Field Theory Roman, Steven
2007, 2005, 2014-07-30, Letnik:
158
eBook
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, ...irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included. About the first edition: " ...the author has gotten across many important ideas and results. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study." -J.N. Mordeson, Zentralblatt "The book is written in a clear and explanatory style. It contains over 235 exercises which provide a challenge to the reader. The book is recommended for a graduate course in field theory as well as for independent study."- T. Albu, MathSciNet.
This book provides an advanced look at the basic theory of groups. It integrates classic material and new concepts and offers an introduction for those new to the theory of groups.
This graduate level textbook provides encyclopedic treatment of linear algebra theory, both classical and modern. This new edition has been revised and expanded with many new chapters.
Completely rewritten for its second edition, this book concentrates on discrete derivative pricing models, culminating in a thorough derivation of the Black-Scholes option pricing formulas as a ...limiting case of the Cox-Ross-Rubinstein discrete model.
This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, ...linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with important applications.
The second edition contains two new chapters: a chapter on convexity, separation and positive solutions to linear systems and a chapter on the QR decomposition, singular values and pseudoinverses. The treatments of tensor products and the umbral calculus have been greatly expanded and there is now a discussion of determinants (in the chapter on tensor products), the complexification of a real vector space, Schur's lemma and Gersgorin disks.
This user-friendly book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. The presentation is lucid and the book contains a ...plethora of exercises, examples, and illustrations.
