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

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Good book to give to a student yet to apply to university and who is considering a degree in mathematics. Very superficial, no real "mathematical idea", and not in the least any insight about the levels of depth of mathematical concepts, i. Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Editionpresents some of the most fundamental and beautiful ideas in pure mathematics. Can also make for a fun read over Summer for a student who will be pursuing a maths degree once the term starts.The author introduces the absolutely unnecessary relation "i These new chapters introduce the ideas of limits of sequences and continuous functions as well as several interesting applications, such as the use of the intermediate value theorem to prove the existence of nth roots. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.

This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. These new chapters introduce the ideas of limits of sequences and continuous functions as well as several interesting applications, such as the use of the intermediate value theorem to prove the existence of n th roots.

By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. 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. 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; Eulers 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. In addition to preparing students to go on in 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.