Instructor(s): Vladimir Chernov
Course on canvas.dartmouth.edu.⇗
Syllabus
Math 54 Topology I
ORC Course description: This course begins with the definitions of topological space, open sets, closed sets, neighborhoods, bases and subbases, closure operator, continuous functions, and homeomorphisms. The course will study constructions of spaces including subspaces, product spaces, and quotient spaces. Special categories of spaces and their interrelations will be covered, including the categories defined by the various separation axioms, first and second countable spaces, compact spaces, and connected spaces. Subspaces of Euclidean and general metric spaces will be among the examples studied in some detail.
Prerequisites: Math 13 and Math 22 or Math 24
This course meets Monday, Wednesday, Friday 2:10-3:15 PM. We will have the occasional x-hours on Thursday 1:20-2:10 PM. We will have the x-hours frequently in the beginning of the term to make up for the classes we have to miss later. The course meets in Kemeny 108.
Course Textbook: James Munkres, Topology, Second Edition
Instructor: Vladimir Chernov, Office Hours Monday, Wednesday, Friday 12 - 1 PM, Thursday 9-10 AM. My office is 304 Kemeny. If you can not come to the office hours please do not hesitate to make an appointment in Zoom or in person.
TA for this course is Filip Rupchin and he will have office hours on Thursdays 4:30-5:30 PM in Kemeny 343.
Course grade will be based on regular homework assigned every week 20% usually due Monday 4 PM in writing under my office door, Take Home Midterm Exam 40% and Take Home Final Exam 40%.
Take home Midterm exam will be Friday October 24 - Monday October 27 and it should be submitted on Canvas.
Take home Final Exam will be Thursday November 18 - Sunday November 23 and it should be submitted on Canvas.
Tentative Course Schedule:
Weeks 1,2 Chapter 1
Weeks 3, 4, 5 Chapter 2
Weeks 6, 7 Chapter 3
Weeks 8, 9 Chapter 4
Academic Honors Principle
Cooperation on daily and weekly homework is permitted (and encouraged), but you should write up the solution on your own. In other words, you might share your thoughts on a sheet of paper or blackboard to get started together, but then work on your own submission afterwards using only your understanding. For weekly homework, please acknowledge any cooperative work by listing your collaborators at the end of each assignment.
AI usage is not allowed.
See also https://policies.dartmouth.edu/policy/academic-honor-policy-undergraduate-students-arts-and-sciences and Academic Honor Principle
On exams no cooperation or human help given or received is allowed. You can not use textbooks or printed matter other than the course textbook, you can not use internet. Using the textbook or our course lecture notes is fine
Plagiarism, collusion, or other violations of the Academic Honor Principle will be referred to the The Committee on Standards. If you have any questions as to whether some action would be acceptable under the Academic Honor Principle, please speak to your instructor beforehand. For more information about standards of conduct, please see these resources.