When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. 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. 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. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts.

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 further 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. 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. The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world .This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. 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 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. 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.

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 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 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. The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … . 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.Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis.