TEXTS: The Keys to Advanced Mathematics : Recurrent
Themes in Abstract Reasoning by Daniel Solow ( Paperback, Books
Set Theory and Related Topics 2nd Ed'n by Lipschutz (McGraw-Hill SOS,1998) (Unexpected!)
How to Solve It by G. Polya (Princeton, 1988)
SCOPE: This course will provide a foundation for further work
in mathematics.This will be accomplished primarily by informal but careful
and rigorous exploration of key topics related to mathematical reasoning.
This will include a discussion of many of the essential tools for any mathematical
discourse and problem solving: sets, functions, and relations; problems
and conjectures; evidence, proofs and refutations; and direct and indirect
Several topics from discrete mathematics will provide additional opportunities for using these tools.
Lectures will organize the topics to present materials not covered in
the texts as well as those treated in the texts. We will cover material
from Solow contained in chapters 1 to 3, 5.1, and 6.2.4; from Lipschutz
chapters ??? being revised due to new edition???, and perhaps others as
time permits. By the end of the first two weeks students will be expected
to have read the textual part of the Polya, and references to relevant
words in his "dictionary" section should be read regularly. Supplementary
readings and materials will be supplied as appropriate.
Summaries of lectures may be available through the course webpage.
TECHNOLOGY: We may use the computer at various stages of this course to illustrate and investigate some of the topics. No particular software will be required though at times we may use X(PLORE) or Geometer's Sketchpad.
TESTS AND ASSIGNMENTS:
Proof Analysis: Each week students will be expected to read at least one proof presented for analysis.These will not be lengthy. A brief analysis responding to a list of questions is to be passed on Wednesdays beginning February 3rd.
The proof analysis will cover briefly the techniques of argument (direct, indirect, induction, etc.) and exposition (forward-backward organization, reference to prior work, definitions, etc.) used in presenting the result. [See the Weekly assignments. The proof analyses and proofs without words will be graded Honors(4)/Good(3)/Credit(2)/NCr(0). (Accepted one day tardy at most!) ]
Proof Without Words: An explanation of a weekly proof without words will be assigned to be done cooperatively and due on Fridays beginning January 29th.
Regular Homework: Shorter problem assignments (about 5-10 problems) will be made on a regular basis for each class. These will not be accepted after 5 p.m. of the due date and will be graded Well-done (++=4), Acceptable (+=3), Unacceptable (-=2), No Credit (--=0)
Reality Check Quizzes: During the term I will give several reality check quizzes. These will usually be distributed on Fridays and collected on Mondays, covering work from the previous recent assignments and class discussions.
Midterm Examinations: There will be two self-scheduled mid-term examinations.These will be announced a week in advance and will be worth 100 points each. There will also be a mid term coorperative assignment which I will grade worth 50 points.
FINAL ASSESSMENT: The final assessment will be in two parts. Part I will be a cooperative team take home examination that will be due on the last day of the final examination period. Part I will be distributed on the Friday before the last week of classes. Part II will be an individual self-scheduled 90 minute examination given during the final examination period. Part I will be worth 100 points. Part II will be worth 150 points.
GRADES: Final grades will be based on the accumulation of points in the various categories of assignments as indicated in the following chart:
|Proof w/o Words||25|
|Reality Check Quizzes||100|
|Final Assessment Part I||100|
|Final Assessmant Part II||150|