In Math 23a and Math23b, Professor Paul Bamberg provides opportunities for students to practice proofs.In this class, students are responsible for 22 proofs. The class is structured to make students comfortable with proofs. Each section, 2 students do the proofs from lecture. Additionally, there are other ways that students are incentivized to practice proofs: students can host a proof party where they will get together and do proofs for one another. They can get extra credit for this. Students also can record themselves writing out a proof and post it to youtube. Students that listen to other students' proofs also get extra credit.

**An example of a posted proof is here:** http://www.youtube.com/watch?v=ne0TqR1eCGE

**Here is the information from the syllabus about the structure of this system:**

One of the goals of this course is to make you comfortable with proving things. Each lecture outline (roughly one per week) typically includes two proofs. Generally these proofs appear in the textbook and will also be done in lecture.

In each week's section two students will present these proofs on the blackboard to the class. They then join the course staff as qualied listeners. Anyone who presents a satisfactory proof to a qualied listener becomes qualied.

Each proof is worth 1 point. Here is the grading system:

- Presenting a proof in section on the Monday after it is done in lecture: 1.1 points. Only one student in a section can receive credit for presenting a proof.
- Presenting a proof privately: 0.9 points.
- Listening to a fellow student's proof: 0.1 point. Only one student can receive credit for listening to a proof.
- Hosting a "proof party" at which at least ve students present proofs and at least ten proofs are presented: 1 point, shared among all hosts. $20 is available for refreshments.

Students who do the proofs early, host proof parties, and listen to lots of other students' proofs can get more than 100%, but there is an upper bound of 25 points.

You may consult the official list of proofs that has the statement of each theorem to be proved, but you may not use notes. That will also be the case when proofs appear on quizzes and on the nal exam. It is OK for the listener to give a couple of small hints.

It is your responsibility to keep an electronic log of all the proofs that you present or listen to, with the presenter, listener, outline and number, date, and score. Also include a line in the log for each "proof party" that you host...

Additionally, once during the term you may make a YouTube video of a proof... for one point of extra credit, but only the first four students to do a video of a given proof can receive credit.