Topology
Topology Spring 2011
TuTh 11am - 1pm
Topology is a major branch of modern mathematics. Topology is often described as rubber sheet geometry. In geometry objects are considered rigid with fixed distances and angles, but in topology distances and angles can be deformed. In topology objects are treated as if they are made out of rubber, capable of being deformed. Objects are allowed to be bent, stretched or shrunk but not allowed to be ripped apart or cut. For example, in topology a coffee mug and a doughnut are the same! In this course we will develop the mathematical framework to understand the above ideas.
Course description: The primary goal of this course is to introduce you to topology, which is a major branch of modern mathematics. This course covers basic point set topology, continuity, compactness, connectedness, quotient topology, surfaces, Euler characteristic and classification of surfaces. Another goal is to learn how to write concise, complete proofs, and how to present to others what you have learned.
Homework: Homework will be announced in class. Incomplete work with good progress will also be rewarded. Homework grade will count 40% towards the final grade. I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.
Exams: There will be one midterm exam and one final exam.
Grading: The course grade will be determined as follows: 30% Homework & Participation + 30% Midterm + 40% Final.
Method of Study: Attend class. Read the textbook. Do the homework. Discuss and talk to other students. Use my office hours or email me to ask questions.
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