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This classic text and standard reference comprises all subjects of a first-year graduate-level course, including in-depth coverage of groups and polynomials and extensive use of categories and functors. 1989 edition.

The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra • Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le.

Author : Barbara R. Sandall
ISBN : 9781580377683
Genre : Juvenile Nonfiction
File Size : 29.46 MB
Format : PDF, Kindle
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Facilitate a smooth transition from algebra to algebra II for students in grades 7 and up using Helping Students Understand Algebra II. This 128-page book includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, and answer keys. The book supports NCTM standards and includes chapters on topics such as solving equations, inequalities, polynomials, rational expressions, roots and radicals, and quadratic expressions.

Develops a new framework for working in schools that helps educators make informed decisions about change at individual, classroom, curricular and school levels on behalf of gender equity. Addresses the issue of understanding the impact of education on the two sexes, and looks at responsibility for creating gender-fair environments, organising work and creating environments for learning. The book draws on a two-year study into the role that gender played as three Catholic high schools prepared to move from single sex to coeducation. It does not weigh the advantages of single sex against coeducative approaches, but studies gender in a setting where the particpants' consciousness of gender issues was heightened: faculty and administration were formally and informally discussing gender concepts and students were talking about male and female issues. The book shows that the combination of leadership, staff and curricular awareness, and an understanding of gender fair and gender affirmative practices can serve to improve institutional effectiveness and lead to higher levels of student achievement.

Author : Alexey L. Gorodentsev
ISBN : 9783319508535
Genre : Mathematics
File Size : 54.95 MB
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This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.

Author : P.M. Cohn
ISBN : 9780857294289
Genre : Mathematics
File Size : 41.59 MB
Format : PDF
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This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.

Algebra is a compulsory paper offered to the undergraduate students of Mathematics. The majority of universities offer the subject as a two /three year paper or in two/three semesters. Algebra I: A Basic Course in Abstract Algebra covers the topic required for a basic course.