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 6 components:

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 small groups of students work 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 with small groups discussing ideas that students have already been working on outside of class. Thus for most class periods you will have problems to 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 and polished solutions produced by your group and class participation, generally.  (This last includes contributing to class discussions, asking good questions, and active participation in the work of your group.) 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.

Cooperative learning for written assignments: I encourage students to discuss problems with me and with each other. This is true for written work as well as for class assignments. If you work with other students on an assignment, you should note this on your paper. (There is no penalty, this is just a matter of academic honesty.) However, write-ups are individual. Be sure that the group discussions stop before the writing begins. Discuss the problems in a group, then go off by yourself to write up the solutions for submission. It is not OK for a group to work out a problem together, copy it down, and turn in identical write-ups----even if all members of the group contributed equally to its production. Individual digestion of the ideas and individual writing must be the end of the process. Note that if you all write something together on a whiteboard, take a picture with your phone, and then separately copy down what is on the phone you have not accomplished the "individual digetion and writing" that I expect. You can use joint work as a guide, but the final write-up should come out of your head. (See Academic Integrity, below.)

You are the authority: Many of the proofs you will do in class are "standard" in the sense that you would have no problem finding full solutions in books or online. But the idea here is for you to struggle with these ideas and produce solutions of your own. (Often with help from Prof. Schumacher or in consultation with other students, as noted above.) Thus when you work on class problems, you may not consult any books except the textbook. You are, of course, free to use any class notes, any previously proved theorems, and anything that is distributed in class.You may not consult outside sources, including on-line sources and human sources not associated with the class. In particular, it is fine to consult with students in your class or with Professor Schumacher, but you should not ask students who took the course previously to help you or to provide you with copies of their work.

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 your real analysis 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 anywhere.
• 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.

In-class midterms: The purpose of these exams will be to encourage everyone to gain a command of the basic mathematical facts that are discussed in class. Typical questions will ask you to define important terms, answer true/false and short answer questions, give examples and counterexamples on the basic material and perhaps state an important theorem or two.  You will also be asked to give proofs of straightforward theorems that have already been presented and discussed in the class.The second midterm is worth more than the first and will thus be commensurately more difficult. This is natural because by the time of the second midterm we will have much more sophisticated skills and will have studied deeper ideas.

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; I am always happy to help with LaTeX questions, even on takehome exams. All the usual rules about good writing apply to tests, as they do to written assignments.

Academic Integrity: You are encouraged to work with other students in our class on everything except exams. It is, however, understood that all written work that you turn in must finally be your own expression. In working alone or with other students on problems, it is understood that your only sources of information will be the book, any notes you took in or for class, and brainpower. (And, of course, Prof. Schumacher, who is happy to answer questions at any time.)

• You are not to consult written sources other than your textbook---this prohibition includes books, journals, online sources and notes/solutions constructed by a Real Analysis student in prior semester.
• Nor are you to consult human resources other than each other or Professor Schumacher. This also includes students who have taken Real Analysis in a prior semester.
  

For further information see the student handbook or consult Prof. Schumacher.

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 Student Accessibility and Support Services (SASS) at 740-427-5453. The Coordinator of SASS, Erin Salva (salvae@kenyon.edu), will review your concerns and determine, with you, what accommodations are appropriate. 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. Except in extraordinary circumstances, accommodations must be arranged with Ms. Salva and with me at least one week before they are to take effect.

Title IX; responsible employee: As a member of the Kenyon College faculty, I am concerned about the well-being and development of my students and am available to discuss any concerns you may have. However, I need for you to know that as a Kenyon faculty member I am obligated by federal law to share certain information with the college's Title IX coordinator. This is to ensure our student's safety and welfare are being addressed, consistent with the requirements of that law. These disclosures include but are not limited to reports of sexual assault, relational/domestic violence, and stalking.