What did we do:

  1. I introduced myself and my background, and discussed about the syllabus, academic integrity, homework policy, etc…For the complete discussion please refer to the syllabus in the main page or contact me.
  2. We discussed mainly 1.1 and 1.2.
    • Discussed the concept of function and how it appears in different manifestations, from the word version which migh be “bad” mathematically to the formula ones which are better, passing through graphs and tables/tabulations.
    • We discussed linear behavior and linear functions and how to detect them from table and drawing and how to deduce its equation from the data.
    • We discussed exponential behavior and exponetial functions and how to detect the from table and drawing (but we mention we have to be careful with drawings here), and we talked how to obtain the equation from the data.
    • Discussed the differences of linear and exponential behavior of functions.

What we did not do:

  1. We barely touched section 1.3. Only the concept of shifting appeared when discussing the behaviour of linear functions.
  2. We did not define increasing, decreasing and monotone functions (section 1.1, page 6).
  3. We did not define concave up or concave down functions (section 1.2, page 14).

Comments on Section 1.2:

We did not discuss any example like Example 4, page 18. Make sure to read through it.

Comments on Section 1.3:

We did not have time to discuss much of section 1.3. The most important parts are “Composition of Functions”: example 1 and 2. And “Inverse functions”. We will return to this next class, but it is a good excercise to read this by yourselves and work out this concepts.

Extra References:

The material that is mentioned here is just for those that are interested in knowing more of ideas and concepts that were mentioned in class. That said, feel free to discuss with me these or other topics mentioned that you might want to know more.

  • Black holes and linear relationships: [To be completed, there is a nice docuentary on this and I can’t find it!]
  • Carbon Dating and Natural Clocks: The book The Greatest Show on Earth of Richard Dawkins explains several Natural Clocks and how they are used to date the age of objects. It appears in chapter 4.
    • You can find this book in the U of T libraries, or by a very cheap prize in bookstores around downtown. You can also contact me if you want to read about it more and for some reason can’t find the resource.
  • Rice and Exponentials:
    • You can read the wikipedia page to get some feeling of the mathematics and the history of the problem: link.
    • Yet, there is an interesting “counter” argument to the intuition put in here that you can read in this article of Forbes: link.
  • The number e: We mentioned that e is the prefered base for exponentials. A very nice video from Numberphile, a youtube channel dedicated (quite seriously) to expanding mathematical knowledge in easy terms (they try, they are good) is the following (many ideas they mention there appear later in the course, others won’t):