Math 121 (Spring 2021)

Introduction to Topology (Math 121, Spring 2021)

Email policy Grading Exams Homework and SYOPs Examples library Schedule Equity Integrity

Instructor: Nina Otter
(lastname AT math dot ucla dot edu)

Office Hours: Monday at 11am Pacific Time; Wednesday at 9am Pacific Time.

Teaching Assistant:
Benjamin Szczesny (ben dot lastname AT math dot ucla dot edu)

TA Office Hours: TBD

Textbook: T.W. Gamelin and R.E. Greene, Introduction to Topology (2nd Edition) , Dover.

Campuswire page: click here


Email policy

Please note that we will use Campuswire as an online discussion platform for this course.

Whenever possible, post your questions on Campuswire, instead of sending an email to the instructor or the TAs. In case you do need to send an email, please follow these guidelines: use your UCLA email address, start the subject of all your emails with "MATH 121", and sign your emails with your full name and UCLA ID number.



The final grade will be compiled as follows:

Homework SYOPs Examples Midterm Final

The homework and SYOPs with the lowest grade will be dropped from the final grade.

Final grades will be absolute, and will be based on the standard letter-grading scheme, available here, with the exception that there will be no A+ grade, because this grade is too difficult to gauge in the remote format.

I might consider modifying this scheme, but only if the modification results in a grade increase.  


There will be one midterm which will count 25% towards the final grade and a final counting 30% towards the final grade. The exams will take place on the dates indicated in the timetable below, and you will have a 24 hour time window to complete and upload the exam. To take into consideration limited access to resources and time that some of you might experience, none of the exams are timed, therefore you will have the full 24-hour time window to work on them.

The time windows will be as follows:

  • Midterm: 8am Pacific time on 30 April to 8am Pacific time on 1 May.
  • Final: 8am Pacific time on 7 June to 8am Pacific time on 8 June.
  • You may use internet resources to clarify definitions and better understand theorems, but the use of any human resources (e.g., Chegg, Math Stack Exchange) is forbidden. The use of any such materials constitutes academic dishonesty.

    No makeup exams. Attendance of the final is a requisite for the successful completion of this course.


    Homework and SYOPs

    There will be two different types of assignments, due each week:

    About the SYOP sheets: A mathematics education will ideally enable you to build your mathematical skillset and pursue mathematical questions on an independent basis. For this I believe that it is crucial that you are given the opportunity to develop your own way of learning and doing mathematics. Each week I will therefore ask you to put in writing a discussion of some topic covered in the lecture, some additional topic that you might find interesting (but is still closely related to the lecture content), or a solution to an exercise of your choice (this does not need to be from the book, but needs to be related to the lecture content). For this assignment I would like you to pay particular attention to the quality of your (mathematical) writing. Of course, it goes without saying that mere transcription of parts of the book or other sources will not be accepted. Be creative!

    There will in total be eight homework assignments and eight SYOPs. Each assignment counts towards 2.5% of the final grade. The homework and SYOPs with the lowest score will be dropped from the final grade. Homework assignments will be released on Mondays, and will be due on Tuesday of the following week at 10am Pacific time, as indicated on the schedule below. SYOPs will be due on Tuesdays at 10am Pacific time.

    We will use Gradescope for submission and grading of homework, as well as for grading the exams. Gradescope is integrated with CCLE, and all students enrolled to the course should have been automatically added to Gradescope. If this is not the case, please contact the instructor.

    Please make sure that you upload readable copies of your solutions to Gradescope. You can find advice on how to scan and sumit your solutions here.

    No late assignments will be accepted.


    Examples library

    To develop an intuitive understanding of new concepts it is usually very important to play with examples. Therefore, in this course, we will build a collective library of examples.

    You are asked to contribute examples each week on Campuswire. Each example should be related to the topics covered during the week in which you are posting it to Campuswire, and it should be described in enough detail to convince your classmates that it is indeed an example (or counterexample) of a specific property or theorem, etc. Each example will be awarded 5% points. You can earn up to 15% points per week, for a total of 100% points over the quarter. The points earned through the examples will contribute 5% to the final grade of this course.  


    The scheduled lecture times are MWF 10-10:50 am Pacific. The lectures will be synchronous, will be recorded and made available to watch later for the students who can't attend. Attendance is not compulsory, but strongly encouraged.

    In the following table you can see the preliminary lecture schedule.

    L# Date Content of Lecture Homework
    1 M, 29 March Metric spaces and open sets Week 1
    no Homework
    no SYOP
    2 W, 31 March Closed sets and sequences
    3 F, 2 AprilComplete metric spaces
    4 M, 5 April Baire Category Theorem Week 2
    Homework 1, due 5 April
    SYOP 1, due 5 April
    5 W, 7 April Corollary of BCT, the real line
    6 F, 9 AprilThe real line (cont.), products of metric spaces
    M, 12 April no lecture Week 3
    Homework 2, due 13 April
    SYOP 2, due 13 April
    7 W, 14 April Continuous maps, products
    8 F, 16 AprilCompactness
    9 M, 19 April Compactness in metric spaces Week 4
    Homework 3, due 20 April
    SYOP 3, due 20 April
    10 W, 21 April Compactness in metric spaces
    11 F, 23 AprilTopological spaces
    12 M, 26 April Subspaces Week 5
    Homework 4, due 27 April
    SYOP 4, due 27 April
    13 W, 28 April Continuous maps
    F, 30 AprilMidterm, no class
    14 M, 3 May Basis for a topology Week 6
    no Homework
    no SYOP
    15 W, 5 May Separation axioms
    16 F, 7 MayProduct spaces
    17 M, 10 May Compact spaces Week 7
    Homework 5, due 11 May
    SYOP 5, due 11 May
    18 W, 12 May no lecture
    19 F, 14 MayQuotient spaces
    20 M, 17 May Connected spaces Week 8
    Homework 6, due 17 May
    SYOP 6, due 17 May
    21 W, 19 May Path connected spaces
    22 F, 21 MayLocally compact spaces; infinite products
    23 M, 24 May Basics about groups and homotopies of paths Week 9
    Homework 7, due 24 May
    SYOP 7, due 24 May
    24 W, 26 May Fundamental group
    25 F, 28 MayFundamental group: dependence on basepoint and induced homomorphisms
    M, 31 May Memorial day, no class Week 10
    Homework 8, due 3 June
    SYOP 8, due 3 June
    26 W, 2 June
    27 F, 4 JuneRevision


    Learning from home exacerbates existing differences. Please contact the instructor at any time if you have difficulties with access to materials, participation or study.  

    Academic integrity

    Academic integrity is of the uttermost importance.

    For any type of evaluation (homework, SYOP, exams, examples library) You may use internet resources to clarify definitions and better understand theorems, but the use of any human resources (e.g., Chegg, Math Stack Exchange) is forbidden. The use of any such materials constitutes academic dishonesty.

    At the beginning of each exam you will be asked to first sign the following code of integrity:

    I certify on my honor that I have neither given nor received any help, or used any non-permitted resources, while completing this evaluation.

    Students suspected of academic dishonesty may be reported to the Dean of Students. This leads to a process which could end in suspension or dismissal.

    Last updated 3 May 2021