COURSE SYLLABUS Course Number: MATH7500 Course Title: Topology I Credit Hours: 3 Prerequisites: MATH 6210 or 6500 or departmental approval. Corequisite: Objectives: To prepare the interested graduate student in the field of topology and give the topological background for further studies in other fields of mathematics such as analysis, probability theory and other. To prepare students for further study in both the areas of algebraic topology and general topology. Course Content: First Semester: Separation and countability axioms. (2 weeks). Covering properties. (2 weeks). Completeness. (2 weeks).v Connectedness. (2 weeks). Metric spaces and metrizability. (2 weeks). Product and quotient spaces. (2 weeks). Functional spaces. (2 weeks). Possible textbook: Topology A First Course, James R. Munkres, 1975, Prentice-Hall Inc. Sample Grading and Evaluation Procedures A graduate student is expected to creatively engage the mathematical material of the course. The student will be given problems to solve; these problems may include the derivation of proofs to theorems. These solutions may be presented in class on the blackboard or be written up to be handed in to the instructor. Extended projects may also be assigned. Grade Calculation Presentation of solutions to problems/theorems, homework: 40% Midterm exam or midterm project: 25% Final Exam or culminating project: 35% There may be variations in these procedures depending on the individual instructors and the nature of the specific material. 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.) JUSTIFICATION FOR GRADUATE CREDIT This course is part of a modified semester version of a 600-level sequence under the quarter system, the Point Set Topology sequence, MATH0654-0655-0656. The quarter system sequence has been expanded into two sequences: MATH7530-7540, Continuum Theory I and II and MATH7550-7560, Set Theoretic Topology I and II. Current research in topology necessitated separate emphases on continuum theory and set theoretic topology. Topics lost from the conversion of the quarter sequence MATH0650-0651-0652 into the semester sequence MATH7500-7510 have been absorbed into these two semester sequences. Outside of modernization, the standard of the course remains at the same graduate level that the department has maintained in the past. The course demands considerable mathematics background and a degree of mathematical maturity traditionally found at the graduate level. The 7000-level course will inculcate the same analytical skills and depth of understanding previously demanded by the comparable 600-level quarter course. In order to successfully complete the course the student will have to demonstrate an ability to creatively examine and apply the mathematics presented in the course.