Topology I
Text: Adams & Franzosa, Introduction to Topology Pure and Applied, Pearson.
Other Resources: You can find a list of other recommended books on point-set topology here.
Schedule: Lectures TTh 12:30 - 2:00 in RLM 5.122
Instructor: Hossein Namazi
hossein at math dot utexas dot edu
RLM 12.156
Office Hours: T 2:00 - 3:30 PM
W 2:00 - 3:00 PM
Prerequisite and degree relevance: One of M361K or 365C with a grade of C- or better, or consent of instructor.
Course description: This course is aimed at an introduction to topology, including sets, functions and the topology of metric spaces.
There are two different approaches to this subject. One emphasizes on the abstract definition of topology and axiomatic proof of the theorems and introduction of the concepts; the other approach concentrates on a study of various examples and an understanding of concrete situations where various topological properties are important. In particular in the latter approach, metric spaces and their properties play a significant role. We try to follow both of these approaches and therefore allow an introduction to different ways of using topology.
The course will be centered around chapter 1 through chapter 7 the textbook. However we feel free to skip some sections and discuss topics that are not necessarily mentioned in the textbook.
Final Grade: Homework: 20%
Exams: 25% each
Quizzes and Participation: 5%
Exams: There will be three exams on Feb 14th, Mar 21st, and one on the last day of the class on May 2nd conducted during the class. The exams are cumulative but with a much more emphasis on the more recent material. Note that there will be no makeup exams except in emergency cases and you need to make sure to leave your schedule empty for that time slot.
Questions and Complains: If you need help or you have a concern about the course, you should contact the Instructor during the office hours and in rare cases when you cannot attend the office hours, you can arrange an appointment via e-mail.
If you have a question about the grading of exams or homework, you must submit a written explanation within a week of the time the grade is posted. Note that all your grades will be posted on blackboard.
Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471- 6259, 471-6441 TTY. If you plan on using accommodations, you need to notify your instructors early in the semester.
Mathematics M367K: Spring 2013 : 56750
Academic dishonesty will not be tolerated and will result in a penalty of failure in the course.
List of Topics:
Week of Jan 14 - Jan 18:
Week of Jan 21 - Jan 25:
Week of Jan 28 - Feb 01:
Week of Feb 04 - Feb 08:
Week of Feb 11 - Feb 15:
Week of Feb 18 - Feb 22:
Week of Feb 25 - Mar 1:
Week of Mar 04 - Mar 08:
Week of Mar 11 - Mar 15:
Week of Mar 18 - Mar 22:
Week of Mar 25 - Mar 29:
Week of Apr 01 - Apr 05:
Week of Apr 08 - Apr 12:
Week of Apr 15 - Apr 19:
Week of Apr 22 - Apr 26:
Week of Apr 29 - May 03:
Set Theory and Definition of Topology
Interior, Closure and Boundary
Bases, Metric Spaces
Subspace and Product topology
Exam 1
Continuity
Connectedness
Separation Axioms
Spring Break
Exam 2
Compactness
Normal Spaces
Tychonoff’s Theorem
Urysohns Lemma
Tietze Extension Theorem
Exam 3
In Class Activities and Quizzes: We will use part of the time in the class to go through some of the theorems discussed in the lecture without a proof or homework problems. The presentation of these will be by the students. We also will have occasional short quizzes where you are supposed to work on a problem or example in a group. The grades for the quizzes and the participation in the in-class activities can earn you an extra 5% credit for the final grade .