A Concise Introduction to Pure Mathematics

by Martin W. Liebeck

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 n th 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.

Genres: Mathematics, Nonfiction, Reference, Textbooks

268 pages, Paperback

First published March 24, 2000

Reviews

[Ronan Dance · Rating 4 out of 5]

university reading

[Jeff · Rating 2 out of 5]

Apparently I like my math messy

[Muhammd Awais]

Need

[M · Rating 3 out of 5]

Ill leave it as an exercise to the reader to determine why this book gets 3 stars

[k4khalid · Rating 3 out of 5]

Interesting and challenging but pure maths is so slow to read 😭

[Jack Taft · Rating 5 out of 5]

An incredibly useful resource, will refer back to it in future study.

[Yekorzh · Rating 3 out of 5]

The chapters theory at first glance is quite enough, but when it comes to solving problems - it gets to hard

[Molidere · Rating 3 out of 5]

Good book to give to a student yet to apply to university and who is considering a degree in mathematics. Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts. 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.e. Spivak). 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.

[Maurizio Codogno · Rating 4 out of 5]

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.

Rispetto a quello che ricordo io del mio primo anno di matematica, il livello è molto più basso; sarà che la facoltà di Pisa voleva mantenere la sua fama e teneva corsi molti teorici, però garantisco che non lo si può certo usare come libro di testo, o forse sì ma per informatica. Ciò detto, non è che sia da buttare: è scritto in maniera molto scorrevole e quindi permette una lettura agevole. 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... sempre che apprezziate i giochi di parole matematici.

[Juan Francisco · Rating 3 out of 5]

The first chapters are a great introduction to advance maths, but some explanations in the last chapters are incredible complex.