# a fresh way to read mathematics

In spite of the title, the main subject of these lectures is not algebra, even less history, as one could conclude from a glance over the table of contents, but methodology. Their aim is to convey to the audience, which originally consisted of undergraduate students in mathematics, an idea of how mathematics is made. (from the preface)

Most of the math courses are organized such that the "historical winners" (the generally accepted theories) are laid out in a top-down manner. It's thus nice to have a bottom-up view of how these theories have developed through trials and errors. It's useful to read this book alongside an Abstract Algebra textbook to get a sense of what problems and concerns have motivated and shaped the field of Algebra. It also makes it more entertaining to study the subject because one can see how the theory has become the way it is today through a chronological progression of ideas, some of which have made it into the final triumph while others have narrowly missed out. However, one might be better equipped to appreciate the contents having taken at least an introductory level Abstract Algebra course or with the equivalent knowledge of the subject.