Course Syllabus for Math 305: Real Analysis (Fall 2009)

Instructor: James Propp


COURSE OVERVIEW:

Real analysis is the bridge from freshman and sophomore mathematics to advanced undergraduate mathematics. My primary goal in teaching this course is to lead you through a rigorous study of the concepts of real numbers and functions, including the fundamental ideas of calculus. My second goal is to help you develop and perfect your skill in communicating mathematics clearly and rigorously; class discussions (in which all students are expected to participate) and homeworks (to be submitted electronically in LaTeX, as discussed below) will give you practice in both oral and written communication.

I want all of you to succeed in this class; below you will find some tips for how you can help make this happen.

USEFUL LINKS:

Lecture-notes

Reading assignments (subject to change)

Homework problems and solutions

CONTACTING THE INSTRUCTOR:

Email: jpropp at cs dot uml dot edu (note: I also have a James_Propp account but I don't read it very often).

Phone: (978) 934-2438. I'll leave a message on my voice mail if the university is open but I'm unable to attend class. To check whether the university has been closed because of weather, call (978) 934-2121.

Fax: (978) 934-3053 (“Attn: James Propp”).

Office: Olney 428C.

Office Hours: Mondays 2-3, Wednesdays 1-2, Thursdays 2-3.
Meetings at times other than my office hours can be arranged by appointment; see me after class, call me on the phone, or send me an email message.

Suggestions about how the course is being run are welcome at any time. If something isn't working for you, please don't wait until the end of the semester to tell me!

GENERAL COURSE INFORMATION:

Meeting times: Mondays, Wednesdays, and Fridays, 10:30-11:20 a.m.

Meeting place: Olney 522.

Prerequisites: 92.221 (Linear Algebra I) and 92.231 (Calculus III).

Expectations: You're expected to attend classes, do the reading in advance, ask questions, and make serious attempts to answer questions raised by me or by other students during class. If you miss a class, it's your responsibility to make sure you obtain all information (course material, assignments, changes in exam dates, etc.) presented that day.

TEXT:

Stephen Abbott, Understanding Analysis (2nd printing, 2002). The Table of Contents can serve as a rough syllabus for the course, though we won't cover all the material in the book. Note that there have been some corrections since the last printing.)

GRADING POLICY:

Course grades

Course grades will be based on three numbers: your Homework score, your score on the in-class Midterm, and your score on the Final. Your average score for the course will be computed as a weighted average of your Homework, Midterm, and Final scores in which the highest of the three scores is assigned weight 40% and the other two scores are assigned weight 30%. (For instance, if your highest score was on the Midterm, your average score for the course would be 30% of your Homework score plus 40% of your Midterm score plus 30% of your Final score.) Your letter-grade will be determined from your weighted average score according to the following table:

Average [90, 100) [87, 90) [85, 87) [80, 85) [77, 80) [75, 77)
Grade A A- B+ B B- C+







Average [70, 75) [67, 70) [65, 67) [60, 65) [0, 60)
Grade C C- D+ D F


(I may raise your grade above what's shown in the table if your class participation is strong. Coming to office hours counts as a form of class participation.)

Exam dates: Midterm October 23; Final TBA.

Exam Policy

It's important that everyone take the same exams under the same conditions for maximum fairness and reliability of testing. I therefore don't give makeup exams unless you have a valid reason for missing the scheduled exam (for example, illness or a religious holiday), and I don't allow extra time on exams unless you have a note from Disability Services (see below). If you have to miss a scheduled exam, please let me know ahead of time if at all possible; I'm much more likely to be sympathetic if you call me the morning of the exam and say “I have the flu and can’t take the exam” than if you come in two days after the exam and say “I missed the exam. When can I take a makeup?”

You may not use a cell phone in any way during an exam.

Use of calculators is prohibited during exams.

You can always reschedule an exam that falls on a day that is a religious holiday for you, but you must make these arrangements ahead of time.

 

Tips on Preparing for Exams

  • Start studying for an exam at least one week ahead of time.
  • Begin by reviewing the homework problems for the sections that will be covered on the exam. Make sure you know how to solve each problem. If you can't solve a particular problem, make a note of the problem number and move on to the next problem; you can go back to the problem later with a fresh head (yours or someone else’s!).
  • Ask me or someone else for help on any homework problem that gave you trouble.
  • Get a good night’s sleep the night before the exam. You'll perform better if you are fresh and able to think clearly.


    • Tips on Taking Exams
     

  • Read every question on the exam before you start working. This will give you a feel for how long the exam is and how you should pace yourself. It'll also give your subconscious mind a chance to start working on the questions.
  • If you're not sure what a question means, please ask me. I'm trying to see how well you know the material, not to trick you with ambiguous wording.
  • Show as much of your work as possible, in as clear a way as possible. Even if you get the wrong answer, I'll try to award you as much partial credit as I feel I can conscientiously give you, but it's hard for me to do this if you don't show your thought-processes.
  • Look at the point value of each question. Obviously, it's more important to do well on the questions that count the most than the ones that count the least.
  • It's generally best to do the easiest problem first, then the next easiest, and so on. You don't have to do the problems in the order they appear on the exam.
  • If you get stuck on one question, move on to the next. Come back later to the question that is giving you trouble.
  • Be aware of how much time you have left. Don't spend too much time on a single question. It's generally better to get partial credit on every question than full credit on a small number of questions.
  • If you have extra time, use it to check your work! Better still, if there's more than one natural approach to the problem, try to solve the problem with a different method; this can be a better way to catch mistakes than just re-reading your calculations. If you get the wrong answer with one approach but the right answer with the other approach, I'll give you nearly full credit (especially if you speculate intelligently on where you might have made an error).
  • If you get an answer that doesn't make sense but don't have time to trace down your error, don't just cross out your answer; explain why you think the answer you got looks wrong, and you may get some extra points for having good instincts.
  • Never be afraid to ask for extra paper. (If you want to write on the reverse side of a page, please write “see other side”.)

    Homework

    All submitted work must be prepared using LaTeX and submitted electronically as both a .tex and a .pdf file. Anything composed by hand, using Microsoft Word, etc., will not be accepted, nor will pdf files created from Word documents.

    Typically there'll be one homework assignment per week, due one week after it is assigned. (We may deviate from this schedule at the beginning of the term and around the time of the midterm.)

    In order for you to understand the material in this course, it's extremely important that you do the assigned homework problems. Working with your classmates can be a great help, and I strongly encourage it, subject to certain provisos (see below). I also urge you to ask questions about any problems that give you trouble.

    Homework will usually be due each week on Friday (except during the week of an exam). Your grade will be based on clarity as well as correctness, so neatness, grammar, and punctuation should not be neglected. Harder problems will in general be worth more points. You are required to include an estimate of how much time you spent on each and every assigned problem; this will help me assess which of the problems are the harder ones. (I reserve the right to throw out a problem entirely if it turns out to be too hard.)

    Barring unusual circumstances, late homeworks will not be accepted.

    Each student will be allowed to skip one assignment without penalty; additional skipped homeworks will only be permitted if a valid excuse is presented, preferably ahead of time rather than afterwards. If you don't skip any assignments, your lowest homework score gets dropped. Don't use up your “free skip” too early in the semester!

    While you can discuss the exercises with classmates, the work you hand in should be your own write-up and not copied from someone else. When leaving a joint homework-solving session, don't carry away anything that doesn't fit in your own brain. Also, you must acknowledge who you worked with in the homework that you hand in. (If you didn't work with anyone, please write “I worked alone on this assignment”.)

    A solution to a problem is an essay of sorts, and you will be expected to respect the rules of spelling, grammar, and punctuation. Sloppily written or unclear solutions may not receive full credit, even if the underlying mathematical ideas are correct.

    Along with your solution to each problem, you will be expected to include information that tells me how much time you spent on each problem. Even if you end up being unable to submit a solution, I would like to know how much time you spent looking for one. This helps me improve the course from year to year by spreading out the work-load more evenly from week to week and eliminating problems that are too hard. Comments on the problems are also welcome.

    Attendance

    Regular attendance is expected. It is not part of the grading scheme, but it may be used to adjust grades upward in the event of a borderline grade. Class participation that shows that you have read the assigned material may also be helpful.

    SPECIAL NEEDS:

    If you have any special needs, e.g., you need more time on exams because of a disability, I'll do my best to accomodate you. Please notify me at least two weeks in advance.