## A Concise Introduction to Pure Mathematics, Second EditionFor 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. |

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### Contents

Sets and Proofs | 1 |

Number Systems | 11 |

Decimals | 17 |

Inequalities | 23 |

nh Roots and Rational Powers | 29 |

Complex Numbers | 33 |

Polynomial Equations | 45 |

Induction | 55 |

The Integers | 87 |

Prime Factorization | 95 |

More on Prime Numbers | 103 |

Congruence of Integers | 107 |

Counting and Choosing | 115 |

Vlll | 127 |

Infinity | 145 |

159 | |

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Answer argument bijection called Cartesian product coefficients common factor complex numbers congruence equation connected plane graph coprime countable countable sets Critic Ivor Smallbrain cube roots cubic equation decimal expressions deduce define DEFINITION Let digits elements equal equivalence classes equivalence relation Euler's formula example Exercises for Chapter faces fifth root finite sets Fundamental Theorem hcf(a Hence implies inequality infinite set inverse function Liebeck lower bound Mathematical Induction modulo n'h roots notation number of choices number of regions number system pairs pentagonal Platonic solids polar form polygon polynomial equation positive integer positive real number prime factorization prime numbers product of prime Proposition 8.1 rational numbers real line regular polyhedron remainder result roots of unity satisfies the formula set consisting solution statement P(n Strong Induction subsets Suppose true vertex vertices write