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, 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.

Genres: Mathematics, Nonfiction, Reference, Textbooks

318 pages, Hardcover

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.