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. The only things that are NOT permitted are collaborating with fellow students or posting questions on study help websites, such as Chegg or Math Stack Exchange. 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.
|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||Quiz1 (lec 1-3)|
|3||4/14 (W)||VID5a: limit theorems||Ch.9|
|3||4/16 (F)||VID6a: monotone sequences||Ch.10|
|4||4/21 (W)||VID7a: limsup and liminf||Ch.10|
|4||4/23 (F)||VID8a: Cauchy sequences||Ch.10|
|5||4/27 (T)||PracticeQuiz2||Quiz2 (lec 5-8)|
|5||4/28 (W)||VID9a: catch up|
|5||4/23 (F)||VID10a: subsequences||Ch.11|
|6||5/5 (W)||VID11a: subsequences, limsup, and liminf||Ch.12|
|6||5/7 (F)||VID12a: review of sequences, part one|
|7||5/11 (T)||PracticeQuiz3||Quiz3 (lec 9-12)|
|7||5/12 (W)||VID13a: review of sequences, part two|
|7||5/7 (F)||VID14a:< continuous functions, part one||Ch.17|
|8||5/19 (W)||VID15a: continuous functions, part two||Ch.18|
|8||5/21 (F)||VID16a: intermediate value theorem, part one||Ch.19|
|8||5/25 (T)||PracticeQuiz4||Quiz4 (lec 13-16)|
|8||5/26 (W)||VID17a: intermediate value theorem, part two||Ch.18|
|8||5/28 (F)||VID18a: uniform continuity, part one||Ch.19|
|9||6/1 (T)||(no quiz)|
|9||6/2 (W)||VID19a: uniform continuity, part two||Ch.19|
|10||6/3 (Th)||PracticeQuiz5||Quiz5 (lec 17-20)|
|9||6/4 (F)||VID20a: review and Math Movie Competition|
|11||6/8 (T)||PracticeFinalExam||FinalExam (lec 1-20)|
Do's and Don'ts:
Here are some of my favorite videos from previous years: