Syllabus for Math 405: Introduction to Real Analysis.
Fall 2009, Prof. Andrew Salch
Office: 412 Krieger
Office hours: 1:00 to 3:00 on Tuesdays
Classroom: Shaffer 300
General notes:
No late work will be accepted and there will be no makeups for any assignments or exams in this course.
Attendance is mandatory. You must come to class (this is what "mandatory" means), but since a professor telling you what you "must" do without mention
of your grade is something of a meaningless gesture, I will give five five-minute quizzes in class throughout the course of the term. These will be
unannounced and if you miss them, there will be no opportunity to make them up (just like any other assignment in the course). I will make sure that
the quiz problems are relatively easy, and I will grade them leniently; the purpose of the quizzes is to give the more grade-oriented students among
you some incentive to come to class consistently.
You should do the reading for a lecture before you come to class. You will need to see every idea in this class at least twice: once from the
textbook, and once from me, during the in-class lecture. This will help you to absorb the material. If you feel that you are bored by seeing the
same material more than once (especially since some of you will have already seen some calculus, in a high school class, for instance), this is not an
indication that you already understand the material; in fact, it is an indication that you have an inadequate grasp of the course material, as there
is so much depth and useful generalization to be made beyond the simple cases of calculus which we cover in this class that a student who truly understands
the course material will not have an opportunity to be bored, because she or he will have so many further avenues to explore. I will give some examples
of this during class lectures.
You have a weekly recitation which you will attend on Fridays; your recitation is run by the course TA, Leili Shahriyari.
Each Wednesday, I will assign you a homework assignment, which you will turn in during your recitation of the following week
(so you will have eight or nine days to work on each homework assignment).
Each homework assignment will consist of a set of problems from your textbook, and possibly
supplementary problems not in your textbook.
During each week's recitation,
your TA will choose students randomly
to present their solution of a problem on week's assignment.
It is not as important that your proof be correct as it is important that you try to prove it, so
if there are problems with your proof, your TA can show you where you've stumbled and how to correct the problem.
You will each need to present one proof in recitation during the semester; this is part of your grade.
No calculators are allowed on any test in the course and in fact you would probably not find a calculator useful in this
course, as most of our effort will go into proofs, not computations.
Grading for the course is as follows:
| Weekly homework | 30% |
| In-class pop quizzes | 10% |
| Midterm 1 | 15% |
| Midterm 2 | 15% |
| Final exam | 20% |
| Proofs during recitation | 10% |
If you need help, try the following things, in approximately this order:
1. Read the relevant sections in your textbook. (If you know the phrase "RTFM" from computer science, it applies here.)
2. Did you read the relevant sections in your textbook? Make sure you did that.
3. See your TA. Your TA will have office hours during the week. During his office hours, you can come in and ask him questions about the class material; you don't need an appointment for this.
4. There is a "Math Help Room" at 213 Krieger. Its hours are 9 AM to 9 PM, Monday through Thursday, and 9 AM to 5 PM on Fridays. It is staffed by graduate students in mathematics who can help answer your math questions.
5. You can come to my office hours, but make sure you tried to answer your questions using the textbook first. My office is 412 Krieger, in a niche off of the stairwell at the west end of the fourth floor; I will announce my office hours for the semester during the second or third week of classes. Again, you are free to come in and ask questions during office hours, without making an appointment with me.
6. If you cannot make it to my usual office hours due to a scheduling conflict, you can email me or talk to me in person, and we can find a time to meet when you can ask me any questions about the class material that you may have; just email me and ask when I am free to make an office hours appointment with you.
7. Keep in mind that human beings took thousands of years to develop calculus. If you can't make sense of it in a single semester, this doesn't make you a dunce.
I will try to tell enough bad jokes in class to make up for the dire tone of this syllabus.
Our textbook, Stricharz's "The Way of Analysis," is a good book but written with a very casual tone. It may be helpful to you to go to the
library and look over some other Real Analysis
textbooks, at some point, if you want to see a more traditional (Definition-Proposition-Proof) way of presenting
mathematics; my lectures will probably be more "traditional" in this regard.
Your first midterm exam will be in class on Wednesday, October 7.
Your first homework assignment, due in your recitation on Friday, September 11: section 1.2.3, problems 3,4; section 2.1.3, problems 5,7,8.
Homework assignment #2, due in recitation on Friday, September 18: section 2.2.4, problems 2,3,4,5,9.
Homework assignment #3, due in recitation on Friday, September 25: section 2.3.3, problem 1,5,9,10; section 3.1.3, problems 1,4,5,12. For next week, read sections 3.1-3.3.
Homework assignment #4, due in recitation on Friday, October 2: section 3.1.3, problems 1,5,8; section 3.2.3, problems 13,14; section 3.3.1, problem 1; section 4.1.5, problems 1,7,8. Additional problem: Let K be a subset of the real numbers. Prove that K is closed and bounded if and only if every open cover of K has a finite subcover.
Homework assignment #5, due in recitation on Friday, October 9: no homework this week, just study for your midterm exam!
Homework assignment #6, due in recitation on Friday, October 23: section 5.1.3, problems 1,2,6; section 5.2.4, problems 1,12; section 5.3.4, problems 1-3, 8. For next week, read sections 5.1-5.3.
Homework assignment #7, due in recitation on Friday, October 30: section 5.3.4, problem 4; section 5.4.6, problems 1,6,9,11; for next week, read chapter 6.
Homework assignment #8, due in recitation on Friday, November 6: section 6.1.5, problems 2,4,13; section 6.2.4, problems 1-4; for next week, read section 6.2.
Homework assignment #9, due in recitation on Friday, November 13: section 6.2.4, problem 8; section 7.1.3, problems 1,4,6; For next week, read sections 7.1, 7.2.
Homework assignment #10, due in recitation on Friday, November 20: section 7.2.4, problems 1,4,7,8,13. For next week, study for your second midterm.