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 proofs Inequalities
Real numbers Decimals
Rational numbers Introduction to analysis
Complex numbers Polynomial equations
Induction Integers and prime numbers
Counting methods Countability
Functions Infinite sets
Platonic Solids Euler'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.

Contenuti:

Preface. Sets and Proofs
Number Systems
Decimals
Inequalities
nth Roots and Rational Powers
Complex Numbers
Polynomial Equations
Induction
Euler's Formula and Platonic Solids
Introduction to Analysis
The Integers
Prime Factorization
More on Prime Numbers, Congruence of Integers
Counting and Choosing
More on Sets
Equivalence Relations, Functions
Infinity
Further Reading

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