This is a comprehensive textbook on modern algebra written by an
internationally renowned specialist. It covers material traditionally
found in advanced undergraduate and basic graduate courses and presents
it in a lucid style. The author includes almost no technically difficult
proofs, and reflecting his point of view on mathematics, he tries
wherever possible to replace calculations and difficult deductions with
conceptual proofs and to associate geometric images to algebraic
objects. The effort spent on the part of students in absorbing these
ideas will pay off when they turn to solving problems outside of this
textbook. Another important feature is the presentation of most topics
on several levels, allowing students to move smoothly from initial
acquaintance with the subject to thorough study and a deeper
understanding. Basic topics are included, such as algebraic structures,
linear algebra, polynomials, and groups, as well as more advanced
topics, such as affine and projective spaces, tensor algebra, Galois
theory, Lie groups, and associative algebras and their representations.
Some applications of linear algebra and group theory to physics are
discussed. The book is written with extreme care and contains over 200
exercises and 70 figures. It is ideal as a textbook and also suitable
for independent study for advanced undergraduates and graduate students.
||E. B. Vinberg
||Orient Blackswan Pvt Ltd.