Math 250 -- Fall 2012
Foundations of Mathematics
Sections 000 and 004
We will cover the following topics.
Here is an official pdf of the syllabus for this course. (There is no information on this pdf that is not on the webpage.)
- Logic -- statements, negation, converse, etc.
- Sets, relations, functions -- the building blocks of mathematics
- Techniques of proof -- proof by contradiction, induction;
non-constructive proofs, "consider a minimal X" proofs, pigeonhole principle
- Cardinality -- different sizes of infinity
- Numbers -- what they are, transcendental numbers vs. algebraic numbers (i.e., the difference between pi and 2^(1/2))
- Mathematical prose and rigor-- how to write mathematics correctly and in complete sentences.
This class will meet 28 times. I will cover roughly one section of
our text each class. Some sections will be skipped and many will be
covered out of order.
There will be lots of short in class activities in addition to
There will be two midterm exams.
Each of the two midterm exams is worth 20 percent,
for a total of 40 percent of the final grade.
The final exam will be comprehensive and will count for 25 percent.
Homework is worth 25 percent. Seriously! If you do not stay on
top of the homework, you will have a bad time in this class.
There will be a number of short in class quizzes; together they will be worth 10 percent.
The quiz and midterm dates below are tenative (and may be adjusted if
the pace of the course is adjusted), but the date of the final exam is set in stone;
make your summer travel plans accordingly. If you have a conflict
with the final exam (e.g., another final) please let me know ASAP.
| Quizzes || 10% || (Sporadic) |
| Homework || 25% || (Weekly) |
| Midterm Exam I || 20% || (Oct 9) |
| Midterm Exam II || 20% || (Nov 15 (Tentative)) |
| Final Exam || 25% || (000 -- Mon, Dec 17, 4:30-7:00, W302)||
| || || (004 -- Fri, Dec 14, 8:30-11:00am, W304)||
Calculators, notes, and textbooks are not allowed in exams or quizzes.
There will be homework assigned every week, usually on Thursday. There
will be many simple problems, checking your understanding of the
definitions, that will be collected and graded for completness but not
correctness. Most weeks there will be a number of proofs assigned. You
are expected to write them up very carefully. I will very carefully grade 1-2 of
these per week; re-writes will be allowed and in fact expected, and students will be able to recover up to half of the missed points. Homework assignments will typically be worth 20-40 points, depending on the length of the assignment.
The homework assignments are available at this link, and will be updated after each lecture.
There will be 2-5 quizzes throughout the semester, dates and
content to be announced. The schedule and content of the quizzes will be available at this link.
Make up quizzes
There will be no make up quizzes. If you miss a quiz for a documented,
legitimate reason, I will simply not count the quiz in your final grade.
Remember that copying another student's work is a violation of the
Honor Code and will be treated as such. If you must leave class during
an exam for any reason, please leave all of your belongings
handheld supercomputer phone!).
For homework: you are free to consult any sources (animate or
inanimate) while doing your homework (working in groups is
encouraged!), but if you use anything (or anyone) other than your
class notes or the texts listed above, you should say so on your
homework -- please state at the end of every problem any sources used.
On the other hand, you are expected to make an honest attempt to do every problem on your own before consulting other sources. Remember that copying another student's work is a violation of the Honor Code and will be treated as such.
A good rule of thumb to avoid plagarism is the following -- when doing
the final write up of a problem, do not have any text books, web
pages, or classmate's write up in front of you. If you get stuck when
writing up an assignment, go back and look again; just make sure that
you organize the mathematics in your head before writing a proof
rather than copying a solution from some source. This is a
generous homework policy. Please do not abuse it.
There is a helpful, 10 minute video of every subtopic we will cover on Khan Academy. When you are confused about a concept, please watch the corresponding video! Remember, you can pause and rewind a video, but you can't pause and rewind lecture!
Ken Mandelberg handles all overloads for the department.
To request an overload you must send an
email to Dr. Mandelberg (firstname.lastname@example.org) with your request.
He is the only person who can approve an overload request.
this link for more information.