Mathematical Proof

Today, we started looking at Chapter 11 in the text. The main idea is that logical proofs can be broken down step by step, sometimes at a level so specific that many of the steps seem obvious (but aren’t).  I added the topic of Euclidean geometry, which we discussed in class (and isn’t in the book). The main axioms we have there are the following.

  1. Given two points, we may draw a line between those points.
  2. Given a line between two points, that line may be extended indefinitely in either direction.
  3. Given a point and a radius (some distance), we can create the circle having the point as the center and containing all points at the radius’ distance from the center.
  4. All right angles are congruent.
  5. Given a point and a line, there exists precisely one line through the point that is parallel to the given line.

I’ll be expending on these in class on Wednesday and Friday. I’ll provide some more detail on the website at that point.

Class Project

We discussed the class project briefly. You will work individually on a topic of your choice, either expanding on something that has been covered in class or following a topic of your own interest related to the spirit of the course. An additional stipulation is that no two students may work on projects that are too closely related. I prefer presentations (10-15 minutes) to the class, but am open to videos that you may produce, and other options. As a last resort, you can write a paper (4-5 pages, with correct citations, etc.). Remember that this is worth 25% of your grade, and you should therefore be trying to impress and interest me. Beyond that, you’re being given a pretty good amount of independence with this project, and my hope is that you take advantage of that and be creative. I’ll give you an example in class on Wednesday (tomorrow).

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