General Information
and Course Policies

Grades. Your grade will be based on your performance on homework, participation (broadly defined, see below), two midterms, and the final exam. Each of the midterms will have two components: an in-class component and a take-home component. The final exam will be entirely take-home. Each will be weighted as follows.

Class Work. Foundations will be different from other math courses you have had. Because the purpose of the class is to change the way that you think and reason about mathematics, it is essential that you become immersed in the work of the course. It is not enough to respond to what an instructor does or tells you. You and your fellow students are the ones that make things happen in class. Without your active participation, nothing will happen. Perhaps more than in any class you take, you will get benefit out of the course in direct proportion to how much effort you put in. Thus class work is the most substantial portion of the grade. It has several components: written assignments, class presentations and class participation generally. (This last includes contributing to class discussions, asking good questions, and active participation when another student is presenting work at the board.) And, I should add, attendance. If you don’t attend you can’t participate. You are expected to be in class on time, if you aren’t your grade will be adversely affected.

Written Assignments: Since Math 222 is primarily a language course, you will be expected to learn clearly and precisely to express mathematical ideas in writing. Several times during the semester you will be asked to write up and turn in the proof of some theorem. My evaluation of your proofs will depend on both the mathematical content of your argument as well as the form of your argument. When grading for content I will be looking to see if you understood the mathematical ideas required for the proof. When grading for form, I will consider your clarity of expression, the completeness of your argument, your proper usage of both English and mathematical grammar and notation, and whether you really said what you meant to say.

Of course, form and content cannot be entirely divorced. If your writing is sufficiently muddled that the reader cannot tell what you meant to say, both grades will suffer. Likewise, if you really don’t understand what it is you are trying to say, the writing will be fuzzy and unclear. However, it is not impossible to distinguish the factors; the grades will be separated so you can see where improvement is needed.

When you write up an assignment, you are expected to include sufficiently many details to enlighten someone who does not already know what you are trying to say. This may require that you restate a definition or previous theorem and say how it is used in your proof. Do not be afraid to include too many details. If you are in doubt about whether or not to say something that you feel is pertinent, always do so!

Class Presentations: I have said that most of the class will consist of students presenting work to each other. You will be expected to do your share in this. To ensure that everybody comes to class prepared on a regular basis, I will often choose who presents at the board with the help of a die. I've found that by introducing an element of randomness, we avoid the problem arising when students expect a bye on one lesson because they presented during the previous lesson. Some times I will rely on volunteers to make presentations. This makes it possible for students to present the work about which they feel most confident. But the fact that so much of the grade depends on this participation means that all students must volunteer on something like a regular basis. Don’t assume that because others volunteer, you (or your grade) are off the hook.

More about class participation: The person who is presenting his or her work at the board is not the only person with responsibilities in a presentation. The students sitting at their desks have a central role to play, as well. Students presenting their work are not meant to replace a seasoned polished lecture that would be given by an experienced instructor. Nor should they be made to. They are counting on their fellow students to help them by making clarifying suggestions and asking questions. I will feel free to ask questions of persons who are sitting down. Also, it is imperative that everyone is respectful. It can be scary for some students (even the very brightest, I will add) to get up to the board to present a proof to a class of twenty people. If you catch a mistake, say so, but do so with respect and encouragement. If you see the correct argument faster than a classmate, then please be patient and avoid making disparaging comments that might make others feel as though they are slow to catch on. The success of Foundations rests on a supportive and encouraging learning environment, and our goal is to get the class to a point where people are competent in (and confident when) presenting mathematical arguments both orally and in writing.

Exam Dates: