Math 117: Real Analysis

Professor: Katy Craig, katy•craig at ucsb • edu

Teaching Assistant: Chris Dare, SH 6431D, dare at math • ucsb • edu

Syllabus:

Lecture: Lectures will be given asynchronously and posted on this website by Tuesday/Thursday at 11:59pm.

Section: Our TA, Chris Dare, will lead a synchronous section each Monday from 1:45-3:45pm. Prof. Craig will lead a synchronous section each Thursday from 9:30-11:00am. This is optional but highly recommended. Math 117 can be a very challenging course, and most students find the extra examples worked during section to be extremely helpful.

Office Hours: Prof. Craig will hold office hours Monday from 3:45-5:15pm. Our TA, Chris Dare, will also hold office hours Tuesdays from 2-4pm.

Grading Scheme: homework: 30%, quizzes and exams: 70%
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

Camera Policy: All students are expected to turn their video camera on and actively participate during section and office hours. Students who are unable to turn their video camera on (e.g. broken webcam, NSFW roommmate) may contact Chris or myself directly to explain your situation.

Textbook: Elementary Analysis by Kenneth Ross, 2nd edition
Using the above link, you can purchase a paperback copy for $24.99 and download a PDF version for free. Do both.

Discord Server: We have a class discord server, where you can ask questions about the course and collaborate with your classmates. A link to the server is available at the top of the Gauchospace page. Please treat this as a public channel and do not post private information.
Quizzes and Exams:

There will be five quizzes and one final exam. The final exam counts as two quizzes.

All assessments will be administered using Gradescope. They will be open book, open note, and open any math website (for example, Wikipedia, Paul’s Online Notes, Wolfram Alpha, …). The only things that are NOT permitted are collaborating with fellow students or visiting websites that help you collaborate with others (for example, Chegg, Math Stack Exchange, Course Hero, Slader,...). Incidences of academic dishonesty will be treated harshly.

There will be no retaking or rescheduling of quizzes or exams under any circumstances, as the grading scheme allows you to drop EITHER your two lowest quiz scores OR your final exam score, whichever results in a higher overall grade.

There are two time options for each quiz. Whichever option you pick, you must stick with the same time for the rest of the quarter.

TIME A: 6:00am-7:15am
TIME B: 9:30am-10:45am

You must log into zoom and turn your video on while taking the quiz. I will be using the Zoom participant log and Gradescope logs to ensure that everyone is starting the quizzes at the correct time. Students who don’t log in to Gradescope at the correct time or who are not on Zoom for the entire time they are taking the quiz on Gradescope will have their quiz grade reduced by 30 points (out of 100). I will be present most of the time to proctor over Zoom, but I will not be present all of the time. In particular, those on TIME A should begin taking their quiz promptly at 6am, even if I don’t log in to Zoom until 6:05am or later.

Homework:
  • Homework assignments will be posted on Gradescope and will be due every other Tuesday at 11:59pm.
  • Only problems marked with an asterisk (*) should be submitted for grading.
  • At least one problem on each of the quizzes will be chosen from the non-asterisked homework problems.
  • No late homework will be accepted.
  • The lowest two homework grades will be dropped and will not count toward the final grade.



Weekly Routine:

Monday Tuesday Wednesday Thursday Friday
  • watch lecture (posted by Tuesday at 11:59pm)
  • watch lecture (posted by Thursday at 11:59pm)


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


Daily Course Materials: (updated throughout quarter)

week day video reading/study materials due today
1 3/31 (W) VID1a: course goals
VID1b: N,Z,Q,R, and induction
VID1c: ordering, density, |•|
VID1d: sqrt(2) is not rational
CraigSectionVideo_040121
LEC1
Ch.1-2, appendix
CraigSectionNotes_040121
1 4/2 (F) VID2a: fields
VID2b: ordered fields
VID2c: supremum, infimum, defn of R
CraigOHVideo_040521
LEC2
Ch.3
CraigOHNotes_040521
DareOHNotes_040521
DareOHNotes_040621
2 4/6 (T) HW1, HW1Sol
2 4/7 (W) VID3a: supremum and infimum, again
VID3b: Archimedean property
VID3c: Q is dense in R
CraigSectionVideo_040821
LEC3
Ch.4-5
CraigSectionNotes_040821
2 4/9 (F) VID4a:sequences
VID4b:convergent/divergence sequences
VID4c:bounded sequences
CraigOHVideo_041221
LEC4
Ch.7-8
CraigOHNotes_041221
DareOHNotes_041221
3 4/13 (T) PracticeQuiz1, PracticeQuiz1Sol Quiz1 (lec 1-3), Quiz1Sol
3 4/14 (W) VID5a: limit of sum
VID5b: limit of product
VID5c: examples, divergence to infinity
CraigSectionVideo_041521
LEC5
Ch.9
CraigOHNotes_041521
3 4/16 (F) VID6a: bounded monotone sequences converge
VID6b: general monotone sequences
CraigOHVideo_041921
LEC6
Ch.10
CraigOHNotes_041921
4 4/20 (T) HW2, HW2SOL
4 4/21 (W) VID7a: limsup and liminf
VID7b: when limsup = liminf
CraigSectionVideo_042221
LEC7
Ch.10
CraigSectionNotes_042221
4 4/23 (F) VID8a: Cauchy sequences
VID8b: Cauchy iff convergent
CraigOHVideo_042621
LEC8
Ch.10
CraigOHNotes_042621
5 4/27 (T) PracticeQuiz2, PracticeQuiz2SOL Quiz2 (lec 4-7), Quiz2SOL
5 4/28 (W) VID9a: subsequences
VID9b: subsequential limits
CraigOHVideo_042921
LEC9
Ch.11
CraigSectionNotes_042921
5 4/23 (F) VID10a: bounded seq. have convergent subseq.
VID10b: subsequences, liminf, and limsup
CraigOHVideo_050321
LEC10
Ch.12
CraigOHNotes_050321
6 5/7 (F) VID11a: sequences and series
VID11b: continuous functions
VID11c: example of epsilon/delta defn
CraigSectionVideo_050621
CraigOHVideo_051021
LEC11
Ch.14 and Ch. 17
CraigSectionNotes_050621
CraigOHNotes_051021
HW3, HW3SOL
7 5/11 (T) PracticeQuiz3 Quiz3 (lec 8-11a)
7 5/12 (W) VID12a: more continuous functions
VID12b: combining continuous functions
CraigSectionVideo_051321
LEC12
Ch.17
CraigSectionNotes_051321
7 5/7 (F) VID13a: attaining maximum/minimum
VID13b: intermediate value theorem
CraigOHVideo_051721
LEC13
Ch.18
CraigOHNotes_051721
8 5/18 (T) HW4
8 5/19 (W) VID15a: continuous functions, part two Ch.18
8 5/21 (F) VID16a: intermediate value theorem, part one Ch.19
9 5/24 (M)
9 5/25 (T) PracticeQuiz4 Quiz4 (lec 12-15)
9 5/26 (W) VID17a: intermediate value theorem, part two Ch.18
9 5/28 (F) VID18a: uniform continuity, part one Ch.19
10 5/31 (M)
10 6/1 (T) PracticeQuiz5 Quiz5 (lec 16-18)
10 6/2 (W) VID19a: uniform continuity, part two Ch.19
10 6/3 (Th)
10 6/4 (F) VID20a: review and Math Movie Competition
11 6/7 (M)
11 6/8 (T) PracticeFinalExam FinalExam (lec 1-20)


Extra Credit Math Movie Competition:
As an opportunity for extra credit, we will hold a math movie competition. The goal is to make the best math movie, lasting three minutes or less. Submissions are due on Sunday, May 23rd. 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.

Submissions should be uploaded to YouTube, Vimeo, or a similar site. Links to the movies can be emailed to me. (Please do not send the movies as email attachments.)

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 use your video as a chance to feature yourself, your roommates, your drawings... anything you create!
  • Do show a list of references at the end of the video, including any articles, books, or websites you consulted while making the video.
  • Do not simply use clunky online tools to quickly make a cartoon. I get tons of these every year, and I have yet to see one that displays creativity.
  • Do not plagiarize. Some students have simply made a video of themselves reading something they found on the internet, without attribution.

Here are some of my favorite videos from previous years: