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):
Xuxing Chen (sec 03):
Zachary Ibarra (sec 01, 02):
Office Hours: Babson 5:00 to 6:00 pm Wed via zoom 7150588313. 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)

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-.

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.

DayDateSection(#s) coveredHomework
MonApr 1Linear Algebra: 1.1 HW1 part 1 Due Apr 12.
WedApr 3Matrix Inverse: 1.2 HW1 parts 1-2 Due Apr 12.
FriApr 5Topology: 1.3 HW1 Due Apr 12.
MonApr 8Compacta: 1.4
WedApr 10Derivatives: 2.5 HW2Due April 26.
FriApr 12Differentiable: 2.5
MonApr 15Continuously Differentiable: 2.6
WedApr 17Review
FriApr 19 Midterm I Solutions, More
MonApr 22Chain Rule Use: 2.7 HW3 Due April 26.
WedApr 24Chain Rule Proof: 2.7
FriApr 26Inverse Fn Thm: 2.8
MonApr 29Integrals: 3.10 HW4 Due May 3.
WedMay 1Int Existence: 3.11
FriMay 3Int Evaluation: 3.12
MonMay 6Int Evaluation: 3.12 HW5 Due May 10.
WedMay 8 Int Bounded: 3.13
FriMay 10Int Bounded: 3.13
MonMay 13Rectifiable Sets: 3.14 HW6 Due May 24
WedMay 15review
FriMay 17 Midterm II PracticeAnswers covers 2.5 - 3.14
MonMay 20Int- Improper: 3.15
WedMay 22Partitioning Unity: 4.16
FriMay 24Change Variables: 4.17
MonMay 27Memorial Day: no class HW7 Due May 31
WedMay 29Diffeomorphism: 4.18
FriMay 31Var Chng Proof: 4.19
MonJun 3Var Chng Appl: 4.20
WedJun 5review
WedJun 12Final 6-8pm.