Kategoria BISAC: Mathematics >> Algebra - Linear

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.

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.