This updated printing of the first edition of Colorado Mathematical Olympiad: the First Twenty Years and Further Explorations gives the interesting history of the competition as well as an outline of all the problems and solutions that have been created for the contest over the years. Many of the essay problems were inspired by Russian mathematical folklore and written to suit the young audience; for example, the 1989 Sugar problem was written in a pleasant Lewis Carroll-like story. Some other entertaining problems involve olde Victorian map colourings, King Authur and the knights of the round table, rooks in space, Santa Claus and his elves painting planes, football for 23, and even the Colorado Springs subway system.
Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year. This book presents a year-by-year history of the CMO from 2004–2013 with all the problems from the competitions and their solutions. Additionally, the book includes 10 further explorations, bridges from solved Olympiad problems to ‘real’ mathematics, bringing young readers to the forefront of various fields of mathematics. This book contains more than just problems, solutions, and event statistics — it tells a compelling story involving the lives of those who have been part of the Olympiad, their reminiscences of the past and successes of the present. I am almost speechless facing the ingenuity and inventiveness demonstrated in the problems proposed in the third decade of these Olympics. However, equally impressive is the drive and persistence of the originator and living soul of them. It is hard for me to imagine the enthusiasm and commitment needed to work singlehandedly on such an endeavor over several decades. —Branko Grünbaum, University of Washingtonp/ppiAfter decades of hunting for Olympiad problems, and struggling to create Olympiad problems, he has become an extraordinary connoisseur and creator of Olympiad problems. The Olympiad problems were very good, from the beginning, but in the third decade the problems have become extraordinarily good. Every brace of 5 problems is a work of art. The harder individual problems range in quality from brilliant to work-of-genius... The same goes for the “Further Explorations” part of the book. Great mathematics and mathematical questions are immersed in a sauce of fascinating anecdote and reminiscence. If you could have only one book to enjoy while stranded on a desert island, this would be a good choice. /ii/i/psup/supp/ppiLike Gauss, Alexander Soifer would not hesitate to inject Eureka! at the right moment. Like van der Waerden, he can transform a dispassionate exercise in logic into a compelling account of sudden insights and ultimate triumph./ii/i/pp— Cecil Rousseau Chair, USA Mathematical Olympiad Committee/ppiA delightful feature of the book is that in the second part more related problems are discussed. Some of them are still unsolved./ii/i/pp—Paul Erdős/ppiThe book is a gold mine of brilliant reasoning with special emphasis on the power and beauty of coloring proofs. Strongly recommended to both serious and recreational mathematicians on all levels of expertise./i/p —Martin Gardner
This book explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.
This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
Bartel Leendert van der Waerden made major contributions to algebraic geometry, abstract algebra, quantum mechanics, and other fields. He liberally published on the history of mathematics. His 2-volume work Modern Algebra is one of the most influential and popular mathematical books ever written. It is therefore surprising that no monograph has been dedicated to his life and work. Van der Waerden’s record is complex. In attempting to understand his life, the author assembled thousands of documents from numerous archives in Germany, the Netherlands, Switzerland and the United States which revealed fascinating and often surprising new information about van der Waerden. Soifer traces Van der Waerden’s early years in a family of great Dutch public servants, his life as professor in Leipzig during the entire Nazi period, and his personal and professional friendship with one of the great physicists Werner Heisenberg. We encounter heroes and villains and a much more numerous group in between these two extremes. One of them is the subject of this book. Soifer’s journey through a long list of archives, combined with an intensive correspondence, had uncovered numerous details of Van der Waerden’s German intermezzo that raised serious questions and reproaches. Dirk van Dalen (Philosophy, Utrecht University) Professor Soifer’s book implicates the anthropologists’ and culture historians’ core interest in the evolution of culture and in the progress of human evolution itself on this small contested planet. James W. Fernandez (Anthropology, University of Chicago) The book is fascinating. Professor Soifer has done a great service to the discipline of history, as well as deepening our understanding of the 20th century. Peter D. Johnson, Jr. (Mathematics, Auburn University) This book is an important contribution to the history of the twentieth century, and reads like a novel with an ever-fascinating cast of characters. Harold W. Kuhn (Mathematics, Princeton University) This is a most impressive and important book. It is written in an engaging, very personal style and challenges the reader’s ability of moral and historical judgment. While it is not always written in the style of ‘objective’ professional historiography, it satisfies very high standards of scholarly documentation. Indeed the book contains a wealth of source material that allows the reader to form a highly detailed picture of the events and personalities discussed in the book. As an exemplar of historical writing in a broader sense it can compete with any other historical book. Moritz Epple (History of Mathematics, Frankfurt University)
Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.
This second edition of Alexander Soifer’s How Does One Cut a Triangle? demonstrates how different areas of mathematics can be juxtaposed in the solution of a given problem. The author employs geometry, algebra, trigonometry, linear algebra, and rings to develop a miniature model of mathematical research.
Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s problems—problems that previously seemed hopeless. Review from the first edition: The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art...Keep this book at hand as you plan your next problem solving seminar. —The American Mathematical Monthly
This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s problems—problems that previously seemed hopeless. Review from the first edition: The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art...Keep this book at hand as you plan your next problem solving seminar. —The American Mathematical Monthly
This second edition of Alexander Soifer’s How Does One Cut a Triangle? demonstrates how different areas of mathematics can be juxtaposed in the solution of a given problem. The author employs geometry, algebra, trigonometry, linear algebra, and rings to develop a miniature model of mathematical research.
Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.
This book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space Rm. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry. The author’s primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly, the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time, the author reveals profound interactions between various facts and statements from different areas of mathematics: the theory of convex sets, finite and infinite combinatorics, graph theory, measure theory, classical number theory, etc. All chapters (and also the five Appendices) end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally, the exercises vary in their difficulty. Among them there are almost trivial, standard, nontrivial, rather difficult, and difficult. As a rule, more difficult exercises are marked by asterisks and are provided with necessary hints. The material presented is based on the lecture course given by the author. The choice of material serves to demonstrate the unity of mathematics and variety of unexpected interrelations between distinct mathematical branches.
Oṃ Maṇipadme Hūṃ, perhaps the most well-known of all Buddhist mantras, lies at the heart of the Tibetan system and is cherished by both layman and lama alike. This book documents the origins of the mantra, and presents a new interpretation of the meaning of Oṃ Maṇipadme Hūṃ, and includes a detailed, annotated precis of the Kāraṇḍavyūha Sūtra, opening up this important Mahayana Buddhist work to a wider audience. The Kāraṇḍavyūha— the earliest textual source for Oṃ Maṇipadme Hūṃ—which describes both the compassionate activity of Avalokiteśvara, the bodhisattva whose power the mantra invokes, and the mythical tale of the search for and discovery of the mantra. Through a detailed analysis of this sutra, Studholme explores the historical and doctrinal forces behind the appearance of Oṃ Maṇipadme Hūṃ in India at around the middle of the first millennium C.E. He argues that the Kāraṇḍavyūha has close affinities to non-Buddhist puranic literature, and that the conception of Avalokiteśvara and his six-syllable mantra is informed by the conception of the Hindu deity Śiva and his five-syllable mantra Namaḥ Śivāya. The sutra reflects an historical situation in which the Buddhist monastic establishment was coming into contact with Buddhist tantric practitioners, themselves influenced by Saivite practitioners.
Most people understand property as something that is owned, a means of creating individual wealth. But in Commodity and Propriety, the first full-length history of the meaning of property, Gregory Alexander uncovers in American legal writing a competing vision of property that has existed alongside the traditional conception. Property, Alexander argues, has also been understood as proprietary, a mechanism for creating and maintaining a properly ordered society. This view of property has even operated in periods—such as the second half of the nineteenth century—when market forces seemed to dominate social and legal relationships. In demonstrating how the understanding of property as a private basis for the public good has competed with the better-known market-oriented conception, Alexander radically rewrites the history of property, with significant implications for current political debates and recent Supreme Court decisions.
This biography of the famous Soviet physicist Leonid Isaakovich Mandelstam (1889–1944), who became a Professor at Moscow State University in 1925 and an Academician (the highest scientific title in the USSR) in 1929, describes his contributions to both physics and technology. It also discusses the scientific community that formed around him, commonly known as the Mandelstam School. By doing so, it places Mandelstam’s life story in its cultural context: the context of German University (until 1914), the First World War, the Civil War, and the development of the Socialist Revolution (until 1925) and the young socialist country. The book considers various general issues, such as the impact of German scientific culture on Russian science; the problems and fates of Russian intellectuals during the revolutionary and post-revolutionary years; the formation of the Soviet Academy of Science, the State Academy; and the transformation of the system of higher education in the USSR during the 1920s and 1930s. Further, it reconstructs Mandelstam’s philosophy of science and his approach to the social and ethical function of science and science education based on his fundamental writings and lecture notes. This reconstruction is enhanced by extensive use of previously unpublished archive material as well as the transcripts of personal interviews conducted by the author. The book also discusses the biographies of Mandelstam’s friends and collaborators: German mathematician and philosopher Richard von Mises, Soviet Communist Party official and philosopher B.M.Hessen, Russian specialist in radio engineering N.D.Papalexy, the specialists in non-linear dynamics A.A.Andronov, S.E. Chaikin, A.A.Vitt and the plasma physicist M.A.Leontovich. This second, extended edition reconstructs the social and economic backgrounds of Mandelstam and his colleagues, describing their positions at the universities and the institutes belonging to the Academy of Science. Additionally, Mandelstam’s philosophy of science is investigated in connection with the ideological attacks that occurred after Mandelstam’s death, particularly the great mathematician A.D.Alexandrov’s criticism of Mandelstam’s operationalism.
This book presents the role of mesostructure on the properties of composite materials. A complex percolation model is developed for the material structure containing percolation clusters of phases and interior boundaries. Modeling of technological cracks and the percolation in the Sierpinski carpet are described. The interaction of mesoscopic interior boundaries of the material, including the fractal nature of interior boundaries, the oscillatory nature of it interaction and also the stochastic model of the interior boundaries’ interaction, the genesis, structure, and properties are discussed. One of part of the book introduces the percolation model of the long-range effect which is based on the notion on the multifractal clusters with transforming elements, and the theorem on the field interaction of multifractals is described. In addition small clusters, their characteristic properties and the criterion of stability are presented.
This book provides the reader with the full panoply of political economy tools and concepts necessary to understand, analyze, and integrate how political and social factors may influence the success or failure of their policy goals.
Volume I, entitled Russian Mathematics Education: History and World Significance, consists of several chapters written by distinguished authorities from Russia, the United States and other nations. It Examines the hostory of mathematics education in Russia and its relevance to mathematics education throughout the world. The second volume, entitled Russian Mathematics education is highly respected for its achievements and was once very influential internationally, it has never been explored in depth. This publication does just that. --Book Jacket.
This book presents the most recent results in the area of bulk nanostructured materials and new trends in their severe plastic deformation (SPD) processing, where these techniques are now emerging from the domain of laboratory-scale research into the commercial production of various bulk nanomaterials. Special emphasis is placed on an analysis of the effect of nanostructures in materials fabricated by SPD on mechanical properties (strength and ductility, fatigue strength and life, superplasticity) and functional behavior (shape memory effects, magnetic and electric properties), as well as the numerous examples of their innovative applications. There is a high innovation potential for industrial applications of bulk nanomaterials for structural use (materials with extreme strength) as well as for functional applications such as nanomagnets, materials for hydrogen storage, thermoelectric materials, superconductors, catalysts, and biomedical implants.
This book presents the theory and practice of product lifecycle management, chiefly focusing on modern approaches suitable for digitalized enterprises. In addition to describing adaptive methods for advanced product creation using big data analytics, it presents economic and mathematical models for managing product lifecycles based on the application of recent methods (e.g. digital design and automated intelligent systems) to control pre-production and production processes. Given its scope, the book appeals to researchers, economic analysts and entrepreneurs alike.
This monograph provides theoretical and practical perspectives on competency management as a key resource for producing competitive products. The authors develop and substantiate a law of dependence between competencies and emergence of new markets, and describe the practical aspects of developing competencies in high-tech companies. Further, they develop economic and mathematical models for managing the competitive advantages of a company based on competencies. Using these models, they present a method for evaluating and ranking core competencies, as well as for multi-criteria ratings of human potential efficiency. The book also discusses the mechanisms of competitiveness management based on a conceptual model of a competence center network.
The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.
Territorial disputes are one of the main sources of tension in Northeast Asia. Escalation in such conflicts often stems from a widely shared public perception that the territory in question is of the utmost importance to the nation. While that's frequently not true in economic, military, or political terms, citizens' groups and other domestic actors throughout the region have mounted sustained campaigns to protect or recover disputed islands. Quite often, these campaigns have wide-ranging domestic and international consequences. Why and how do territorial disputes that at one point mattered little, become salient? Focusing on non-state actors rather than political elites, Alexander Bukh explains how and why apparently inconsequential territories become central to national discourse in Japan, South Korea, and Taiwan. These Islands Are Ours challenges the conventional wisdom that disputes-related campaigns originate in the desire to protect national territory and traces their roots to times of crisis in the respective societies. This book gives us a new way to understand the nature of territorial disputes and how they inform national identities by exploring the processes of their social construction, and amplification.
In this narrative history and contextual analysis of the Thirteenth Amendment, slavery and freedom take center stage. Alexander Tsesis demonstrates how entrenched slavery was in pre-Civil War America, how central it was to the political events that resulted in the Civil War, and how it was the driving force that led to the adoption of an amendment that ultimately provided a substantive assurance of freedom for all American citizens. The story of how Supreme Court justices have interpreted the Thirteenth Amendment, first through racist lenses after Reconstruction and later influenced by the modern civil rights movement, provides insight into the tremendous impact the Thirteenth Amendment has had on the Constitution and American culture. Importantly, Tsesis also explains why the Thirteenth Amendment is essential to contemporary America, offering fresh analysis on the role the Amendment has played regarding civil rights legislation and personal liberty case decisions, and an original explanation of the substantive guarantees of freedom for today's society that the Reconstruction Congress envisioned over a century ago.
Organometallic Chemistry of Five-Membered Heterocycles is a comprehensive source of information on the synthesis, coordination modes and reactivity of coordinated five-membered monoheterocycles and the organometallic complexes of their numerous derivatives, including chelating ligands, oligomers and macrocycles. Applications in modern materials chemistry are examined, including optical materials, catalysts, fuels, and more. An ideal reference for researchers working in organometallic, heterocyclic, materials chemistry, organic chemistry and catalysis, readers will find this book a comprehensive overview on the modern synthetic methods, possible coordination situations, trends in reactivity of the coordinated heteroaromatic ligands, and methods for construction of modern materials. Includes synthesis, structural features and coordination modes of five-membered heterocycles Features a comparative analysis of reactivity of uncoordinated and coordinated ligands Offers coverage of derivatives of fundamental ligands and examines trends in materials applications
With a new focus on evidence-based practice, the 3rd edition of this authoritative reference covers every aspect of infusion therapy and can be applied to any clinical setting. Completely updated content brings you the latest advances in equipment, technology, best practices, guidelines, and patient safety. Other key topics include quality management, ethical and legal issues, patient education, and financial considerations. Ideal as a practical clinical reference, this essential guide is also a perfect review tool for the CRNI examination. Authored by the Infusion Nurses Society, this highly respected reference sets the standard for infusion nursing practice. Coverage of all 9 core areas of INS certification makes this a valuable review resource for the examination. Material progresses from basic to advanced to help new practitioners build a solid foundation of knowledge before moving on to more advanced topics. Each chapter focuses on a single topic and can serve as a stand-alone reference for busy nursing professionals. Expanded coverage of infusion therapy equipment, product selection, and evaluation help you provide safe, effective care. A separate chapter on infusion therapy across the continuum offers valuable guidance for treating patients with infusion therapy needs in outpatient, long-term, and home-care, as well as hospice and ambulatory care centers. Extensive information on specialties addresses key areas such as oncology, pain management, blood components, and parenteral nutrition. An evidence-based approach and new Focus on Evidence boxes throughout the book emphasize the importance of research in achieving the best possible patient outcomes. The user-friendly design highlights essential information in handy boxes, tables, and lists for quick access. Completely updated coverage ensures you are using the most current infusion therapy guidelines available.
Comprehensive and lavishly illustrated, McKee’s Pathology of the Skin, 5th Edition, is your reference of choice for up-to-date, authoritative information on dermatopathology. You’ll find clinical guidance from internationally renowned experts along with details on etiology, pathogenesis, histopathology, and differential diagnosis – making this unique reference unparalleled in its wealth of clinical and histopathological material. The 5th Edition of this classic text is a must-have resource for practicing dermatopathologists and general pathologists who sign out skin biopsies. Covers pathological aspects of skin diseases in addition to providing superb descriptions and illustrations of their clinical manifestations – the only available reference with this unique combination of features. Integrates dermatopathology, clinical correlations, and clinical photographs throughout, and features bulleted lists of clinical features and differential diagnosis tables for easy reference. Contains more than 5,000 superb histopathologic and clinical illustrations that demonstrate the range of histologic manifestations. Brings you fully up to date with key molecular aspects of disease, the capabilities and limitations of molecular diagnostics, and targeted/personalized medicine. Features up-to-date information on biologics, drug eruptions, and other developments in therapeutics. Helps you stay current with the latest diagnostic tumor markers and other new developments in immunohistochemistry. Includes a completely revised chapter on cutaneous lymphoma that reflects recent WHO-EORTC classification changes, as well as new coverage of sentinel lymph node biopsy for melanoma. Shares the knowledge of the main editor Dr. J. Eduardo Calonje, along with co-editors Thomas Brenn, and Alexander Lazar, and new co-editor Steven D. Billings who offers expertise on both dermatopathology and soft tissue tumors.
This biography of the famous Soviet physicist Leonid Isaakovich Mandelstam (1889-1944), who became a Professor at Moscow State University in 1925, describes his contributions to both physics and technology, as well as discussing the scientific community which formed around him, usually called the Mandelstam school. Mandelstam’s life story is thereby placed in its proper cultural context. The following more general issues are taken under consideration: the impact of German scientific culture on Russian science; the problems and fates of Russian intellectuals during the revolutionary and post-revolutionary years; the formation of the Soviet Academy of Sciences; and transformation of the system of higher education in the USSR during the 1920's and 1930's.The author shows that Mandelstam’s fundamental writings and his lectures notes allow to reconstruct his philosophy of science and his approach to the social and ethical functions of science and science education. That reconstruction is enhanced through extensive use of hitherto unpublished archival material as well as the transcripts of personal interviews conducted by the author.
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