Accessible to all students with a sound background in high school mathematics, **A Concise Introduction to Pure Mathematics, Third Edition** presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations, the use of Euler’s formula to study the five Platonic solids, the use of prime numbers to encode and decode secret information, and the theory of how to compare the sizes of two infinite sets.

*New to the Third Edition*The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis. These new chapters introduce the ideas of limits of sequences and continuous functions as well as several interesting applications, such as the use of the intermediate value theorem to prove the existence of

By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. Written in a rigorous yet accessible style, it continues to provide a robust bridge between high school and higher level mathematics, enabling students to study further courses in abstract algebra and analysis.

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Divided into 22 short chapters, this title offers a selection of exercises ranging from routine calculations to the challenging problems. It discusses real and complex numbers and explains how these concepts are applied in solving natural problems. It introduces topics in analysis, geometry, number theory, and combinatorics.

It would in fact be difficult to find in this excellent book three consecutive pages that do not contain material useful to students or practitioners. ... A diligent, active reader of this outstanding book will have the best foundation at minimum cost for making meaningful contributions to mathematics, science, or engineering.

―*Computing Reviews*, November 2011

Now in an updated and expanded third edition, **A Concise Introduction to Pure Mathematics** provides an informed and informative presentation into a representative selection of fundamental ideas in mathematics ... . Of special note is the inclusion of solutions to all of the odd-numbered exercises. An ideal, accessible, elegant, student-friendly, and highly recommended choice for classroom textbooks for high school and college level mathematics curriculums, **A Concise Introduction to Pure Mathematics** is further enhanced with a selective bibliography, an index of symbols, and a comprehensive index.

―*Library Bookwatch*, December 2010

This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. The material is very well chosen and arranged, and teaching from Liebeck’s book has in many different ways been among my most rewarding teaching experiences during the last decades.

―Boris Hasselblatt, Tufts University, Medford, Massachusetts, USA

In addition to preparing students to go on in mathematics, it is also a wonderful choice for a student who will not necessarily go on in mathematics but wants a gentle but fascinating introduction into the culture of mathematics. ... This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. At the very least, the student will have an appreciation of mathematics. As usual, Liebeck’s writing style is clear and easy to read. This is a book that could be read by a student on his or her own. There is a wide selection of problems ranging from routine to quite challenging.

―From the Foreword by Robert Guralnick, University of Southern California, Los Angeles, USA

**Praise for Previous Editions:**

The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world ... .

―Gerald A. Heuer, *Zentralblatt MATH*, 2009

...a pleasure to read ... a very welcome and highly accessible book.

―Michael Ward, *The Mathematical Gazette*, March 2007

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