FOUNDATIONS OF ADVANCED MATHEMATICS -- MATH 251 – Spring, 2004

Time: M T Th F 10:20 – 11:10 am Location: Collins 306

Professor: Steve Prothero Office: Collins 307

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

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

Office Hours: M T Th F 9 – 10:15; W 8 - noon

Afternoons by appointment

{In class: M T Th F 8 – 8:50 & 10:20 – 11:10}

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 will 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 power 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 try to use correct grammar, punctuation, and spelling. The journal will be handed in on a regular basis (see schedule) and will be graded each time. The grad will be base primarily on the whether or not the journal was on time and complete.

Proofs Without Words: Most classes will begin with a student presenting a “Proof Without Words” of some mathematical theorem or formula. Each student will present three of them. The presentation schedule will be determined by lot.

Problem Sets: There will be regularly assigned proofs/problems. Some will be done in

groups; others will be individual assignments.

Papers: There will be two required papers. The topics will be announced later.

Special Lectures: There will be three or four special lectures given outside of class time.

You will be expected to attend and to write about two or three of these.

Grading:
	Journal Submissions	5 @ 10 points	50
	Proofs Without Words	3 @ 20 points	60
	Problem Sets	~ 10 @ 20 points	~ 200
	Papers	2 @ 40 points	80
	Special Lectures	2-3 @ 20 points	40 - 60
	Mid - Terms	2-4 @ 40 points	80 - 160
	Final	(may be part take-home)	100
		Total	~ 610 - 710

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. written discussions of pieces of established mathematics

3. problem solutions

4. your personal journal

5. expository papers relating to mathematics