# Math 411. Real Analysis II

Spring 2016

• Instructor:         Enrique Treviño

• Lectures:           MTRF 11:00 - 11:50 pm in Young Hall 207

• Office Hours:    MWF between 10:00am and 11am. You can also arrange a meeting by appointment.

• Office:               Young Hall 105

• Email:

• Phone Ext.:        #6187

Announcements

Final Exam. The final exam is due on Friday April 29 at 1:30pm in my office. The rules are listed in the pdf. Enjoy!

Homework 10, due on Thursday April 21, consists of the following exercises from the textbook:
6.2.2, 6.2.5, 6.2.7, 6.2.18, 6.2.19.
6.3.3, 6.3.4, 6.3.5, 6.3.9, 6.3.11.
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 10 is in pdf, and
Homework 10 Solutions.

No class on Friday April 8.

Homework 9, due on Thursday April 14, consists of the following exercises from the textbook:
6.1.1, 6.1.2, 6.1.6, 6.1.8, 6.1.9, 6.1.11, 6.1.13, 6.1.20.
6.2.1, 6.2.4.
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 9 is in pdf, and
Homework 9 Solutions.

Homework 8, due on Thursday April 7, consists of the following exercises from the textbook:
5.3.4, 5.3.5, 5.3.8, 5.3.9, 5.3.17
5.4.1, 5.4.4, 5.4.5, 5.4.6, 5.4.11 (for this problem you may assume 5.4.8,5.4.9,5.4.10 are true).
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 8 is in pdf, and
Homework 8 Solutions.

Homework 7, due on Tuesday March 29, consists of the following exercises from the textbook:
5.1.3, 5.1.5, 5.1.9, 5.1.13, 5.1.20
5.2.2, 5.2.3, 5.2.5, 5.2.8, 5.2.13
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 7 is in pdf, and
Homework 7 Solutions.

Stirling's Approximation. This is part of the proof I did in class on Tuesday. It's not complete.

Homework 6, due on Monday March 21, consists of the following exercises from the textbook:
4.3.4, 4.3.5, 4.3.8, 4.3.9, 4.3.10
4.4.1, 4.4.2, 4.4.7, 4.4.8, 4.4.11
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 6 is in pdf, and
Homework 6 Solutions.

No class on Tuesday February 23.

Homework 5, due on Thursday February 25, consists of the following exercises from the textbook:
4.1.1, 4.1.2, 4.1.3, 4.1.5, 4.1.6, 4.1.12
4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.2.5, 4.2.9
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 5 is in pdf, and
Homework 5 Solutions.

Homework 4, due on Tuesday February 16, consists of the following exercises from the textbook:
3.2.2, 3.2.3, 3.2.4, 3.2.5,
3.3.3, 3.3.4, 3.3.11, 3.3.12,
and two more exercises (not from the book) which you can find in the pdf below. I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 4 is in pdf, and
Homework 4 Solutions.

No class on Thursday February 4.

Homework 3, due on Tuesday February 9, consists of the following exercises from the textbook:
3.1.1, 3.1.3, 3.1.5, 3.1.7, 3.1.11, 3.1.12, 3.1.13, 3.1.15, 3.1.17, 3.1.19.
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 3 is in pdf, and
Homework 3 Solutions.

Homework 2, due on Tuesday February 1, consists of the following exercises from the textbook:
2.2.1, 2.2.4, 2.2.5, 2.2.6, 2.2.7, 2.2.8, 2.2.9,
2.3.1, 2.3.2, 2.3.5, 2.3.10, 2.3.11.
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 2 is in pdf, and
Homework 2 Solutions.

Section 1.2 in the Textbook. The link includes the exercises from section 1.1 and section 1.2. Section 1.2 is the list of definitions and theorems we'll take for granted in this class.

Homework 1, due on Tuesday January 26, consists of the following exercises from the textbook:
1.1.3, 1.1.18
2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.9, 2.1.10, 2.1.11, 2.1.15.
I wrote out the problems in tex to help you have a template for the homework solutions you will turn in.
Homework 1 is in pdf, and
Homework 1 Solutions.

Textbook

A radical approach to Lebesgue's theory of integration by David Bressoud.

The textbook is mandatory.

Supplemental Textbook
An introduction to Measure Theory by Terence Tao. The book can be found free online here and a hardcover copy is available on reserve in the library. You can also purchase a cheap copy in several places. This book can help as an extra reference.

Topics we will cover

This course is a survey of important concepts in real analysis. The main purpose will be to learn Lebesgue integration.

The course grade will be based on:
Homework 20%,
Midterm 40%,
Final Exam 40%.

Homework

There will be written homework roughly every week. The most recent homework will be posted in the announcements and a copy of all homeworks can be accessed here. Each homework assignment will consist of roughly 10 problems. Each student will submit the solutions to the problems written in LaTeX. Collaboration on the homework is permitted (and encouraged), however the solutions turned in must be written individually.

You may not use the internet or any resource other than the textbook, course notes, and the supplementary textbook when working on the homework assignments.

Exams

There will be two midterms and one final exam. The three exams will be take home exams. You can use your notes and both textbooks. You are not allowed to use the internet or any other book. You can ask for two free hints in each exam. You can ask for more hints at the expense of points in the test. You must work on the problems on your own. No collaboration permitted in the exams.

The tentative dates are:
• The first midterm will be handed out on Monday February 29 and due in class on Friday March 4.
• The second midterm will be handed out on Monday April 11 and due in class on Friday April 15.
• The final exam will be handed out on Monday April 25 and it will be due on Friday April 29 by 4:30pm.

Attendance

Students are expected to come to every lecture and every exam.

If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.

Accommodations Statement

If you believe that you need accommodations for a disability, please consult with The Learning and Teaching Center. Since accommodations may require early planning and are not retroactive, please contact the center as soon as possible. For details about the services for students with disabilities and the accomodations process, visit http://www.lakeforest.edu/academics/resources/disability/.

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Teryn Robinson at the Learning and Teaching Center.