Chapter 1: Cartesian Coordinate Systems

So I didn't complete a chapter yesterday like I wanted to, mostly because I was out most of the day (Prometheus makes me feel things about things) and just didn't feel like doing work upon my return. Today however, I went through the first chapter of the book. This first chapter has the same title as this post, but is mostly prepping the reader and making sure they understand the expected knowledge level required coming into the book.

Chapter 1 is broken into the following sections.

• 1.1 One Dimensional Mathematics
  This section explained natural numbers, real numbers, and the like. Basic stuff everyone should know.
• 1.2 Two Dimensional Mathematics
  Again, very simple introduction to the Cartesian coordinate system. Points as ordered pairs of numbers, orientation of axes etc. More simple stuff.
• 1.3 Three Dimensional Mathematics
  Introduces the concept of "Left-handed" and "Right-handed" coordinate systems. Left-handed axes can never be rotated to match right-handed axes perfectly. Introduced rotation direction around an axis for each system. Also introduced the conventions the book itself uses. (Left-handed)

• 1.4 Odds & Ends
  This section actually made up the bulk of the content and time spent on this chapter. It reviews the content required to understand the following chapters of the book. Topics briefly covered included: Summation Notation, Product Notation, Interval Notation, Angles, Degrees and Radians.
  The last part of this section covered all the standard Trigonometry Functions and Identities which I picked up fairly quickly considering how much I have[n't] used them since first learning them. The identities gave me a little trouble (mainly the Double Angle Identities for cos and sin), but I made sure to derive them from the Sum and Difference Identities which was quite satisfying once I understood how they worked.

 I think I've also stopped being annoyed and ashamed that I feel the need to go over highschool level math again. I realise that most people are like me and just forget the specifics once they stop using it every week. It actually feels really good to see how easy it is for me now that I'm older (damn you undeveloped brain, hindering me in highschool).

All in all, it was a fairly smooth chapter. The next chapter is on Vectors and I don't expect them to give me any large amount of trouble. I have an exam coming up though, so I don't believe I will post for another 3 or so days. </transmission>

P.S. There are slides associated with the book for anyone who wants to take a gander. They're nowhere as near as thorough as the book though. The slides for this particular chapter can be found here and the page with all the slides here.

"Careful. We don't want to learn from this." — Bill Watterson (1958–) from Calvin and Hobbes