Math 117: Real Analysis
| 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.
|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|
|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
|1||4/2 (F)||VID2a: fields
VID2b: ordered fields
VID2c: supremum, infimum, defn of R
|2||4/6 (T)||HW1, HW1Sol|
|2||4/7 (W)||VID3a: supremum and infimum, again
VID3b: Archimedean property
VID3c: Q is dense in R
| LEC3 |
|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
| LEC5 |
|3||4/16 (F)|| VID6a: bounded monotone sequences converge
VID6b: general monotone sequences
| LEC6 |
|4||4/20 (T)||HW2, HW2SOL|
|4||4/21 (W)|| VID7a: limsup and liminf
VID7b: when limsup = liminf
|4||4/23 (F)|| VID8a: Cauchy sequences
VID8b: Cauchy iff convergent
| LEC8 |
|5||4/27 (T)||PracticeQuiz2, PracticeQuiz2SOL||Quiz2 (lec 4-7), Quiz2SOL|
|5||4/28 (W)|| VID9a: subsequences
VID9b: subsequential limits
|5||4/23 (F)|| VID10a: bounded seq. have convergent subseq.
VID10b: subsequences, liminf, and limsup
| LEC10 |
|6||5/7 (F)|| VID11a: sequences and series
VID11b: continuous functions
VID11c: example of epsilon/delta defn
Ch.14 and Ch. 17 CraigSectionNotes_050621
|7||5/11 (T)||PracticeQuiz3, PracticeQuiz3SOL||Quiz3 (lec 8-11a), Quiz3SOL|
|7||5/12 (W)|| VID12a: more continuous functions
VID12b: combining continuous functions
|7||5/7 (F)||VID13a: attaining maximum/minimum
VID13b: intermediate value theorem
| LEC13 |
|8||5/18 (T)||HW4, HW4SOL|
|8||5/19 (W)||VID14a: uniform continuity, part one
VID14b: uniform continuity, part two
VID14c: uniform continuity, part three
VID14d: cts on [a,b] implies unif cts
VID14e: unif cts sends cnvgt to cnvgt
| LEC14 |
|8||5/21 (F)|| VID15a: limits of functions, part one
VID15b: limits of functions, part two
| LEC15 |
|9||5/25 (T)||PracticeQuiz4, PracticeQuiz4SOL||Quiz4 (lec 11b-14), Quiz4SOL|
|9||5/26 (W)||VID16a: limits of functions VID16b: sequences of functions, pointwise conv VID16c: sequences of functions, uniform conv VID16d: pointwise conv does not imply unif conv CraigSectionVideo_052721|| LEC16
|9||5/28 (F)|| VID17a: unif limit of cts is cts
VID17b: unif Cauchy iff unif convergent
VID17c: series of functions, part one
VID17d: series of functions, part two
Ch.23, 25 |
|10||6/1 (T)||PracticeQuiz5, PracticeQuiz5SOL||Quiz5 (lec 15-16) , Quiz5SOL|
|10||6/2 (W)|| VID18a: review of unif convergence
VID18b: review of triangle inequality
VID18c: review of Archimedean property, part one
VID18d: review of Archimedean property, part two
VID18e: review of subsequences
VID18f: review of continuous functions
First Place in Math Movie Comp., Natalie Churchley
Second Place in Math Movie Comp., Amner Guzman Third Place in Math Movie Comp., Siyue Liu
| LEC18 |
|11||6/8 (T)||PracticeFinal||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:
Here are some of my favorite videos from previous years: