# Omar Abuzzahab

Department of Mathematics
University of Pennsylvania

Office: DRL 4N29
Email: omarab (a) sas (dot) upenn (dot) edu
Office Hours: Monday 5:00-6:00 pm, Thursday 10:00-11:00 am

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### Course Information

Instructor: Herman Gluck

#### Lecture:

T, Th 3:00 - 4:30 p.m DRL 4C4

#### Recitation Sections:

M, W 6:30-8:30 p.m. in DRL 4C6.

During our recitation sessions you will presenting solutions to homework problems (those that you have already worked on the previous week and handed in) in front of the class at the blackboard. The goal is to practice laying out a mathematical argument, communicate it effectively, and be able to spot gaps in proofs.

Homework problems are handed in at lecture and returned to you at recitation after it has been graded. Selected problems from each assignment will be graded in detail while the rest may be graded less in depth.

### Presenting Solutions:

The goal in written mathematics is to communicate a formal proof clearly enough that a reader can understand the proof without special ingenuity on their part. One must therefore have an idea of who the hypothetical reader is. For us, the hypothetical reader is someone who hasn't thought about the problem and therefore doesn't know what details will come up in the proof or how they will be addressed. We assume though that the reader knows what we know outside of the particular problem at hand and, likewise, is as competent with the current material as we are. This means they know the definitions and they are comfortable taking facts for granted that have been proven earlier in the course.

It is necessary, then, that when we present the solutions to the class that we engage in a little bit of acting - none of us fits the description of the hypothetical reader! The audience should also act the part, asking questions where the solution is ambiguous or unclear. Of course, if you legitimately don't see a step then definitely ask a question too. Likewise for the speaker, feel free to break character and ask a question. (When standing at the blackboard, it is normal to get confused about what you knew when sitting down - don't be ashamed!).

When you present the problem at the blackboard you should be both speaking and writing your solution. Normally it is a good idea to verbally give an overview or an intuitive idea before you do each step. When you write, you should speak aloud what you are writing, either literally or paraphrasing. To reiterate: you should almost always be speaking, either facing the class (while not writing) or while writing (and speaking what you write). As for what you write, it should be complete sentences and self contained, meaning there should not be an essential step which you spoke but did not write. Make sure to use the whole blackboard instead of erasing a single panel over and over.