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Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years hasbeen studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them.
But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation's defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed otherspectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved forNumber theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years hasbeen
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
About the Series: Oxford's Very Short Introductions offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, and Literary Theory to History. Not simply a textbook of definitions, each volume provides trenchant and provocative--yet always
In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. Robin Wilson's book has been widely used as a text for undergraduate courses in mathematics,
This Very Short Introduction might prove disappointing to those expecting an introduction to a very short man. Dispelling the myth of Napoleon Bonaparte's short stature, as well as the other rumors and legends, David A. Bell provides a concise, accurate, and lively portrait of Napoleon Bonaparte's
Utilitarianism may well be the most influential secular ethical theory in the world today. It is also one of the most controversial. It clashes, or is widely thought to clash, with many conventional moral views, and with human rights when they are seen as inviolable. Would it, for example, be right
This is an elementary undergraduate level introduction to number theory, with carefully explained proofs and numerous exercises and worked examples. A feature of particular interest is a concise account of Fermat's Last Theorem and its recent proof by Andrew
In this Very Short Introduction, Kenneth Morgan provides a wide-ranging thematic introduction to modern Australia, examining the main features of its history, geography and culture since the beginning of European settlement in New South Wales in 1788. It highlights the distinctive features of
A comprehensive and authoritative short guide, this Very Short Introduction to Medieval Britain covers the establishment of the Anglo-Norman monarchy in the early Middle Ages, through to England's failure to dominate the British Isles and France in the later Middle Ages. Out of the turbulence came
Banks are of central importance for economic growth, the allocation of capital, competitiveness, and financial stability. Propelled by technological advances in financial analysis and financial deregulation, the banking industry's investment played a key role in enhancing national economic growth
Epicureanism is commonly associated with a carefree view of life and the pursuit of pleasures, particularly the pleasures of the table. However it was a complex and distinctive system of philosophy that emphasized simplicity and moderation, and considered nature to consist of atoms and the void
Critical theory emerged in the 1920s from the work of the Frankfurt School, the circle of German-Jewish academics who sought to diagnose -- and, if at all possible, cure -- the ills of society, particularly fascism and capitalism. In this book, Stephen Eric Bronner provides sketches of
The Brain: A Very Short Introduction provides a non-technical introduction to the main issues and findings in current brain research and gives a sense of how neuroscience addresses questions about the relationship between the brain and the mind. Short, clear discussions on the mechanical workings
Games are everywhere: Drivers maneuvering in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. The supermarket's price for corn flakes is decided by playing an economic game. This Very Short Introduction offers a succinct tour of the
An isotope is a variant form of a chemical element, containing a different number of neutrons in its nucleus. Most elements exist as several isotopes. Many are stable while others are radioactive, and some may only exist fleetingly before decaying into other elements. In this Very Short
Since its inception, psychoanalysis has been hailed as a revolutionary theory of how the mind works, whilst some of its ideas such as the Oedipus complex have become part of everyday conversation. In Psychoanalysis: A Very Short Introduction, Daniel Pick offers a lucid, lively, and wide-ranging
In A Very Short Introduction to Politics, Kenneth Minogue begins with a discussion of issues arising from a historical account of politics, and goes on to offer chapters dealing with the Ancient Greeks and the idea of citizenship; Roman law; medieval Christianity and individualism; freedom since
This Very Short Introduction introduces readers to the key concepts of political philosophy: authority, democracy, freedom and its limits, justice, feminism, multiculturalism, and nationality. Accessibly written and assuming no previous knowledge of the subject, it encourages the reader to think