Course Design and Strategy
There is a tremendous amount of material to learn in
this course! The design of the learning strategy for the
course must be chosen with this fact in mind.
This class is designed to optimize the learning experience
for students who are making full use of all of the available
resources. Note that this means that if you do not
make full use of the resources, then not only will you not get the
benefit of those resources but furthermore the rest of the course
will not be designed optimally for you.
As the learning strategy for this course is designed, the
expectation is that students will:
- preview the material before class on their own (through the
book and the lecture notes);
- attend with focus during class meetings, during which the
instructor will present the ideas that achieve the greatest
balance of (a) importance to the course and (b) benefits from
being presented live (these are tough, subjective choices for
the instructor!);
- review the material extensively after class (through the
lecture recordings, the book, and the lecture notes), in
addition to working on the assigned homework exercises.
Each of these steps assumes the previous and serves as a foundation
for the next, making each of these steps critical to full
learning. If you take away any of these steps
then, your experience in the course will suffer
disproportionately as a result.
For example then, the lectures (2. above) are designed on the
assumption that students will have done the preview (1. above), and
will move at a corresponding pace. If you have not done the
preview, then you will also find the lecture correspondingly hard to
follow and will have a less effective learning experience than you
could have. The lectures are also designed on the assumption
that students will subsequently review extensively (3. above); if
you do not review sufficiently, then you will also find the lectures
to have been insufficient, as you will likely not make the expected
subsequent connections after the lectures, and not achieve the
expected subsequent proficiency with the ideas and methods.
Note then, all of these sorts of possible shortcomings in your
approach to the course cause disproportionate resulting problems in
your experience in the course.
Importantly, note that with this design, much if not most of
the learning is expected to happen outside of the class meetings,
in the students' subsequent work. This important aspect of the
learning strategy of the course is necessary due to the nature of
the material, being so challenging and extensive -- there is just
too much to learn, and that learning takes too much time, for it to
be feasible to expect all of that learning to happen in class.
This might be a new experience for some students, whose previous
math courses might have covered less material so as to allow for the
expectation that all learning would take place in class, or easier
material such as might have allowed the student to fill in the
blanks from the lectures with relatively low effort if any. If
you think this might be the case for you, then you are urged to make
a deliberate and serious effort to think through how you will
change your approach to math courses, to help you form a
reasonable plan for taking full advantage of all available
resources, to ensure your best possible experience in this
course. Feel free to talk to your instructor about this if you
feel you need help forming this plan.