How to write up your solutions

The sample problems provided here should be used as guidelines for writing up solutions to the course assignments. The basic point to keep in mind when writing up your own solutions is that the explanation you give should be comprehensible to someone who has almost no knowledge of Maple. In other words, do not assume that the marker knows how to solve the problem since, in fact, this will not always be the case. Here are some other points to keep in mind:

• State the problem clearly; do not expect the marker to have the problem at hand. Your problem statement should also explain any notation you will be using, as well as the definitions of variables you use. Hand drawn diagrams are sometimes useful in this regard.
• State clearly any simplifying assumptions you make. You may not be able to solve a problem as stated but, may be able to come up with a partial solution by making a simplfying assumption. This may be acceptable in some cases (depending on how reasonable the simplifying assumption is) but you shold not try to hide your assumption. Instead, state it as clearly as possible and justify it as well as you can.
• Explain the key Maple commands you use in straigtforward English. (In some cases this explanation can be omitted but, if you are not sure, include an explanation.)
• It is not always necessary to show the Maple output of each command. This is especially true for commands which generate long lists or algebraic expressions which go on for many pages. Maple output can be supressed by ending a command with a colon ":" instead of a semicolon ";".
• Your assignment should usually end with a short paragraph containing concluding remarks. These might include: observations on unexpected outcomes of calculations, the accuracy of numerical answers and their source of errors, the effect of simplfying assumptions, questions left unanswered by the solution and conjectures for further study.

The sample problems provided cover different types of problems which might be covered in MATH2041 or MATH2042.

• How to dig ditches of minimal length in order to find hidden pipelines.
• How to cover a triangle with four circles whose total area is as small as possible.
• How to determine whether two knots are the same using the colouring invariant.
Notice that in some cases you may only be able to provide a partial solution or, your solution may have some defect which you do not know how to correct. It is important to behonest in such cases. See the last example to see one way of handling such situations.

Instructor

Juris Steprans
Department of Mathematics and Statistics.
Ross 624 South, ext. 33952
York University
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