Math 410-03, Problem
solving and math Contests, Fall 2008
Syllabus
Course Description
Techniques of solving mathematical
problems will be reviewed, and
the
seminar will also prepare the students for college level mathematical
competitions, like Putnam Exam,
and Virginia
Tech competition.
Parallel to a systematic review of knowledge on algebra, combinatorics,
number theory, calculus, geometry and other topics, students will also
solve problems from selected problem sets, present and discuss their
solutions in seminar.
Instructors:
There are 5
professors who will give lectures/lead discussion for this seminar:
Junping Shi (coordinator, Jones 122, shij@math.wm.edu); Tanujit
Dey (Jones 110, tdey@wm.edu);
David Hasler (Jones 119,dghasler@wm.edu);
Ryan Vinroot (Jones 130, vinroot@math.wm.edu);
Gexin Yu (Jones 127, gyu@wm.edu). See schedule on course webpage: http://jxshix.people.wm.edu/math410-problem-solving/index-2008.html
Meeting times and
location
Tuesday 3:30-4:30pm, Jones Hall 131
Plan
of the seminar
The structure of each meeting is as follows: first 20-30 minutes, the
instructor will give a presentation on a mathematical topic, including
main concepts and theorems, problem solving techniques, and a few
typical examples to illustrate the
theory; next 30-40 minutes, the class will discuss a
problem set assigned prior week. Students should think
about these
problems before the
class, and if you
can solve some problems in the set, sketch your answer in notebooks,
and try to
present your answer in class. For each problem set, one or two problem
will be
assigned to each student, and he/she will lead the discussion of the
problem, or present his/her solution. We
may have one or 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 effect on your grade. Our "midterm exam" is
Virginia Tech competion in November 1,
Saturday, and our "final exam" is Putnam exam in December 6, Saturday.
Again, the results has no effect on your grade.
Grades
Your grade will mainly be
determined by participation of
discussions, and your presentations.
Resource
Resource for this seminar
course is from (1) several books on
this subject; and (2) internet. For the books, the instructor has now a
collection of 6 books, and students in the seminar are welcomed to use
these books for their need. For the internet resource, plese check the
course
website: http://jxshix.people.wm.edu/math410-problem-solving/index-2008.html
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
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
The William Lowell Putnam Mathematical
Competition Problems and Solutions: 1938-1964 By Andrew M. Gleason