FOUNDATIONS OF ADVANCED MATHEMATICS – MATH 251 – Fall, 2006

Time: M F 1:50 – 2:40 pm W 1:50 – 3:30 pm Location: Collins 306

Professor: Steve Prothero Office: Collins 303

Phones: Office: 370 - 6484 Home: (503) 393 - 5143

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

Office Hours: M W Th F 9:10 – 10:15; W 8:30 – 11:30

Afternoons by appointment

{In class: M W Th F 8:10 – 9 & 10:20 – 11:10}

Text: Proofs and Fundamentals: A First Course in Abstract Mathematics

by Ethan D. Bloch

The Course: The purposes of this course are 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, and will learn how to use them to approximate functions.

Proofs Without Words: Students will be expected to orally present a “Proof Without Words” in class. Each is a highly visual proof of

some mathematical theorem or formula. The presentation

schedule will be determined by lot.

Class Participation: Students will be called upon to present solutions / proofs of

problems / theorems from the book or from outside sources.

It is expected that the student will be present and will be

prepared to present.

Assigned Homework: There will be regularly assigned proofs/problems. See the class schedule for the due dates.

Writing: Writing for this course will consist of, but may not be limited to, some

of the following:

1. proofs of theorems

2. written discussions of pieces of established mathematics

3. problem solutions

4. expository papers relating to mathematics

Grading:
	Assigned Homework	10 @ 20 points	200
	Proof Without Words	40 points	40
	Class Participation	50 points	50
	Exams	5 @ 40 points	200
	Final	(may be part take-home)	100
		Total	590

The total points earned will determine the course grade. The grade will not be based on fixed percentages. However,

531 points (90%) guarantees at least an A-,

472 points (80%) guarantees at least a B-,

413 points (70%) guarantees at least a C-,

354 points (60%) guarantees at least a D.