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Synopsis
A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.
The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.
What's New in the Second Edition:
The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.
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Review
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.
Robert Guralnick, Chair of the Mathematics Department, University of Southern California, from the Foreword
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