Introduction to Modern Algebra and Matrix Theory: Second Edition (Dover Books on Mathematics)

This unique text provides students with a single-volume treatment of the basics of calculus and analytic geometry. It reflects the teaching methods and philosophy of Otto Schreier, an influential mathematician and professor. The order of its presentation promotes an intuitive approach to calculus, and it offers a strong emphasis on algebra with minimal prerequisites.
Starting with affine space and linear equations, the text proceeds to considerations of Euclidean space and the theory of determinants, field theory and the fundamental theorem of algebra, elements of group theory, and linear transformations and matrices. Numerous exercises at the end of each section form important supplements to the text.

German mathematician Otto Schreier (1901-29) made important contributions to combinatorial group theory in the course of his tragically short life. This book was assembled from his lecture notes by his student, Emmanuel Sperner.