Peter Russell

James B. Carrell

A. V. Geramita

University of British Columbia

Geramita A. V.

Conference in Algebraic Geometry (1984, Vancouver, British Columbia)

Natural Sciences and Engineering Research Council Canada

The research and expository papers in this book cover a cross-section of the latest developments in modern algebraic geometry. The volume will be especially beneficial to researchers and to those who want to keep abreast of the latest directions in the field. Aimed at those with an expert background in the field, the topics covered include algebraic groups and representation theory, enumerative geometry, Schubert varieties, rationality, compactifications, and surfaces.

Proceedings of the 1984 Vancouver Conference in Algebraic Geometry

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

A Group Theoretic Approach to Linear Algebra

Groups, Matrices, and Vector Spaces

James B. Carrell

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