Professors' Tips and Suggestions
Scott Smith

Use vocabulary correctly.
Mathematical vocabulary is precise. Synonyms in everyday English are not necessarily synonyms in mathematics. Words do not mean the same thing in mathematics that they do in everyday English. For example, curve in everyday English means something that is bent in a rounded shape while a line segment is an example of a mathematical curve.

Pay attention to the usage of vocabulary terms.
For example, two angles are complementary to each other; you cannot describe a single angle as complementary.

Use symbols correctly.
Although there are some exceptions, an entire phrase should be made up of either all words or all symbols. For instance, “these two numbers are equal” and “1 + 2 = 3” are correct, but “these two numbers are =” is wrong.

Provide justifications for all but the most obvious steps in a solution or a proof.

In mathematics, it is acceptable to state a commonly accepted definition word-for-word without citing the source.
You should cite the source if the author of the source (or the subject, if the source is a biography) created the definition or if the definition provided is not the usual one.

Take time to do the writing.
Write rough drafts. Do scratch work. Proofread. Fill in details. If you are writing an answer to an in-class test question, there is some need to balance time and completeness. Many students choose the time side of the balance. I would prefer students to err on the side of too much completeness than too little time.

Making connections between subjects is a big deal for me.
Expect to see written questions on my tests asking you to make connections within a course and between courses.

Use writing assignments to increase your own knowledge of the material.

Use writing assignments to demonstrate your knowledge of the material.
It takes one level of understanding to be able to solve problems; it takes another to be able to write about the concepts.

The reaction papers are not summaries of the discussion.
You should write about your own personal reactions to the material.