1. What is combinatorics?

Source abstract

<p>Combinatorics can loosely be described as the branch of mathematics concerned with selecting, arranging, constructing, classifying, and counting or listing things. ‘What is combinatorics?’ explains that the subject can be dated back some 3000 years to ancient China and India. For many years, especially throughout the Middle Ages and the Renaissance, it consisted mainly of problems involving the permutations and combinations of certain objects, but over the succeeding centuries the range of combinatorial activity has broadened greatly. Combinatorics now includes a wide range of topics such as the geometry of tilings and polyhedra, the theory of graphs, magic squares and latin squares, block designs and finite projective planes, and partitions of numbers.</p>