Structure for Proof-based Courses

Expectations

It is essential that you are prepared for EACH class. Being passive in your discovery of the material (i.e., waiting for someone to tell you how to do a problem), or being passive in class (i.e., saying that you did not know how to work a problem) will not work in this class. You must be proactive in working with other students or meeting with me if you are stuck. This lack of preparedness affects the class dynamic and will be reflected in your grade.

Do not wait until class to discover how to do the problems – the point of the class is for you to do a lot of the discovery outside of class. Making mistakes is a BIG part of learning and discovery. It is better to take risks and be wrong than to do nothing at all. To reiterate: you will not be adversely affected (in grade) by making mistakes; you will, however, be adversely affected by not being prepared (i.e., doing nothing).

By the end of the semester, I expect that you will have made significant progress towards mastery of

• reading and understanding mathematics
• giving coherent logical and formal arguments in BOTH written and verbal forms of communication
• independent problem-solving
• effectively communicating to and with peers (not as trivial as it may seem)

I assume a lot of responsibility on you; however, you would not have made it this far in your academic career if you did not have the skill set to handle it. You should expect a lot from me too. My responsibilities to you are to

• create a safe learning environment
• guide you in the discovery process
• help you master some concepts in the course, as well as the skills I listed above

Class Flow

In order to facilitate the development of the soft skills mentioned below, I have created an active learning environment for our course. A typical class session will be divided into 3 parts: mini-lecture, working in groups, warm-up presentations. The general flow is as follows.

1. You will read a section and submit questions based on your reading (Class Notebook).
2. I will give a mini-lecture based on your questions.
3. You will submit warm-up exercises (Class Notebook) and present them in class.
4. You will submit a proof for a main problem (Canvas) which is often more advanced than warm ups.

In essence, you will interact with the material in triads: each week you will encounter a concept in 3 ways (reading on your own, my lecture in class, your presentations of warm ups in class) and each day you will encounter 3 topics.  Below is a table illustrating the two triads.

(Note that red + blue = purple.)