\( \newcommand{\sech}{\operatorname{sech}} \) \( \newcommand{\inverse}[1]{#1^\leftarrow} \) \( \newcommand{\<}{\langle} \) \( \newcommand{\>}{\rangle} \) \( \newcommand{\vect}{\mathbf} \) \( \newcommand{\veci}{\mathbf{\hat ı}} \) \( \newcommand{\vecj}{\mathbf{\hat ȷ}} \) \( \newcommand{\veck}{\mathbf{\hat k}} \) \( \newcommand{\curl}{\operatorname{curl}\,} \) \( \newcommand{\dv}{\operatorname{div}\,} \) \( \newcommand{\detThree}[9]{ \operatorname{det}\left( \begin{array}{c c c} #1 & #2 & #3 \\ #4 & #5 & #6 \\ #7 & #8 & #9 \end{array} \right) } \) \( \newcommand{\detTwo}[4]{ \operatorname{det}\left( \begin{array}{c c} #1 & #2 \\ #3 & #4 \end{array} \right) } \)

MA 434/542

Topology - 2018 Fall

Course Information

  • Semester: 2018 Fall
  • Title: Topology
  • Sections:
    • MA 434-101 (Undergraduate)
    • MA 542-101 (Graduate)
  • Class Time:
    • MW 3:00-4:15pm
    • MSPB 360
  • Office Hours
    • MW 1:15-2:45pm and TR 1:45-3:15pm
    • MSPB 314

Course Content

This course is a survey of various introductory topics in general topology. To this end, students will be provided a Theorem Sequence outlining several results from the field.

In particular, the following areas will be covered this semester:

  • topological spaces,
  • curves and surfaces,
  • continuity and homeomorphisms,
  • compactness,
  • connectedness,
  • metric spaces,
  • product spaces, and
  • quotient spaces.


Grades in this course are determined based upon satisfactory completion of four grade specifications:

  • Presentations
  • Notes
  • Knowledge
  • Proofs

Letter grades are assigned at the end of the semester as follows:

  • A: All specifications satisfied
  • B: 3/4 specifications satisfied
  • C: 2/4 specifications satisfied
  • D: 1/4 specifications satisfied
  • F: No specifications satisfied

Article specification for grad students

Graduate students will have an additional specification: Article, described below. Letter grades for graduate students will be assigned at the end of the semester as follows:

  • A: 5/5 specifications satisfied
  • B: 4/5 specifications satisfied
  • C: 3/5 specifications satisfied
  • D: 2/5 specifications satisfied
  • F: 1/5 or less specifications satisfied

Textbook and Resources

No textbook is required for this course; in fact, using a text is discouraged except in desperate circumstances. Students will be provided a Theorem Sequence that outlines all the content that may be covered in the course, and students will be tasked with presenting original proofs for these facts.


The majority of in-class time will be spent on presentations. At the beginning of each class, students will report which topics from the Theorem Sequence they are prepared to present on. The instructor will choose which topics will be presented that day and will choose which student will present each (randomly, or based upon needed progress).

After each presentation, the class will agree whether the topic was satisfactorily covered. If not, the student may be given the opportunity to make corrections and reattempt the presentation during the next class.

If the presentation is accepted by the class, the instructor will award between 1-3✓ for the presentation based on its quality and difficulty.

Satisfying the Presentation Specification

Around midsemester, the class will decide on a positive integer. All students who earn at least this number of marks from presentations will have satisfied the Presentation Specification.


All students are expected to keep a \(\LaTeX\) notebook containing proofs of all theorems presented within their teams. The easiest way to do this is by using Overleaf.com.

Satisfying the Notes Specification

Around two-thirds through the semester, the instructor will secretly choose three topics that have been satisfactorally presented in class. Students will submit their full notebook, and the instructor will evaluate the notes on these topics, as well as for coverage of the semester.

Students who have satisfactorily taken notes on all three topics and have notes on nearly all topics covered in class will have satisfied the Notes Specification; students will be given the opportunity to correct minor errors.

Students with more significant issues in their notes will be given the opportunity to resubmit their notebook at the end of the semester.


Periodically multiple-choice closed-note Knowledge Quizzes will be given during class to assess coverage of the nine areas outlined above in Course Content. Up to five questions from each topic will be asked.

Students that answer at most one question incorrectly for a area will be given a mark for that area. Only one may be earned per area. If two or more questions are answered incorrectly, then that area may be reattempted on a future quiz.

Satisfying the Knowledge Specification

Students that earn at least 7/8 in this way will have satisfied the Knowledge Specification.


Periodically full-response open-note Proofs Quizzes will be given during class to assess student ability to discover and write proofs, including constructing examples and counterexamples. Students will be given one or more theorems related to (but not identical to) the topics satisfactorally presented in class, and will be allowed to submit proofs for one or more. These will be marked for understanding by the instructor and returned; satisfactorily written proofs (modulo minor errors) must be corrected (as needed) and typeset in \(\LaTeX\) for resubmission. Each typeset correct proof will be worth one .

Satisfying the Proofs Specification

At midsemester, the class will decide on a positive integer. Students who earn at least that many from proofs will have satisfied the Proofs Specification.


Each graduate student will choose a topic related, but not directly covered, by our course content, with the advice of the instructor. They will then author a short article in the genre of a research paper, the scope of which will be agreed upon with the instructor.

Satisfying the Article Specification

A draft of this article may be submitted up to twice for grading during the semester, and will either be accepted as satisfactory, or returned with suggested revisions. The third submission of an article is final and will be marked as either satisfactory or unsatisfactory.

Graduate students who have an article accepted as satisfactory will have satisfied the Article specification.


Students are given the responsibility and privilege to help make many choices during the course that affect content coverage and grade assignments. In the (hopefully rare) case that consensus cannot be reached in a team/class decision, the instructor will make the final decision.

When deciding on thresholds for each specification, the instructor reserves the right to overrule the class if they choose a threshold that is too high or low.

Final Exam

The Final Exam will be a combination of a Knowledge Quiz and Proof Quiz, which can be used to help students complete the Knowledge and Proof Specifications. There is no added benefit to taking the final exam for a student who has already satisfied both specifications.

Minor errors in proofs will be accepted without needing revisions.

Makeup Policy

Due to the nature of assessment in this course, quiz makeups are not needed and won’t be offered since that credit may be made up on future quizzes. However, additional time may be given on the Final Exam by request to students who have one or more excusable absences. Also, in exceptional cases the requirements to meet other specifications may be lowered due to multiple excusable absences.

Academic Honesty

Academic Honesty is defined in USA’s Student Academic Conduct Policy. Any student who is caught cheating will immediately lose credit for all earned , either for the relevant specification or the whole semester as appropriate. In addition, the incident will be reported to the university.

In particular, cheating includes copy-pasting and blind rewriting of results from other students, books, or the internet and submitting these results as original work (i.e. plagarism). \(\LaTeX\) source files may be required to assist with automatic detection of plagarized work.

USAOnline and USA Course Policies

The official syllabus for this course is available on. Grade data will be provided to students via periodic printed progress reports.

USA’s Course Policies apply to this course.