A Concise Introduction to Pure Mathematics, Second EditionA Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic 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. What's New in the Second Edition: The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly 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. |
Contents
Sets and Proofs | 1 |
Number Systems | 13 |
Decimals | 21 |
Inequalities | 27 |
nth Roots and Rational Powers | 31 |
Complex Numbers | 35 |
Polynomial Equations | 47 |
Induction | 57 |
Congruence of Integers | 111 |
More on Congruence | 121 |
Secret Codes | 131 |
Counting and Choosing | 137 |
More on Sets | 149 |
Equivalence Relations | 157 |
Functions | 163 |
Permutations | 173 |
Eulers Formula and Platonic Solids | 71 |
Introduction to Analysis | 81 |
The Integers | 91 |
Prime Factorization | 99 |
More on Prime Numbers | 107 |
Infinity | 187 |
Further Reading | 197 |
| 199 | |
| 201 | |
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Common terms and phrases
2-cycle a₁ answer bijection called choose codes coefficients complex numbers congruence equation connected plane graph contradiction coprime countable critic Ivor Smallbrain cube roots cubic equation cycle notation cycle-shape decimal expressions deduce define DEFINITION Let digits divides edges elements equal equivalence classes equivalence relation Euler's formula example Exercises for Chapter Fermat's Little Theorem finite sets function Fundamental Theorem hcf(a,b Hence infinite set integers s,t isin Liebeck lower bound Mathematical Induction mathematics Miller's test modulo multiple nth roots number system odd permutations P₁ permutations plane graph Platonic solids polyhedron polynomial positive integer positive real number prime factorization prime numbers prove r₁ rational number real line real number result roots of unity s₁ sends sequence set consisting solution solve statement P(n subsets Suppose symbol total number true upper bound vertices words write α₁
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