Course Information
Course Goals and Topics
- To gain mastery of the basics of analysis in the real numbers, especially notions of convergence
applied to sequences, series, differentiation, integration, and the relations between these concepts. Also, how
these ideas extend to more general contexts.
- To improve problem solving skills---what do you do when confronted with a problem so hard you
don't even know where to start?!
- To improve your mathematical proof writing and communcations skills---what consitutes a valid proof? What does a good proof look like? What does a beautiful proof look like?
- To learn how to read an actual mathematical text, one that doesn't have pretty pictures of balloons
or airplanes or carnival rides.
- To learn to think like a mathematician.
- Here is a rough list of the
topics we'll cover from the book.
Intellectual Honesty
- Exams: For in-class exams and quizzes your work must be your own, of course, using only the authorized resources stated. For take-home exams you must also work individually, and ask for help or clarification only from me! As with in-class exams, use only the resources that are authorized on the exam cover page.
- Homework: You are expected/encouraged to collaborate with other students, but when the time comes to write up the homework solutions you should be able to do this on your own with complete understanding, and
in YOUR OWN WORDS. Homework will be assigned three or four (or more) days in advance. START WORKING ON IT THE DAY IT'S ASSIGNED. Unless you're a total friggin' genius, in which case you should start it the night before it's due.
- If you did cooperate significantly with one or more other students please indicate this on the front page of the homework set, problem by problem if necessary, e.g., "I worked with "student A" on problems 3 and 5", "student B" on problem 14".
- If you can't solve a given problem, just say so. It's OK.
- If you're not sure about whether what you're doing for the course is in accordance with the above, ask me!
Course Work Guidelines
- Check the course web page frequently! All homework will be posted there, as well as additional
study info and resources.
- Homework is due at 5 pm on the due date. One day late is automatic half credit, after that zero!
- A significant amount of the homework in this course consists of writing (and reading) proofs. As
such, this is a writing-intensive course, sort of "Tech Comm for Mathematicians." Homework, especially
proofs, will be graded with respect to both technical correctness AND clarity of exposition. I'll give
you examples of good and bad homework write ups, after we get started.
- Homework should be written up VERY NEATLY and all pages stapled.
- In relation to the above point, you really should consider learning TeX/LaTeX. It can be installed
from the IAIT software server, or see the links on the Course Document page. Check out the "LED" editor as well (www.latexeditor.org).
- If you know you're going to be gone on a given day, let me know AHEAD of time. If there's a quiz that day you can make it up ahead of time, not after.
- If you miss class YOU are responsible for learning the material you missed. Although you can ask me specific questions about the material (see "Office Hours" below),
you cannot ask me to repeat the class for you personally---I have too many students for this to be feasible.
- The final grade will be weighted 50 percent for turned in homework, 50 percent for exams/quizzes/final.
- To encourage you to start the homework early, YOU MAY NOT ASK QUESTIONS ABOUT THE HOMEWORK ON THE DAY IT IS DUE!!!!
Office Hours
- Come to office hours if you're confused!
- But please come somewhat prepared, having at least read the book and tried the problems. It's not very helpful if you come in and say "I don't understand anything we're doing."
- Once your questions are answered, do not sit in my office to finish your work---many other people probably want to see me.
- Coming by to talk about math not related to the course (just because it's interesting) is encouraged!
This page last updated November 19, 2015