Math 117: Real Analysis

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

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

Syllabus:

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, PracticeQuiz3SOL Quiz3 (lec 8-11a), Quiz3SOL
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, 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
CraigSectionVideo_052021
LEC14
Ch.19
CraigSectionNotes_052021
8 5/21 (F) VID15a: limits of functions, part one
VID15b: limits of functions, part two
CraigOHVideo_1_052421
CraigOHVideo_2_052421
LEC15
Ch.20
CraigOHNotes_052421
9 5/24 (M)
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
Ch.24
CraigSectionNotes_052721
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
CraigOfficeHours_053121
LEC17
Ch.23, 25
CraigOfficeHour_053121
10 5/31 (M)
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
CraigOfficeHours_060621
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
CraigOfficeHour_060631
11 6/8 (T) PracticeFinal FinalExam (lec 1-20)

Here is a list of the most important problems in the course:

• Practice Quiz 1: 3, 5, 6, 8
• Quiz 1: 1, 2, 3
• Homework 2: 11, 14, 15
• Practice Quiz 2: 1, 2, 4 ,5, 12
• Quiz 2: 2
• Homework 3: 7, 9, 11
• Practice Quiz 3: 7, 9
• Quiz 3: 1, 2
• Homework 4: 3, 6, 7
• Practice Quiz 4: 1, 2, 5, 7
• Quiz 4: 2, 3
• Practice Quiz 5: 1, 2, 3, 8
• Quiz 5: 1, 3, 4.2
• Practice Final: 2, 4, 5, 6

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: