Fall 2019: Math 341, Real Analysis

Class: Math 341, Real Analysis

Time: MWF, 1030-1120 and 1130-1220

Location: UNIV 201

Office hours: W 1230-200 PM and F 830-1000 AM.

Book: I do not plan to have an official textbook for the class. There are many resources for analysis that are freely available online (for example, this book). Here is a list of some popular ones:

I will have class notes that will be updated throughout the term for the class; it is located at the bottom of this page. I will have links to web pages (mostly wikipedia) that give lengthier discussions of the various topics we cover. You should utilize the free information that abounds. The hyperlinks in the class notes are meant to make that easier. There are also several hyperlinks to YouTube videos that discuss concepts, proofs, and topics that arise in this class.

Problem sets: I will post weekly problem sets here in .pdf format. I will try to post the problem sets a week before they are due.

Grades: I assign grades based on your rank within the class. I usually employ 3-4 schemes for producing a ranking. They are based on exams and homework. I give you the best grade among the different schemes.

The class: The two primary goals for the course are to introduce you to proof based mathematics and to provide you with a good working knowledge of real analysis.

Class Announcements

September 25: Only problems 1-5 on Pset will be graded this week. The remaining problems will be graded in a future problem set.
September 11: #6 and #7 on Pset 3 are optional.
September 6: Pset 3 has been updated.
September 1: Pset 1 and 2 merged to become Pset 1-2. Pset 1-2 is due on Friday September 6 and will count as two problems sets. Pset 3 will be due September 13.
August 26: Fixed problem 8 in Pset 1. As stated, the problem was false.
August 19: Read Chapter 1, Section 1 of the class notes on sets and functions.

Class Schedule

(Week 1) August 19: Class logistics.
August 21: Fun lecture.
August 23: Sets and functions.
(Week 2) August 26: Sets and functions.
August 28: No class.
August 30: Problem set discussion.
(Week 3) September 2: No class. University holiday.
September 4: Distance, metrics, and metrics spaces.
September 6: Metric spaces and sequences.
(Week 4) September 9: Bounded, Cauchy, and convergent sequences. Subsequences.
September 11: Sick day.
September 13: Open and closed sets. Topologies.
(Week 5) September 16: Another sick day.
September 18: What makes the reals the real?
September 20: Continuity and convergence.
(Week 6) September 23: Review for Midterm 1.
September 25: Overview of module 1.
September 27: Midterm 1.
(Week 7) September 30: Hand back midterm 1.
October 2: Infinite series.
October 4: Day off. No lecture.
(Week 8) October 7: No class. Fall break.
October 9: Series.
October 11: Series.
(Week 9) October 14: Series and continuity.
October 16: Continuity and connectedness.
October 18: Save the fish day.
(Week 10) October 21: Continuity, connectedness, and compactness.
October 23: Continuity, connectedness, and compactness.
October 25: Continuity, connectedness, and compactness.
(Week 11) October 28: Review for Midterm 2
October 30: Review for Midterm 2
November 1: No class
(Week 12) November 4: Midterm 2
November 6: Handback Midterm 2
November 8: Distributions and Integration
(Week 13) November 11: Integration
November 13: Integration
November 15: Integration
(Week 14) November 18: Integration.
November 20: Integration
November 22: Midterm 3. Tentative.
(Week 15) November 25: Handback Midterm 3.
November 27: No class. University holiday.
November 29: No class. University holiday.
(Week 16) December 2: Dead week. Derivatives.
December 4: Dead week. Derivatives.
December 6: Dead week. Derivatives.