This is an unintentional detour for our little course. I didn’t plan to investigate the factorial function in so much detail, but it came about quite by accident (or stupidity) as we’ll see in later [more…]
Here we’ll look at some more probability calculations before moving on to permutations, combinations and the binomial theorem. More Probability… If you recall from the last part, we used set notation to describe a general [more…]
Subsets Let’s suppose that set \(S\) contains a full deck of playing cards. Therefore, \(|S|=52\). We can split the cards into four suits: \(♠,♣,♥,♦\). Let’s make a set \(T\) that contains only the clubs suit [more…]
Before we can start to solve some counting problems we need to know a little of combinatorics’ notation. Luckily, a few simple rules should get us started. Don’t worry if it doesn’t make sense, that [more…]
Mathematics is not everyone’s cup of tea – fair enough. The Monday morning ‘double maffs’ articles by our resident mathematician, OldTrout, can present some GP’ers with a feeling of bewilderment. Myself included. I’m no mathematician. [more…]
We touched on quadratic residues when discussing Pythagorean triples. We relied upon the quadratic residues and non-residues in modulo for our proof that and took opposite parities. These residues have important results in encryption, integer [more…]
There is another way of generating the primitive Pythagorean triples using matrices which was discovered by Berggren in 1934 and again by Barning in 1963.