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 1:453:45pm. Prof. Craig will lead a synchronous section each Thursday from 9:3011:00am. 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 3:455:15pm. Our TA, Chris Dare, will also hold office hours Tuesdays from 24pm. 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.
Homework:

Monday  Tuesday  Wednesday  Thursday  Friday 






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 BolzanoWeierstrass 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 CraigSectionVideo_040121 
LEC1 Ch.12, 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  
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.45 CraigSectionNotes_040821  
2  4/9 (F)  VID4a:sequences VID4b:convergent/divergence sequences VID4c:bounded sequences 
LEC4 Ch.78  
3  4/13 (T)  PracticeQuiz1  Quiz1 (lec 13)  
3  4/14 (W)  VID5a: limit theorems  Ch.9  
3  4/16 (F)  VID6a: monotone sequences  Ch.10  
4  4/20 (T)  HW2  
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 58)  
5  4/28 (W)  VID9a: catch up  
5  4/23 (F)  VID10a: subsequences  Ch.11  
6  5/4 (T)  HW3  
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 912)  
7  5/12 (W)  VID13a: review of sequences, part two  
7  5/7 (F)  VID14a:< continuous functions, part one  Ch.17  
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  
8  5/25 (T)  PracticeQuiz4  Quiz4 (lec 1316)  
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 1720)  
9  6/4 (F)  VID20a: review and Math Movie Competition  
11  6/8 (T)  PracticeFinalExam  FinalExam (lec 120) 
Do's and Don'ts:
Here are some of my favorite videos from previous years: