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

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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. Of course here the ambiguity reigns supreme, as it is not clear how to define the notion of "people living in Denmark" with precision, unless (and this should be specified when defining such a set) we add the sentence "according to a given population census". 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. 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.

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.

By using the Web site, you confirm that you have read, understood, and agreed to be bound by the Terms and Conditions. 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 … . Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for. 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.

Rispetto a quello che ricordo io del mio primo anno di matematica, il livello è molto più basso; sarà che la facoltà di Pisa voleva mantenere la sua fama e teneva corsi molti teorici, però garantisco che non lo si può certo usare come libro di testo, o forse sì ma per informatica.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.

Martin Liebeck is a professor and head of the Pure Mathematics Section in the Department of Mathematics at Imperial College London. 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.Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts. To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average.

The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis. 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. 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.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. 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, the use of Euler’s formula to study the five Platonic solids, the use of prime numbers to encode and decode secret information, and the theory of how to compare the sizes of two infinite sets. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.

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