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

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

applied mathematicians also need to know about proofs, counting, inequalities, bounds, and even groups ― and this book could help them learn all that. 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. 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.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. 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. This book displays a unique combination of lightness and rigor, leavened with the right dose of humor.

Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for. The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … . 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. 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. 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.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. The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis. 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. 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.

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. 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 . 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. 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.

Ciò detto, non è che sia da buttare: è scritto in maniera molto scorrevole e quindi permette una lettura agevole. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. 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". 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 further courses in abstract algebra and analysis.