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. 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. Easier to sink one's teeth into and requires less mathematical maturity than something like Spivak's Calculus yet stills maintains the flavour of undergraduate mathematics - thereby making it a better fit for students who are either yet to settle on studying maths or whose backgrounds at such a point in time may not yet be strong enough to cope with a more challenging text (i.

The author introduces the absolutely unnecessary relation "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. 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. 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 n th roots. 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.

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 … . To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average.

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. 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. 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. 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.