MATH 351                     Analysis I                       Fall 2011

Welcome to Analysis, a course devoted entirely to the study of infinity – from the infinitely small, to the infinitely small, to infinite processes. Along the way, we will work hard to understand into the foundations of calculus.  In addition to proving many of the unproven claims of those courses, we will lay the foundation for the majority of mathematics invented over the last 150 years.

The Text: We will use a text by Steve Abbott called Understanding Analysis.  This is an incredibly readable text; unlike the FOM text some of you used, however, there are no signposts for when you should stop and think, write or get your hands dirty. YouÕve had an entire semester of experience in FOM, and I expect you to continue those habits into this course. I strongly suggest that you keep a journal or notebook of notes while you read and do problems. Unlike in FOM, this journal will not be collected (though when you visit me in my office, please bring it along if youÕve been keeping it up to date.)

The Course:  This is the first semester of a two semester sequence. In the fall, we will start with a review of some of the material covered in FOM, including the key properties of the real numbers, and cover the idea of completeness. Chapter 2 covers sequences and series, which you should have seen in a very elementary fashion in Calc. II.  Chapter 3 looks at the topological properties of the real numbers. Chapter 4 digs into limits and continuity.  Chapter 5 covers the derivative and theorems related to it.  Chapter 6 returns to the ideas of chapter 2, this time in the context of sequences and series of functions.  Chapter 7 covers the integral, leading toward the Fundamental Theorem of Calculus, and chapter 8 contains a few miscellaneous topics.

During the fall semester, we will get as far as we can through this text – hopefully through Chapter 4.  As mentioned above, additional topics will be sprinkled throughout the semester.

You may have noticed while registering or looking for a seat: this class is packed. This means that you will have to rely on your classmates for help at many points in the semester. Get to know them. Plan study sessions early and often. It also means weÕve been granted two TAs for this class – both of them were top students in Analysis last year, Marissa Smith and Nick Pasko.

Random Facts:

Name:

Dave Kung

Office:

175 Schaefer Hall

Email:

dtkung@smcm.edu

Phone:

x4433 (240-895-4433)

My favorite moment:

Sunrise (not everyday!)

Office Hours:

 Tue 9:00-10:00am Wed 2:00-3:00pm Thurs 10:00-11:00am

TAs:

Marissa Smith (msmith@smcm.edu)

My schedule this year is more limited than usual – I am getting some time off to hang out with Ellie (who is roughly ¹/10 years old). If you want to meet with me, email me and weÕll set something up.

You will work your butt off in this class. It's hard stuff. You won't learn it by sitting and listening to me talk. Instead, you will read the book before class, come to class with questions, work on problems at home, put in endless hours working on problem sets with your classmates, and present problems in class. As for grades they will be determined as follows:

 Type of Work Percent Class Participation 10 Problem Sets (roughly every week) 30 In-Class ÒDefinitionsÓ quizes (Oct. 13th and Dec. 1st) 20 Midterm (in class Oct 25th, 2-?pm) 15 Comprehensive Final (Takehome – due Dec. 14th, 2pm) 25 Total 100

For the problem sets, I encourage you to work together.  The midterm exam will be taken in class – plan your schedule so you can stay late if needed. The final will be take-home exams during which working with a classmate -- or with any living organism other than me and Ellie -- is strictly forbidden.  The in-class Definitions Quizes (two of them) will be designed to make sure that you know and understand the definitions which are critical to analysis.  As you undoubtedly know from FOM, precise definitions hold the key to rigorous mathematical proofs; these exams will reinforce that idea.

The Software:

At least two of your homework sets (or take-home exams) will be typed using LaTeX, and typesetting language which allows you to easily write mathematics using code that looks like this:

$\int_0^1 \frac{dx}{\sqrt x}$  (Does this integral converge or diverge? Find the appropriate discussion board at smcm.blackboard.com . Please note that this is not the normal Blackboard server. Our class is one of the lucky ones piloting a new version of Blackboard.

We will spend a day in class familiarizing ourselves with LyX, a program which makes LaTeX easy, which will be available on the computers in the Schaefer Hall lab.