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

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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.

applied mathematicians also need to know about proofs, counting, inequalities, bounds, and even groups ― and this book could help them learn all that. 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". 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. Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts.The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world . 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. Ciò detto, non è che sia da buttare: è scritto in maniera molto scorrevole e quindi permette una lettura agevole. 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. 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.

The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … . 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. 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. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average.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.

When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. The author introduces the absolutely unnecessary relation "i In addition to preparing students to go on into mathematics, it is also a wonderful choice for a student who will not necessarily go on in mathematics but wants a gentle but fascinating introduction into the culture of mathematics.Web icon An illustration of a computer application window Wayback Machine Texts icon An illustration of an open book.