Precalculus, Calculus and Infinitesimals

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SUMMARY

This discussion presents an innovative approach to teaching Precalculus and Calculus, proposing a single text that integrates Algebra 1, Geometry, Algebra 2, and Precalculus, allowing students to complete the material in two years, or even one year for advanced learners. The method addresses gaps in traditional curricula, such as the premature introduction of concepts like 2^x without proper definition, by incorporating Calculus to clarify these topics. Additionally, the text introduces set theory and infinitesimals in a manner suitable for the target audience, enhancing comprehension and application.

PREREQUISITES
  • Understanding of Algebra 1 concepts
  • Familiarity with Geometry principles
  • Basic knowledge of Algebra 2
  • Introductory Calculus awareness
NEXT STEPS
  • Research effective methods for integrating Algebra and Geometry in curriculum design
  • Explore advanced Calculus techniques for teaching complex concepts
  • Study set theory fundamentals and their applications in mathematics
  • Investigate the use of infinitesimals in modern calculus education
USEFUL FOR

Educators in mathematics, curriculum developers, and students seeking an accelerated understanding of Precalculus and Calculus concepts.

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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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