MAT 300, Introduction to Proof, Analysis, and Topology
Spring, 2008

Tue/Thu, 8:30-9:45 a.m.
Chambers 3234


Outline


Instructor:
Stephen L. Davis; click here for my weekly schedule.

Text:
R. B. Maddox, Mathematical Thinking and Writing, Harcourt/Academic Press, 2002

Overview:

Our goal is to develop your capacity for reading, writing, and speaking mathematics. The first two-thirds of this course concentrates on a core which investigates basic mathematical paradigms and objects: proof techniques, sets, relations, and functions (chapters 1--3 of our text). We follow this with an foray into the basic principles of analysis (chapters 4 and 5). A rough approximation for our progress toward address these topics is shown in the Schedule Guesstimate below.

We hope that your experience in this course will serve as a gentle initiation into the larger mathematical community. One technical aspect of this initiation will be an introduction to LaTeX, a markup system for producing mathematical documents on a computer. Other ways this will be fostered will be through outside readings and participation in activities of the Bernard Mathematics Society, including Math Coffees. Your involvement in some of these activities may have tangible rewards towards your course grade, but others will be expected of you as fledgling members of the fellowship of mathematicians.

Evaluation:

We will have two take-home writs, one in-class review, and a self-scheduled final examination. Homework will be assigned regularly and collected weekly. Auxiliary activities may include the D. H. Hill Problem Contest, Math Coffees, the Bernard Lecture and other mathematics events on campus.

A culminating activity in the course (along with the final examination) will be the compliation of a proof portfolio. The portfolio will include at least a dozen examples of your proof-writing from homework, each showing your progression from initial effort to polished revision. Your choices for inclusion in the portfolio should provide a broad representation of topics and proof techniques from our course.

A rough recipe for the proportions in which these events combine to produce your evaluation is

Class Policies:

The portfolio, writs, review and final examination are pledged events; you are expected to be vigilant in upholding the Honor Code.

You should come to class prepared to discuss readings and problems from the text. Collaboration on homework is encouraged. However, anything you present or turn in should represent your own understanding of the material. If you have any questions regarding ground rules for individual events, do not hesitate to ask for clarification.

Each member of the class is a valuable resource for others in the class. Absences and tardiness diminish the quality of the course; come to class and come on time. I monitor attendance; missing 20% of class meetings can trigger action to encourage more faithful attendance. In any event, you are responsible for all material discussed in class, whether you are present or absent.

Schedule Guesstimate:

( volatile! )
Date Chapter Event/Topic
Jan 15, 17 0.1, 0.2 1.1, 1.2 ch 0: Notation & Assumptions
Jan 22, 24 1.3, 1.4 LaTeX Intro ch 1: Logic
Jan 29, 31 2.1 2.2 ch 2: Beginner-Level Proofs
Feb 5, 7 2.3 2.4 Writ #1 (due Feb 12)
Feb 12, 14 2.5 2.6 ..
Feb 19, 21 2.7 2.8 ..
Feb 26, 28 2.9 3.1 ch 3: Functions
Mar 4, 6 no class no class Spring Break
Mar 11, 13 3.2 Review ..
Mar 18, 20 3.3 .. ch 4: The Real Numbers
Mar 25, 27 no class 4.1 Easter Break
Apr 1, 3 4.2 4.3 ..
Apr 8, 10 4.4 4.5 (Portfolio draft due Apr 10)  Writ #2 (due Apr 15)
Apr 15, 17 4.6 .. ..
Apr 22, 24 5.1 5.2 ch 5: Functions of a Real Variable
Apr 29, May 1 5.5? 5.6? (Portfolio due May 1)
May 6 .. Reading Day ..
May 9--14 Final Examination