Math 117: Methods of Analysis — Fall 2026
Professor: Katy Craig, katy•craig at ucsb • edu , SH 6507
Teaching Assistant: Connor Marrs, cmarrs@ucsb.edu, SH 6607Q
Learning Assistant: Kaia Behrstock
Syllabus:
Class Meetings: Monday and Wednesday, 9:30-10:45am, South Hall 1431
Prof. Craig Office Hours: Wednesdays 12:45-1:45pm and Fridays 10-11am (SH 6507)
Grading Scheme:
-
Your course grade will be determined by whichever of
the following two schemes gives you the higher score:
- Scheme A: Participation: 5%, Homework: 15%, Highest of Two Midterm Grades: 35%, Final: 45%
- Scheme B: Participation: 5%, Homework: 15%, Midterm 1: 25%, Midterm 2: 25%, Final: 30%
- The grading cutoffs are as follows: [97,100]: A+, [93,97): A, [90,93): A-, ... , [70,73): C-, [0,70): F
- If you have questions about the grading of any assignment or exam, you have one week after it is graded to request a regrade.
Textbook: Elementary Analysis by Kenneth Ross, 2nd edition
Using the above link, you can purchase a paperback copy for $39.99 and download a PDF version for free. Do both.
Exams:
- There will two in class midterms and one in class final exam.
- There will be no retaking or rescheduling of exams under any circumstances. Since I understand that unexpected things happen (illness, family responsibilities, etc), the grading scheme allows you to drop your lowest midterm.
- In order to reduce time pressure and stress during midterms, I am giving you twice the usual amount of time to take the midterms, while keeping the number of questions the same. You will receive half of the questions on the first day and half on the second day.
- Incidences of academic dishonesty will be treated harshly.
- Midterm 1: Monday, October 26th and Wednesday, October 28th
- Midterm 2: Monday, November 16th and Wednesday, November 18th
- Final Exam: Wednesday, December 9th, 8-11am
- Midterm 1: Monday, October 26th and Wednesday, October 28th
- In order to help motivate everyone to watch the videos before class, each class will begin with a 5 minute quiz over the material discussed in the videos. The quizzes will be straightforward if you have watched the videos and taken handwritten notes.
- During the quizzes, you are allowed to use your own handwritten notes (on paper or tablet), but not the textbook, the videos, the internet, or another person's notes.
- You must take the quiz while physically in the classroom. Incidences of academic dishonesty will be treated harshly.
- Quizzes will be taken via Gradescope.
- I understand that many unexpected things can happen over the course of the quarter (illness, family responsibilities, etc). Consequently, I automatically drop the four lowest quiz grades. No further exceptions will be offered.
- Homework assignments will be posted on the course website and will be due Sundays at 11:59pm.
- Homework will be turned in via Gradescope.
- Only problems marked with an asterisk (*) should be submitted for grading.
- At least one problem on each of the exams will be chosen from the non-asterisked homework problems.
- I understand that many unexpected things can happen over the course of the quarter (illness, family responsibilities, etc). Consequently, I automatically drop the two lowest homework grades. No further extensions will be offered.
Students graduating with any undergraduate degree in mathematics will demonstrate proficiency in mathematical communication, including the ability to read and write detailed, well-organized, and logically sound proofs in complete sentences.
Weekly Routine:
| Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|
| attend class, take quiz | watch assigned videos and take notes for quiz | attend class, take quiz | work on the problem set and begin the next videos | finish the problem set and the next videos; take notes for quiz |
Outline of Course:
| Part I: Sequences | Part II: Functions |
|---|---|
| the real numbers, inf, and sup | continuous functions |
| limit, liminf, limsup | cts functions attain max and min on closed interval |
| bounded, monotone, and Cauchy sequences | intermediate value theorem |
| subsequences and the Bolzano-Weierstrass theorem | uniform continuity and limits of functions |
Daily Course Materials:
(updated throughout quarter)Extra Credit Math TED Talk Competition:
As an opportunity for extra credit, we will hold a math TED Talk competition. The goal is to give the best math "TED talk," lasting five minutes or less. Each talk should have accompanying slides (Powerpoint, Keynote, etc.). To enter the competition, slides must be submitted by 11:59pm on Sunday, November 29th. Among the submitted slides, the top three will be chosen to present on the last day of class. The winner of the competition will receive ten points of extra credit on their final exam. Second place will receive five points of extra credit, and third place will receive three points of extra credit. (You are allowed to work in groups, but then the extra credit points will be distributed equally among all members of the group.)Potential topic ideas for inspiration...
- Chat GPT proves ill-posedness of Navier Stokes: Who Gets Credit in the AI Era?
- Lean and Automating Formalization of Mathematics
- Math Research in the Age of AI
- Math and Gerrymandering
- Different sizes of infinity
- Any chapter from Jordan Ellenger's How Not to Be Wrong, including amazing topics such as the math of the lottery, dating, politics... the whole book is incredible.
- The Kakeya Conjecture and here
- How Wavelets Allow Researchers to Transform, and Understand, Data
- The Journey to Define Dimension
- New Math Book Rescues Landmark Topology Proof (Michael Freedman is a professor here at UCSB!)
- The Math of Counting Votes
- The Chaos of Weather Forecasts
- Conducting the Mathematical Orchestra from the Middle
- The Math of Goat Grazing
Do's and Don'ts:
- Do let me know if you choose one of the above topics, so I can remove it from the list, to prevent duplicates.
- Do show a list of references at the end of your presentation, including any articles, books, or websites you consulted while preparing the presentation.
In an earlier era, this used to be a Math Movie competition. Here are some of my favorite videos from previous years:
- The Cauchy Sequences that Don't Converge, Kevin Petersen
- AI and Counterexample Proofs, Joe DiGiovanni
- Banach Tarski Paradox, Hunter Lin
- Benford's Law, Winnie Ouyang
- A Brief History of the Real Numbers, Casey Gatlin
- Absolute vs Conditional Convergence, Connor Ding
- The Math of Elections, Morgan Falkowski