Instructions for Problems to be Graded

All problems should be self-contained in the sense that

1.  It should be clear as to what problem is being solved.  From a practical standpoint this means that each problem must have a problem statement, usually the actual statement of the problem from the textbook.   [Note:  Some problems have part of the statement given with the problem number and part given with general instructions for a set of problems.  Your statement should be complete.]

2.  The solution of the problem should be clear.  Your work should be well-organized, with steps in logical order.  You should not turn in scratch work as part of the solution unless it is clearly labeled as scratch work.

In mathematics we are concerned with solutions to problems, not with answers.  In most cases unsupported answers will carry no credit, even if correct. Correct solutions with minor technical errors will usually earn most of the credit for the problem

You should look over your solutions with the following three things in mind:

1.  Rigor.  Your work should be both mathematically correct and logically correct.

2. Simplicity.  Make the argument as simple as possible within the level of rigor.

3. Completeness.  Include all important steps, but do not belabor the obvious.

### Theorems

All theorems should have the following format:

Theorem:  [Formal statement of the theorem to be proved.]
Proof:  [Formal or informal argument to prove the theorem.  The last statement in the proof should be the conclusion of the theorem.]