COURSE SYLLABUS Course Number: MATH4970 Course Title: SPECIAL PROBLEMS Credit Hours: 1-4 Prerequisites: Departmental approval, junior standing. Corequisite: Objectives: To provide for the interested mathematics student the opportunity to study mathematical problems of special interest to the student. Course Content: Students will work under the direction of a staff member on a problem of mutual interest. Sample Outline Sample Problem Topic: Special Problems in Fixed Points and Periodic Points. Fixed and periodic points on the closed interval and the circle [5 weeks]: The fixed point theorem for the closed interval. Periodic points on the closed interval. Fixed points on the circle. Repelling and attracting periodic points. Fixed point iteration [5 weeks]: The fixed point theorem for contractive maps. The fixed point iteration algorithm. Applications of iteration. Existence of a unique solution of a first order differential equation. Fixed points on cubes and spheres [5 weeks]: Fixed points and retractions to the boundary. Sperner's lemma. Brouwer fixed point theorem. Fixed points on the sphere. Sample Grading and Evaluation Procedures: Students will be expected to have prepared assigned homework. Homework will occasionally be collected. This will be part of the participation grade. Students will be expected to present problems on the blackboard. A term project will be assigned, the student may be required to present the project to the class. Grade Calculation Class presentations: 30% Projects: 20% Midterm: 20% Final Exam: 30% Tentative Test Schedule Hour tests are given approximately every three weeks and will be announced a week ahead of time. Quizzes may or may not be announced; at least four quizzes will be given in the course of the semester. Friday is typically a good day for quizzes. Sample Statement Re: Accommodations Students who need accommodations are asked to arrange a meeting during office hours the first week of classes, or as soon as possible if accommodations are needed immediately. If you have a conflict with my office hours, an alternate time can, be arranged. To set up this meeting, please contact me by E-mail. Bring a Copy of your Accommodation Memo and an Instructor Verification Form to the meeting. If you do not have an Accommodation Memo but need accommodations, make an appointment with The Program for Students with Disabilities, 1244 Haley Center, 844-2096 (V/TT). (Note: Instructor office room, office hours and email address will be made available on the course syllabus and on the first day of class.)