Academic Expectations for University Mathematics Courses
You are no longer in high school. The great majority
of you, not having done so already, will have to discard high school
notions of teaching and learning and replace them by university-level
notions. This may be difficult but it must happen sooner or later, so
sooner is better. Our goal is more than just getting you to reproduce what
was told to you in the classroom.
Expect to have material covered at two to three times the
pace of high school. Above that, we aim for greater command of the
material, especially the ability to apply what you have learned to new
situations (when relevant).
Lecture time is at a premium, so it must be used efficiently. You
cannot be "taught" everything in the classroom. It is
your responsibility to learn the material. Most of this
learning must take place outside the classroom. You should be
willing to put in two hours outside the classroom for each hour of
The instructor's job is primarily to provide a framework, with some of the particulars, to guide you in doing your learning of the
concepts and methods that comprise the material of the course. It is not
to "program" you with isolated facts and problem types nor to monitor your
You are expected to read the textbook for comprehension. It gives the
detailed account of the material of the course. It also contains many
examples of problems worked out, and these should be used to supplement
those you see in the lecture. The textbook is not a novel, so the reading
must often be slow-going and careful. However, there is the clear
advantage that you can read it at your own pace. Use pencil and paper to
work through the material and to fill in omitted steps.
As for when you engage the textbook, you
have the following dichotomy:
[recommended for most students] Read for the first time the
appropriate section(s) of the book before the material is
presented in lecture. That is, come prepared for class. Then the
faster-paced college-style lecture will make more sense.
If you haven't looked at the book beforehand, try to pick up what
you can from the lecture (absorb the general idea and/or take thorough
notes) and count on sorting it out later while studying from the book
outside of class.
Exams will consist largely of fresh problems that fall within the
material that is being tested.