OverviewIn the early 19th century, Fourier described a method for expressing an even function f(x) as an infinite sum of cosines:During the semester, we will look at the issues raised by the Fourier series and the mathematics that was developed in response to these issues. In particular, we will explore why there is the need for rigorous definitions of continuity and differentiability and understand that there are many subtleties from Calculus~I & II that we glossed over in those courses. EvaluationYour final grade will be determined by
Reading AssignmentsYou will have a reading assignment due each Monday. I think that the text is very well-written and is very readable. This does not mean that the material is easy -- it's not. We are studying material that took mathematicians many years to work their way through, so you should expect to re-read each section several times. But don't be scared or get discouraged.HomeworkA major emphasis in this course is that you learn how to write rigorous and precise mathematical proofs. This can be a challenging endeavor and may require several iterations, but the process will not only aid your mathematical development but can also great improve your clarity of thought in other disciplines and areas as well.With this emphasis, your homework should be precise, comprehensible, completely justified, and written in complete sentences. Most of the homework problems will be worth 5 points, and the possible grades will be 5, 4, or No Grade. A few of the problems may be worth 10 points, and the possible grades will be 10, 9, 8, or No Grade. After I have returned the homework, I will allow you one opportunity to rewrite any problem that you have made a serious effort to complete. However, you must turn in your rewrite, along with your original paper, within one week of when I return the homework to the class. An important aspect of your mathematical development is that you learn to discuss mathematics with others and collaborate on problems. The homework assignments will alternate between Individual assignments and Group assignments. On the group homework assignments, you will work in groups of two and turn in one paper. It is extremely important that both of you understand every solution that your group produces. On each assignment, one student will be designated as the primary author who writes-up the solutions, and the role of primary author must alternate between the members of the group. You may discuss the Individual assignments with other students, but each person must turn in a separate paper that represents his/her own work. Homework will usually be due at my office on Fridays at 2:00 pm. ExamsThe two exams during the semester will have a closed-book inclass component, which count for 10-20% of the total grade. The remaining part of the exam will be open-book and takehome. You will have at least five days to complete each takehome exam and at least one week to complete the final exam. I would strongly suggest that you begin these early to leave time to ask me questions about the exam.Writing ProjectsDuring the semester you will have two or three writing projects. In the first project, you will be asked to explore a mathematical argument and point out any assumptions which were not proved. The later assignment(s) will consist of filling in the gaps in the original argument. The projects should be written using a word processor. I will correct each project and you will have a chance to submit a revised version. I will give you more details of my expectations for the projects later in the semester.Group PresentationYou will give one group presentation (on Thursday evening, November 8) on a topic related to the course that we have not covered during the semester. I will give you more details as the time gets closer.A Few Notes on Your Homework and ExamsHere are a few guidelines for the presentation of your written work. If you do not follow these, I reserve the right to return your homework ungraded.
I strongly recommend that you turn in all assignments on time. For each class period that an assignment is late, you will lose 25%.Be aware that this 25% cannot be regained through a rewrite. Grading of Group AssignmentsEach group assignment will receive a single grade, and the group will determine how the points are allocated to each member. For example, if a group of two receives an 85 on a presentation, then the group will have 2 x 85=170 points to distribute among them. I will be available to mediate this process, if necessary.Class AttendanceAlthough class attendance is not a specified percentage of your grade, I will keep a class roll to help me determine borderline grades at the end of the semester. If you do miss class, you are responsible for the material that was covered.Getting HelpPlease come see me during my office hours! If you have a conflict and cannot make my office hours, please call or email me and we can set up an appointment for another time.
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