Yet another climate protest against our use of fossil fuels. Spokes-persons berate us over air-waves driven by generated electricity carried by steel pylons cemented into the ground. They sit in a studio with its array [more…]
A binary operation is said to commute if the order of the operands does not alter the result. In the real numbers, , the following commutative laws hold : for all for all Although these [more…]
Or : Multiplying by . The beginning of complex numbers is often attributed to Cardano (1501 – 1576). Complex numbers provide a solution to the equation . They are an extension of the number system [more…]
Diophantus of Alexandria wrote a collection of books called Arithmetica in the 3rd century AD. He noted that natural numbers of the form cannot be expressed as the sum of two square numbers. He also [more…]
Part of a conversation between Mission Control and Apollo 11 : 104:59:27 Garriott: Columbia, Houston. Over. 104:59:34 Collins: Columbia. Go. 104:59:35 Garriott: Columbia, Houston. We noticed you are maneuvering very close to gimbal lock. I [more…]
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…]
So far, we’ve looked at sets and how they contain information that we wish to count in some way. How the power set \(\wp(S)\) can count all of the possible sub-sets of a given set [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…]
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