Please read this syllabus carefully. You will be responsible for all the information given here, and for any modifications to it that may be announced in class.

The Mathematics Senior Seminar is a course designed to fulfill the Senior Capstone Experience requirement, described in the Provost's Advisory Committee for General Education Oversight (PACGEO) Policies, Procedures, and Guidelines as "Designed to culminate a student's undergraduate field of study and place it in a larger social, intellectual and professional context, the capstone experience should be an intensive experience in the major of interdisciplinary field at the senior level of performance. The capstone must include an in-depth writing component."

Reflecting the different natures of their disciplines, departments and colleges use a very wide range of educational experiences and structures to meet this requirement. The Mathematics Senior Seminar does not have a fixed curriculum, and traditionally the course design is left to the instructor's judgment. In designing this course, I have considered many objectives, and I intend to use a flexible and wide-ranging approach. Among the most important objectives is to fill some of the gaps that inevitably develop as one moves through a formal curriculum. Accordingly I will present a number of lectures that address matters not usually treated in courses, and make connections between subjects (such as linear algebra and multivariable calculus) that were not possible when you were first learning them. Another objective is to increase your experience and skill in expressing your mathematical ideas, both in writing and verbally, in various formal and informal environments. For this we will use class discussions, student presentations, and writing assignments. To meet the required "in-depth writing component," we will study the art of mathematical writing and will have assignments that focus on this critically important skill. Another course objective is to increase your familiarity with the "culture" of mathematics. To this end, assignments may include attendance at mathematical events such as OU Math Club talks, departmental colloquia, and so on, and reporting on them verbally or in writing.

The first class of the semester will be a brainstorming session, developing ideas for class activities that address the many course objective.

Text: We will not be using a textbook for this course (please enjoy the hundred bucks or so that you will be saving).

Instructor: Darryl McCullough, Professor of Mathematics

Office:	804 Physical Sciences Center
Phone:	325-2743
Email:	dmccullough at math.ou.edu
Office hours:	Mondays, Wednesdays and Fridays 11:30-12:20, and by appointment.

Class Participation: I expect you to arrive on time and to participate fully in all of the classes and in any other scheduled activities. Among other things, this includes arriving properly prepared and in good physical condition--- in particular, adequately rested and up to date on the course so that you are ready for whatever the day's activities will be. Structure your schedule and life so that nothing other than illness or an absolutely unavoidable conflict such as a scheduled University-sanctioned activity interferes with your participation. Unreasonable absence from class will have a serious impact on your course grade.

Obviously, use of electronic devices is incompatible with class participation, and no electronic devices of any kind are to be used during the lectures. All electronic devices including cellular telephones and texting devices are to be turned off before the class hour begins at 2:30.

Homework: The homework assignments and their due dates will be posted on our course website, and the assigned homework must be prepared by the due date. If it is a written assignment, it must be turned in at the start of class on the due date. If it is preparation for a class discussion, then you will be expected to be ready to discuss the topic, with whatever materials you may need in hand. If it is another task, it is expected to be completed no later than the start of class on the due date.

Testing: During the semester, I will decide how much to do in the way of in-class quizzes and tests. Any tests or major quizzes will be announced in advance, shorter quizzes may be given unannounced at any time, if I determine that it will be pedagogically beneficial.

The final examination will be held in the usual lecture room on Monday, May 9, 4:30 to 6:30 p. m. University regulations require that you take it at that time.

Grading system and class participation: Because of its mix of so many activities, this course will require an adaptive, non-quantitative grading system. Your initial grade is a B. It will stay the same or change up or down as we go along in the semester, depending upon your cumulative performance in the many aspects of the course. I will post the current grades at various times during the semester, also I will be meeting with students individually to discuss their progress and performance in the course, so you will have ample feedback as you go along.

Getting Help: For help with any aspect of the course, come to my office hours, or to make an appointment to meet with me at another time. If my regular office hours do not fit your schedule, I urge you to arrange another time to meet with me. Success for my students is a very high priority with me, and helping my students learn mathematics is a pleasure, not an inconvenience. Email is an efficient way to contact me.

Withdrawal Policy: Until January 31, there is no record of a grade for dropped courses. From February 1 through February 25, the University gives you an automatic W if you withdraw from the course. From Feburary 28 through April 1, the rule is that you receive a W or an F at the instructor's discretion, but I will give you a W if you withdraw, regardless of your performance in the course up to that point. After April 1, University regulations specify that you may withdraw only in “very unusual circumstances,” and only with the permission of the Dean. Avoidance of a low grade is not sufficient reason to obtain permission to withdraw after April 1.

Grade of Incomplete: The grade of “I” is a special-purpose grade given when a specific task needs to be completed to finish the coursework. An “I” cannot be given to avoid receiving a low grade.

Academic Misconduct: If cases of academic misconduct arise, they will be dealt with according to University policies. In math classes it's rather obvious what is acceptable conduct and what is not, but just to make sure you understand the policies, you should be familiar with the OU Student's Guide to Academic Integrity. There's really no way that any misconduct could be worth the risk, so just don't go there. As in the rest of life, totally ethical behavior is always the smart choice in the long run.

Students with Disabilities: The following is the University's Reasonable Accomodation Policy: The University of Oklahoma is committed to providing reasonable accomodation for all students with disabilities. Students with disabilities who require accomodations in this course are requested to speak with the professor as early in the semester as possible. Students with disabilities must be registered with the Office of Disability Services prior to receiving accomodations in this course. The Office of Disability Services is located in Goddard Health Center, Suite 166, phone 405/325-3852 or TDD only 405/325-4173.

Final Grades: Grades will be posted on our course website as soon as they are available.

Advice: Think about mathematics, and in particular this course, daily or almost daily. Every day you move either forward or back, and when you move back, you have to spend time and effort simply regaining lost ground.

Learn definitions immediately, or you won't really have any idea what is going on. You don't need to memorize definitions word-for-word, but you should be able to give a correct definition and explain it to anyone who happens to ask you about it.

Be able to state major theorems. They are the key information in any subject.

Pay attention to correct notation and use it at all times. Sloppy, imprecise notation reflects sloppy thinking and lack of understanding. Good notation will do some of the mathematical work for us, and frees our minds to work with the underlying ideas.

Always be aware of the type of mathematical object you are thinking about (is it a number, a set, a variable, an equation, an identity, a function, a vector, a vector space, a power series, a Kleinian group, a Banach space, a de Rham cohomology class, etc.?). If you are not clear about the type of object you are working with, then you are lost and need to backtrack until you are reoriented.

Learn the language. Beyond just knowing the types of objects, learn the terminology and call things what they are--- integral, derivative, vector-valued function, set, linear transformation, or whatever. Use words like implies, evaluate, equality, identity, definition, and so on. Speak it, write it. The goal is to get the math happening in your head, and the language is a major enabler of that process.

The bottom line: Be involved and give full focus to mathematics when you are thinking about it, otherwise you are wasting your time. Know the definitions, know the statements of major theorems, use good mathematical notation, and always know the type of object you are thinking about. Experience mathematics as much as you can. Mathematics can be one of life's great pleasures, and the more you give to it, the more you will enjoy it.