Here are books that were recommended to me.
You can find other similar books in the QA43.* area of the library.
International Student Competition in Europe.
Virginia Tech Regional Mathematics Contest.
There are seven problems for two hours and a half.
This competition has problems of a different type.
I am told that they often have a relatively "quick" solution (if
you find the right idea/method).
Information from the web-site:
Highlights of this Course: This seminar is geared toward
Freshmen. The course website features extensive problem sets and
supplementary problems. Students in this course are expected to
compete in a nationwide mathematics contest for undergraduates.
Course Description This course is an undergraduate seminar
on mathematical problem solving. It is intended for students who
enjoy solving challenging mathematical problems and who are
interested in learning various techniques and background
information useful for problem solving.
Information from the web-site:
Highlights of this Course: This undergraduate subject on
"The Art of Counting" features a comprehensive set of 233
problems for students to solve. The course is structured with one
lecture session per week, and student presentations to report on
their work in one problem session per week.
Course Description The subject of enumerative
combinatorics deals with counting the number of elements of a
finite set. For instance, the number of ways to write a positive
integer n as a sum of positive integers, taking order into
account, is 2n-1. We will be concerned primarily with
bijective proofs, i.e., showing that two sets have the same number
of elements by exhibiting a bijection (one-to-one correspondence)
between them. This is a subject which requires little mathematical
background to reach the frontiers of current research. Students
will therefore have the opportunity to do original research. It
might be necessary to limit enrollment.
ORGANIZATION:
- By default, there are two windows that will pop-up: one for problems and solutions, and one for hints.
You can open more windows, as described below:To open a link in a new window, check the menu provided by the right mouse button (when it is over the link).
Often the middle button is a shortcut.COMMENTS:
- The hints are only a suggestion. You could find many other solutions following your own ideas.
Sometimes the posted solutions also offer more ways to solve a given problem.- I suggest that you write (at least a sketch of) your solution, so that I can take a look.
Of course, checking could go faster if you have also time to explain the solution on the blackboard.
Let me know if you would like to see me.- You might have already worked through these problems - I will add more as we go along.