Fundamental structures of algebra / George D. Mostow, Joseph H. Sampson, Jean-Pierre Meyer

This book provides a sound foundation for beginners in algebra. It is clearly written and seems to conform to the Bourbaki canon. There are numerous exercises which can lead to the acquisition of a good technique. These, along with the text, contain a significant number of topics which are considered old-fashioned in some quarters, for example, the Lagrange interpolation formula and a complete treatment of partial fractions. All the usual topics of elementary analytic geometry up through the conics and quadrics are included as part of linear algebra. The chapter on tensors provides the first treatment, known to the reviewer, of multilinear algebra available at this level, and should prove especially useful. The authors use the book with first-year undergraduates. Others will not hesitate to use it at a later stage. Contents: (1) Binary operations and groups, (2) Rings, integral domains, the integers, (3) Fields, the rational numbers, (4) The real number system, (5) The field of complex numbers, (6) Polynomials, (7) Rational functions, (8) Vector spaces and affine spaces, (9) Linear transformations and matrices, (10) Groups and permutations, (11) Determinants, (12) Rings of operators and differential equations, (13) The Jordan normal form, (14) Quadratic and hermitian forms, (15) Quotient structures, (16) Tensors. (MathSciNet)