Funded by a National Science Foundation grant, "Discovering Higher Mathematics" emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses.

* Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization
* Guidelines for effective mathematical thinking, covering a variety of interrelated topics
* Numerous problems and exercises designed to reinforce the key themes

A collection of prisoner of war and concentration camp survivor stories from some of the toughest World War II camps in Europe and the Pacific, this book details the daring escapes and highlights the fundamental aspects of human nature that made such heroic efforts possible. Levine takes a comprehensive approach, including evasion efforts by those fleeing before the enemy who never reached formal prisoner of war camps, as well as escapes from ghettoes and labor camps.

Levine pays particular attention to dramatic escapes by small boat. Many are not widely known, although some were made over vast distances or in fantastically difficult conditions from enemy-occupied areas. Accounts include attempts at freedom from both German and Japanese prisoner of war camps, stories that reveal much about the conditions prisoners endured. Some of these escapes are far more amazing than the famed Great Escape from Stalag Luft III. German and Austrian prisoners also recount their amazing flights from India to Tibet and Burma. This study challenges some ideas about behavior in extreme situations and casts interesting light on human nature.

Here is a history of the development of military missiles and space travel from World War II to the American visits to the Moon in 1969-1972. It stresses the relationship between the early stages of space exploration and the arms race, and that a dual path led to space flight. One was the development of unmanned long-range war rockets, the other, less often noted, was the rocket-powered research plane. The first path led through the intercontinental ballistic missile to the first artificial satellites and space capsule; the latter, more uniquely American, through the X-series and Skyrocket rocket planes to the X-15, and ultimately to the Space Shuttle. The early part of the book focuses on the Soviet-American race to develop the ICBM in the 1950s, and the first satellites, with particular attention paid to the events and reactions that followed the flight of Sputnik I in 1957 and the subsequent missile gap era.

In this volume, Alan Levine traces the development of the Soviet Union and the Communist movement from 1917 to the Nazi invasion of the USSR in June 1941. Arguing that the Cold War between the Soviet Union and the Western democracies can only be fully understood by examining the doctrine and practices of the Soviet Union and the world Communist movement from their inception, Levine offers a detailed account of the development of the state parties in Russia and China, the Communist seizure of power, the Soviet Union's role in international relations between the two world wars, and the development of the techniques of conflict management used by the Communist powers later in the era of the Cold War. By treating together a number of topics and elements that are closely related but usually treated separately, Levine offers important new insights into the origins of the Cold War, showing that the devices used successfully by the Soviet state during these years--building satellite states, the use of proxy forces to influence the outcomes of revolutions, the use of Soviet military aid, and the inconspicuous employment of Soviet advisors--were already seen in the 1920s and 1930s.

Levine stresses throughout the continuity exhibited by Soviet policies between the world wars and those used during the Cold War after World War II. He examines in depth such topics as Soviet foreign policy and territorial expansion, the development of Communist movements and doctrines, the successes and failure of the Communists' enemies, the history of the Russian and Chinese revolutions, and the history of Communist attempts to seize power. Based on his analysis, Levine concludes that rather than beginning in 1945, following the end of World War II, the Cold War actually had its origins in the development of a totalitarian Communist regime in the former Russian Empire under the shattering impact of World War I. Levine argues further that there has also been a strong element of continuity in the characteristic features of Western responses to the Soviets. Students of twentieth-century international politics will find Levine's work illuminating reading.

This bold and controversial book takes a hard look at an old subject-race relations in the Western world. Using history as a backdrop, the author illustrates how racism and ethnic chauvinism are, sadly, common. The author warns against the harm of colorthink-an excessive obsession with race and racism-and explores the impact of such thinking on race relations today. He gives no comfort to either racists or more fashionable contemporaries obsessed with the supposedly unique evils of the Western past. Racial issues, and misconceptions about race and race relations, are among the most divisive and confusing features of contemporary society. Race Relations Within Western Expansion is designed to provide an overall account of the development of the issues involved, relating them to global history and putting them squarely within the framework of the expansion of the Western world, an expansion that began much earlier than is generally realized, far back in the Middle Ages. Levine analyzes the reasons for that expansion and how it took different forms and brought many different peoples into several different sorts of contact with the West, and how these contacts, and conceptions about other peoples, changed, or remained fixed over time. He also shows the impact within Europe of pseudo-scientific racial ideologies, and criticizes contemporary misconceptions about the history of relations between European settlers and native peoples, slavery, and the age of imperial rule in Asia and Africa. It stresses the complexity and variety of those relationships rather than attempting, as is currently fashionable, to pigeonhole more and more data into fewer and fewer ideological categories. This is a necessarily controversial book, one that collides with many cherished beliefs, both traditional and contemporary, and exposes how bizarre they really are. It acidly exposes both traditional racist myths, and more recently fashionable postures that often prove little more factually based.

This book puts American policy in Southeast Asia and the traumatic events of the second Indochina War into the larger perspective of the Cold War. Levine's wide-ranging work treats everything from the local appeals of Communist parties in the region and the peculiarities of Vietnamese Communism to the development of the domino theory and its consequences, from helicopter warfare to the antiwar movement. Treating harshly some of the orthodoxies that have developed about Vietnam and scathing in its treatment of the Kennedy, Johnson, and Nixon administrations, it will interest scholars, students, and veterans of the conflict.

A brief, yet complete history of the Allied campaign for the liberation of Europe from the Normandy invasion to the surrender of Germany, this study describes not only what happened, but "why" it happened. While an enormous amount has been written about this campaign, most of it focuses upon a single army or an individual battle. This book stresses a true inter-Allied and all arms approach with a balance of both strategy and tactics; accounts of effort by land, sea, air forces; as well as the strong influence of logistics. Levine deals extensively with the German side, particularly morale issues, and he includes the role played by Canadian forces--a topic usually neglected in American accounts.

Rapid changes in warfare rendered the character of the battles of 1944-1945 quite different from battles earlier in the war, and Levine finds that old-fashioned fortifications often had an unexpected and formidable impact on the fighting. Logistics played a central role in the struggle, and supply problems would continuously plague the U.S. Army during this campaign. Levine considers whether the war could have been won in 1944, and he discusses the lost opportunities on both sides. Casting new light on some familiar subjects and recounting many neglected issues, this book places the campaign within the larger context of European events in both the east and the Mediterranean.

An exciting account of a little-known, yet vital part of World War II, the Allied effort to blockade Axis forces in North Africa with a relatively small number of planes and submarines included some of the war's most spectacular air battles, and opened the way to the attack on Fortress Europe from the south. This is the first book-length treatment of the crucial struggle to cut Axis supply lines in the Tunisian campaign of 1942-1943, a battle often ignored or played down even by official historians. The campaign marked the first big U.S. victory against the Axis powers and served as a proving ground for several top Allied commanders. This study fills an important gap in the history of the war, reevaluating the development of Allied airpower and the role of Italy in the campaign.

Allied success in interdiction was a critical factor in the greatest Allied victory in the Mediterranean campaign, a victory which left the enemy so weakened that it could not stop the subsequent invasion of Europe from the south. Despite initial disorganization and early disappointments, the British waged one of only two successful submarine campaigns ever fought. This study describes some of the war's most amazing air battles, notably Operation Flax against the enemy's air transport fleet, and attacks on convoys, all interwoven with the events of the ground war in the desert and comparisons with the Pacific effort. It details the struggle to reorganize and improve the Allied effort, the belated success of sea sweeps against enemy ships, and the final victory in the spring of 1943, in which an air blockade was clamped on the sea and sky approaches to Tunisia.

This book is the only full-scale account of the strategic air offensive against Germany published in the last twenty years, and is the only one that treats the British and the Americans with parity. Much of what Levine writes about British operations will be unfamiliar to American readers. He has stressed the importance of winning air superiority and the role of escort fighters in strategic bombing, and has given more attention to the German side than most writers on air warfare have. Levine gets past a simple account of what we did to them and describes the target systems and German countermeasures in detail, providing exact yet dramatic accounts of the great bomber operations--the Ruhr dams, Ploesti, and Regensburg and Schweinfurt. The book is broad-guaged, touching many matters, from the development of bombing doctrine before the war to the technical development of the Luftwaffe and the RAF, jets and V-weapons, to the role of the heavy bombers in supporting land and sea operations.

Levine stresses the impact of bombing on the war, and generally endorses the strategic air campaign as worthwhile and effective. But he concludes that many mistakes were made by the Allies--both the British and the Americans--in tactics, the development of equipment, and in the selection of targets. Levine sees strategic bombing as a powerful tool that was often misused, particularly when the doctrine of area bombing flourished. Scholars, students, and buffs interested in World War II and/or the history of aviation will find this study of great interest.

Nineteen ninety-five is a year of celebration and remembrance of the Axis collapse that signaled the end of the Second World War. In August, the world will mark the 50th anniversary of V-J Day. Particularly important, then, is this new historical study o the Pacific phase of World War War II that coers not just the military, but also the political side of the war. Rejecting recent trends that tend to whitewash or demonize the Japanese, this book casts new light on many controversial issues from Pearl Harbor to Hiroshima. It treats the submarine campaign, the air attacks on Japan, the use of the atomic bombs, and Japan's surrender in unusual detail. Finally, it emphasizes that the war was primarily a struggle for the air and sea.

The recent economic crisis in the United States has highlighted a crisis of understanding. In this volume, Bradley C. S. Watson and Joseph Postell bring together some of America's most eminent thinkers on political economy an increasingly overlooked field wherein political ideas and economic theories mutually inform each other. Only through a restoration of political economy can we reconnect economics to the human good. Economics as a discipline deals with the production and distribution of goods and services. Yet the study of economics can-indeed must be employed in our striving for the best possible political order and way of life. Economic thinkers and political actors need once again to consider how the Constitution and basic principles of our government might give direction and discipline to our thinking about economic theories, and to the economic policies we choose to implement. The contributors are experts in economic history, and the history of economic ideas. They address basic themes of political economy, theoretical and practical: from the relationship between natural law and economics, to how our Founding Fathers approached economics, to questions of banking and monetary policy. Their insights will serve as trusty guides to future generations, as well as to our own."

Two generations of students inspired by Harvey Mansfield come together here to demonstrate how their diverse approaches illuminate the topic of the arts of rule and speak to the wide scope of Mansfield's contributions. The essays collected here cover both ancient and modern ground. The first section covers topics such as Xenophon's question of what it is to be a gentleman, Aristotle's view of friendship, Montaigne's account of the highest good, and Montesquieu's elevation of modesty. The second section engages Machiavelli's political theory and its influence on subsequent thinkers, such as Bacon, Hobbes, and Hume. Authors in the third section examine the sources, conditions, and practices of freedom in the context of modern politics, drawing on writers from Shakespeare to Tocqueville to shed light on contemporary debates. The arts of rule cover the exercise of power by princes and popular sovereigns, but they range beyond the domain of government itself, extending to civil associations, political parties, and religious institutions. Artful rule both directs the use of authority toward a specific end and posits a more comprehensive vision of the best way of life for human beings. Making full use of political philosophy and benefiting from a range of backgrounds, this collection recognizes that although the arts of rule are comprehensive, the best government is a limited one.

Two generations of students inspired by Harvey Mansfield come together here to demonstrate how their diverse approaches illuminate the topic of the arts of rule and speak to the wide scope of Mansfield's contributions. The essays collected here cover both ancient and modern ground. The first section covers topics such as Xenophon's question of what it is to be a gentleman, Aristotle's view of friendship, Montaigne's account of the highest good, and Montesquieu's elevation of modesty. The second section engages Machiavelli's political theory and its influence on subsequent thinkers, such as Bacon, Hobbes, and Hume. Authors in the third section examine the sources, conditions, and practices of freedom in the context of modern politics, drawing on writers from Shakespeare to Tocqueville to shed light on contemporary debates. The arts of rule cover the exercise of power by princes and popular sovereigns, but they range beyond the domain of government itself, extending to civil associations, political parties, and religious institutions. Artful rule both directs the use of authority toward a specific end and posits a more comprehensive vision of the best way of life for human beings. Making full use of political philosophy and benefiting from a range of backgrounds, this collection recognizes that although the arts of rule are comprehensive, the best government is a limited one.

Almost since their publication, the writings of Michel de Montaigne (1533-1592) have provided rich fodder for the work of scholars in myriad disciplines. Philosophers have considered Montaigne's views on skepticism; historians have examined his views on the Indians; deconstructionists and literary scholars have examined Montaigne's view of the self; and, political scientists have touched on his arguments for toleration. However, because each of these projects has been done largely in isolation, most scholars have failed to see the relationships between the various aspects of Montaigne's thought. Alan Levine, in Sensual Philosophy, unites Montaigne's thought for the first time, ably and convincingly demonstrating the significant role Montaigne played in establishing the liberal ethos in the West. In exploring Montaigne's grounding for liberalism, Levine considers Montaigne's conceptualization of skepticism and its relationship to toleration. He argues that Montaigne's theories of self ground his idea of toleration without leaving it open to the corrosive charges of relativism and nihilism. Levine also articulates the importance of Montaigne's thought for contemporary conceptions of personal freedom, individuality, subjectivity, and self-creation by bringing him into dialogue with modern and postmodern political theorists such as Heidegger, Nietzsche, and Richard Rorty. This lively book persuades those who might be tempted by postmodernism that they should turn to Montaigne instead.

Almost since their publication, the writings of Michel de Montaigne (1533-1592) have provided rich fodder for the work of scholars in myriad disciplines. Philosophers have considered Montaigne's views on skepticism; historians have examined his views on the Indians; deconstructionists and literary scholars have examined Montaigne's view of the self; and, political scientists have touched on his arguments for toleration. However, because each of these projects has been done largely in isolation, most scholars have failed to see the relationships between the various aspects of Montaigne's thought. Alan Levine, in Sensual Philosophy, unites Montaigne's thought for the first time, ably and convincingly demonstrating the significant role Montaigne played in establishing the liberal ethos in the West. In exploring Montaigne's grounding for liberalism, Levine considers Montaigne's conceptualization of skepticism and its relationship to toleration. He argues that Montaigne's theories of self ground his idea of toleration without leaving it open to the corrosive charges of relativism and nihilism. Levine also articulates the importance of Montaigne's thought for contemporary conceptions of personal freedom, individuality, subjectivity, and self-creation by bringing him into dialogue with modern and postmodern political theorists such as Heidegger, Nietzsche, and Richard Rorty. This lively book persuades those who might be tempted by postmodernism that they should turn to Montaigne instead.

This collection of original essays by the nation's leading political theorists examines the origins of modernity and considers the question of tolerance as a product of early modern religious skepticism. Rather than approaching the problem through a purely historical lens, the authors actively demonstrate the significance of these issues to contemporary debates in political philosophy and public policy. The contributors to Early Modern Skepticism raise and address questions of the utmost significance: Is religious faith necessary for ethical behavior? Is skepticism a fruitful ground from which to argue for toleration? This book will be of interest to historians, philosophers, religious scholars, and political theorists--anyone concerned about the tensions between private beliefs and public behavior.

Why does the Civil War still speak to us so powerfully? If we listen to the most thoughtful, forceful, and passionate voices of that day we find that many of the questions at the heart of that conflict are also central to the very idea of America-and that many of them remain unresolved in our own time. The Political Thought of the Civil War offers us the opportunity to pursue these questions from a new, critical perspective as leading scholars of American political science, history, and literature engage in some of the crucial debates of the Civil War era-and in the process illuminate more clearly the foundation and fault lines of the American regime. The essays in this volume use practical dilemmas of the Civil War to reveal and probe fundamental questions about the status of slavery and race in the American founding, the tension between moralism and constitutionalism, and the problem of creating and sustaining a multiracial society on the basis of the original principles of the American regime. Adopting a deliberative approach, the authors revisit the words and deeds of the most important political actors of era, from William Lloyd Garrison, John C. Calhoun, and Abraham Lincoln to Alexander Stephens and Frederick Douglass, with reference to the American Founders and the architects of Reconstruction. The essays in this volume consider the difficult choices each of these figures made, the specific problems they were responding to, and the consequences of those choices. As this book exposes and explores the theoretical principles at play within their historical context, it also offers vivid reminders of how the great controversies surrounding the Civil War continue to shape American political life to this day.