Peter's Blog

Mdoular arithmetic is essentially arithmetic on remainders. Recall that whenever we have two integers , with , there exist unique integers and , with such that The number is the remainder. Doing arithmetic on remainders is usually much easier than doing arithmetic on the original numbers, especially if is small. In addition, since the set…

The Pythagorean Theorem is of course a well-known theorem. Basically, it states that the sum of squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. There are many proofs of this. The following is perhaps my favourite. Consider the diagram below:…

The transition from grade school mathematics to a mathematics specialist program in university is a big one, even for those who are in enriched high school mathematics programs.  The primary change in my opinion is the shift from computations to abstractions.  In grade school mathematics, the emphasis is on concrete examples involving numbers.  In university…