MATH 127C Spring 2024: Analysis
Lectures: Teaching Learning Complex 2215 from 1:10 to 2:00 on MWF.
Sections A01-A03: Thursdays between 3 and 5 pm: check time and location with the registrar.
Teaching Staff: Eric Babson (lecture): babson@math.ucdavis.edu
Xuxing Chen (sec 03): xuxing@math.ucdavis.edu
Zachary Ibarra (sec 01, 02): zribarra@ucdavis.edu
Office Hours:
Babson 5:00 to 6:00 pm Wed via zoom 7150588313.
Changed for Wed June 5 only: 2:30-3:30 in MSB 2109.
I will also be in my office much of Mon June 10 and Wed June 12. Feel free to drop in or email.
April 17 .
Xuxing 3:00 to 4:00 pm Thurs in MSB 3219.
Ibarra 12:00 to 1:00 Tues and 4:00 to 5:00 Fri in MSB 2202.
Homework: A few problems will be assigned at the end of most lectures and they will be collected weekly.
Discord:(created by a student)https://discord.gg/7rq7PTDq2p
Exams: One sheet of hand written notes (both sides) is allowed.
Grading: There will be 200 points for homework, 200 points for the final and 200 points between the two midterms. I will double the largest of the three for a total of 800 possible points. For final grades a score of at least 720 yields an A+, at least 680 an A, at least 640 a A-, at least 616 a B+, at least 584 a B, at least 560 an B-, at least 536 a C+, at least 504 a C, at least 480 an C-, at least 456 a D+, at least 424 a D and at least 400 a D-.
More explicitly there were seven twenty point homework assignments. The first midterm adjusted score had a maximum of 100 and the second midterm had a maximum of 80. The final will have a maximum of 200.
I erred in making the final one problem too long so I will call the last problem extra credit.
That changes the grading formulae to the following:
To compute your grade take HW to be the sum of your seven homework scores, MI to be the adjusted score on your first midterm, M2 to be the raw (only) score on the second and F to be your score (up to 200) on the final.
Your point total to compare to the above letter grades is the largest of the three:
(20/7)HW + MI + (5/4)M2 + (8/7)F
(10/7)HW + 2MI + (5/2)M2 + (8/7)F
(10/7)HW + MI + (5/4)M2 + (16/7)F
Course Outline: Following the department syllabus from Analysis on Manifolds by James Munkres chapters 1-4 (sections 1-20).
This stack exchange thread discusses other good references.
Banach-Tarski Theorem: Why only some sets can get measures.
Dehn Theorem and Hilberrt's third problem: Why cube disections do not give all polyhedra.
This table is a rough outline of when topics will be covered and will be edited as the term progresses. The first chapter is meant to be mostly review and will be covered only briefly. The exam scheduling will not change. Homework problems will be added.
| Day | Date | Section(#s) covered | Homework |
| Mon | Apr 1 | Linear Algebra: 1.1 | HW1 part 1 Due Apr 12. |
| Wed | Apr 3 | Matrix Inverse: 1.2 | HW1 parts 1-2 Due Apr 12. |
| Fri | Apr 5 | Topology: 1.3 | HW1 Due Apr 12. |
| Mon | Apr 8 | Compacta: 1.4 | |
| Wed | Apr 10 | Derivatives: 2.5 | HW2Due April 26. |
| Fri | Apr 12 | Differentiable: 2.5 | |
| Mon | Apr 15 | Continuously Differentiable: 2.6 | |
| Wed | Apr 17 | Review | |
| Fri | Apr 19 | Midterm I | Solutions, More |
| Mon | Apr 22 | Chain Rule Use: 2.7 | HW3 Due April 26. |
| Wed | Apr 24 | Chain Rule Proof: 2.7 | |
| Fri | Apr 26 | Inverse Fn Thm: 2.8 | |
| Mon | Apr 29 | Integrals: 3.10 | HW4 Due May 3. |
| Wed | May 1 | Int Existence: 3.11 | |
| Fri | May 3 | Int Evaluation: 3.12 | |
| Mon | May 6 | Int Evaluation: 3.12 | HW5 Due May 10. |
| Wed | May 8 | Int Bounded: 3.13 | |
| Fri | May 10 | Int Bounded: 3.13 | |
| Mon | May 13 | Rectifiable Sets: 3.14 | HW6 Due May 24 |
| Wed | May 15 | review | |
| Fri | May 17 | Midterm II | PracticeAnswers covers 2.5 - 3.14 |
| Mon | May 20 | Int- Improper: 3.15 | |
| Wed | May 22 | Partitioning Unity: 4.16 | |
| Fri | May 24 | Change Variables: 4.17 | |
| Mon | May 27 | Memorial Day: no class | HW7 Due May 31 |
| Wed | May 29 | Diffeomorphism: 4.18 | |
| Fri | May 31 | Var Chng Proof: 4.19 | |
| Mon | Jun 3 | Var Chng Appl: 4.20 | |
| Wed | Jun 5 | review | HW8 Not Due |
| Wed | Jun 12 | Final 6-8pm. Practice answers | |