Math 3283W, Spring '02

Last changed: May 15, 2002.

Sequences, Series and Foundations - Writing Intensive.

The course meets 5 times a week: Lectures, 9:05am-9:55am MWF in 1701 Univ. Ave, Rm 3
Max Jodeit, VinH 258, 5-3855, jodeit@math.umn.edu
and
Discussion sessions at 9:05 or 10:10, depending on section. Your TA is
Leonard Blackburn
or
Kyle Calderhead respectively. See their Web pages for locations and more information.

The TEXT is Infinite Sequences and Series, by Konrad Knopp. It's a Dover publication, $8.95

We don't need the text right away. Your class notes will do at first, along with the PDF document "The Peano Postulates" available from this site (link below).

In addition, you may want to obtain a copy of the notes by Prof. Wayne Richter used before for Math 3283W and for Math 2283. The notes are available at Alpha Prints on 4th St in Dinkytown, between 14th and 15th Avenues, for $15.

Max Jodeit's Office Hours: 10:30 - 11:30 MWF, chat after class, -- or call 5-3855 to see if I'm in and available.

Links, if any, to other Web pages or documents related to this course will go here. Announcements, hints, "news" will also be here.

Announcements, hints, "news"
News May 15: Weights: Final 32%, Tests 23%, writing 22.5%, Quiz/Homework 20%, Problems 2.5%.

The Final will be May 13, 1:30 - 4:30pm, Room 14 at 1701 University

News: Reading for Monday May 6: pages 18 - 29; In pages 30 - 36.5, read Definitions 2 and 3, Theorems 2.3.3.1 - 2.3.3.11. Read from 36.5 thru 40, and 42, 43. Read the Complex notes on the Web. Read the nth-power notes -- one of you pointed out that the first time the Difference-of-Powers Formula is stated in the nth-power notes, the factor (a - b) is omitted -- that is now corrected. Read 43.75 - 51. Read the Exponential Saga. Preread "The Logarithm: exponential in reverse."

On page 40, under Example 5, where it says "2.5.1,3" it should say "2.6.1,3" which is on page 46.

Reread 44 - 48.5 (i.e., thru Theorem 1) more than once. There is a lot there that says "what's going on" with regard to series. 48.5 - 51 are important too, just technical. Read 52 - 53.5. Read twice: 53.5 - 60.25 (3.1.2.3 - 3.3). Preread again: "The Logarithm: exponential in reverse." For the moment, ignore log and powers that are not rational. Preread 60.25 - 66. We'll re-do Theorem 2 as the "Cauchy Condensation Test;" Theorem 2 is the CCT with Bells ans Whistles. Theorem 3 is the very useful Integral Test.

Go thru all the Series Tests we have dealt with in class; ignore the other series stuff in Knopp.

Advice: when you find a Definition or a Theorem with a name, memorize it! The exercises may help you learn without memorizing; you need to read and at least understand a l l the exercises!

We will cover "log" and powers x^a when "a" is not a rational number on Monday May 6!

Please make a list, as you read, of places where Knopp baffles you. Let me know what's in your list!!

Test 3 gradelines: "pseudotop" is 110, average was about 72.
A: 85 or more;
B: 65 or more;
C: 50 or more;
D: 40 or more.

Test 2 gradelines: "pseudotop" is 92, average was about 48.
A: 73 or more;
B: 58 or more;
C: 45 or more;
D: 36 or more.

Test 1 gradelines: "pseudotop" is 100, average was about 55.
A: 80 or more;
B: 64 or more;
C: 51 or more;
D: 40 or more.
Tests will occur on Wednesdays now, on Feb 20, Apr 3 and May 1.

What does "Writing Intensive" mean? This course will have some assignments emphasizing writing. In most cases, the quality of the writing will be most important, after the mathematics. Succinct is good, prolix bad. You are encouraged to write about the intuitive ideas behind your proofs! This can serve as your introduction to a mathematical argument, as a bridge between parts of a mathematical argument, or as the conclusion to a mathematical argument. The writing scores will amount to about 25% of your grade, and the writing scores will have separate gradelines. You must have a grade of C or brtter to pass the writing part of the course (this may have to be adjusted later). Approximately 15 pages of writing assignments will be given. You'll write a first draft, turn it in for critique, then prepare a final draft for grading. Your drafts, both first and final, must be neatly written, with one-inch margins. The assignments will use about 45 of you "good" hours (more if you work on them when you are tired or distracted!).

On tests and quizzes (when you are under time pressure) the important thing is that your answer must be on the paper, not in the scorer's mind. Your writing on quizzes or exams won't count against you unless it is mathematically incorrect.

Math 3283W is a "bridge" between "factual" Mathematics courses and proof-oriented ones. The course introduces you to proofs dealing with Sequences and Series and some of their important applications.

The course consists of Lectures, the more formal part, and Discussion Sessions, that are very important, because they allow you to see how important your intuition and your past experience, both mathematical and otherwise, are! They are the "back room," the "kitchen," the space behind the Wizard's curtain! The material in the Lectures will always be treated with "high seriousness," presented with gentle humor, greatly influenced by your questions in Lecture and your answers to the questions I ask in Lecture.

We will begin with Logic, Sets, Functions and the Peano Postulates (for the Natural Numbers), to introduce the Foundations of the subject. You'll learn about Truth Tables, quantifiers, writing mathematical statements "in logic," translating them back to mathematical English, and the mechanics of working with denials of mathematical statements. We'll also see how difficult it is to "suspend belief" in the things mathematical you take for granted, by developing the operations of addition and multiplication of Natural Numbers, and the concept of order there.

When you finally get your copy of Knopp's book, you'll find that Chapter One outlines how the Real and Complex numbers can be built from the Natural Numbers.

This descriptive information and more is contained in the Syllabus (link below).