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

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I would imagine that this book must be perfect for maths undergraduates in their first year - or even in the summer before starting.

Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems. 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.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. 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. 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. The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems.

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 . Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Editionpresents some of the most fundamental and beautiful ideas in pure mathematics.Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts.

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. 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. 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. 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.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. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. 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". The author introduces the absolutely unnecessary relation "i

The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. The 103 third parties who use cookies on this service do so for their purposes of displaying and measuring personalized ads, generating audience insights, and developing and improving products. Moreover, the book is confusing at times: concepts are often not precisely defined, and if you have the gift of critical thinking you will find lots of places where the logic standards of the book are less than acceptable.Martin Liebeck is a professor and head of the Pure Mathematics Section in the Department of Mathematics at Imperial College London. Non garantisco sulla difficoltà degli esercizi, che ovviamente non ho nemmeno provato a risolvere, non avendone al momento necessità alcuna; dateci comunque un occhio, perché alcuni sono carini almeno come formulazione. This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. 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.

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