# Math 321 — Real Analysis — Fall 2017

Instructor: Mark Meckes (pronounced "MECKess")
Email: mark dot meckes at case dot edu
Office: Yost 223
Phone: 368-4997
Office hours: Tuesday 1:15–2:45 p.m. and Friday 10:45–12:15 p.m.

Class time and location:
Section 1: MW 12:45–2 p.m., Sears 480.
Section 2: MW 2:15–3:30 p.m., Sears 480

http://www.case.edu/artsci/math/mwmeckes/math321-17f/

This site is where to go for all information about this class, including assignments. Canvas may be used for the online grade book, but will not be used for anything else.

Text
Elementary Real Analysis, 2nd edition, by B. S. Thomson, A. M. Bruckner, and J. B. Bruckner.

The textbook is available for free online at the link above, or can be ordered from various places (see the web site).

Official course description
Abstract mathematical reasoning in the context of analysis in Euclidean space. Introduction to formal reasoning, sets and functions, and the number systems. Sequences and series; Cauchy sequences and convergence. Required for all mathematics majors. Prereq: MATH 223.

This is a first course in real analysis, which roughly speaking is a deeper treatment of the two most fundamental ideas you encountered in calculus: convergence and continuity. (You thought I was going to say derivatives and integrals, didn't you? We'll get to those eventually, but convergence and continuity come first.) Math 321 will cover the first several chapters of the textbook, and some material from some later chapters. Math 322 will cover much of the rest of the book, and probably a substantial amount of material not in the book.

Here are some things for you to know heading into this class, or deciding whether to take it.

• If you've never taken a proof-oriented math class before, you might consider taking Math 305 first. If you're not sure which is the right course for you, then please discuss it with me, but here are some things for you to look at to help you decide.

1. The Math 305 self-test.
2. The Appendix of the textbook.
3. My handout A few words about proofs.

If you're not already comfortable with most of the material in all three of these, then Math 305 may be for you. (I'll only cover some of the material in the Appendix of the book explicitly, and I will assume everyone is comfortable with all of it throughout the semester.)

• Historically, most students have taken Math 307 (linear algebra) either before Math 321 or at the same time. In Math 321 we will cover and use some basic concepts from linear algebra; Math 322 will cover and use some more substantial linear algebra concepts. We will cover everything about linear algebra that's needed in Math 321–322, but students who have already taken Math 307 will have the advantage of seeing those ideas for the second time.

You are expected both to attend lecture (and take notes!) and read the textbook. The lectures and textbook partly reinforce each other and are partly complementary. You will be responsible for knowing material from the textbook which is not covered in lecture, and material from lecture which is not in the textbook.

For most lectures there will be a reading assignment. The lecture will begin with a short group quiz based on the reading (so don't be late!). I will assign groups for the quizzes. You will receive an email with your group assignment before the first quiz. (Note that for this reason, you will need to attend the section of the class for which you are registered.)

After each lecture, there will be homework problems based on the reading and lecture material, normally due at 4 p.m. on the next class day.

There will be no make-up quizzes and late homework will not be accepted. If unusual circumstances arise and you contact me in a timely manner, then we can discuss alternative arrangements.

Throughout this class, you need to explain your answers even when the problem doesn't explicitly ask for a proof; this typically means writing in complete English sentences. When deciding how much detail to include, here's the standard to keep in mind: your solution to a problem should be complete and clear enough that one of your classmates, who has paid attention in class but hasn't thought about that specific problem yet, could read your solution and understand exactly how it works. If you only try to convince me that you understand the solution, then you almost certainly won't write enough.

Students may work together on homework. However, each student must figure out how to write up his or her own solution to be turned in. That means for example that you and a friend may figure out together how to prove a statement, but the written-out proofs you turn in should not be verbatim copies of each other.