A Concise Introduction to Pure Mathematics

Martin Liebeck

A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon essential topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.

The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.

The textbook allows for courses with various points of emphasis because it can be divided into four reasonably independent sections related to an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.