Conquest of the Planefor a didactic primer on Analytic Geometry and Calculus ISBN 9789080477469 March 2011 EUR 24.95
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Cover text CONQUEST OF THE PLANE provides:
For the professions that apply mathematics like physics, engineering, biology, economics and evidence based medicine, the book provides documentation to judge on the proposal to let the national parliaments look into mathematics education, as explained in the book Elegance with Substance by the same author. Calculus can be developed with algebra and without the use of limits and infinitesimals. Define y / x as the outcome of division and y // x as the procedure of division. Using y // x with x possibly becoming zero will not be paradoxical when the paradoxical part has first been eliminated by algebraic simplification. The Weierstrasz epsilon and delta and its Cauchy shorthand with limits are paradoxical since those exclude the zero values that are precisely the values of interest at the point where the limit is taken. Much of calculus might well do without the limit idea and it could be advantageous to see calculus as part of algebra rather than a separate subject. This is not just a didactic observation but an essential refoundation of calculus. Didactic issues in trigonometry concern the opaque names of sine and cosine and the cluttering of questions with or 360 degrees whereas a simple 1 suffices. Basically the plane itself gives that unit of 1, and angles are mere sections. The solution is to use the unit turn or unit of measurement (meter) around (UMA) as the yardstick for angles. This gives the Xur and Yur functions, defined on the circle with unit circumference and generating the {X, Y} coordinates on the circle with unit radius. Finally students will understand what Cos and Sin are. The common term 'dimensionless' appears to confuse 'no unit of measurement specified' (with a metric, in planimetry and trigonometry) with 'no dimension' (a pure number, in number theory). The relevant mathematical constant is = 2(capital theta, reminiscent of a circle) rather than and it comes into use much less when we use UMAs instead of radians. The sine and cosine remain relevant the derivative, and that can also be shown in an elegant manner. You can benefit from this book also when you don't have the software. However, with the software, you will have an interactive environment in which you can test the propositions in this book and your own deductions. The software is included in The Economics Pack  by the same author  which is an application of Mathematica, a system for doing mathematics with the computer. The Pack has users in many countries in the world. The Pack is available for Windows XP, Macintosh and Unix platforms and requires Mathematica 8.0.1 or later. It can be freely downloaded, but you need a licence to run it. 
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Reading Notes for COTP August 2011 Neoclassical Mathematics for the Schools
EMS Review
October 2011
Review by
Richard Gill (KNAW, Leiden) January 2012
(published
version NAW, March
2012, without corrections)
Presentation
of Workshop D5 of the Dutch Teachers of Mathematics Day, November 9 2013
(English version).
Also available with spoken discussion at YouTube.
Warning: This book proves radical new ideas and must be read with care. If you spend more than a cursory glance on the PDF then it is advisable to get the hardcopy and continue reading from paper. I tend to focus my research on misconceptions that lead society away from common sense, and then I select pivots that cause crucially different points of view depending on how the argument is resolved. Such a pivot only works well if the argumentation gets proper attention. 
Dutch
(1) "Review" van "Conquest of the Plane", Euclides, februari 2012, 874,
p168170
(2) Reactie
op deze laatste "review", 9 februari 2012
(3) Detailkritiek,
13 februari 2012
(4) Emails van Joop
van Dormolen over COTP
uit 2012
(5) Christiaan Boudri over
COTP, 15 maart 2013. Zie ook de Forum
pagina bij de NVvW, 18 maart 2013
(6) Presentatie D5
voor de NVvW Studiedag,
9 november 2013 (of neem de Engelse
versie of op YouTube).
Hier is de NVvW download pagina voor alle workshops.
Type  Price  Description 
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One copy of "Conquest of the Plane" (COTP) Ordering 
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See The Economics Pack (TEP) 
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