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

Product Information

I would imagine that this book must be perfect for maths undergraduates in their first year - or even in the summer before starting.

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.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. applied mathematicians also need to know about proofs, counting, inequalities, bounds, and even groups ― and this book could help them learn all that. 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. Martin Liebeck is a professor and head of the Pure Mathematics Section in the Department of Mathematics at Imperial College London.

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.

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

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. To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average.More Hamburger icon An icon used to represent a menu that can be toggled by interacting with this icon. 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. This book will give a student the understanding to go on in further courses in abstract algebra and analysis. 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". The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems.