Modern Algebra : Time for Change

Introduction

So what is modern about Modern Algebra anyhow? It is an old subject, to be sure, and calling it "modern" in the sense of "recent" is a misnomer. The first conception of an abstract group-a set of elements whose natures were completely unspecified but which operated on one another according to a multiplication table that often came out of the blue-goes back to Cayley [1854].

The early date of Cayley's work makes clear that, when your Modern Algebra course was created and named (around the middle of the 20th century in the case of many colleges), the idea of it being modern in the sense of recent was not true even then. However, there was a different sense in which the adjective was reasonable. (And, after all, something was needed to distinguish it from College Algebra, which dealt only with the real and complex numbers.) By now, however, even that further justification is less persuasive than it once was. Mystifying right? OK, so let's fill in a little context.