**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 **Web site (this page):**- 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.
**About this class**- 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.
- The Math 305 self-test.
- The Appendix of the textbook.
- 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.

- 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.
**Reading, quizzes, and homework**-
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.

Reading assignments and homework problems will be posted on this page (again:

**not**on Canvas). **Exams**- There will be four 45-minute
in-class midterm exams, on September 20, October 16, November 13, and
December 6. The final exam will be Wednesday, December 20 at
8–11 a.m. for the 2:15 section and 12–3 p.m. for the 12:45
section. location TBA. All exams are closed-book, closed-note exams
with no calculators, phones, or collaboration. You must take each
exam in the class section for which you are registered.
**Grading**- Your grade for the semester will be computed as follows:

Quizzes: 5%

Homework: 25%

Midterm exams: 12% each (48% total)

Final exam: 22% **Links**- Reading, homework, and exam information
- Forget what you know about good study habits: Read this, and think about what it implies about how you should study.
- U Can't Talk to Ur Professor Like This and the author's guidelines about email etiquette for students
- Useful posts on Tim Gowers's blog:
- Welcome to the Cambridge Mathematical Tripos
- Basic logic — connectives — AND and OR
- Basic logic — connectives — NOT
- Basic logic — connectives — IMPLIES
- Basic logic — quantifiers
- Basic logic — relationships between statements — negation
- Basic logic — relationships between statements — converses and contrapositives
- Basic logic — tips for handling variables
- Basic logic — summary

- A few words about proofs: a short handout with some hints about basic techniques in writing proofs. I wrote this with Math 307 in mind but it applies just as well for anybody who's writing mathematical proofs for the first time, or is still getting used to it. I recommend that you read this before doing the first homework.