# Real Analysis II

**Course:** Math 461, Spring 2016

**Time & Place:** TR 11:50–1:10 pm in RKC 101

**Instructor:** Jim Belk (belk@bard.edu)

**Office Hours:** Friday 1 – 5 pm (Albee 3rd Floor)

## Announcements

#### Extra Office Hours

I am having extra office hours this Monday and Tuesday evening:

- Monday, 7–9 pm (3rd floor Albee)
- Tuesday, 7–9 pm (3rd floor Albee)

#### Takehome Final

The takehome final is due next Tuesday at 11:59 pm. Here is the final:

Since this is an exam, you should make sure not to discuss the problems with anyone else in the class, or with anyone on the internet.

#### Notes

Here are all of the notes in order:

#### Homework 11

The eleventh homework assignment is due this Friday, May 13. Here is the assignment:

#### Homework 10

The tenth homework assignment is due this Friday, May 6. Here is the assignment:

#### Homework 9

The ninth homework assignment is due this Friday, April 22. Here is the assignment:

#### Homework 8

The eighth homework assignment is due this Friday, April 15. Here is the assignment:

#### Homework 7

The seventh homework assignment is due this Friday, April 8. Here is the assignment:

#### Midterm Solutions

Here are the solutions to the takehome midterm:

#### Homework Solutions

Here are the solutions to the first four homework assignments. Please take a look:

- Homework 1 Solutions (PDF, TeX)
- Homework 2 Solutions (PDF, TeX)
- Homework 3 Solutions (PDF, TeX)
- Homework 4 Solutions (PDF, TeX)

#### Extra Office Hours

I will be having extra office hours this week on Wednesday and Thursday evening, in addition to my usual Friday office hours:

**Wednesday** 7 – 9 pm (**RKC 100**)
**Thursday** 7 – 9 pm (**RKC 100**)

#### Takehome Midterm

The takehome midterm is due this Sunday at 11:59 pm. Here is the midterm:

Since this is an exam, you should make sure not to discuss the problems with anyone else in the class, or with anyone on the internet.

#### Homework 6

The sixth homework assignment is due

**next** Friday, March 18. Here is the assignment:

You should feel free to work together with other members of the class, though everyone must turn in their own copy of the assignment, and you must acknowledge any collaborators. You can turn in the assignment by e-mailing your solutions to

belk@bard.edu.

#### Homework 5

The fifth homework assignment is due this Saturday, March 5. Here is the assignment:

You should feel free to work together with other members of the class, though everyone must turn in their own copy of the assignment, and you must acknowledge any collaborators. You can turn in the assignment by e-mailing your solutions to

belk@bard.edu.

#### Homework 4

The fourth homework assignment is due this Friday, February 26. Here is the assignment:

You should feel free to work together with other members of the class, though everyone must turn in their own copy of the assignment, and you must acknowledge any collaborators. You can turn in the assignment by e-mailing your solutions to

belk@bard.edu.

#### Homework 3

The third homework assignment is due this Friday, February 19. Here is the assignment:

You should feel free to work together with other members of the class, though everyone must turn in their own copy of the assignment, and you must acknowledge any collaborators. You can turn in the assignment by e-mailing your solutions to

belk@bard.edu.

#### Homework 2

The second homework assignment is due this Friday, February 12. Here is the assignment:

You should feel free to work together with other members of the class, though everyone must turn in their own copy of the assignment, and you must acknowledge any collaborators. You can turn in the assignment by e-mailing your solutions to

belk@bard.edu.

#### Homework 1

The first homework assignment is due this Friday, February 5. Here is the assignment:

You should feel free to work together with other members of the class, though everyone must turn in their own copy of the assignment, and you must acknowledge any collaborators. You can turn in the assignment by e-mailing your solutions to

belk@bard.edu.

#### Welcome!

Welcome to Math 461. I will be using this course webpage to post all announcements and documents, including class notes, homework assignments, and takehome exams.

## Course Description

This course is a continuation of math 461. Our goal is to cover those topics in analysis typically required for beginning graduate courses. The first half of the course will be an introduction to Lebesgue measure and Lebesgue integration on the real line and in higher dimensions. The second half will cover a variety of topics, including Hilbert and Banach spaces, applications of measure theory to probability, differentiation and integration in multiple dimensions, and so forth. The prerequisite is Math 361 (Real Analysis).

#### Textbook

There is no textbook for the course, but there are several books that you may find it helpful to consult:

The last of these is available for free online, and is quite good. I especially recommend reading through §2.1 on problem-solving strategies in analysis.

## Homework, Exams, and Grading

#### Homework

There will be weekly homework assignments, which will consist almost entirely of formal proofs. You are encouraged to work together on the homework, but you should write up your own solutions individually, and you must acknowledge any collaborators. Homework solutions must be written in LaTeX, and should be submitted to me by e-mail.

#### Exams and Grading

The grade will be based on the weekly homework, the takehome midterm exam, the takehome final exam:

Homework | 50% |

Midterm Exam | 25% |

Final Exam | 25% |