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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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The Forward says this book can "be read by a student on his or her own". The Preface restates this slightly differently, by saying that as "well as being designed for use in a first university course, the book is also suitable for self-study". However, debatably, this text does not serve both purposes equally well, as it seems less suitable for a self-study target audience.
A " Solutions Manual for a Concise Introduction to Pure Mathematics" is listed on-line. The Solutions Manual described is about 70 pages in length. If this is correct, it's contents could easily have been included with this text, while still keeping the text relatively concise at less than 300 pages. At the time of this review, this manual was not available from Amazon or other on-line sellers.
The lack of fully-worked solutions to exercises is typical of many books designed for classroom use. This allows faculty to assign problems that students must work out on their own, as solutions are not readily available. While this approach is, arguably, appropriate for a classroom environment, the lack of detailed exercise solutions considerably reduces the value of this text for self-study. For self-study, the opportunity to work through a considerable variety of problems and check results against detailed solutions is quite important. This is perhaps the key deficiency of this text. However, it is enjoyable to read, with explanations that are very well done. Thus, although not self-contained, it could be excellent for self-study if supplemented by a source of problems with fully worked solutions.
Conclusion: Excellent for self-study but not standalone, as it is best supplemented by problems book with solutions. For classroom use, this is clearly in the top tier of mathematics transition texts.
Prof. Read more
quite noticeable. I found this book to be an excellent book
to prep a smooth landing to university... Read more
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