The Queen of Mathematics : a Historically Motivated Guide to Number Theory /: a Historically Motivated Guide to Number Theory. (1997)

• Record Type: Book
• Further Information: Note: Jay Goldman.
• Authors: Goldman, Jay
• Contents: Cover; Half Title; Title Page; Copyright Page; Dedication Page; Preface; Acknowledgements; Notation and Numbering; Table of Contents; Preface; Acknowledgements; Notation and Numbering; PART 1: FROM FERMAT TO LEGENDRE; Chapter 1. The Founding Fathers; 1. The Beginnings; 2. Fermat's Mathematical Background; 3. Pythagorean Triples; Appendix: Properties of the Integers; Chapter 2. Fermat; 1. Fermat (1601-1665); 2. Infinite Descent; 3. Fermat's Last Theorem; 4. Pell's Equation; 5. y3 = x2 + k; 6. Sums of Squares; 7. Perfect Numbers and Fermat's Little Theorem; 8. Fermat's Error; Chapter 3. Euler 1. Euler2. Partitions of a Number; 3. The Beginning of Analytic Number Theory; Prime Numbers, Zeta Functions, Bernoulli Numbers; 4. Arithmetic Functions; 5. The Beginning of Algebraic Number Theory; Chapter 4. From Euler to Lagrange; The Theory of Continued Fractions; 1. Introduction; 2. The Basic Notions: Finite and Infinite Continued Fractions; The Continued Fraction Algorithm; 3. The Early History; 4. The Algebra of Finite Continued Fractions; 5. The Arithmetic of Finite Continued Fractions; 6. Infinite Continued Fractions; 7. Diophantine Approximation and Geometry 8. Quadratic Irrationalities9. Pell's Equation; 10. Generalizations; Chapter 5. Lagrange; 1. Lagrange and His Work; 2. Quadratic Forms; Chapter 6. Legendre; 1. Legendre; 2. Rational Points on Conics; 3. Distribution of Prime Numbers; 4. Quadratic Residues and Quadratic Reciprocity; PART 2: GAUSS AND THE DISQUISITIONES ARITHMETICAE; Chapter 7. Gauss; 1. Gauss and His Work; 2. An Overview of the Disquisitiones Arithmeticae; Chapter 8. Theory of Congruence 1; 1. Section I of the Disquisitiones; 2. Residue Classes; 3. Congruences and Algebraic Structures; 4. Applications; 5. Linear Congruences Chapter 9. Theory of Congruences 21. Introduction; 2. Reduced Residue Classes; 3. The Structure of Z/nZ; 4. Polynomial Congruences; 5. Polynomial Congruences and Polynomial Functions; 6. Congruences in Several Variables; Chevalley's Theorem; 7. Solutions of Congruences and Solutions of Equations; The Hasse Principle; Chapter 10. Primitive Roots and Power Residues; 1. Primitive Roots; 2. Indices; 3. kth Power Residues; Chapter 11. Congruences of the Second Degree; 1. Introduction; 2. Elementary Properties of Quadratic Residues; 3. Gauss's Lemma; 4. Computing (a/p); 5. Quadratic Reciprocity 1 6. Quadratic Reciprocity 27. Some History and Other Proofs; 8. The Jacobi Symbol; Chapter 12. Binary Quadratic Forms 1: Arithmetic Theory; 1. Introduction; 2. Equivalence of Forms; 3. Matrix Notation and the Discriminant; 4. Reduced Forms and the Number of Classes; 5. Representation and Equivalence; 6. Representations and Quadratic Residues; 7. Proper Equivalence; 8. Definite and Indefinite Forms; 9. Positive Definite Forms; 10. Primitive Forms and the Class Number; Chapter 13. Binary Quadratic Forms 2: Geometric Theory; 1. Introduction; 2. The Roots of a Form
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 1997
• Extent: 1 online resource
• Subjects: 512.7-dc20; Mathematics; Statistics; Mathematics -- Philosophy; Number theory; Mathematics; Mathematics -- Philosophy; Number theory; Statistics; Electronic books
• Languages: English
• ISBNs: 9781439864623; 1439864624
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.