Assignments
1. During the semester each
student will give two presentations
in class about a
mathematcial subject, or students can choose to do it in
two-person group. The topic will be chosen by the instructor, and also
some material, but the presenter can choose his (her) favorite
part. (The student do the presentation on Week 2 will only do one
presentation.)
2. After one week's discussion, one student will write up the solution
of one designated problem in that week's problem set. The solution
needs to be typed, in Words or LaTeX. The solutions should be sent to
the instructor by email, every two or three weeks. Since we have 13
students, 3 students will be exempted of writing problems each week,
usually 2
of them will be the ones doing presentation next week. So at the end of
semester, each
student will write the solutions for exactly 10 problems.
3. We will have two take-home midterm "tests", similar to mathematical
competitions. You can think these tests as mock competitions. You will
be given a period of 4-5 days try to solve the problems. But the
results of the tests has no big effect on your grade.
4. Our "midterm exam" is Virginia Tech competion in October 29,
Saturday, and our "final exam" is Putnam exam in December 3, Saturday.
Again, the results has no effect on your grade.
Grades
Your grade will mainly be
determined by participation of
discussions, your presentations, and your weekly problem solutions.
Resource
Resource for this seminar
course is from (1) several books on
this subject; and (2) internet. For the books, thanks to the support
from chairman of the math department Prof. Li, the instructor has now a
collection of 6 books, and students in the seminar are welcomed to use
these books for their need. Some part of the book will be photocopied
for everyone. For the internet resource, plese check the course
website:
http://www.math.wm.edu/~shij/math490-fall2005.html
The problem sets and answer (which is written by you!) will also be
available on the website.
Textbooks and refererence books
There is no required textbook
for the class. There are many good books on the subject of problem
solving, and student can choose to pruchase one or more books for their
interests. Recommended general problem solving books are
Problem
Solving Through Problems By: Loren C. Larson
Problem-Solving
Strategies (Problem Books in Mathematics) By: Arthur Engel
Mathematical
Olympiad Challenges By: Titu Andreescu and Razvan Gelca
Mathematical
Miniatures (New Mathematical Library) By: Svetoslav
Savchev, Titu Andreescu
The
William Lowell Putnam Mathematical Competition 1985-2000: Problems,
Solutions, and Commentary By: Kiran S. Kedlaya, et al
The
William Lowell Putnam Mathematical Competition Problems and
Solutions: 1965-1984 By: Gerald L. Alaxanderson, et al
Presentation Topics and Schedule
The first round of presentation
is from Aug. 30 to Oct 18, and the second round is from Oct. 20 to Dec
1.