Every aspect of Math 121 is highly interactive: Students spend most of class time working in groups on problems and they then present their work and discuss as a class. Each student is responsible for some part of the in-class problems.Each week is structured around modules. A module handout is posted on the website with all the information relevant to that week or class. Each module includes "warmup exercises" that students do before class. Each class starts with a student presenting a proof at the start of class, which was assigned ahead of time. Professor Paul Bamberg then gives a lecture, which draws from notes in the module handout. Paul then does a few sample problems, and then the students spend the rest of the time working in small groups. Two students from each group present their answers and the other two write up the solutions after class to be posted on the website.

Given that every single student in a given group has to write up some aspect of the problem, all students have to have some understanding. This led to high scores on the final exam, which used a randomly chosen set of problems similar to those done throughout the semester.

**See below for the description on the syllabus, and see the attachment for an example of a module handout.**

Modules:

Each module, to be posted on the course web site, consists of several parts:

- Reading from the textbook. This will often not make complete sense on the first try, but you should look it over before class anyway.
- A couple of "warmup exercises." These are intended to be simple enough so that you can do them, perhaps rather mechanically, before coming to class.
- An important proof that may appear verbatim on a quiz or exam. A student will be assigned to present this at the start of section in the next class. You are expected to present each proof orally to Paul or Mariel or to a student who has done the proof.
- Three to five pages of notes { just the facts, with examples and most proofs omitted. These will eventually serve as a nice review. I will typically spend 30 minutes talking about them.
- Sample problems. These illustrate the key concepts listed in the notes and will serve as an introduction to the small-group problems.
- Small-group problems. Usually there is one set of four problems, one set of four proofs. Each team of three to five students will do one from each set. Two students will write the group's solutions on the blackboard; two will write up the solutions in LaTeX and email them to the course assistant for posting on the Web site. The solutions on the board will be discussed at the end of class.
- Three or four homework problems. These will be due either once per class or once per week, as the class prefers.

After the first week, it will become your responsibility to print the modules (or download them to your laptop or iPad), do the reading and warmups, and bring them to class.

a-projectivedual.pdf | 151 KB |