FOUNDATIONS OF ADVANCED MATHEMATICS -- MATH 251 – Fall, 2003

Time: M T Th F 10:20 – 11:10 am Location: Olin 214

Professor: Steve Prothero Office: Collins 307

Phones: Office: 370 - 6484 Home: 393 - 5143

e-mail: prothero@willamette.edu home: prothero4@comcast.com

webpages: http://www.willamette.edu/~prothero

Office Hours: M T Th F 8 – 9; W 8 - noon

Afternoons by appointment

{In class: M T Th F 9:10 – 10, 10:20 – 11:10, and 11:30 – 12:20}

Text: Reasoning and Writing, Foundations of Mathematics – class notes, Janeba

The Course: The purpose of this course is three-fold.

1. to introduce and practice the methods of mathematical proof

2. to become familiar with mathematical tools to be used in other courses

3. to learn to read and write concise mathematics

Coverage: We will discuss set theory, logic, and methods of proof while learning some of the fundamental aspects of higher mathematics.

We may develop the primary number systems of mathematics (natural numbers,

integers, rational, real and complex numbers) from fundamental concepts.

We will study sequences and series of numbers and functions including Taylor series.

Journal: Sometime between the end of one class and the beginning of the next you are to do the

following in your journal.

1. Indicate the date of your entry.

2. Summarize the previous class.

3. Indicate what (if anything) was good or bad, easy or hard, interesting or boring.

4. Indicate your feelings (hopes, fears, etc.) about what went on in that class session

or that is going on in the course.

This is informal and primarily for your own personal use. However, you should use

correct grammar, punctuation, and spelling. The journal will be handed in on a regular

basis (see schedule) and will be graded each time.

Proofs Without Words: Most classes will begin with a student presenting a “Proof Without Words” of some mathematical theorem or formula. These will be furnished a few days in advance. Each student will present four or five of them.

Problem Sets: Will be done with a partner. A single set of solutions will be turned in for each

partnership. Throughout the semester you will partner with each of the students

at least once and no more than twice. When the enrollment is an odd number

there will be one three-person partnership. Solutions should be carefully written

and word-processed. Problem sets will be graded on the quality of the exposition

as well as the quality of the mathematics.

Papers: There will be two required papers during the semester. The topics to be announced later.

Grading:	Proofs Without Words	~ 4 @ 10 points	~ 40
	Problem Sets	~ 10 @ 20 points	~ 200
	Papers	2 @ 30 points	60
	Journal Submissions	5 @ 10 points	50
	mid -terms	2 @ 50 points	100
	Final	(may be part take-home)	100
		Total	~ 550

The total points earned will determine the course grade. The grade will not be based on fixed percentages. However, 90% guarantees at least an A-, 80% guarantees at least a B-, etc.

Writing: Writing for this course will consist of, but may not be limited to, several of the following:

1. proofs of theorems

2. discussions of pieces of established mathematics

3. problem solutions

4. your personal journal

5. expository papers relating to mathematics