Review: Functional approach to precalculus

Functional approach to precalculus by Mustafa A. Munem
My rating: 4 of 5 stars

This text came out the year I was born as a textbook for a community college in a county adjacent to the one I teach at 45 years later. This was a fully digested of the New Mathematics or New Math brief, dramatic change in the way mathematics was taught in American grade schools during the 1960s. While the phrase is often used now to describe this change as a short-lived pedagogical fad which quickly became highly discredited, the set of teaching practices introduced in the U.S. shortly after the Sputnik crisis in order to boost science education and mathematical skill in the population, introduced topics seen here including modular arithmetic, algebraic inequalities, and abstract algebra. These topics have been greatly de-emphasized or eliminated in US elementary schools and high schools curricula since then while built upon outside of the US. Consequently, a typical US math student is a good academic year behind foreign students who also tend to school for longer during the year. The rules of sets would later prove to be very valuable with the onset of databases and other formations of data that were emerging in society. I find it is the area my incoming students are weakest at when I meet them in their final semester before calculus where the readers of this text were grappling with the idea of a set algebraically closed under an operation. This is something we cannot approach at the level of a first-year college student, any longer. This allows such concepts as the circle as a set of equidistant points from a center as well as proofs and theorems – all notions current students are allergic to. I see the readers of this text could handle mathematical induction, now an optional and often foregone topic, as well as periodic function, basic trigonometry to inverses of the sine and cosine as well as vectors and polar coordinates. Now, these topics, a good engineering foundation, have their own semester.

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