## Solving problems with graphs

I saw this question on Quora: A teacher assigns each of her 18 students a different integer from 1 through 18. The teacher forms pairs of study partners by using the rule that the sum of the pair of numbers is a perfect square. Assuming the 9 pairs of students follow this rule, the student...

## Markov chain

A Markov chain is a mathematical system that undergoes transitions from one state to another on a state space in a stochastic (random) manner. Examples of Markov chains include the board game snakes and ladders, where each state represents the position of a player on the board and a player moves between states (different positions...

## Probability

The fundamental idea of inferential statistics is determining the probability of obtaining the observed data when we assume the null hypothesis is true. For example, if we roll a die 10 times and got 10 sixes, what is the probability of observing this result if we assume the null hypothesis that the die was fair?...

## Combinations and permutations in R

Time to get another concept under my belt, combinations and permutations. While I'm at it, I will examine combinations and permutations in R. As you may recall from school, a combination does not take into account the order, whereas a permutation does. Using the example from my favourite website as of late, mathsisfun.com: A fruit...

## Calculus

I remember studying calculus in school and there were so many concepts that never clicked. I could solve the equations, find derivatives, work out the area under the curve, etc. but I didn't see the use of calculus, i.e. the application of calculus. I'm revisiting calculus now because I've been taking part in a biostatistics...

## Set notation

I've just started the Mathematical Biostatistics Boot Camp 1 and to help me remember the set notations introduced in the first lecture, I'll include them here: The sample space, (upper case omega), is the collection of possible outcomes of an experiment, such as a die roll: An event, say E, is a subset of ,...

## Using LaTeX with WordPress

I've been meaning to learn LaTeX for a while now (among all the other things I want to learn). Here I just illustrate examples of using LaTeX with WordPress, with respect to displaying vectors and matrices. To display LaTeX, I just need to surround the code with two starting dollar signs (\$\$) and two closing...