The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems.

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 nth roots.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. 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. Liebeck’s book stands out from the crowd of similar books by being short (as the title says, it is concise) and by trying to expose students to mathematical ideas beyond the basics of sets and logic. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems. The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis.

Particularly able prospective maths students with stronger backgrounds will likely get more out of self-studying either Spivak's Calculus or Apostol's Calculus Volume I. The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world . Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses.Easier to sink one's teeth into and requires less mathematical maturity than something like Spivak's Calculus yet stills maintains the flavour of undergraduate mathematics - thereby making it a better fit for students who are either yet to settle on studying maths or whose backgrounds at such a point in time may not yet be strong enough to cope with a more challenging text (i. By using the Web site, you confirm that you have read, understood, and agreed to be bound by the Terms and Conditions. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. 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. 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.

Through careful explanations and examples, this popular textbook illustrates the power and beauty of basic mathematical concepts in number theory, discrete mathematics, analysis, and abstract algebra. 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. 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. This book displays a unique combination of lightness and rigor, leavened with the right dose of humor.In addition to preparing students to go on into 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. In addition to the pre-Analysis and pre-Algebra chapters, there are chapters on complex numbers, inequalities, some number theory and combinatorics, and the Platonic solids. 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. 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 . the author does not explain that the very first condition that a set should satisfy consists in giving a set through an expression which must be as unambiguous as possible.