MAT 451-551 Syllabus

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Instructor: Dr. R. Herman
Class Meeting Times: TR 9:30-10:45 A.M., OS 2009
Office Hours: TR 8:30-9:30. Other hours by appointment

Texts:

• Introduction to Topology, 2nd Ed., T. W. Gamelin and R. E. Greene, 1999.

• Essential Topology, M. D. Crossley, 2010.

• Optional: Introduction to Topological Manifolds, 2nd Ed., J. M. Lee, 2011.

Course Objectives:

1. Students will learn the fundamentals of point-set topology.
2. Students will learn the some fundamentals of algebraic topology.
3. Students will learn how topological ideas were discovered.

Student Learning Outcomes: Students will

• Understand terms, definitions and theorems related to topology.
• Know how to read and write proofs in topology.
• Demonstrate understanding of concepts like open and closed sets, interior, closure and boundary, continuity, connectedness, compactness.
• Form topological spaces by using subspace, product and quotient topologies.
• Use continuous functions & homeomorphisms to understand structure of topological spaces.
• Demonstrate understanding of metric and other spaces.
• Construct examples and counterexamples, solve problems, and prove theorems in topology.
• Know about the fundamental group and covering spaces.
• Demonstrate understanding of the historical developments leading to topology.

Webpages:

This syllabus as well as a variety of other relevant information for this class is posted on the internet. The website is located at

http://people.uncw.edu/hermanr/Topology

You are encouraged to log onto this page often to check the homework assignments and read text material. You can email me for help on using LaTeX or any other concerns with the topics you are researching.

Course Requirements:

Homework: Assignments will be assigned and collected periodically. Assignments will be posted online at http://people.uncw.edu/hermanr/Topology/assign.htm. As doing homework is important for learning the material in this course, it will count as 30% of your grade.

Attendance: YOU ARE EXPECTED TO ATTEND ALL OF THE CLASSES! After three excused absences there will be a penalty of 1% for each absence from your total grade.

Exams and Grades: There will be a midterm and no final for this course. The exams will cover the material up to the date of the exam. The tentative dates for the exams are below.

Due to COVID-19, the final will be replaced with a paper and presentation.

Your final grade will be based on the following:

Academic Honor Code
Students are expected to adhere to the UNCW Honor code found at http://www.uncw.edu/odos/honorcode/. In particular, you will become familiar with what plagiarism is, as this is one from of academic dishonesty which is covered by the code.

Student Disabilities
UNCW Disability Services supplies information about disability law, documentation procedures and accommodations that can be found at http://uncw.edu/disability/. To obtain accommodations the student should first contact Disability Services and present their documentation to the coordinator for review and verification.

Campus Respect Compact
UNCW has a Respect Compact to affirm our commitment to a civil community, characterized by mutual respect. That Compact is affixed to the wall of each classroom and can be accessed at: http://uncw.edu/diversity/documents/ApprovedSeahawkRespectCompact8x10.08.09.pdf .