A concise introduction to pure mathematics - Martin Liebeck

For many students interested in pursuing - or required to pursue - the study of mathematics, a critical gap exists between the level of their secondary school education and the background needed to understand, appreciate, and succeed in mathematics at the university level. A Concise Introduction to Pure Mathematics provides a robust bridge over this gap. In nineteen succinct chapters, it covers the range of topics needed to build a strong foundation for the study of the higher mathematics.

Sets and proofsInequalities
Real numbersDecimals
Rational numbersIntroduction to analysis
Complex numbersPolynomial equations
InductionIntegers and prime numbers
Counting methodsCountability
FunctionsInfinite sets
Platonic SolidsEuler's Formula

Written in a relaxed, readable style, A Concise Introduction to Pure Mathematics leads students gently but firmly into the world of higher mathematics. It demystifies some of the perceived abstractions, intrigues its readers, and entices them to continue their exploration on to analysis, number theory, and beyond.