Policy on Missed Exams
======================

Generally speaking, I do not offer make-up exams because they are
problematic for many reasons.  Since the original and make-up exams are
written at different points in time, the make-up exam clearly cannot
be identical to the original exam, as this would raise serious issues
with respect to cheating.  For example, a student writing the exam at
an earlier time could communicate what questions are on the exam to
the students writing the exam at a later time.  So, for this reason,
the make-up exam would need to be different from the original exam.
Furthermore, the make-up exam cannot simply be a modified version of
the original exam with only trivial changes.  In particular, the make-up
exam cannot have all the same types of questions as the original exam.
If the types of questions on the two exams were the same, the student
writing the make-up exam could direct all of their exam preparation
efforts at only the types of questions that are known (in advance) to
be on the exam.  This would give a very unfair advantage to the student
writing the make-up exam.

For the above reasons, the make-up exam would have to be a completely
different exam from the original exam, with completely different types
of questions.  This causes another significant practical problem, namely,
that it is impossible to set a make-up exam that has exactly the same
difficulty level as the original exam, since the two exams would have to
be completely different (i.e., the two exams cannot have any similar types
of questions).  This, in turn, raises significant fairness issues since
students writing the easier of the two exams would have a significant
advantage over the students writing the more difficult one.

To avoid all of the above problems, I simply never offer the option of a
make-up exam.  In cases where a student misses an exam for a legitimate
reason (such as illness/injury, severe weather events, or travelling
out of town to attend a university-sanctioned event), I handle this
as follows:

    1. If the student has written 50% or more of the exams in the course,
    the weight of each missed exam will be moved onto the other exams in
    the course that the student did write.  The precise manner in which
    the exam weights are adjusted is described in detail in Appendix A
    (titled "Adjustment of Exam Weights").

    2. If the student has not written 50% or more of the exams in the
    course, the only academic concession that the instructor would approve
    is a late withdrawal from the course without penalty.  Please note
    that this type of major concession needs the formal approval of the
    University (not just the instructor), and the University is likely
    to require the student to provide formal documentation (e.g., doctor's
    notes, etc.) in support of a request for this type of concession.

The second case above is necessary because it is impossible for the
instructor to assess the student's understanding of the course material
if they have not written the majority of the exams in the course.

Normally, when a student misses an exam for medical reasons, a doctor's
note is required.  Due to the current COVID-19 pandemic, however,
this requirement for a doctor's note has been waived (i.e., no doctor's
note is required).

Appendix A: Adjustment of Exam Weights
======================================

In the case that exam reweighting is necessary (due to a student being
excused from one or more exams for legitimate reasons), this is performed
using the procedure described in very precise detail below.

IMPORTANT NOTE: In the event of any typos/errors in the formulas that
follow, the correct formulas take precedence over ones with typos/errors.

- Let e denote the exam component of the course grade for the student (i.e.,
  the quantity that this section is explaining how to determine).
- Let n denote the number of exams in the course.
- Let the exams be numbered from 1 to n.
- Let e_i denote the student grade on exam i for i = 1, 2,..., n,
  where e_i = 0 for each exam from which a student was excused.
- Let w_i denote the weight of exam i (as a fraction of 1) as specified on
  the course outline (where, by definition, \sum_{i=1}^{n} w_i = 1).
- Let w_i' denote the effective weight for exam i.  The effective weight
  is the actual weight that is used for the purposes of grade calculation.
- The quantity e is computed as
    e = \sum_{i=1}^{n} w_i' e_i
- In the case that a student is not excused from any exams, w_i' is given by
    w_i' = w_i for i = 1, 2, ..., n
  (i.e., the original and effective weights are identical).
- In the case that a student is excused from one or more exams, the
  determination of w_i' for i = 1, 2,..., n is slightly more complicated,
  and is computed in the manner described below.
- Let s denote the sum of the weights of the exams from which the student
  was not excused (i.e., the exams for which a grade was assigned).
- Then, w_i' is given by
    w_i' = 0 if the student was excused from exam i
    w_i' = w_i / s otherwise

Weight Calculation Example
--------------------------

Suppose that
  n = 5 (i.e., 5 exams in course)
  w_1 = w_2 = w_3 = w_4 = 5/24 and w_5 = 4/24
  student misses exam 1 and writes exams 2, 3, 4, and 5
Then, we have
  s = \sum_{i=2}^{5} w_i = 5/24 + 5/24 + 5/24 + 4/24 = 19/24
Thus, the effective weights are given by
  w_1' = 0
  w_2' = w_3' = w_4' = (5/24) / (24/19) = 5/19
  w_5' = (4/24) / (24/19) = 4/19