A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability. Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him. Math has a bad reputation: dull, difficult, detached from daily life. As a talking Barbie doll opined, “Math class is tough.” But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function (“The year: 1972. The scene: Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey”), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

The world is filled with difficult people; it is impossible to avoid them. You've tried confrontation, passivity-- now discover what works. Gain the tools you need to get along with others and conduct your relationships in a manner that honors God-- and preserves your sanity!

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

This “uncommonly astute study” examines the early development of the US-UK military alliance that would eventually lead to victory in WWII (Paul Miles, author of FDR’s Admiral). On December 12, 1937, Japanese aircraft sank the American gunboat Panay outside Nanjing, China. Although the Japanese apologized, President Roosevelt set Captain Royal Ingersoll to London to begin conversations with the British admiralty about Japanese aggression in the Far East. While few Americans remember the Panay Incident, it was the start of what would become the “Special Relationship” between the United States and Great Britain. In The Origins of the Grand Alliance, William T. Johnsen provides the first comprehensive analysis of Anglo-American military collaboration before the Second World War. He sets the stage by examining Anglo-French and Anglo-American coalition military planning from 1900 through World War I and the interwar years. Johnsen also considers the formulation of policy and grand strategy, operational planning, and the creation of the command structure and channels of communication. He addresses vitally important logistical and materiel issues, particularly the difficulties of war production. Drawn from extensive sources and private papers held in the United Kingdom, Canada, and the United States, Johnsen’s exhaustively researched study casts new light on the twentieth century’s most significant alliance.

In 1939 Hitler went to war not just with Great Britain; he also went to war with the whole of the British Empire, the greatest empire that there had ever been. In the years since 1945 that empire has disappeared, and the crucial fact that the British Empire fought together as a whole during the war has been forgotten. All the parts of the empire joined the struggle and were involved in it from the beginning, undergoing huge changes and sometimes suffering great losses as a result. The war in the desert, the defence of Malta and the Malayan campaign, and the contribution of the empire as a whole in terms of supplies, communications and troops, all reflect the strategic importance of Britain's imperial status. Men and women not only from Australia, New Zealand and India but from many parts of Africa and the Middle East all played their part. Winston Churchill saw the war throughout in imperial terms. The British Empire and the Second World War emphasises a central fact about the Second World War that is often forgotten.

Following on from her acclaimed study of the collapse of international security during the early 1930's, Zara Steiner gives an account of the coming catastrophe. She shows that the era of Hitler's rise to power, an ascent bent on war, was founded on ideologies which the democratic perceptions could neither penetrate nor arrest. --

When Singapore fell to the Japanese in February 1942, Churchill called it the “largest capitulation in British history.” Till today, the myth persists that this was due to the British forces’ being caught off-guard, with their guns facing the wrong direction—towards the sea. This book offers an alternative insight into why Malaya and Singapore were captured by the Japanese. The question of the landward defence of Singapore and Malaya was first raised as early as 1918, eventually taking the form of Operation Matador, the elaborate planning and preparations for which amply demonstrate that the British fully expected the Japanese to attack Singapore from the rear, and had formulated a plan to stop the Japanese at the Kra Isthmus. Yet, when the Japanese forces landed, they found Malaya and Singapore defended by an emasculated fleet, obsolescent aircraft, inadequate artillery and no tanks. The battle for Malaya and Singapore was lost even before the first shot was fired—in the corridors of power at Whitehall. Churchill’s half-hearted support for Operation Matador meant that Malaya was starved of the necessary reinforcements, and the commanders on the spot were expected to “make bricks without straw.” The question that remains: If implemented, might Operation Matador have stopped the Japanese?