Lesson 4: Mathematics, The M Word

4. Lesson 4: Mathematics, The M Word#

A tiny bit of mathematics. Really.

“When I imagine a triangle, even though such a figure may exist nowhere in the world except in my thought, indeed may never have existed, there is nonetheless a certain nature or form, or particular essence, of this figure that is immutable and eternal, which I did not invent, and which in no way depends on my mind.”
René Descartes (1596-1650), Meditations on First Philosophy (1641)

This lesson is constructed like most. We’ll start with some goals, move smoothly into a short biography of an important character in the story, and then to the content. This one’s a little different. I’m going to use some mathematics in QS&BB and it’s important for you to understand why and gain confidence that like Goldilocks, we’ll do just enough.

This lesson is a little more review and reference-like than the rest. Some of you may have seen much of the content of this lesson. I’d point you to the Descartes, M Word, and Functions, the QS&BB Way sections.

Note

  Goals of this lesson Understand, Appreciate, Familiarity

I’d like you to Understand:

  • Simple one-variable algebra.

  • Exponential notation.

  • Scientific notation.

  • Unit conversion.

  • Graphical vector addition and subtraction.

I’d like you to Appreciate:

  • The approximation of complicated functions in an expansion.

I’d like you to become Familiar With:

  • Aspects of Descartes’ life.

  • The importance of Descartes’ merging of algebra and geometry.