Conquest of the Plane
This book is a primer on Calculus and Analytic Geometry and not a text book, but it has a textbook format. It has different functions for different readers: students, teachers and professionals that apply mathematics. The first four parts have been written with the students in mind, while the fifth part explains the didactics to both teachers and students in didactics of mathematics.
It is claimed that the book can be studied with and without "The Economics Pack, Applications of Mathematica", but it is worthwhile mentioning that the book does not include exercises, this program provides the exercises required by the reader to confirm he has understood the matter correctly.
The contents of the book are the following:
(1) Arithmetic, Algebra and Geometry with coordinates: lines, circles and vectors.
(2) Trigonometry, the Complex plane and Linear Algebra.
(3) Calculus, developped fully from algebra.
(4) Applications from physics, economics and statistics.
(6) An extensive discussion of the didactics.
The reading must be aware that this book can produce disquieting feelings. Indeed, I felt myself uncomfortable, since I was reading very elementary mathematics I knew well, but the unusual notations and presentation created a barrier to my understanding. Moreover, according to the author style, he introduces surprisingly rather deep digressions explaining why he has chosen a concrete approach to introduce some notion. The reader must be very attentive at this point, since this kind of comments constitutes one of the most valuable characteristics of this book.
Once the reader becomes familiar with the notations and the author style, he/she will enjoy the book. I am convinced that this work will help the students to recognize what they should know but they ignore, and so it could be intended as a refresher course. It also helps those parents who try to help their kids with math and, mainly, the book provides new insights for the teacher both in didactics and mathematics itself.
Some words are needed to warn researchers in Physics, Economics or Biology that the mathematical background needed by theme exceeds enormously the contents of this book.