*Logarithm : *Logarithm of a number *N* to the base *a* is the number *x *to which the base must be raised to equate with the original number *N*. *i.e*., if log_{a}*N * = *x, *then *a ^{x} = N. *The number

*Factorial n : *Factorial* n*, denoted by *n*!, is defined as *n*!* = n(n-1)(n-*2)…1. Thus 5! = 5.4.3.2.1 = 120. It is convenient to define 0! = 1.

*Combinations : *A combination of *n* different objects taken *r* at a time is a selection of *r* out of the *n* objects with no attention given to the order of arrangement. The number of combinations of *n* objects taken *r* at a time is denoted by and is given by _{ }

=

For example, the number of combinations of the letters a, b, c taken two at a time is These are *ab, ac, bc*. Note that *ab* is the same combination as *ba*, but not the same permutation.

*Mathematical expectation : *If *X* denotes a discrete random variable which can assume the values *X*_{1}, *X*_{2}, …,* X _{k}* with respective probabilities

E(*X*) = *p*_{1}*X*_{1 }+ *p*_{2}*X*_{2 }+ …+ *p*_{k}*X*_{k} .

In the case of continuous variables, the definition of expectation is as follows. Let *g*(*X*) be a function of a continuous random variable *X*, and let *f*(*x*) be the probability density function of *X*. The mathematical expectation of *g*(*x*) is then represented as

where *R* represents the range (sample space) of *X, *provided the integral converges absolutely.

*Matrix* : A matrix is a rectangular array of numbers arranged in rows and columns. The rows are of equal length as are the columns. If *a _{ij}* denote the element in the

A* _{r }*x

A simple example of a 2 x 3 matrix is A* *_{2 x 3}=

A matrix containing a single column is called a column vector. Similarly a matrix that is just a row is a row vector. For example, x = is a column vector. y’ = is a row vector. A single number such as 2, 4, -6 is called a scalar.

The sum of two matrices A* *= {*a _{ij}*} and B

A = and B = , then C =

The product of two matrices is defined as C* _{r}* x

A* *= and B = , then C =

For further details and examples from biology, the reader if referred to Searle (1966).