MATH 352            Analysis II: d Strikes Back                    Spring 2012

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.  You know it, and judging by your comments from Analysis I, you like it.

The Course:  This is the second semester of a two semester sequence. In the fall, we started with a review of some of the material covered in FOM, including the key properties of the real numbers, and covered the idea of completeness. Chapter 2 covered sequences and series; Chapter 3 looked at the topological properties of the real numbers. We left off in Chapter 4 digging 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.

 

In Analysis II, we will finish this text, and move on to discuss other topics of interest.  An additional textbook may be assigned for that course. Stay tuned.

Random Facts:

Name:

Dave Kung

Office:

175 Schaefer Hall

Email:

dtkung@smcm.edu

Phone:

x4433 (240-895-4433)

My safe place:

Running trails with my dogs

Office Hours:

Tue

9:00-10:00

Wed

2:00-3:00

Fri

1:00-2:00

TAs:

Nick Pasko & Marissa Smith

 

 

I will also be around at other times - if you need to meet with me and the times above don't work for you, let me know and we can schedule an appointment. And of course you are always welcome to stop by and see if I'm around.

 

Course Work and Grades:

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, due Friday)

25

In-Class Definitions Quizzes (Jan. 26th, Mar 1st, Apr. 19th)

24

Midterm (in class, March 8th)

15

Infinity License

1*

Comprehensive Final (take-home – due May 4th 2pm)

25

Total

100

 

á      Your score on the ÒInfinity LicenseÓ assignment will either be a 1 or a 0. If 1, that score will be added to your other grades. If a 0, it will be multiplied by your other grades.

 

For the problem sets, I encourage you to work together. What you turn in must be your own work in the sense that it should reflect, in your own words, your understanding of the problem. The midterm (in class) and final (take-home) exams are individual assessments and working with anyone is strictly forbidden.  The in-class Definitions Quizzes (three of them) will be designed to make sure that you know and understand the definitions that are critical to analysis.  As you undoubtedly know from FOM & Analysis I, 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}$