Abstract algebra

Paul B. Garrett

Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal mapping properties, rather than by constructions whose technical details are irrelevant. Addresses Common Curricular Weaknesses In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.

「Nielsen BookData」より

[目次]

  • n Worked examples PRIMES IN ARITHMETIC PROGRESSIONS Euler's theorem and the zeta function Dirichlet's theorem Dual groups of abelian groups Non-vanishing on Re(s) = 1 Analytic continuations Dirichlet series with positive coefficients GALOIS THEORY Field extensions, imbeddings, automorphisms Separable field extensions Primitive elements Normal field extensions The main theorem Conjugates, trace, norm Basic examples Worked examples SOLVING EQUATIONS BY RADICALS Galois' criterion Composition series, Jordan-Holder theorem Solving cubics by radicals Worked examples EIGENVECTORS, SPECTRAL THEOREMS Eigenvectors, eigenvalues Diagonalizability, semi-simplicity Commuting endomorphisms ST = TS Inner product spaces Projections without coordinates Unitary operators Spectral theorems Corollaries of the spectral theorem Worked examples DUALS, NATURALITY, BILINEAR FORMS Dual vector spaces First example of naturality Bilinear forms Worked examples DETERMINANTS I Prehistory Definitions Uniqueness and other properties Existence TENSOR PRODUCTS Desiderata Definitions, uniqueness, existence First examples Tensor products f x g of maps Extension of scalars, functoriality, naturality Worked examples EXTERIOR POWERS Desiderata Definitions, uniqueness, existence Some elementary facts Exterior powers ?nf of maps Exterior powers of free modules Determinants revisited Minors of matrices Uniqueness in the structure theorem Cartan's lemma Worked examples

「Nielsen BookData」より

この本の情報

書名 Abstract algebra
著作者等 Garrett, Paul B
Garrett Paul B.
出版元 Chapman & Hall/CRC
刊行年月 c2008
ページ数 451 p.
大きさ 26 cm
ISBN 9781584886891
NCID BA83531733
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想