Real Analysis - Fall 2020

Basic Course Information

Instructor:	Patrick Guidotti.
Teaching Assistant:	Matthew Powell.
Class Meetings:	Monday and Wednesday 5-6:20pm (via Zoom).
Office Hours:	Wednesday 3-4pm and Thursday 4-5pm (via Zoom).
Weekly Homework due by:	Saturday, 11:59pm, starting Oct 10.
Midterm Examination:	November 9, 2020
Final :	December 16, 2020
Textbook:	Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, Wiley (2nd edition).
Complementary Reading:	H.L. Royden and P.M. Fitzpatrick, Real Analysis, Prentice Hall-Halsey (4th edition). W. Rudin, Real and Complex Analysis, McGraw-Hill (3rd edition). S. Axler, Measure, Integration, and Real Analysis, Springer Open.

Course Goals

Gain working knowledge of measure and integration theory.
Develop and practice learning independence.
Learn to assess own learning and understanding.
Grow by exchange of ideas and points of view, collaboration.
Develop written and oral presentation skills.

Course Components

Assigned Reading

Before each zoom meeting each student will read the assigned portion of the textbook in preparation for the class meeting and the group discussions. Groups will comprise four members, each with one of four roles. The latter are discussion leader, presenter, devil's advocate, and notetaker and will change from session to session.
The presenter is tasked with elaborating the designated textbook material (see prompts) into a presentation (see samples) to be given at the following class meeting during the group activities. During a presentation each group will act as a mini classroom in which the discussion leader is the moderator and each group member is encouraged to ask questions, offer comments, share alternative points of view, ...
The devil's advocate will keep the conversation "honest" by raising testing questions and advocating alternative simpler approaches, when appropriate and possible, even only for the purpose of making the reasons explicit for the approach chosen in the by now traditional development of the subject. The notetaker will keep a written record of the issues that triggered interesting and lively reactions/discussions in the group and of the questions, the answers to which could be of general interest or were not found within the group. The notetaker will eventually record this information in the class journal in the form of a question, answer, or comment.
Presentations, in PDF-format, need to be uploaded to Canvas, regardless of whether you gave a tablet, beamer, or hand-written presentation.

Zoom Meetings

We will meet twice a week online. During each session we will address issues of common interest altogether before breaking into groups of four. Each group member will play one of four roles: discussion leader, presenter, notetaker, and devil's advocate. The roles will rotate each class and will be recorded in a file in Overleaf. Each group will act as a mini classroom with assigned presentations and discussions about the material. While some prompts for conversation will be provided, everyone is encouraged to raise any issue of their interest or concern.

Class Journal

As we go through the course material we will use a shared Overleaf Project as a class blog, in which questions can be asked, answers can be given, and comments can be posted. Everyone is invited to participate and the course's instructor and TA will monitor the discussion and provide input as needed. The journal reflects the structure of the class meetings so that it can be used during the reading and class preparation phase, as a recap of the major issues discussed during the team work, and as a useful future reference when reviewing the material.

Homework Assignments

While collaboration and exchange of ideas are an integral part of this course, it remains important to set aside some time for individual work. Weekly omework assignments are reserved for this. They are an opportunity to assess your progress and your understanding of the material. Once you turn in your assignments via Overleaf, the courses TA will mark them and leave feedback. If you only obtain partial credit, you will have the opportunity to improve your work for additional credit.

Discussions

During discussion selected homework problems are discussed along with old exam problems relevant to the topic at hand.

Evaluation Policy

The final grade of this course will be based on

(15%) Active participation in the Zoom meetings and in the team activities.
(15%) Contributions to the class journal in the form of questions, answers, or comments.
(20%) Presentations.
(20%) Homework.
(30%) Midterm and final examinations.

Additional Information

UCI Health Guidelines.
School's Expectations for Students During Remote Instruction.
Online Etiquette.

Plese notice that Section 102.23 of Policies Applying to Campus Activities, Organizations, and Students states that the following activities constitute grounds for discipline: Selling, preparing, or distributing for any commercial purpose course lecture notes or video or audio recordings of any course unless authorized by the University in advance and explicitly permitted by the course instructor in writing. The unauthorized sale or commercial distribution of course notes or recordings by a student is a violation of these Policies whether or not it was the student or someone else who prepared the notes or recordings.

$\LaTeX$ Distributions

MacTex (OS X), MikTex (Windows), TeX Live (Linux), The LaTex Project