Course Procedures

Mathematics 341---Real Analysis

Instructor: Carol S. Schumacher

Text: Closer and Closer: Introducing Real Analysis by Carol S. Schumacher. Jones and Bartlett Publishers, 2008.

Grade will be based on 7 com ponents:

Test dates

Daily Work: Written assignments, in-class presentations, and class participation expectations are the major work of the course: You will be asked to prepare problems/proofs for presentation in class. Other problems that I will designate "notebook" problems, I will expect you to write up and accumulate in a notebook until the periodic "turn in dates." You will be expected to use proper mathematical and English grammar in both written work and oral presentation.

Inquiry-Based Learning: The classroom approach used in this class is called Inquiry-Based Learning, or IBL. IBL is a pedagogical strategy in which students are led to develop mathematical concepts and discover mathematical connections for themselves. The faculty member serves as mentor and moderator. The time in class is structured as a collaborative learning experience in which everyone works together to deeply understand the mathematical ideas. There is a lot of evidence that, when students actively discuss mathematical ideas with other students on a regular basis, they learn more deeply and the knowledge stays with them longer than when they work in isolation. Thus I encourge you to work together in small groups outside of class as well as in the class.

Much of the time in class is spent in discussing ideas that students have already been working on outside of class. Thus for most class periods you will have problems that work on in preparation for class. That work will serve as a springboard for class discussion that deepens the insights gained before class with careful class discussion that teases out subtleties and sharpens understanding.

Thus class preparation and class work form the most substantial portion of the grade.  The grade for classwork has several components: class preparation, class presentations and class participation, generally.  (This last includes contributing to class discussions, asking good questions, and active participation when another student is presenting work at the board.) And, I should add, attendance.  If you don’t attend you can’t participate.  You are expected to be in class, if you aren’t your grade will be adversely affected.

Working with your fellow students: It has been my experience that most students who thrive in this course are part of a small group of 2-4 students who work together regularly outside of class.  This not only provides a more profound learning experience, I think it also makes the class more fun.

Office hours: Most students need to consult with me as they work through the problems for this class. Thus frequent work in office hours is an expected part of the course. I encourage you to plan Foundations work time around my office hours so that we can chat at times when you feel stuck or confused.

Notebooks: I will ask you to keep a loose-leaf notebook in which you write up the problems designated "notebook problems". I will collect the notebook problems about every two weeks and look them over. The problems will be graded on a scale of 1 to 5. (I reserve the right to assign 6 points to an exceptionally well written or elegant proof!) You should not think of the grade as representing a percentage but, rather, as delivering a message:

• 5 --- excellent work; no real complaints on content or on writing.
• 4 --- argument basically correct but missing some details/less clearly argued than I would like.
• 3 --- argument mostly correct, but there is a misstep in the mathematics; an especially poorly written proof might merit a 3, as well.
• 2 --- serious gaps in the mathematics.
• 1 --- some ideas in the right direction, but didn't really get there.
• 0 --- didn't do the problem or it was completely wrong.

I will use my reading of the notebook problems to keep track of your progress in the course and give helpful feedback as I can. As you work on the notebook problems, I encourage you to work together, come see me outside of class, etc. I expect that the problems will be written up neatly and fully. In each set of notebook problems, at least one problem must be typeset in LaTeX.

Quizzes: I will give periodic short quizzes in class. The quizzes may include a definition or two, a short answer or example question, and you will be asked to reproduce a proof from the text. I will always tell you ahead of time which proofs you will be responsible for. The purpose of these quizzes is just to make sure you that internalize a handful of very important standard ideas and proofs as you go along.

In-Class exams: The in-class exams will consist of definitions, short answers, true-false questions, examples, and very straightforward short proofs: the sorts of questions that should be fairly routine if you have been digesting the material as you go along.

Takehome exams: In the takehome exams you will be asked to prove theorems that you have not previously seen. I will expect takehome exams to be typed using LaTeX, so I will make myself available early in the semester to help anyone who doesn't know how to use it. All the usual rules about good writing and speaking apply to tests, as they do to written assignments and in-class presentations.

Academic Honesty: When I assign a problem, the idea is for you to work the problem yourself. Thus, you are not to look for the solution in other sources (this includes other books and internet sources.) On daily homework you may consult freely with me or with your fellow students. In the end, however, I expect every piece of work that you turn in to be written by you. You will be expected to maintain the usual standards of giving credit where credit is due by letting me know if you worked with a fellow student (there is no penalty for this, it is just academic honesty). On exams you may consult with no one except me. You may make free use of the textbook, the Foundations book, and any notes you have made in or for the Real Analysis class. You may not consult any outside sources, including print and electronic sources.

Disabilities: If you have a physical, psychological, or learning disability that may impact your ability to carry out assigned course work, feel free to discuss your concerns in private with me, but you should also consult the Office of Disability Services at 5453. The Coordinator of Disability Services, Erin Salva (salvae@kenyon.edu), will review your concerns and determine, with you, what accommodations are appropriate. (All information and documentation of disability is confidential.) It is Ms. Salva that has the authority and the expertise to decide on the accommodations that are proper for your disability. Though I am happy to help you in any way I can, I cannot make any special accommodations without proper authorization from Ms. Salva.