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Course Responsibilities:

This course serves as a transition between the calculus courses where you are primarily using mathematics to upper-level math courses where you are actually doing mathematics. We will spend a lot of time thinking about how to interpret definitions and mathematical statements, and especially how to prove them. Writing will play a significant role in this course, but this writing is of a formal type, with certain rules and accepted practices. It is not creative writing, though you need to be creative in your thinking. In many ways, this is more like poetry than prose, as it is very concerned with the form of the writing as well as its subtle meanings.

This has the following consequences for this course:

Some students are not sure of how much detail to go into, and where to draw the line in terms of justifying the steps of their proofs. I can offer you two pieces of advice here: first, if you had to think about it for more than a moment or two, you should explain and justify your steps; and second, if your steps involve facts or definitions that we have discussed in class, you should justify your conclusions, but if they only involve things we haven't treated in the course, you can assume the reader is aware of the fact you are using. For example, we will treat the relationship "A is a subset of B" in considerable detail, so arguments involving subsets need to be handled precisely and be fully explained. However, we will not treat the relationship "x < y" in detail, so if you know that "2x < 4", you can claim "x < 2" without further justification. I hope this will become clearer as we move through the course.

[HOME] Math 199 (Fall 2020) web pages
Created: 02 Sep 2020
Last modified: 02 Sep 2020
Comments to: dpvc@union.edu
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