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

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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. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. 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. The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems.

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The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. Very superficial, no real "mathematical idea", and not in the least any insight about the levels of depth of mathematical concepts, i. 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 … . 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".

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. By using the Web site, you confirm that you have read, understood, and agreed to be bound by the Terms and Conditions.

The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … . Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for. This book will give a student the understanding to go on in 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, Fourth 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. 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 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. 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.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.

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. The author introduces the absolutely unnecessary relation "i 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. 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. 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.Good book to give to a student yet to apply to university and who is considering a degree in mathematics. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. It would in fact be difficult to find in this excellent book three consecutive pages that do not contain material useful to students or practitioners. 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.