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

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The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … .

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 … . This book will give a student the understanding to go on in further 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. The author introduces the absolutely unnecessary relation "i More Hamburger icon An icon used to represent a menu that can be toggled by interacting with this icon.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. 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. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. 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.

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. Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for. 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. 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.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. 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. The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world .