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Here is a genuine probability question I once tackled: “In your sock drawer there are 6 blue socks, 2 red socks and 2 white socks , distributed so that the probability of picking each is equal. Without looki...

Often, it can seem daunting when you are asked to differentiate a function that looks particularly messy. However, it's really quite simple if you break it down in easy to manage steps. I find students seem ...

How to integrate ln(x)? In order to integrate log x of base e, we are going to apply integration by parts. Recall that the formula for integration by parts is: / / | f(x) g'(x) = f(x) g(x) - | f'(x) g(x) / /...

We all know the the square root of 2 is irrational. So, the answer should be no. But how do we prove it?Let's assume for contradiction that x 2 =2 and that x is rational. Then x can be expressed as a rationa...

Let's take a positive integer n.We can write it as a product of prime numbers:n=p 1 p 2 ...p r , where p 1 , p 2 , ..., p r are prime factors of n.Now, assume that n 2 is even. Then one of the p i equals 2. ...