Introduction to Math 444 Assignments

Thewritten homework assignments are a very important part of Math 444. For one thing, they count as an major part of your course grade; you can't get a good grade in the course without turning in most of the assignments. More importantly, the assignments are where you learn skills in problem solving and writing proofs and can get feedback on your work.

Proofs

A proof is just a logical explanation of how you can establish that something is true, based on what you already know is true. It need not be in two columns. Many students feel uneasy about proofs, and Math 444 provides an opportunity to practice and learn how to write proofs in geometry. It is perfectly normal to have some trouble at the beginning. But even if you have not done many proofs before, there is plenty of chance and support to learn this skill during the course. You will need to be proficient in writing proofs to succeed in the course.

Problem Solving

Some assignments will require the discovery of geometrical relations. There is not usually a recipe to follow, but there are lots of problem-solving techniques that can be employed. Again, there will be opportunity to practice problem solving and learning approaches to problem solving during the course.

Guidelines for Writing up Assignments

Your answers are a place to demonstrate your math communication skills.

• Write in complete sentences.
• Include all information and explanation necessary to make this a clear communication -- including the statement of the problem.
• You do NOT have to include proofs of earlier theorems you are citing. However, it should be clear how you are citing the earlier result.
• Write very clearly or word-process your answers.
• Use figures to make your answers clearer.
• Leave adequate white space
• Don't turn in a first draft of your answer unless it satisfies the preceding criteria. It is very appropriate to try out different strategies, scratch out text, etc., but don't turn this in. Turn in a finished product.

Guidelines for writing proofs

• They should be readable without referring back to the problem set, so state completely the proposition to be proved at the beginning.
• Analyze the statement and make it clear what you are given (what you know).
• Also, write clearly what you are trying to prove.
• Then fill in the gap by proving a sequence of statements, justifying yourself each step of the way, using axioms or theorems already proved.