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

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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. This book displays a unique combination of lightness and rigor, leavened with the right dose of humor.

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. Ciò detto, non è che sia da buttare: è scritto in maniera molto scorrevole e quindi permette una lettura agevole. 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.Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for…applied mathematicians also need to know about proofs, counting, inequalities, bounds, and even groups — and this book could help them learn all that. 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. 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 … . 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.

More Hamburger icon An icon used to represent a menu that can be toggled by interacting with this icon. 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.Web icon An illustration of a computer application window Wayback Machine Texts icon An illustration of an open book. Questo libro è fondamentalmente un'introduzione all'analisi matematica e all'algebra che si studiano (negli USA) nel primo anno di università, il che significa che è tranquillamente alla portata di un liceale nostrano dell'ultimo anno, tenuto conto che le dimostrazioni più complicate sono omesse. 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. 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. Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts.

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.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.