Textbooks: Topology by James R. Munkres (second edition) and Algebraic
Topology by. Allen Hatcher. Homework problems will be assigned each Monday
and ...
Math 527
Math 527: Topological and Metric Spaces Instructor: Paul Baum Office: 312 McAllister Building Telephone: 863-0545 Email Address:
[email protected] Class Hours: 2:30 – 3:20 MWF, 304 Boucke Office Hours: MWF 12 noon to 1PM – and by appointment Course Description: This course is an introduction to topological spaces and metric spaces. The course will begin with a brief survey of set theory. Countability, the axiom of choice, and Zorn's lemma will be briefly discussed. Topological space and metric space will then be defined and basic general (i.e. point set) topology will be developed. Continuous maps, separation axioms, compact spaces, connected spaces, product topology, and the Tychonoff theorem will be studied. Next, the course will take up the theory of covering spaces and fundamental group. Various examples of fundamental groups and covering spaces will be considered. If time permits, the course will give an introduction to simplicial complexes, CW complexes, and homology. Textbooks: Topology by James R. Munkres (second edition) and Algebraic Topology by Allen Hatcher. Homework problems will be assigned each Monday and are due at the beginning of each Friday class. Late papers will not be accepted. Halfway through the semester and at the end of the semester each student will be required to write an essay explaining what he/she has learned in the course. Grades will be based 50% on the homework and 50% on the two essays. There will be no exams. Academic Integrity: All Penn State Policies regarding ethics and honorable behavior apply in this course. Students with Disabilities: Penn State welcomes students with disabilities into the University’s educational programs. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) Website provides contact information for every Penn State campus: http://equity.psu.edu/ods/dcl. For further information, please visit the Office for Disability Services Website: http://equity.psu.edu/ods PLEASE NOTE: Homework assignments begin on next page.
Math 527
1. Due Friday, August 30, Munkres, page 28, problems 1-5. 2. Due Friday, September 6, Munkres, page 51, problems 1 – 5. 3. Due Friday, September 13, Munkres, pages 83-84, problems 1, 7, 8; Munkres, pages 91-92, problems 1, 3, 4, 6. 4. Due Friday, September 20, Munkres, page 100, problems 2, 3 Munkres, page 101, problems 12, 13, 14 Munkres, page 102, problems 19, 20 Munkres, page 111, problems 1, 3, 5, 6 Munkres, page 112, problems 10, 11, 12 5. Due Friday, September 27, Munkres, page 118, problems 3, 6, 7, and 8 Munkres, page 126, problem 1 Munkres, page 127, problems 4 and 5 6. Due Friday, October 4, Munkres, pages 133-134, problems 3, 6, and 9 Munkres, pages 135-136, problem 12 Munkres, page 145, problems 3 and 4 Munkres, page 145 (Supplementary Exercises), problem 1 Munkres, page 146, problems 5 and 6 7. Due Friday, October 11, Munkres, page 152, problems 1, 2, 3, 4, 5, 6, and 11 Munkres, page 157, problem 1 Munkres, page 158, problems 2, 3 and 8 Munkres, page 162, problem 4 8. Due Friday, October 18, Munkres, page 163, problem 10 Munkres, page 170, problem 1 Munkres, page 171, problems 2, 3 and 4 9. Due Friday, October 25, Munkres, page 177, problem 2 Munkres, page 178, problems 4 and 6 10. Due Friday, November 1, Munkres, page 181, problem 6 Munkres, page 181-182, problem 7 Munkres, page 186, problems 1 and 7 11. Due Friday, November 8, Munkres, page 212, problems 1, 2 and 3 Munkres, page 214, problem 11 12. Due Friday, November 15, Munkres, page 223, problems 1, 3, 4, 5 and 6 Munkres, pages 223-224, problem 7 Munkres, page 224, problems 8 and 9
Math 527 13. Due Friday, November 22, Munkres, page 270, problems 4 and 5 Munkres, page 271, problems 9 and 10 14. Due Monday, December 9, Hatcher, page 38, problems 1 through 8
