Leseprobe
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Algebraic Theory of Numbers. (AM-1), Volume 1
Hermann Weyl
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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 "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.
Kundenbewertungen
Prime ideal, Equation, Prime number theorem, Mathematics, Principal ideal, Galois theory, Theorem, Galois group, Finite field, Calculation, Irreducible polynomial, Sign (mathematics), Algebra, Divisibility rule, P-adic number, Automorphism, Analytic function, Logarithm, Vector space, Algebraic number field, Prime factor, Algebraic number theory, An Introduction to the Theory of Numbers, Coefficient, Ring (mathematics), Commutative ring, Subgroup, Division algebra, Root of unity, Quadratic field, Algebraic theory, Natural number, Identity matrix, Cyclotomic field, Big O notation, Adjunction (field theory), Algebraic equation, Complex number, Infinite product, Variable (mathematics), Commutative property, Number theory, Ring of integers, Dirichlet series, Ideal number, Modular arithmetic, Polynomial, Algebraic number, Fundamental theorem of algebra, Quadratic equation, Abelian group, Irreducibility (mathematics), Algebraic operation, Riemann surface, Algebraic surface, Geometry, Multiplicative group, Theory of equations, Quadratic form, Summation, Additive group, Integer, Algebraic function, Square number, Prime number, Quadratic residue, Divisor, Scientific notation, Abstract algebra, Quadratic reciprocity