The back cover here promises that topics in algebra will be done in a way “useful for computer science applications and the symbolic treatment of algebraic problems, pointing out and discussing their algorithmic nature.” There is nothing here, however, that is as modern and current as hyperbolic or elliptic functions, or nonlinear PDEs. There is no discussion on what about a method may be inefficient and costly or how issues related to time and space complexity may be confronted. A final short, one-page section on n log n complexity feels as if it should be a lead-in to something more substantial.
Dozen-line pseudocode algorithms are sparsely offered: for Euclidean division, square-free form of a polynomial, polynomial factorization and one or two others. These are no more — in quantity or intricacy — than what one finds in a typical modern algebra textbook.
The result is a concisely presented range of classical results, including the Chinese remainder theorem, polynomial interpolation, p-adic expansions of rational and algebraic numbers, discrete Fourier transform, and more. There is a small number of examples and exercises which would benefit from implementation details for software packages such as matlab or Maple.
As an instructor at Oakland Community College, Tom Schulte prepares students for a life in algebra.