Insights Precalculus, Calculus and Infinitesimals

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An unconventional approach to Precalculus is proposed, combining Algebra 1, Geometry, Algebra 2, and Precalculus into a single text, allowing average students to complete the material in two years and advanced students in one. The text presents challenges, such as introducing concepts like 2^x without prior definitions, which necessitates the inclusion of calculus for proper understanding. Calculus is introduced at the relevant point in the text to clarify these concepts. Additionally, the material includes an introduction to set theory and infinitesimals, tailored for the intended audience. This method aims to accelerate learning and deepen comprehension in mathematics.
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See my insights article for those interested in an unconventional approach to doing Precalculus at an accelerated pace and beginning Calculus.

It is different from the usual way that a precalculus is done text in that it covers in the US what is called Algebra 1, Geometry, Algebra 2, and Precalculus in one text. Instead of taking 4 years to cover the material, IMHO, an average student can do it in 2 years; a good student could do it in a year. The text has some 'issues' in that it uses things like 2^x without first defining 2^x, where x is a real number. There is only one way to fix this - with calculus. So when it reaches that point in the text, I introduce calculus and define it properly. This also includes an introduction to set theory and infinitesimals but at a level appropriate for the audience.

Thanks
Bill
 
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