id: 00976389
dt: b
an: 2014a.00593
au: Wolfart, Jürgen
ti: Introduction to number theory and algebra. (Einführung in die
Zahlentheorie und Algebra.)
so: Vieweg Studium: Aufbaukurs Mathematik. Braunschweig: Vieweg. x, 223 S.
(1996).
py: 1996
pu: Braunschweig: Vieweg
la: DE
cc: F65 H45
ut: number theory; algebra; congruences; Sylow subgroups; abelian groups;
Euclidean rings; Diophantine problems; Fermat’s equation;
$abc$-conjecture; quadratic reciprocity law; ramification in quadratic
fields; prime number tests; factorization; field theory; Galois theory;
Kummer theory; transcendence
ci:
li:
ab: The concern of this book is to present the contents of a two semester
course in number theory as well as in algebra, the range of which is
based upon the idea that problems in number theory are instantly
understood as questions which are worth studying, and that algebra is
the language which must be developed for doing so. In this respect the
book is quite different from the many existing ones in this area, no
matter whether they regard algebraic or analytic number theory on the
one hand or algebra on the other ‒ none of them really include both
at the same time. However, the actual presentation of the individual
topics follows the standard pattern. The material covers congruences,
groups (including Sylow subgroups and abelian groups), rings (including
Euclidean rings and some Diophantine problems, such as Fermat’s
equation and the $abc$-conjecture), arithmetic modulo $n$ together with
the quadratic reciprocity law and ramification in quadratic fields,
prime number tests and factorization, fields and Galois theory
(including Kummer theory and the transcendence of e.g. $π$ and $e$).
The feature I like most about the book is that, in connection with the
introduction of the classical items, the author constantly refers to
today’s research work, thereby hinting at new theories, giving
numerous references, and, most importantly, directing the reader’s
attention to current mathematics and, in this way, arousing her or his
curiosity.
rv: J.Ritter (Augsburg)