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; Euleras 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 Euleras 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.way, and some of the answers may appear strange at first sight; for example, the set of all integers and the set of all ... In them I introduce a topic known as mathematical analysis, which is the study of the real numbers and functions defined on them. ... 11, 13, 14 Introduction to discrete mathematics: Chapters 16, 17, 19, 20 Functions, relations and countability: Chapters 18, ... students more for a future course in analysis, one should use all the chapters in the first, fourth and fifth sections.

Title | : | A Concise Introduction to Pure Mathematics, Fourth Edition |

Author | : | Martin Liebeck |

Publisher | : | CRC Press - 2015-10-28 |

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