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Combinatorics is the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. Combinatorics: A Very Short Introduction provides an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to draw a map with different colours for neighbouring countries.Less

Networks: A Very Short Introduction considers the basic elements of network theory and its applications using everyday examples from society, technology, nature, and history. It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena. The ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse are all considered. The findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology.Less