Math403  Introduction to Analysis, I   Fall 2008


Daily Syllabus     Peter Greim's home page    MACS home page   Registrar's page   Citadel home page  
 

Class  Mo, We, Fr 10:00-10:50,  TH 316

P. Greim, Thompson 329, Tel. 953­5035, E­mail: peter.greim@citadel.edu
http://macs.citadel.edu/~greimp

Office hours are posted at my door and at my class schedule  web page. You can read it as long as you are using a Citadel terminal. The class schedule will give you an idea which times might be available if you need to make an appointment.

Text:

An Interactive Introduction to Mathematical Analysis
by Jonathan Lewin

Cambridge University Press 2003
ISBN-10: 0521815894 (with CDRom)

 

Covered material: Chapters 5 – 8 (after a brief review of chapters 2-4)

(MATH404 will cover chapter 11, parts of chapters 12, 14, and 15, and selected topics if time permits)

Course description

At first glance, it looks like there is not much new in this course: you have seen, in Calculus, in one form or other, most of the objects of study in the text. Nevertheless, we won't be able to cover all of them in one semester, because we will approach the subject with a different attitude.
We will build the development of familiar Calculus topics  -  limits, continuity, derivatives, integrals   -  on your thorough study (mostly done in MATH 206) of a few basic notions (sets and relations), being well aware, and precise in the use, of the rules of logic that we employ.
Please review the Discrete Math topics Logic, Sets, and Functions before the course begins. Alternatively, read chapters 1-4 of the text. [In detail: Read chapter 1. Review chapter 2. You should be able to do all the exercises. Read chapter 3. The notion of an algebraic number (example 2 in 3.5.1 might be new to you). You should be able to do most of the exercises. Review chapter 4. The exercises are excellent. The ones involving Scientific Notebook can wait until you begin your 30-day trial or have access to Thompson 220.]

A considerable part of the course work is outside the classroom. You need time to contemplate, look at an issue from different viewpoints, discuss it among yourselves. Activity on your part is crucial, as opposed to consumption and development of some computational skills. I will ask you to present selected homework problems in class after you had an opportunity to discuss your solutions with me. In this way you will be sure to understand your own work and you learn to present mathematics.

The (out-of-print) text comes in hardcopy with a CD that contains the full text and supplementary chapters. The cadet store has sufficiently many copies for the present enrollment. If you can get your hands on a paperback copy (with CD), that will work as well. You are welcome to write your homework with Scientific Notebook, but you don’t have to. A 30-day trial version of Scientific Notebook is included on the CD. At the end of the trial period you will still be able to read the text, but not use the built-in computer algebra system (Maple). Scientific Notebook is installed in the lab in Thompson Hall 220.

Grades

are based on the final, 2 tests, homework assignments, and projects. Each test counts 20%, homework 25%, projects 10%, and the final exam counts 25%. You'll receive 0.5 percentage points extra credit for each correctly solved problem of the week. (Look out for weekly announcements on the classroom bulletin boards.)  I will follow the usual 10% per grade scheme.

Missing a test unexcused will result in a score of zero. I will not allow you to miss a test because of a lack of preparation. If your absence is excused, I may choose to drop it and prorate the other test and homework scores, or give you a make­up test.

You can check your standing in the course here.
You'll need to know your code number to identify your record. It will be on your first returned assignment.

When you work problems, first try to do them by yourself. After that, whether you succeed or not, you may discuss them with others. You will learn from talking about mathematics. However, do not copy homework from others. I want you to understand a problem solution (either through own research or discussion) and then formulate it in your own words. Discussing a problem solution with a classmate, understanding it, and then formulating it in your own words is allowed. Copying a solution from others is not.

Occasionally I may let you do or redo part of a test as take-home. In that case you are completely on your own - almost. I am the only person with whom you may discuss a test problem before turning it in.

Help

is available: you may work with other students, see me after class, during office hours, or make an appointment (or just drop by my office, taking a chance that I may be busy).  I’m on campus Monday nights and, by appointment only, Thursday nights.

One last advice: when you are getting behind (or can't even get started right) - let me know right away. I'll go out of my way to help you if you try. Your grade will be based on your success - not on your effort. However, your effort will determine how much I help.