Number Theory An Introduction to Mathematics Second Edition

Number Theory An Introduction to Mathematics by W. Coppel

PDF Free Download | Number Theory An Introduction to Mathematics Second Edition by W. A. Coppel

Contents of Number Theory Introduction to Mathematics

  • Part A. The Expanding Universe of Numbers
  • Sets, Relations and Mappings
  • Natural Numbers
  • Integers and Rational Numbers
  • Real Numbers
  • Metric Spaces
  • Complex Numbers
  • Quaternions and Octonions
  • Groups
  • Rings and Fields
  • Vector Spaces and Associative Algebras
  • Inner Product Spaces
  • Further Remarks
  • Selected References
  • Additional References
  • Divisibility
  • Greatest Common Divisors
  • The B´ezout Identity
  • Polynomials
  • Euclidean Domains
  • Congruences
  • Sums of Squares
  • Further Remarks
  • Selected References
  • Additional References
  • More on Divisibility
  • The Law of Quadratic Reciprocity
  • Quadratic Fields
  • Multiplicative Functions
  • Linear Diophantine Equations
  • Further Remarks
  • Selected References
  • Additional References
  • IV Continued Fractions and Their Uses
  • The Continued Fraction Algorithm
  • Diophantine Approximation
  • Periodic Continued Fractions
  • Quadratic Diophantine Equations
  • The Modular Group
  • Non-Euclidean Geometry
  • Complements
  • Further Remarks
  • Selected References
  • Additional References
  • Hadamard’s Determinant Problem
  • What is a Determinant?
  • Hadamard Matrices
  • The Art of Weighing
  • Some Matrix Theory
  • Application to Hadamard’s Determinant Problem
  • Designs
  • Groups and Codes
  • Further Remarks
  • Selected References
  • VI Hensel’s p-adic Numbers
  • Valued Fields
  • Equivalence
  • Completions
  • Non-Archimedean Valued Fields
  • Hensel’s Lemma
  • Locally Compact Valued Fields
  • Further Remarks
  • Selected References
  • Part B The Arithmetic of Quadratic Forms
  • Quadratic Spaces
  • The Hilbert Symbol
  • The Hasse–Minkowski Theorem
  • Supplements
  • Further Remarks
  • Selected References
  • VIII The Geometry of Numbers
  • Minkowski’s Lattice Point Theorem
  • Lattices
  • Proof of the Lattice Point Theorem; Other Results
  • Voronoi Cells
  • Densest Packings
  • Mahler’s Compactness Theorem
  • Further Remarks
  • Selected References
  • Additional References
  • The Number of Prime Numbers
  • Finding the Problem
  • Chebyshev’s Functions
  • Proof of the Prime Number Theorem
  • The Riemann Hypothesis
  • Generalizations and Analogues
  • Alternative Formulations
  • Some Further Problems
  • Further Remarks
  • Selected References
  • Additional References
  • A Character Study
  • Primes in Arithmetic Progressions
  • Characters of Finite Abelian Groups
  • Proof of the Prime Number Theorem for Arithmetic Progressions
  • Representations of Arbitrary Finite Groups
  • Characters of Arbitrary Finite Groups
  • Induced Representations and Examples
  • Applications
  • Generalizations
  • Further Remarks
  • Selected References
  • Uniform Distribution and Ergodic Theory
  • Uniform Distribution
  • Discrepancy
  • Birkhoff’s Ergodic Theorem
  • Applications
  • Recurrence
  • Further Remarks
  • Selected References
  • Additional Reference
  • Elliptic Functions
  • Elliptic Integrals
  • The Arithmetic-Geometric Mean
  • Elliptic Functions
  • Theta Functions
  • Jacobian Elliptic Functions
  • The Modular Function
  • Further Remarks
  • Selected References
  • Connections with Number Theory
  • Sums of Squares
  • Partitions
  • Cubic Curves
  • Mordell’s Theorem
  • Further Results and Conjectures
  • Some Applications
  • Further Remarks
  • Selected References
  • Additional References
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Number Theory An Introduction to Mathematics Second Edition

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