Math 289 – Problem Solving
(Winter 2007)
· Time and Location: Wed 3-5 (2866 East Hall).
· Instructor: Richard Kollár,
East Hall 1847, phone: (734)
936-2879.
· E-mail: kollar....umich.edu (a preferred way of communication) .
· Office Hours: Mon 1-2, Tue 1-2, Thu 1-2 or by appointment.
· Textbook: Problem-Solving Through Problems by Loren C. Larson (Not Required)
· Additional Information: Winter
2006 course home page Fall
2006 course home page
· Syllabus: Very flexible.
· Grading Policy: Grades will be based on participation and on
individual homework. No final exam will be given. The homework
assignments (problem sets) will be regularly posted below. Each problem set
contains 6-8 problems of a various difficulty, each 10 points, 15 points or 20
points worth. The score from the best 4 problems will be added to form
the total HW score. There will be approximately 11 problem sets assigned. The
grade will be based on total from each student’s 10 best assignment scores
(these number are just guidelines and may be adjusted – lowered – later):
|
|
A+ |
451 and more |
A |
391 – 450 |
A- |
331 – 390 |
|
|
B+ |
271 – 330 |
B |
211 – 270 |
B- |
171 – 210 |
|
|
C+ |
141 – 170 |
C |
101 – 140 |
C- |
71 – 100 |
|
|
D+ |
41 – 70 |
D |
11 – 40 |
D- |
1 – 10 |
· Course Description: Some theories say that the best way to learn
mathematics is through problem solving. In fact, all the mathematical knowledge
we have today was obtained by solving various kinds of mathematical problems.
Also, problem solving is a day-to-day-bread of every mathematician since every
theorem or lemma they want to prove contains within itself a series of small
steps, each forming a small or a bigger challenge. The common feature of these
problems is that before solving them it is often hard to tell whether they are
easy or hard to solve and it is not clear which method is the most suitable for
attacking them. Therefore each mathematician has his/her own virtual library of
mathematical methods, recipes and tricks, which are always handy. Of course, as
in each library it is very important to have the entries well organized. The
goal of this course is to build a decent library of mathematical methods and to
organize it. This will be done almost solely through individual problem solving
although some topic reviews will be given over the semester. Most of the
problems will be various Mathematical Olympiad and Putnam contest problems. The
important part of the course is also interest, curiosity, fun and joy
from solving mathematical problems as these
are the main driving forces in the field. Therefore a significant out-of–class-time
dedication is expected from all students in the course. It is important to
emphasize that the skills developed through-out the course may be extremely
useful in further study of mathematics, statistics or related fields.
· Recommended Literature for Further Reading
(Not Required):
Problem
Solving Strategies by Arthur
Engel,
The
William Lowell Putnam Mathematical Competition: Problems and Solutions
1965-1984,
The
William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions,
and Commentary (MAA Problem Book Series),
Mathematical
Olympiad Challenges by Mark
Saul,
103
Trigonometry Problems: From the Training of the USA IMO Team by Titu Andreescu,
Mathematical
Olympiad Treasures by Titu
Andreescu, Bogdan Enescu,
102 Combinatorial
Problems by Titu Andreescu,
Zuming Feng,
Number
Theory and Its Mathematical Structures: A Problem-Solving Approach by Titu Andreescu, et al,
How To
Solve It – A New Aspect of Mathematical Method by G. Polya.
· Problem sets:
|
Jan 10 |
Problem Set 0 – in
class |
|
|
Jan 17 |
Due Problem Set 1 |
|
|
Jan 24 |
Due Problem Set 2 |
|
|
Jan 31 |
Due Problem Set 3 |
|
|
Feb 7 |
Due Problem Set 4 |
|
|
Feb 14 |
Due Problem Set 5 |
|
|
Feb 21 |
Due Problem Set 6 |
|
|
Mar 7 |
Due Problem Set 7 |
|
|
Mar 14 |
Due Problem Set 8 |
|
|
Mar 21 |
Due Problem Set 9 |
|
|
Mar 28 |
Due Problem Set 10 |
|
|
Apr 4 |
Due Problem Set 11 |
|
|
Apr 11 |
Last Class |
|
Page Updated: 03/28/2007