# Real Analysis

**Course:** Math 361, Spring 2018

**Time & Place:** TR 10:10 – 11:30 am in HEG 308

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

**Course Tutor:** Andres Mejia (am8248@bard.edu)

**Upcoming Office Hours:**

## Announcements

#### Final

Here is the takehome final exam:

The final must be written in LaTeX, and is due next Tuesday, May 22. Late submissions will not be accepted.

#### Homework 9

The last homework assignment consists of the following problems from the textbook.

- Section 3.3 # 10
- Section 4.4 # 13, 14

For problems 3.3.10 and 4.4.14, you will probably want to follow the outline given in class on Tuesday.

#### Homework 8

The eighth homework assignment consists of the following problems from the textbook.

- Section 4.2 # 5, 7, 11
- Section 4.3 # 9, 12

The homework must be written up in LaTeX, and is due this

**Friday** (April 27). You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### Homework 7

The seventh homework assignment consists of the following problems from the textbook.

The homework must be written up in LaTeX, and is due this

**Friday** (April 20). You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### Homework 6

The sixth homework assignment can be found at the following link:

The homework must be written up in LaTeX, and is due this

**Friday** (April 13). You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### Homework Solutions

Here are the solutions to the first three homework assignments:

#### Midterm

Here is the takehome midterm exam:

The midterm must be written in LaTeX, and is due next Sunday, April 8th. Late submissions will not be accepted.

#### Homework 5

The fifth homework assignment consists of the following problems from the textbook. Note that this assignment is a bit long, so it will count a bit more than a typical homework assignment:

- Section 2.4 # 2.4.6 and 2.4.7
- Section 2.5 # 2.5.5 and 2.5.8

The homework must be written up in LaTeX, and is due

**next Friday** (March 16). You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### No Class Next Week

There will be no class next Tuesday or Thursday. Of course, there will also be no class the following week because of spring break.

#### Homework 4

The fourth homework assignment consists of the following problems from the textbook:

- Section 2.2 # 2.2.6
- Section 2.3 # 2.3.3 and 2.3.5

The homework must be written up in LaTeX, and is due this

**Tuesday**. You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### Homework 1 Solutions

Here are the solutions to the first homework assignment:

#### Homework 3

The third homework assignment consists of the following problems from the textbook:

- Section 1.5 # 1.5.8, 1.5.10
- Section 2.2 # 2.2.2

The homework must be written up in LaTeX, and is due this Friday. You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### Room Change

We will be meeting in Hegeman 308 for the rest of the semester.

#### Homework 2

The second homework assignment consists of the following problems from the textbook:

- Section 1.4 # 1.4.2 and 1.4.8
- Section 1.5 # 1.5.6

The homework must be written up in LaTeX, and is due this Friday. You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### Reading

Please read Sections 2.1 through 2.4 of the textbook as soon as possible.

#### Homework 1

The first homework assignment consists of the following problems from the textbook:

- Section 1.3 # 1.3.6, 1.3.10, and 1.3.11

The homework must be written up in LaTeX, and is due this Friday. You should feel free to work together with other students in the class, but everyone must type up their own version of the solutions.

#### Practice Problems

Here are some quick practice problems from the book. I recommend that you try to solve these problems, but you do not need to type up your solutions:

You can click on each problem above to see the answer.

#### Reading

Please read Chapter 1 of the textbook as soon as possible. Here is a PDF version of the first chapter for those who don't yet have the book:

The PDF is password-protected. You can open it using the password announced in class.

#### Welcome!

Welcome to Math 361. I will be using this course webpage to post all announcements and documents, including homework assignments, homework solutions, and takehome exams.

## Office Hours

All my office hours are in my office (Albee 315). I've also listed the office hours and math study room hours for the course tutor Andres Mejia (shown in red).

## Textbook Information

The textbook is

*Understanding Analysis, 2nd edition* by Stephen Abbott. You will need a copy of the textbook for reading and homework problems, but you do not need to bring it to class. You can buy a hardcover copy from Amazon.com

for $38, or rent it for $15.

## Course Policies

#### Introduction

This course studies the fundamental ideas of analysis in one-dimensional Euclidean space. Topics covered include the completeness of the real numbers, sequences, Cauchy sequences, continuity, uniform continuity, the derivative, and the Riemann integral. As time permits other topics may be considered, such as infinite series of functions or metric spaces.

#### Prerequisites

The prerequisites are Proofs & Fundamentals (Math 261) and a course covering sequences and series, such as Math 241, Math 245, or Physics 221. We also recommend that students in Real Analysis take at least one other proofs-based 300-level math course beforehand, such as Abstract Linear Algebra (Math 331), Abstract Algebra (Math 332), Graph Theory (Math 317), or Game Theory (Math 315).

#### Homework

There will be a weekly homework assignment due each Friday, consisting mostly 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.

#### Exams and Grading

The grade will be based on the weekly homework and two exams:

Homework | 50% |

Midterm Exam | 25% |

Final Exam | 25% |

The exams will most likely be takehome, possibly with an in-class component as well.