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. |
Contents
Sets and Proofs | 1 |
Number Systems | 13 |
Decimals | 21 |
nth Roots and Rational Powers | 29 |
Complex Numbers | 43 |
Polynomial Equations | 53 |
Eulers Formula and Platonic Solids | 69 |
Introduction to Analysis | 81 |
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Common terms and phrases
1-1 function An+1 Answer bijection Cartesian product choose coefficients common factor complex numbers congruence equation connected plane graph contradiction coprime countable Critic Ivor Smallbrain cube roots cubic equation decimal expressions define DEFINITION Let digits divides edges elements equal equivalence classes equivalence relation Euler's formula example Exercises for Chapter faces fifth root finite sets function f Fundamental Theorem hcf(a Hence implies inequality infinite set inverse function irrational Liebeck lower bound Mathematical Induction modulo notation nth roots number system pentagonal plane graph Platonic solids polar form polygon polyhedron polynomial equation positive integer positive real number prime factorization prime numbers product of prime PROOF Let prove r₁ rational number real line real number regular polyhedron result roots of unity set consisting statement P(n Strong Induction subsets Suppose true vertices write