A Concise Introduction to Pure Mathematics, Fourth Edition (Chapman Hall/CRC Mathematics)

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The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. 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. Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics.

You can change your choices at any time by visiting Cookie preferences, as described in the Cookie notice. 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; Euler's formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions. By using the Web site, you confirm that you have read, understood, and agreed to be bound by the Terms and Conditions. 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. 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.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 more advanced courses in abstract algebra and analysis. Web icon An illustration of a computer application window Wayback Machine Texts icon An illustration of an open book. 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. 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. Very superficial, no real "mathematical idea", and not in the least any insight about the levels of depth of mathematical concepts, i.

New to the Fourth EditionTwo new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applicationsNew material on inequalities, counting methods, the inclusion-exclusion principle, and Eulers phi function Numerous new exercises, with solutions to the odd-numbered onesThrough 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. The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … . 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. Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for.

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. 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; Eulers formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions. It is many years since I did my engineering degree and I wanted to brush up my maths and learn the modern approach to the subject.

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. 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. 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.

The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis. 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.