Introduction to Higher Mathematics, Spring 2011
Instructor: Andrew Obus
email: obus [at] math.columbia.edu
office: Mathematics 609
TA: TBA. I will try to organize a weekly one hour recitation/Q&A, led by the TA.
Schedule of Lectures
Transition to Higher Mathematics, by Bob A. Dumas and John E. McCarthy. This is available at the Columbia Bookstore, on amazon.com, and in the Mathematics Library.
Expected Background: There are no formal
prerequisites beyond high-school algebra and some exposure to
calculus/limits (Calculus I is more than enough). The biggest
requirement is mathematical curiosity and the willingness to think hard
about problems that are not necessarily straightforward.
If you have any questions concerning your background, please speak to me as soon as possible.
Mondays 4:00-5:00, Wednesdays 10:30-11:30. Mathematics 609 (my office). If these times do not work for you, we can try to set up an appointment.
Homework will be due on Wednesdays. It is due IN CLASS. If you are going to miss class for whatever reason, you must either submit the homework to my box outside of Mathematics 410 BEFORE the beginning of class, or have a friend submit your homework in class. Late or improperly submitted homework will never be accepted. If you know in advance you will be unable to turn in homework when it is due, you should plan to turn it in ahead of time. If you have a conflict with a religious holiday, you must let me know BEFORE the fact. I will not be sympathetic if you do not tell me in advance. I will drop your lowest homework score to allow for missed assignments or for assignments that pose special difficulty.
Homework must be neat, well-organized, and legible. In addition, it must be STAPLED or PAPER CLIPPED (no folding over the top-left corner or anything like that). Please write in paragraphs, sentences, and English words (oh my!) when they are called for. The TA should not have to decipher what you are doing--you should be clear and unambiguous about your methods on a homework problem. You may work on the homework in groups (in fact, I encourage this), but your writeup must be done by yourself. Please write down the names of classmates you have worked with on the homework.
Each homework assigment will have a problem or two marked as "bonus"
problems. You may choose either to do these and hand them in, or
to give an oral presentation (see below). Even if you choose to
give a presentation, feel free to discuss and attempt the bonus problems!
Keep in mind that, unlike in other math classes you have taken, you will often not
be able to solve a homework problem simply by a straightforward
application of what has been covered in lecture. Homework will
require some thought and ingenuity!
Homework will be graded thoroughly (perhaps more thoroughly than you
are used to)! Every effort will be made to hand it back
promptly. Grades will be posted on Courseworks.
Schedule of Homework (will also be posted on Courseworks)
Instead of doing the bonus homework problems throughout the
semester, you may instead choose to make a 10-15 minute oral
presentation to me (privately) toward the end of the semester, where
you will present some proof on the blackboard. More guidelines on this will follow toward the middle of the semester.
Midterms will be in class on Wednesday February 16th, and Wednesday March 30th. If you have a conflict with one of these days, you must let me know now. Another exam on the same day is not considered a conflict.
The final exam is (tentatively) on Wednesday, May 11th, from 1:10PM-4:00PM.
Calculators are not permitted on exams.
I will tolerate no cheating, plagiarism, or other forms of academic dishonesty. Cheating on an exam will result in an automatic grade of zero for that exam. For more serious matters, the Office of Academic Affairs may be contacted.
Calculus Placement/Information Page
Columbia Undergraduate Math Page
Columbia Math Department
If you have (anonymous) comments for me about teaching style or anything related to the course, click here for a feedback form.