1. To teach you to think clearly and carefully about mathematics.
2. To teach you to write clearly and carefully about mathematics.
3. To teach you some strategies for solving mathematical problems.
4. To teach you some basic concepts that are common to many areas of advanced mathematics.

This course will very likely be quite different from any other math course you've taken previously, since we will be more concerned with reasoning and communication than with computation. The problems you'll be asked to do will often not have routine, algorithmic solutions; often, you won't be able to start writing down a solution right away, but will have to think and experiment for a while first. Once you've found a solution, you'll be required to communicate your solution effectively. Some things to keep in mind are:

1. As part of your answer, you usually need to present an argument that your solution is correct.
2. Arguments are made up of statements (possibly using symbols and numbers).
3. Statements contain verbs.
4. Verbs are not interchangeable.

Homework problems, which are typically assigned each class period, will be of two types: "Hand-in Problems" and "In-Class Problems".

Hand-in Problems will be collected once a week on Fridays at the beginning of class. Problems assigned on a Monday are due in 4 days, those assigned on a Wednesday are due in 9 days, and those assigned on a Friday are due in 7 days. Assignments that are turned in late, but less than one week late, will be eligible for 50% credit. Assignments that are turned in one to two weeks late will be eligible for 25% credit. Assignments that are turned in two to three weeks late will be eligible for 12.5% credit, etc. In case of an emergency (such as serious illness) or absence because of official university business, these deadlines may be extended by mutual agreement with the instructor. The length of the extension should be negotiated with the instructor as early as possible. In particular, extensions for foreseeable absences must be negotiated before the absences occur. Indeterminate extensions will not be given. Under no circumstances will assignments be accepted (for any credit) after midnight, April 17.

In-Class Problems have due dates similar to Hand-in Problems, but instead of turning in solutions to be graded, students will present their solutions in class at the board. The job of critiquing these solutions will be done mainly by other students. Your grade on In-Class Problems will be based on how often you volunteer to present solutions, how often you present solutions, how actively you participate in critiquing others' solutions, and, of course, on the quality of your solutions and critiques.

You are permitted to discuss the homework problems with your classmates, but you should spend some time thinking about the problems on your own first. Also, you are required to write up your answers on your own in your own words. Do not consult any written notes taken during such discussions when writing your final answers. If you have any questions at all about the difference between permissible and impermissible collaboration, consult BYU's Academic Honesty Policy or ask your instructor.