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## Guidelines for Written Homework

1. Your homework should be neat, legible, and identified with your name and the assignment number. Staple all sheets together before turning them in. It's also a good idea to put your name on each page.
2. It should be comprehensible. Solutions and proofs should be like good programs: clear, concise, well organized, complete, and most of all, well documented. You will often need to explain, in a few complete sentences of good English, what you are doing and why. If the problem calls for some type of programming or algorithm construction, YOU MUST DOCUMENT in order to receive full credit, unless the solution/construction is so simple that no explanation is needed. The definition of `simple' is decided by the instructors.
3. If a problem calls for an answer, program, formula, etc, to receive full credit you must satisfactorily demonstrate that your answer is correct. See 'How to present algorithms' specifically for answer for an algorithm.
4. For a proof, don't be verbose or handwavy, but state clearly what you are going to prove, and the manner in which you will do so. Use statements such as "to show x, we first must show that y and z are true", to indicate the structure of your argument. Each statement you make should assert something. There are syntactic constructs which occur at all levels of mathematical arguments. These include "there exists", "for all", `"such that", "implies", etc. These phrases are the glue. You must make sure that what you glue together are well specified and unambiguous statements, with each variable quantified.
5. Interspersed with a proof you may (and if the proof is at all nontrivial, you must provide intuitions helping the reader understand your proof. This is the documentation. Be sure however that your proof can stand alone and is both meaningful and correct without the documentation and intuition.
6. Make sure your proof or solution is correct for ``boundary'' conditions. (For example, what if a set A is empty? or if x = 0 you don't want to divide by x.) You may have to handle these cases separately.
Some of the guidelines above are not intended as a curse, but rather as a blessing: You will often discover in the process of developing a careful and complete explanation that your tentative answer was wrong. (I never learn anything well until I teach it.) Moreover, if you make a mistake, the graders/TAs have to know what your reasoning was in order to help you by pointing out the flaw (and awarding partial credit). The more clearly you express yourself, the easier and fairer the grading is. This doesn't mean though that you should belabor the obvious to convince us that you understand it. On the other hand, the ability to judge what is "obvious" and can be safely glossed over and what is not is a skill that only comes with experience. (Also, if you are long-winded and verbose about something, then it is usually an indication that you are unsure about it.)

Solutions to the homeworks will be distributed on the web page, which you should use to get an idea of the general style and amount of detail that is expected. After a couple of homework sets, you'll have a pretty good idea of how to go about writing up your answers.

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Topic revision: r2 - 2017-08-25 - 04:45:05 - Main.tanyabw

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