MCS-236: Proof Portfolio

Since one of the main objectives of this course is for you to learn how to write mathematical proofs, you will create a portfolio of examples of perfect proofs. Proofs should be written in complete sentences. Mathematical expressions should be embedded in the text in a grammatically sensible way. Every step in a proof is or can be justified by a reason. Valid reasons include assumptions, definitions, and previously established results. The extent to which reasons are omitted and proofs abbreviated depends on the audience.

You should submit size proofs for your portfolio, which should include a variety of techniques, of difficulty and of topic. At least one of each of the following techniques should be included:

Proofs:

Direct proof
Proof by contrapositive
Proof by contradiction
Weak induction proof
Strong induction proof by top-down induction
Proof by cases

While some proofs can be ones you did for homework (and for which I have not handed out a solution), you should also include some proofs (at least half) which are ones which have not been assigned in the course. The problems in the book requiring you to prove something which are marked "(-)" are good candidates.

Portfolio:

You should buy a green two-pocket folder at the bookmark and keep all your proofs in it. You should hand this folder in whenever you have added a new proof for me to read. You may revise proofs as you wish, but be aware that toward the end of the semester, I may not be able to give you feedback as promptly. If you decide to rewrite a proof, you should hand in previous versions, together with any comments. The portfolio should include at least one example of each of the types listed above.

Grading:

Most proofs should be perfect. This means your proof should be carefully typed with correct grammar, with the logic of the proof made very clear with paragraphs and/or indentation. Each time you cite a Theorem or Lemma, you should quote or paraphrase the Lemma. For example,
You'll be graded primarily on how many proofs are perfect, with some partial credit given only for nearly perfect proofs. If a proof is not acceptable, I will write some comments about why, and I will be quite happy to discuss these with you.