This is the last of three volumes that,
together, give an exposition of the mathematics of grades 9–12 that
is simultaneously mathematically correct and grade-level
appropriate. The volumes are consistent with CCSSM (Common Core State
Standards for Mathematics) and aim at presenting the mathematics of
K–12 as a totally transparent subject.

This volume distinguishes itself from others of the same genre in
getting the mathematics right. In trigonometry, this volume makes
explicit the fact that the trigonometric functions cannot even be
defined without the theory of similar triangles. It also provides
details for extending the domain of definition of sine and cosine to
all real numbers. It explains as well why radians should be used for
angle measurements and gives a proof of the conversion formulas
between degrees and radians.

In calculus, this volume pares the technicalities concerning limits
down to the essential minimum to make the proofs of basic facts about
differentiation and integration both correct and accessible to school
teachers and educators; the exposition may also benefit beginning math
majors who are learning to write proofs. An added bonus is a correct
proof that one can get a repeating decimal equal to a given fraction
by the “long division” of the numerator by the
denominator. This proof attends to all three things all at once: what
an infinite decimal is, why it is equal to the fraction, and how long
division enters the picture.

This book should be useful for current and future teachers of
K–12 mathematics, as well as for some high school students and
for education professionals.

Readership

Teachers of middle school mathematics; students and
professionals interested in mathematical education.