editions, this edition presents two new chapters that give an introduction to Abstract Algebra via group theory. While this is a standard topic and there are many texts on group theory, this is a "taster" as an introduction to more abstract reasoning. Additional material has been added to the chapters "Counting and Choosing" and "More on Sets." The book also contains new exercises with solutions to the odd-numbered ones.
AI Overview
"A Concise Introduction to Pure Mathematics, 4th Edition" by Martin Liebeck is a textbook designed to introduce students to the fundamental concepts of pure mathematics. Here is a comprehensive overview of the book:
Key Themes
- Number Systems: The book begins with an introduction to number systems, including the real numbers and complex numbers, providing a solid foundation for further mathematical exploration.
- Abstract Algebra: Two new chapters in the 4th edition introduce students to abstract algebra via the theory of groups, covering abstract reasoning and numerous examples and applications.
- Inequalities and Counting Methods: The book includes new material on inequalities, counting methods, the inclusion-exclusion principle, and Euler's phi function, which are essential for advanced mathematical studies.
- Analysis and Number Theory: It covers the rigorous theory of limits and continuous functions, as well as interesting topics like the theory of solving cubic equations and Euler’s formula for the numbers of corners, edges, and faces of a solid object.
- Discrete Mathematics: The book explores the use of prime numbers to encode and decode secret information, and the theory of comparing the sizes of two infinite sets, which are fascinating applications of pure mathematics.
Plot Summary
The book is structured to provide a robust bridge between high school and higher-level mathematics. It starts with foundational concepts and gradually introduces more advanced topics, making it accessible to students with a sound background in high school mathematics. The text is written in a rigorous yet accessible style, ensuring that students can grasp complex ideas through careful explanations and examples.
Critical Reception
The book has received positive reviews for its ability to make pure mathematics accessible to a wide range of students. It is highly recommended for classroom use in both high school and college-level mathematics curriculums due to its student-friendly approach and elegant presentation of mathematical concepts.
Edition Details
- ISBN-13: 9781498722926
- ISBN-10: 149872292X
- Weight: 1.05 Pounds
- Dimensions: 6.13 x 0.72 x 8.75 In
- List Price: $84.95
- Edition: 4th Edition
- Format: Paperback
- Language: English
- Pages: 320 pages
- Publisher: Routledge
- Published On: 2015-11-03
Overall, "A Concise Introduction to Pure Mathematics, 4th Edition" by Martin Liebeck is an ideal textbook for students transitioning from high school to more advanced mathematical studies, offering a comprehensive and engaging introduction to the beauty and power of pure mathematics.