Math 347 Midterm Exam 1 Information
Basic Information
Date/time: The exam will be given in class, in the regular
classroom, at the date announced on the Course
Information Sheet:
Wednesday, Feb. 15, 12 pm - 12:50 pm.
Rules: No books, notes, formula sheets, etc.,
and, of course, no cheating.
Exam Content
The exam will be on the material covered in class through Wednesday, February
8. In particular, this includes all class handouts through the first
Induction Worksheet (passed out Monday, Feb. 6), and HW assignments 1 - 3.
(Strong induction and its applications will not be on this exam.)
The exam will have 4-6 problems, generally with
several parts, and will be worth approximately 100 points. The questions
will be of one of the following types:
-
Theorems, definitions, logical statements, negations, etc.:
These are problems that simply ask for an answer (e.g., a precise
statement of a definition). If you are well prepared, you should be
able to rattle off the answers in no time ... For these problems,
precision in your answers is crucial. You must use correct notation and
terminology, supply any necessary quantifiers, in the right order, etc.
As we have seen in class, small changes in a definition (e.g., changing
the order of quantifiers or using the wrong quantifier) can turn the
definition on its head and completely change its meaning; this can mean
the difference between full credit and no credit on a problem!
-
Questions asking for short justification.
Some of the questions may request, in addition to an answer, a brief
justification. Here usually one or two sentences, rather than a
detailed proof, are all that is expected.
-
Problems asking for a proof.
Two or three of the problems will ask for full-fledged proofs, of the
type that came up in the hw and the worksheets.
Here, the write-up must include all steps, in
a logically correct sequence, with proper mathematical notation and
terminology, and any necessary quantifiers included, in the same way as
was done in class and in the homework problems. Missing steps, missing
or incorrect quantifiers, will result in loss of credit.
Tip: For better readability, put each step in the argument on a
separate line (as was done in the hw and worksheet solutions), rather
than writing up the proof as a single continuous paragraph of prose.
Homework versus exams:
While most of the exam problems will be at a level comparable to the
homework problems, and reworking the homework problems (and worksheet
problems) is an excellent preparation for the exam, an exam is not
just a scaled-down version of a homework assignment. Homework and exam
serve different purposes, and there are some important differences
between the two: First, questions asking to state a theorem, definition,
formula, etc., would not make sense in homework assignments (where you
could just look up the answer in the book), but are perfectly appropriate for an
exam. Second, some of the homework problems (e.g., most of the problems
from the honors homework) would be inappropriate for an exam because
they are too lengthy or are too nonroutine. Finally, the grading of the
homework is different from that of an exam problem. HW problems are
graded more crudely, and to some extent more generously, than exam
problems. A typical homework problem has possible scores of 0,1,2, or 3
points, whereas an exam problem might have a maximal score of 10 or 15
points. Thus, a minor error that would not result in a loss of a point on
a 3 point hw problem might cost a couple of points on a 15 point exam
problem.
Click on the above link for sample exams from a past Math 347 honors class.
These should give you an idea of the length and difficulty of the exams,
and types of problems.
Math 347 Course Homepage
Last modified Mon 13 Feb 2012 01:05:31 PM CST