StatlectThe Digital Textbook
Index

Mathematical tools

Review some mathematical tools that are frequently used in probability theory and statistics.

Sets

Set theory

The basics of sets and set operations (union, intersection, complement)

Combinatorics

k-permutations

Generalizing the concept of permutation, counting k-permutations

Permutations

Ordering objects, counting permutations, the factorial function

Partitions

Subdividing objects into groups, counting the number of possible subdivisions

Combinations

Choosing groups of objects, counting them, the binomial coefficient

Sequences

Limit of a sequence

Convergence, convergence criteria, metrics

Sequences

Definition of sequence, countable and uncountable sets

Calculus

Review of integration rules

Definite and indefinite integrals, computation rules

Review of differentiation rules

The basic rules used to compute the derivative of a function

Matrix algebra

Matrix algebra

A short course on the fundamentals of matrix algebra

Special functions

Beta function

A ratio of Gamma functions

Gamma function

A generalization of the factorial function

The book

Most of the learning materials found on this website are now available in a traditional textbook format.