Math 322 — Real Analysis II — Spring 2012

Instructor: Mark Meckes (pronounced "MECKess")
Email: mark dot meckes at case dot edu
Office: Yost 211
Phone: 368-4997
Office hours: Monday 11–12, Wednesday 10–11, Thursday 11–12, or by appointment.

Class time and location:
MW 12:30–1:45 p.m. in Yost 101.

Web site (this page):
http://www.case.edu/artsci/math/mwmeckes/math322/

Text
Real Mathematical Analysis, by Charles Chapman Hugh.

Official course description
Continuation of MATH 321. Point-set topology in metric spaces with attention to n-dimensional space; completeness, compactness, connectedness, and continuity of functions. Topics in sequences, series of functions, uniform convergence, Fourier series and polynomial approximation. Theoretical development of differentiation and Riemann integration. Required for all mathematics majors.

About this class
This is of course a continuation of Math 321. With a thorough grounding in the concepts of convergence and continuity from Math 321, we will focus on some of the most important applications of those ideas: differentiation, integration, and Fourier series. We will spend roughly the first half of the semester covering chapter 5 of the textbook (omitting some topics and adding some things not in the book), and the second half covering Fourier series (which are not covered in this textbook — you'll have to come to class).

As the syllabus from last semester pointed out, this class will require some linear algebra. We will cover what is needed at the beginning of the semester — contrary to what the book says at the beginning of chapter 5, I will not take it for granted that you are familiar with linear transformations, matrices, determinants, and dimension. However, those students who have already taken Math 307 will have the advantage of seeing these ideas for at least the second time.

Reading and homework
You are expected both to attend lecture (and take notes!) and — when we're covering material from it — read the textbook. The lectures and textbook partly reinforce each other and are partly complementary. In particular, I will sometimes cover material in lecture which is not in the textbook, and you will sometimes be responsible for material in the textbook which is not covered in lecture.

There will be homework problems based on the material from each lecture, normally due on Friday. All homework assignments are due by 4 p.m. on the listed date, at my office. 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 the grader 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 and homework problems will be posted on this page.

Exams
There will be four in-class midterm exams, on February 13, March 5, April 9, and April 30. Each midterm will take place in the first 45 minutes of class; the rest of class will cover new material. The final exam will be May 9 at 8:30–11:30 a.m. All exams are closed-book, closed-note exams with no collaboration.

Grading
Your grade for the semester will be computed as follows:
Homework 25%; each midterm exam 12.5%; Final exam 25%.

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