General Topology
MA366 Fall 2017: Northern Michigan University

Homework Guidelines & Suggestions for Well-Written Work

I was told in graduate school that, "I really need to improve my writing", in order to succeed. Indeed, if we look at our written work, usually we can find a knob to twist somewhere which might make it easier for someone else to read it. Given the small amount of time we have to spend on such things we are forced to choose which aspects of our papers to tweak. Here are some things I've seen and learned over the years that makes a written work much better, quickly.

  • Think of the reader
  • The reader has their own perspective and it is your job to guide them so that they can follow what you are writing (and thinking).

  • Use English descriptions
  • Phrases like, "step 1", "by the usual method", "now we compute the determinant", "expand the right hand side", "as in the previous problem", etc., and countless others will help the reader to follow your work.

  • Organize your solutions
  • Are there several steps to the solution to your problem? Dilineate them, and indicate on paper the places where they occur and change. Use words, arrows and white space to seperate and connect ideas as well as focus the reader's attention. After we "get it" it's often easier to partition ideas into parts ... but one key to "getting it", is to try to break the idea down into little familiar pieces. Add energy to this system by making these changes to your writing.

  • Exercises should be compact
  • Find a way to keep your printed work and your handwritten work nearby (on the same or adjacent page). Five consecute pages of minimally labeled sparse computerized printout is an unfortunate combination of multiple flaws.

  • Figures should be relatively dense, and well-labeled.
  • If a problem has multiple plots, find a way to plot them all on the same axis. With the figures close together in space, distinguish them with different symbols, labels and legends. This usually looks good and allows the reader to easily compare the related figures.

  • State the question.
  • I know you're in a hurry, and you don't have much time. You don't have to write out every word, but at the beginning write out the relevant equations, and perhaps draw a figure.

  • Help the reader think what you're thinking.
  • If you are thinking "correctly", AND you are able pull this off, you win because the reader will agree with you. If you are thiking "incorrectly", BUT you are still able to share your thoughts with the reader, you still win since the reader should then able to identify where you went off track.