MATH 240H - Topology (Honors)

Course description

Platonic solids

The Klein bottle

This course is an introduction to point set topology. The main topics covered are the following:

  • Review of set theory.
  • Topological spaces and continuous functions.
  • Metric spaces, convergence and completeness.
  • Connectedness, compactness and the Tychonoff Theorem.
  • Dimension Theory
  • Homotopy Theory and The fundamental group.

Lectures

The class meets for 75 minute lectures twice a week.
Schedule: Monday-Wednesday 12:30-1:45 PM.
Location: Hylan 105.

Classes and office hours are held online during the month of January as per the University COVID-19 safety guidelines
Zoom link https://rochester.zoom.us/j/94466188848
Zoom link for office hours can be found on Blackboard.

Passcode can be found on Blackboard.

Attendance is not mandatory, but strongly encouraged. Lecture notes will be posted on Blackboard after each meeting.

Instructor

Sergio Chaves
Email: schavesr at math.rochester.edu.
Office hours: Tuesdays 10-11 AM (On zoom), Wednesdays 2:30-3:30 PM (in-person). Other times by appointment.
Office: Hylan 1001.

Teaching Assistant

Conor Taliancich
ctalianc@u.rochester.edu
Reach out to our TA through the Blackboard forum.

Textbook

Topology (2nd edition - Pearson - Classic Version 2018) by J. Munkres. ISBN-10 9780134689517.

Any other version of the texbook should work.

Prerequisites

These are strict prerequisites,

  • (MATH 171 - MATH 174) or (MATH 161 - MATH 162).
  • MATH 200 or MATH 235.
  • Permission of instructor.

Homework

Weekly homework will be posted on the course page and collected through Gradescope. You are encouraged to work with other students on the homework problems, but you must write up and submit your own solutions. The two lowest homework scores will be dropped. Late homework will only be accepted with prior arrangements and/or due to exceptional circumstances.

Getting Help

In addition to regularly attending class, you are strongly encouraged to come to office hours. No appointment is necessary to come to office hours — just drop in! You are welcome collaborate with your classmates (although all work you turn in must be your own!). Use the Blackboard forum to connect with the instructor or TA for help anytime outside office hours!

Finally, some strategies students at UR found successful include the following:

  • Always go to class and take good notes.
  • Review your notes soon after class — within the next day or so!
  • Read (or at least skim) each section in the text before it is covered in class.
  • Do all of the homework thoroughly, write out all of the details, keep it organized, and use it to help you study.
  • If you don’t understand something, ask right away.
  • Go over tests and look at solutions until you know what you did wrong and understand the solution.
  • Figure things out rather than memorize them.
  • Arrange your schedule so that you have enough time every week to study and do homework.
  • Start studying for exams early.
  • Get plenty of rest the night before an exam.
  • Don’t stress out and don’t give up!

Academic Honesty

All assignments and activities associated with this course must be performed in accordance with the University of Rochester’s Academic Honesty Policy. More information is available at https://rochester.edu/college/honesty.

In particular, exams must be submitted with a signed Honor Pledge.

This course is also subject to the Mathematics Department’s statement on online resources: Any usage whatsoever of online solution sets or paid online resources (chegg.com or similar) is considered an academic honesty violation and will be reported to the Board on Academic Honesty. In particular, any assignment found to contain content which originated from such sources is subject to a minimum penalty of zero on the assignment and a full letter grade reduction at the end of the semester (e.g. a B would be reduced to a C). This applies even if the unauthorized content was obtained through indirect means (through a friend for instance) and/or the student is seemingly unaware that the content originated from such sources. If you have any questions about whether resources are acceptable, please check with your instructor.

Disability Support

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of a disability, please contact the Office of Disability Resources. The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. You can reach the Office of Disability Resources at: disability@rochester.edu; (585) 276-5075; Taylor Hall; https://rochester.edu/college/disability.