Algebraic Theory of Numbers (eBook)

Hermann Weyl (Autor)

eBook Download: PDF

2016
240 Seiten
Princeton University Press (Verlag)
978-1-4008-8280-9 (ISBN)

Infos

WeylHermann:

Hermann Weyl held the chair of mathematics at Zyrich Technische Hochschule from 1913 to 1930; from 1930 to 1933 he held the chair of mathematics at the University of Göttingen; and from 1933 until he retired in 1952 he was a Permanent Member of the Institute for Advanced Study in Princeton.Hermann Weyl held the chair of mathematics at Zyrich Technische Hochschule from 1913 to 1930; from 1930 to 1933 he held the chair of mathematics at the University of Göttingen; and from 1933 until he retired in 1952 he was a Permanent Member of the Institute for Advanced Study in Princeton.

---

In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "e;will be of some use,"e; has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.

Produkt-Details

• Erscheint lt. Verlag: 21.4.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Princeton Landmarks in Mathematics and Physics
• Reihe/Serie: Princeton Landmarks in Mathematics and Physics
• Zusatzinfo: 30 halftones
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Schlagworte: abelian group • absolute value • abstract algebra • Addition • Additive group • Adjunction (field theory) • Algebra • algebraic equation • Algebraic function • Algebraic manifold • algebraic number • algebraic number field • algebraic number theory • Algebraic operation • algebraic surface • algebraic theory • analytic function • An Introduction to the Theory of Numbers • automorphism • axiomatic system • Bernhard Riemann • Big O notation • Calculation • Class Number • coefficient • commutative property • Commutative Ring • complex number • Cyclic group • Cyclotomic field • Dimension • direct product • Dirichlet series • discriminant • Divisibility rule • division algebra • Divisor • Entire function • Equation • Euler function • existential quantification • finite field • Fractional ideal • functional equation • Fundamental Theorem of Algebra • Galois group • Galois Theory • Geometry • Ground field • Hermann Weyl • Ideal number • Identity matrix • Infinite product • Integer • Irreducibility (mathematics) • irreducible polynomial • Lattice (group) • Legendre symbol • Linear map • logarithm • Mathematics • Meromorphic Function • modular arithmetic • Multiplicative group • Natural number • Nth root • Number Theory • P-adic number • polynomial • prime factor • Prime Ideal • Prime number • prime number theorem • Prime power • Principal ideal • Quadratic equation • Quadratic field • quadratic form • Quadratic Reciprocity • Quadratic residue • real number • Reciprocity law • Riemann surface • Ring (mathematics) • Ring of integers • Root of unity • scientific notation • Sign (mathematics) • Special case • S-plane • Square Number • SUBGROUP • Summation • symmetric function • Theorem • theoretical physics • theory • theory of equations • Variable (mathematics) • Vector Space
• ISBN-10: 1-4008-8280-X / 140088280X
• ISBN-13: 978-1-4008-8280-9 / 9781400882809