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
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.
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 lettergrading 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.
The time windows will be as follows:
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.
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.
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.
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 April  Complete 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 April  The 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 April  Compactness  
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 April  Topological 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 April  Midterm, 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 May  Product 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 May  Quotient 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 May  Locally 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 May  Fundamental 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 June  Revision 
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:
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