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

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This book will give a student the understanding to go on in further courses in abstract algebra and analysis. 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. By using the Web site, you confirm that you have read, understood, and agreed to be bound by the Terms and Conditions. Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts. 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.

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. 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. To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. 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. 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".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 . 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. 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. Martin Liebeck is a professor and head of the Pure Mathematics Section in the Department of Mathematics at Imperial College London. Good book to give to a student yet to apply to university and who is considering a degree in mathematics.

applied mathematicians also need to know about proofs, counting, inequalities, bounds, and even groups ― and this book could help them learn all that. I would imagine that this book must be perfect for maths undergraduates in their first year - or even in the summer before starting. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. Ciò detto, non è che sia da buttare: è scritto in maniera molto scorrevole e quindi permette una lettura agevole. You can change your choices at any time by visiting Cookie preferences, as described in the Cookie notice.

Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. 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.