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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; 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.

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 Euler's 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.



Table of Contents
Sets and Proofs

Number Systems

Decimals

nth Roots and Rational Powers

Inequalities

Complex Numbers

Polynomial Equations

Induction

Euler's Formula and Platonic Solids

The Integers

Prime Factorization

More on Prime Numbers

Congruence of Integers

More on Congruence

Secret Codes

Counting and Choosing

More on Sets

Equivalence Relations

Functions

Permutations

Infinity

Introduction to Analysis: Bounds

More Analysis: Limits

Yet More Analysis: Continuity

Introduction to Abstract Algebra: Groups

Introduction to Abstract Algebra: More on Groups

Solutions to Odd-Numbered Exercises

Further Reading

Index of Symbols

Index