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

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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. 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. 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. Liebeck’s book stands out from the crowd of similar books by being short (as the title says, it is concise) and by trying to expose students to mathematical ideas beyond the basics of sets and logic.

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.the author does not explain that the very first condition that a set should satisfy consists in giving a set through an expression which must be as unambiguous as possible. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. 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. Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts. An ideal, accessible, elegant, student-friendly, and highly recommended choice for classroom textbooks for high school and college level mathematics curriculums, A Concise Introduction to Pure Mathematics is further enhanced with a selective bibliography, an index of symbols, and a comprehensive index.

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. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. I would imagine that this book must be perfect for maths undergraduates in their first year - or even in the summer before starting. It would in fact be difficult to find in this excellent book three consecutive pages that do not contain material useful to students or practitioners.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. The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … .

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. 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. 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. An ideal, accessible, elegant, student-friendly, and highly recommended choice for classroom textbooks for high school and college-level mathematics curriculums, A Concise Introduction to Pure Mathematics is further enhanced with a selective bibliography, an index of symbols, and a comprehensive index. It will just give you a superficial overview of a bunch of theories and theorems that you will encounter sooner or later, in better form, in your college years.The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. A diligent, active reader of this outstanding book will have the best foundation at minimum cost for making meaningful contributions to mathematics, science, or engineering. 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; 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 introduces the absolutely unnecessary relation "i

You can change your choices at any time by visiting Cookie preferences, as described in the Cookie notice. 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". 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 . Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.