Kategoria BISAC: Mathematics >> Algebra - Linear

Taking up the works of Harish-Chandra, Langlands, Borel, Casselman, Bernstein and Zelevinsky, among others, on the complex representation theory of a p -adic reductive group G, the author explores the representations of G over an algebraic closure Fl of a finite field Fl with l1 p elements, which are called 'modular representations'. The main feature of the book is to develop the theory of types over Fl, and to use this theory to prove fundamental results in the theory of modular representations.

"The present book is of evident importance to everyone interested in the representation...

From a review of the first edition:

"A logical development of the subject . . . all the important theorems and results are discussed in terms of simple worked examples. The student's understanding . . . is tested by problems at the end of each subsection, and every chapter ends with exercises."

CURRENT SCIENCE

A cornerstone of undergraduate mathematics, science, and engineering, this clear and rigorous presentation of the fundamentals of linear algebra is unique in its emphasis and integration of computational skills and mathematical abstractions....

Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other extreme, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience. Instead, "Essential Linear Algebra" clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as...

In his new undergraduate textbook, Harold M. Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra. Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century.

Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience.

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role.

The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references...