How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal)
Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. 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. In...

Translation is everywhere and matters to everybody. Translation doesn't only give us foreign news, dubbed films and instructions for using the microwave: without it, there would be no world religions, and our literatures, our cultures, and our languages would be unrecognizable.
In this Very Short Introduction, Matthew Reynolds gives an authoritative and thought-provoking account of the field, from ancient Akkadian to World English, from St Jerome to Google Translate. He shows how translation determines meaning, how it matters in commerce, empire, conflict and resistance, and why...

What is learning? How does it take place? What happens when it goes wrong?
The topic of learning has been central to the development of the science of psychology since its inception. Without learning there can be no memory, no language and no intelligence. Indeed it is rather difficult to imagine a part of psychology, or neuroscience, that learning does not touch upon. In this Very Short Introduction, Mark Haselgrove describes learning from the perspective of associative theories of classical and instrumental conditioning, and considers why these are the dominant, and best...

Adolescence is a turbulent period to live through, and a time of importance and concern to parents, teachers, and social workers. Marking the transition from the world of childhood to adult life, the adolescent faces many challenges and opportunities, including forming their own identity, relating to often conflicting demands from parents and peers, and negotiating first romantic relationships.
In this Very Short Introduction, Peter K. Smith provides an engaging and informative overview of what we know and what we are learning about adolescence. Including both a guide to the classical...

The idea of saints and sainthood are familiar to all, irrelevant of religious faith. In this Very Short Introduction, Simon Yarrow looks at the origins, ideas, and definitions of sainthood, sanctity, and saints in the early Church, tracing their development in history and explaining the social roles saints played in the ancient, medieval, and modern worlds.

Along the way, Yarrow considers the treatment of saints as objects of literary and artistic expression and interpretation, and as examples of idealized male and female heroism, and compares Christian saints and holy figures to...

One film out of every five made anywhere on earth comes from India. From its beginnings under colonial rule through to the heights of Bollywood, Indian Cinema has challenged social injustices such as caste, the oppression of Indian women, religious intolerance, rural poverty, and the pressures of life in the burgeoning cities. And yet, the Indian movie industry makes only about five percent of Hollywood's annual revenue.
In this Very Short Introduction, Ashish Rajadhyaksha delves into the political, social, and economic factors which, over time, have shaped Indian Cinema into a...

The Sikh religion has a following of over 20 million people worldwide, and is ranked as the world's fifth largest religion. However, events such as the verbal and physical attacks on Sikhs just after September 11, where Sikhs were being mistaken for Muslims, suggest that the Sikh faith still remains mysterious to many.
This Very Short Introduction introduces newcomers to the meaning of the Sikh religious tradition, its teachings, practices, rituals and festivals. Eleanor Nesbitt highlights and contextualizes the key threads in the history of Sikhism, from the first Gurus to...

Agriculture, one of the oldest human occupations, is practised all over the world, using techniques ranging from the profoundly traditional to the most scientifically advanced. Without it we would starve. Yet how many of us understand what is happening in the fields that we see as we drive through the countryside? How often do we think about the origins of the food in our trolley?
In this Very Short Introduction Paul Brassley and Richard Soffe explain what farmers do and why they do it. Beginning with the most basic resource, the soil, they show why it is important, and how...

Crystals have fascinated us for centuries with their beauty and symmetry, and have often been invested with magical powers. The use of X-ray diffraction, first pioneered in 1912 by father and son William and Lawrence Bragg, enabled us to probe the structure of molecules, and heralded the scientific study of crystals, leading to an understanding of their atomic arrangements at a fundamental level. The new discipline, called X-ray crystallography, has subsequently evolved into a formidable science that underpins many other scientific areas. Starting from the determination of the structures of...

Savannas form one of the largest and most important of the world's ecological zones. Covering one fifth of the Earth's land surface, they are home to some of the world's most iconic animals and form an extremely important global resource for plants and wildlife. However, increasing recognition of their land potential means that they are extremely vulnerable to accelerating pressures on usable land.
This Very Short Introduction considers savannas as landscapes. Discussing their origin, topography, and global distribution, Peter A. Furley explores the dynamic nature of savannas and...