Mathematics

Ergodic Theory

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REU 2001

Math Consulting Services

Knots in Maple

A favourite elementary problem

A favourite advanced problem

Math Links

 

 

Changing of the Guard

You are given a 3x3 checkerboard with 2 black knights and 2 white knights positioned as shown. Your problem is to exchange the positions of the white knights with the black knights using only knight's moves. What is the minimum number of moves required? Why?

BLACK
KNIGHT

 

WHITE
KNIGHT

 

 

 

BLACK
KNIGHT

 

WHITE
KNIGHT

This is an old question known to many people, and discussed by Martin Gardner in several of his books.

The Magic Hole Punch

The magic hole punch can be placed over a single point p in the plane. When you press the punch it removes all points in the plane that are a rational distance away from p, the position of the punch. How many times do you have to punch and where, to remove all points in the plane?

This question was on a Putnam exam from the early nineties.

Mathematical Consulting and Tutoring Services

I welcome all interesting challenges. The initial consultation and estimate is of course free.  Please contact me.

My skills include:

Mathematical programming.

Expertise in the computer algebra system Maple.

Tutoring experience at all levels .

Mathematical and analytical  problem solving skills.

Good presentation and business skills.

Organizational experience.

Course design and presentation skills.

Editing and proofreading experience with math and computer science texts.

 

Previous Consulting Activities

Developing and delivering one and two day courses on Maple for many customers including Memorial University of Newfoundland, John Abbot College, Seton Hall University, and Waterloo Maple Software.

Providing mathematical solutions to efficiency questions in assembly line processing for Carlson Wagonlit Travel.

Reviewing and editing for MATHPOWER 12 Western Edition - McGrawHill Ryerson's high school math text.

Developed math equations for use in advertising.

Solving math equations for medical technology.

 

Reviewed/Updated January 2006 by Blair Madore