-PDF Download- A Concise Introduction To Pure Mathematics Second Edition EBOOK

A Concise Introduction to Pure Mathematics, Second Edition

Author: Martin Liebeck

Publisher: CRC Press

Published: 2000-03-24

Total Pages: 180

ISBN-13: 9781584881933

For many students interested in pursuing - or required to pursue - the study of mathematics, a critical gap exists between the level of their secondary school education and the background needed to understand, appreciate, and succeed in mathematics at the university level. A Concise Introduction to Pure Mathematics provides a robust bridge over this gap. In nineteen succinct chapters, it covers the range of topics needed to build a strong foundation for the study of the higher mathematics. Sets and proofs Inequalities Real numbers Decimals Rational numbers Introduction to analysis Complex numbers Polynomial equations Induction Integers and prime numbers Counting methods Countability Functions Infinite sets Platonic Solids Euler's Formula Written in a relaxed, readable style, A Concise Introduction to Pure Mathematics leads students gently but firmly into the world of higher mathematics. It demystifies some of the perceived abstractions, intrigues its readers, and entices them to continue their exploration on to analysis, number theory, and beyond.

A Concise Introduction to Pure Mathematics

Author: Martin Liebeck

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 320

ISBN-13: 1315363283

DOWNLOAD EBOOK →

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; 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. New to the Fourth Edition Two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications New material on inequalities, counting methods, the inclusion-exclusion principle, and Euler’s phi function Numerous new exercises, with solutions to the odd-numbered ones 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. 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 Concise Introduction to Pure Mathematics

Author: Martin Liebeck

Publisher: CRC Press

Published: 2010-08-16

Total Pages: 266

ISBN-13: 1439888922

DOWNLOAD EBOOK →

A Concise Introduction to Pure Mathematics, Second Edition

Author: Martin Liebeck

Publisher: CRC Press

Published: 2005-11-02

Total Pages: 230

ISBN-13: 9781584885474

DOWNLOAD EBOOK →

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. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems. The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics. What's New in the Second Edition: Contains extra material concerning prime numbers, forming the basis for data encryption Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics Discusses Permutations and their importance in many topics in discrete mathematics The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.

A Concise Introduction to Pure Mathematics, Third Edition

Author: Martin Liebeck

Publisher: CRC Press

Published: 2011-07-06

Total Pages: 266

ISBN-13: 1439894582

DOWNLOAD EBOOK →

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. 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. New to the Third Edition The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis. 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. This edition also includes solutions to all of the odd-numbered exercises. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. 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.