Welcome to Real Analysis!

Instructor: Dr. Karen Shuman
Class Meetings: 9:00 - 9:50 Noyce 2517
Text: Introduction to Analysis, by Arthur Mattuck

Contact Information for Dr. Shuman:

Office: 2249 Noyce Science Center
Phone: (641) 269-4927
Email: shumank@math.grinnell.edu
Drop-in office hours:

• Monday, 10:30 - 11:50, 3:15 - 4
• Tuesday, 10:30 - 11:50, 2:15 - 4
• Friday, 10:30 - 11:50
• In addition, if you drop by when I am not busy (my door will be open), I will be more than happy to work with you!

Why are you taking analysis?

Real analysis and abstract algebra are the foundation courses in upper-level mathematics here at Grinnell. If you are in this class, you already have a deep appreciation of mathematics, and you are on the brink of exciting and rigorous study of fundamental analytical thought.

Studying

Time studying. Upper-level mathematics courses require regular and dedicated study. You should expect to spend approximately three to four hours studying (this includes your reading and homework sets) outside class for every hour we spend in class.

Why? In order to understand mathematical ideas fully, your brain needs time to absorb them. Even if you feel as if you are not making progress at times during your studying (this is a very common phenomenon in mathematics!), every exposure you give yourself to analysis will pay off in the end!

What is studying? At this stage of your mathematical career, you know you have to study to learn the material. Here is what studying analysis will entail.

• You will be introduced to new definitions on almost every page of your text; these definitions should be committed to memory along with examples and non-examples. You should not keep reading until you have learned the new definitions!

• You will encounter theorems and proofs in your text; in order to work the problems in your text, you will need to understand how the proofs work.

  There are two phases of understanding proofs. First, see the overall picture. What are the hypotheses? What are the conclusions? What tools are needed to go from the hypotheses to the conclusions? If you can't remember the fundamental results or definitions used in the proof of a theorem, look them up!

  After you have read a theorem, understood the structure of its proof, and read the accompanying text, you are ready for the second part---seeing the details. What estimates are needed along the way? How do they work? Is there an epsilon-delta technique, a clever use of sequences, etc.?

• Every section has questions at the end. You should try to answer the assigned questions before checking the solutions at the back of the chapter. If you can do the questions, you have read the material well!

• Now you are ready to attempt the exercises. Exercises will be assigned daily along with your reading. If you can do the exercises, you have learned the basic ideas in a section!

Graded work

• Problem sets

  Problems will be assigned every week. Problems sets form the core of your graded work in this class and come from handouts as well as from the "Exercises" and "Problems" part of your text. Selected problems will be graded every week.

  Typesetting your work. You will be doing a lot of writing in this class, and I will be reading your writing and responding to it. In order to facilitate this process, I highly encourage you to typeset your problem sets in the mathematical typesetting program LaTeX. However, typesetting your work is not a requirement for the course. If you are planning on participating in a mathematical research program or plan to go on to graduate studies in mathematics, you may want to take advantage of the opportunity to learn LaTeX now.

  You will need a MathLAN account to typeset your problem sets. If you do not already have a MathLAN account, see John Stone to get one. Your first introduction to LaTeX can be found here: UIUC TeX help pages.

  Whether you type or handwrite your work, please use the following guidelines when turning in your problem sets:

  • No rough drafts!
  • Each problem needs to be written on a separate sheet of paper.
  • Staple papers which belong to one problem. Separate problems should not be stapled.
  • Your name must appear on each problem.
  • Work must be neat and legible.

  Working with others and consulting external sources. You are highly encouraged to work with others on homework; however, the problem write-ups must be your own. A good way to tell whether your work is your own is to make sure you can explain your solutions to someone else.

  When you do work with other students on a particular problem, note this on your paper. For example, "I worked with X and Y on this problem" is all you need to write.

  The use of external sources for problem set solutions (except for your classmates in both sections of Math 316 and your instructor) is prohibited. This policy includes using the world wide web and other textbooks.

  All papers which violate these policies will be given to the Committee on Academic Standing.
  

  Late problem sets. Late problem sets will not be accepted. You have one drop for the term. (If you complete all assignments, your lowest grade will be dropped.) In cases of extended illness or other unforeseen problems, please come talk to me as soon as possible, and we will work out an alternate schedule for you.

• Quizzes

  There will be a 10-minute quiz at the end of class every Monday. Quizzes will test your knowledge of definitions and theorems. You will not work extensive problems on these quizzes!

  Missed quizzes. Missed quizzes will not generally be given, except at the discretion of the instructor.

• Presentations

  You will be asked to present at least two problems during class. You will know about the presentations ahead of time.

• Exams

  There will be two exams for this class: an in-class midterm exam on Wednesday, March 12, and a three-hour final exam during the regular exam period on Friday, May 16, at 9:00 am in our usual classroom. Final exams must be given when scheduled.

  Missed midterm. A make-up midterm will not be given, except at the discretion of the instructor.

Computing your final grade

The table below shows how your final grade will be determined.

Determining your letter grade

Accommodations

If you have specific physical, psychiatric or learning disabilities and require accommodations, please let me know early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the Associate Dean and Director of Academic Advising, Joyce Stern, whose office is located on the third floor of the Rosenfield Center (x3702).