Serge Lang

Together with Linear Algebra, Undergraduate Algebra is part of the algebra program’s curriculum geared toward students in their first year of college. The separation of linear algebra from the other basic algebraic structures conforms to all current undergraduate education trends, and I agree with these trends. I have ensured that this work can stand on its own, rationally speaking.

However, it is highly recommended that students first get familiar with linear algebra before moving on to the more abstract concepts of groups, rings, and fields, as well as the methodical development of the fundamental abstract features of these concepts. Because I attempted to make this book stand alone, there is some duplication between it and the book Linear Algebra. I begin by defining vector spaces, matrices, and linear maps, then proceed to demonstrate the fundamental properties of each one.

The present book has the potential to be utilized for either a single semester or an entire academic year’s worth of instruction, with the inclusion of Linear Algebra as an option. I believe it is vital to do the field theory and the Galois theory; more importantly, I would say that to do much more group theory than we have done here. Specifically, I think doing the field theory and the Galois theory is important. A section on finite fields demonstrates characteristics that come from general field theory and characteristics that are unique because of characteristic p. These interdisciplinary disciplines have recently become significant in coding theory.