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Algebra geometry, 2nd edition

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Cấu trúc

  • Cover

  • Half Title

  • Title Page

  • Copyright Page

  • Dedication

  • Contents

  • Preface to the Second Edition

  • Preface to the First Edition

  • Prolegomena

  • SECTION I: IDEAS

    • CHAPTER 1: The Nature of Mathematics

      • 1.1. MATHEMATICS IN HISTORY

      • 1.2. MATHEMATICS TODAY

      • 1.3. THE SCOPE OF MATHEMATICS

      • 1.4. WHAT THEY (PROBABLY) DIDN’T TELL YOU IN SCHOOL

      • 1.5. FURTHER READING

    • CHAPTER 2: Proofs

      • 2.1. MATHEMATICAL TRUTH

      • 2.2. FUNDAMENTAL ASSUMPTIONS OF LOGIC

      • 2.3. FIVE EASY PROOFS

      • 2.4. AXIOMS

      • 2.5. UN PETIT PEU DE PHILOSOPHIE

      • 2.6. MATHEMATICAL CREATIVITY

      • 2.7. PROVING SOMETHING FALSE

      • 2.8. TERMINOLOGY

      • 2.9. ADVICE ON PROOFS

    • CHAPTER 3: Foundations

      • 3.1. SETS

      • 3.2. BOOLEAN OPERATIONS

      • 3.3. RELATIONS

      • 3.4. FUNCTIONS

      • 3.5. EQUIVALENCE RELATIONS

      • 3.6. ORDER RELATIONS

      • 3.7. QUANTIFIERS

      • 3.8. PROOF BY INDUCTION

      • 3.9. COUNTING

      • 3.10. INFINITE NUMBERS

    • CHAPTER 4: Algebra Redux

      • 4.1. RULES OF THE GAME

      • 4.2. ALGEBRAIC AXIOMS FOR REAL NUMBERS

      • 4.3. SOLVING QUADRATIC EQUATIONS

      • 4.4. BINOMIAL THEOREM

      • 4.5. BOOLEAN ALGEBRAS

      • 4.6. CHARACTERIZING REAL NUMBERS

  • SECTION II: THEORIES

    • CHAPTER 5: Number Theory

      • 5.1. REMAINDER THEOREM

      • 5.2. GREATEST COMMON DIVISORS

      • 5.3. FUNDAMENTAL THEOREM OF ARITHMETIC

      • 5.4. MODULAR ARITHMETIC

      • 5.5. CONTINUED FRACTIONS

    • CHAPTER 6: Complex Numbers

      • 6.1. COMPLEX NUMBER ARITHMETIC

      • 6.2. COMPLEX NUMBER GEOMETRY

      • 6.3. EULER’S FORMULA FOR COMPLEX NUMBERS

      • 6.4. MAKING SENSE OF COMPLEX NUMBERS

    • CHAPTER 7: Polynomials

      • 7.1. TERMINOLOGY

      • 7.2. THE REMAINDER THEOREM

      • 7.3. ROOTS OF POLYNOMIALS

      • 7.4. FUNDAMENTAL THEOREM OF ALGEBRA

      • 7.5. ARBITRARY ROOTS OF COMPLEX NUMBERS

      • 7.6. GREATEST COMMON DIVISORS OF POLYNOMIALS

      • 7.7. IRREDUCIBLE POLYNOMIALS

      • 7.8. PARTIAL FRACTIONS

      • 7.9. RADICAL SOLUTIONS

      • 7.10. ALGEBRAIC AND TRANSCENDENTAL NUMBERS

      • 7.11. MODULAR ARITHMETIC WITH POLYNOMIALS

    • CHAPTER 8: Matrices

      • 8.1. MATRIX ARITHMETIC

      • 8.2. MATRIX ALGEBRA

      • 8.3. SOLVING SYSTEMS OF LINEAR EQUATIONS

      • 8.4. DETERMINANTS

      • 8.5. INVERTIBLE MATRICES

      • 8.6. DIAGONALIZATION

      • 8.7. BLANKINSHIP’S ALGORITHM

    • CHAPTER 9: Vectors

      • 9.1. VECTORS GEOMETRICALLY

      • 9.2. VECTORS ALGEBRAICALLY

      • 9.3. GEOMETRIC MEANING OF DETERMINANTS

      • 9.4. GEOMETRY WITH VECTORS

      • 9.5. LINEAR FUNCTIONS

      • 9.6. ALGEBRAIC MEANING OF DETERMINANTS

      • 9.7. QUATERNIONS

    • CHAPTER 10: The Principal Axes Theorem

      • 10.1. ORTHOGONAL MATRICES

      • 10.2. ORTHOGONAL DIAGONALIZATION

      • 10.3. CONICS AND QUADRICS

    • CHAPTER 11: What are the Real Numbers?

      • 11.1. THE PROPERTIES OF THE REAL NUMBERS

      • 11.2. APPROXIMATING REAL NUMBERS BY RATIONAL NUMBERS

      • 11.3. A CONSTRUCTION OF THE REAL NUMBERS

  • Epilegomena

  • Bibliography

  • Index

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