Advanced Problems in Mathematics


Book Description

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.










Euclidean Geometry in Mathematical Olympiads


Book Description

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.




Devil-Land


Book Description

*WINNER OF THE WOLFSON HISTORY PRIZE 2022* A BOOK OF THE YEAR 2021, AS CHOSEN BY THE TIMES, NEW STATESMAN, TELEGRAPH AND TIMES LITERARY SUPPLEMENT 'A big historical advance. Ours, it turns out, is a very un-insular "Island Story". And its 17th-century chapter will never look quite the same again' John Adamson, Sunday Times A ground-breaking portrait of the most turbulent century in English history Among foreign observers, seventeenth-century England was known as 'Devil-Land': a diabolical country of fallen angels, torn apart by seditious rebellion, religious extremism and royal collapse. Clare Jackson's dazzling, original account of English history's most turbulent and radical era tells the story of a nation in a state of near continual crisis. As an unmarried heretic with no heir, Elizabeth I was regarded with horror by Catholic Europe, while her Stuart successors, James I and Charles I, were seen as impecunious and incompetent. The traumatic civil wars, regicide and a republican Commonwealth were followed by the floundering, foreign-leaning rule of Charles II and his brother, James II, before William of Orange invaded England with a Dutch army and a new order was imposed. Devil-Land reveals England as, in many ways, a 'failed state': endemically unstable and rocked by devastating events from the Gunpowder Plot to the Great Fire of London. Catastrophe nevertheless bred creativity, and Jackson makes brilliant use of eyewitness accounts - many penned by stupefied foreigners - to dramatize her great story. Starting on the eve of the Spanish Armada in 1588 and concluding with a not-so 'Glorious Revolution' a hundred years later, Devil-Land is a spectacular reinterpretation of England's vexed and enthralling past.




The World's Game


Book Description

Known as much for the emotional outbursts and violence of its fans as for its own stars, soccer (or football, as it is known outside the United States) is a global game. Its international controlling body, FIFA, boasts more members than the United Nations. Bill Murray traces the growth of what during pre-industrial times was called "the simplest game" through its codification in the nineteenth century to the 1994 World Cup, held for the first time in the United States. Murray weaves the sport's growth into the culture and politics of the countries where it has been taken up, analyzing its reputation as a game that has seen more riots and on-field brawls than all other types of football combined. He vividly illustrates how soccer has become the world's most popular sport, one that has resisted the interference of politicians, dictators, and profiteers and - more recently - the demands of television, through which it has spread to virtually every corner of the globe. The World's Game will be entertaining and enlightening to anyone from the most avid, knowledgeable fan to those who merely hope to learn a little about the sport.




The Cambridge History of Ireland: Volume 4, 1880 to the Present


Book Description

This final volume in the Cambridge History of Ireland covers the period from the 1880s to the present. Based on the most recent and innovative scholarship and research, the many contributions from experts in their field offer detailed and fresh perspectives on key areas of Irish social, economic, religious, political, demographic, institutional and cultural history. By situating the Irish story, or stories - as for much of these decades two Irelands are in play - in a variety of contexts, Irish and Anglo-Irish, but also European, Atlantic and, latterly, global. The result is an insightful interpretation on the emergence and development of Ireland during these often turbulent decades. Copiously illustrated, with special features on images of the 'Troubles' and on Irish art and sculpture in the twentieth century, this volume will undoubtedly be hailed as a landmark publication by the most recent generation of historians of Ireland.




Trinity College, Cambridge


Book Description

A history of Trinity College, Cambridge, from its foundation by Henry VIII in 1546 to the Victorian era.