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:

Flipped Class: This is a flipped class. Before class, you will watch lecture videos asynchronously. During class, I will give targeted "mini-lectures" to explain important points, and you will work in groups on the homework, guided by our teaching assistant and learning assistants.

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.
Prerequisites: Math 8

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
Quizzes:
  • 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:
  • 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.
Technology in class: Laptops are permitted to be briefly opened for checking references, but should typically remain put away during class, in order to prioritize group discussion and in person mini-lectures. Phones should remain put away. Tablets are permitted for notetaking. Only in the past year have I had to make rules about this, lol (:

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)

week day topics/videos reading/study materials assignments
1 9/28 (M) N,Z,Q,R & induction (no videos for first class) Sec1-2, appendix
LEC1
1 9/30 (W) Lec2a: Sqrt(2) is not rational
Lec2b: Definition of a field
Sec3
LEC2
LEC2_Highlights
HW1 HW1SOL
2 10/5 (M) Lec 3a: Ordered field, max, min, bounded above, bounded below
Lec 3b: Supremum, infimum, definition of real numbers
Sec4
LEC3
LEC3_Highlights
210/7 (W) Lec 4a: Archimedean property
Lec 4b: Q is dense in R, unbounded above/below
Sec5 and 7
HW2
3 10/12 (M) Lec 5a: Sequences
Lec 5b: Convergence
Lec 5c: Bounded Sequences
Sec8
3 10/14 (W) Lec 6a: Limit of Sum
Lec 6b: Limit of Product
Sec9
4 10/19 (M) Lec 7a: Divergence to Infinity
Lec 7b: Bounded Monotone Sequences Converge
Sec10
4 10/21 (W) Lec 8a: Unbounded Monotone Sequences Diverge
Lec 8b: Liminf and Limsup
Sec10
5 10/26 (M) Midterm 1a (Covering Lectures 1- 8a)
5 10/28 (W) Midterm 1b (Covering Lectures 1- 8a)
6 11/2 (M) Lec 9: When does Lim = Liminf = Limsup? Sec10
6 11/4 (W) Lec 10a: Cauchy sequences
Lec 10b: Cauchy iff convergent; review types of sequences
Sec10
7 11/9 (M) Lec 11a: Subsequences
Lec 11b: Main Subsequences Theorem
Sec11
7 11/11 (W) Veterans Day Holiday — no class
8 11/16 (M) Midterm 2a (Covering Lectures 1-11)
8 11/18 (W) Midterm 2b (Covering Lectures 1-11)
9 11/23 (M) Lec 12: Bolzano Weierstrass
Lec 13: limsup/liminf & subsequential limits
Sec11
Sec12 and 14
9 11/25 (W) No class
10 11/30 (M) Lec 14a: continuous functions
Lec 14b: continuous functions example
Optional: Lec14z: more examples of continuous functions

Lec 15a: combining continuous functions
Lec 15b: cts functions attain max and min on closed interval
Sec17-18
10 12/2 (W) Lec 16a: intermediate value theorem
- 12/4 (F) Optional final exam review session, 9:30-10:45am
- 12/9 (W) Final Exam, 8-11am


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...

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: