We will begin class with a very short quiz (surprise!) that I predict you will do well on, but I need to confirm that hypothesis to plan well going forward.

Test Review

Next we'll review the results of Wednesday's test. The grade distribution was: A: 4, B: 4, C: 2, and D: 2. Here are the solutions to the test questions.

I blame myself for giving you the last problem, which only Stephen proved correctly. We did not spend adequet time in class on problems like this and it was not fair of me to select it. With that in mind I gave 2/3 credit for anyone who correctly identified elements of the problem statement.

Looking Forward

The main tools you have when writting a proof are:

• definitions
• propositions
• specific givens

We'll talk about how each of these are used in the proofs on the test.

The Principle of Mathematical Induction

I am going to use a bit of class time to talk more about something mentioned in section 2.2, but not developed (with promised development in a later section) - Mathematical induction. We will look at José Ejemplo's induction proofs.

Recursive Definitions

We will also take a very brief look at José's musings on the Tree ADT and how it is a recursive defintion.

Additional Exercises

The remainder of class time will be spent sharing solutions to the additional exercises you chose last class.

Read Section 2.3: Planar Graphs and complete the Preview Activity, Reading Questions, and Practice Problems.

We will spend the beginning of class sharing solutions to the Additional Problems from Section 2.1: Problems and Definitions that you chose last Friday. No one emailed me the list of problems you selected, so we will have to determine that in class.

Next I will introduce you to a very helpful tool for rendering and experimenting with graphs, Geogebra.

Then we will introduce Section 2.2: Trees in our textbook, and chose exercises to present in class on Thursday.

Trees Additional Exercises
Exercise	Presenter	Exercise	Presenter	Exercise	Presenter	Exercise	Presenter
1	Robbie	5	Mason	9	Robbie	13	Sean
2	Delanie	6	Nathan	10	Stephen	14	Sean
3	Delanie	7	Gizelle	11	Waleed	15	Evan
4	Dimitri	8	Nathan	12	Waleed	16	Antoan

Complete all Practice Problems, the exercise you chose in class to present from this section, and as many Additional Problems from Section 2.2: Trees as time enables.