Math 127C - Real Analysis

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. 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.

Fun Directed Reading Program: Applications are being accepted for another day for small group enrichment topics. See the website.
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-.

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 Bounded: 3.13

Wed May 8 Rectifiable Sets: 3.14

Fri May 10 Int- Improper: 3.15

Mon May 13 Int- Improper: 3.15

Wed May 15 review

Fri May 17 Midterm II

Mon May 20 Partitioning Unity: 4.16

Wed May 22 Change Variables: 4.17

Fri May 24 Change Variables: 4.17

Mon May 27 Memorial Day: no class

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

Tue Jun 11 Final 6-8pm.

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 Bounded: 3.13
Wed	May 8	Rectifiable Sets: 3.14
Fri	May 10	Int- Improper: 3.15
Mon	May 13	Int- Improper: 3.15
Wed	May 15	review
Fri	May 17	Midterm II
Mon	May 20	Partitioning Unity: 4.16
Wed	May 22	Change Variables: 4.17
Fri	May 24	Change Variables: 4.17
Mon	May 27	Memorial Day: no class
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
Tue	Jun 11	Final 6-8pm.