Vector Spaces & Field Extensions

Abstract algebra provides many foundations for other branches of mathematics. This book, based upon over a decade of independent study outside the classroom, is the second in a series of books which provide a detailed and thorough introduction to the subject. The work builds upon the work in the first book on groups and rings by leading the reader through the study of vector spaces, linear maps, field extensions and field-fixing ring automorphisms. Throughout this development, the topics are presented with an emphasis on theory over application. The reader is assumed to have no previous knowledge of abstract algebra, although some experience with logic as used in mathematical proofs such as induction and contraposition will be helpful. The book is not intended as a textbook and is suitable for someone pursuing the study of abstract algebra as a hobby outside the classroom.