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• Preliminaries: A complex dynamics primer Introduction: Dynamics of a complex history Iteration and differential equations I: The Poincare connection Iteration and differential equations II: Small divisors The core (1906-1920): Early overseas results: The United States The road to the Grand Prix des Sciences Mathematiques Works written for the Grand Prix Iteration in Italy The giants fall After-maths (1920-1942): Branching out: Fatou and Julia in the 1920s The German wave Siegel, the center problem, and KAM theory Iteratin' around the globe Tying the future to the past: Report on the Grand Prix des Sciences Mathematiques in 1918 A history of normal families Singular lines of analytic functions Kleinian groups Curves of Julia Progress in Julia's extension of Schwarz's lemma The Denjoy-Wolff theorem Dynamics of self-maps of the unit disc Koebe and uniformization Permutable maps in the 1920s The last 60 years in permutable maps Understanding Julia sets of entire maps Fatou: A biographical sketch Gaston Julia: A biographical sketch Selected biographies Remarks on computer graphics Glossary Bibliography Index Color plates.
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The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book by Alexander, Iavernaro, and Rosa paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others. A recurrent theme of the authors' treatment is the center problem in complex dynamics. They present its complete history during this period and, in so doing, bring out analogies between complex dynamics and the study of differential equations, in particular, the problem of stability in Hamiltonian systems. Among these analogies are the use of iteration and problems involving small divisors which the authors examine in the work of Poincare and others, linking them to complex dynamics, principally via the work of Samuel Lattes, in the early 1900s, and Jurgen Moser, in the 1960s. Many details will be new to the reader, such as a history of Lattes functions (functions whose Julia set equals the Riemann sphere), complex dynamics in the United States around the time of World War I, a survey of complex dynamics around the world in the 1920s and 1930s, a discussion of the dynamical programs of Fatou and Julia during the 1920s, and biographical material on several key figures. The book contains graphical renderings of many of the mathematical objects the authors discuss, including some of the intriguing fractals Fatou and Julia studied, and concludes with several appendices by current researchers in complex dynamics which collectively attest to the impact of the work of Fatou, Julia, and others upon the present-day study.
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Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions. He revolutionized celestial mechanics, discovering deterministic chaos. In physics, he is one of the fathers of special relativity, and his work in the philosophy of sciences is illuminating. For this book, about twenty world experts were asked to present one part of Poincare's extraordinary work. Each chapter treats one theme, presenting Poincare's approach, and achievements, along with examples of recent applications and some current prospects. Their contributions emphasize the power and modernity of the work of Poincare, an inexhaustible source of inspiration for researchers, as illustrated by the Fields Medal awarded in 2006 to Grigori perelman for his proof of the Poincare conjecture stated a century before. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, or physics, or more generally by anyone who likes mathematical and physical ideas. Rather than presenting detailed proofs, the main ideas are explained, and a bibliography is provided for those who wish to understand the technical details.
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Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks.

The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions under which sums of independent random variables, suitably standardized, have cumulative distribution functions close to the Gaussian distribution. As the name Central Limit Theorem suggests, it is a centerpiece of probability theory which also carries over to statistics. Part One of "The Life and Times of the Central Limit Theorem, Second Edition" traces its fascinating history from seeds sown by Jacob Bernoulli to use of integrals of exp(x2) as an approximation tool, the development of the theory of errors of observation, problems in mathematical astronomy, the emergence of the hypothesis of elementary errors, the fundamental work of Laplace, and the emergence of an abstract Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov. This closes the classical period of the life of the Central Limit Theorem, 1713-1901. The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920-1937), in particular through contributions of Lindeberg, Cramer, Levy, and Feller. The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.
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• Introduction
• Family background and precollege education
• Undergraduate education
• Graduate education
• Employment issues
• Career patterns
• Scholarly and professional contributions
• Epilogue.

More than 14 per cent of the PhD's awarded in the United States during the first four decades of the twentieth century went to women, a proportion not achieved again until the 1980s. This book is the result of a study in which the authors identified all of the American women who earned PhD's in mathematics before 1940, and collected extensive biographical and bibliographical information about each of them. By reconstructing as complete a picture as possible of this group of women, Green and LaDuke reveal insights into the larger scientific and cultural communities in which they lived and worked.The book contains an extended introductory essay, as well as biographical entries for each of the 228 women in the study. The authors examine family backgrounds, education, careers, and other professional activities. They show that there were many more women earning PhD's in mathematics before 1940 than is commonly thought. Extended biographies and bibliographical information are available from the companion website for the book. The material will be of interest to researchers, teachers, and students in mathematics, history of mathematics, history of science, women's studies, and sociology. The data presented about each of the 228 individual members of the group will support additional study and analysis by scholars in a large number of disciplines.
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• Introduction by M. Rosen Books by Emil Artin: The Gamma Function by E. Artin Galois Theory by E. Artin Theory of Algebraic Numbers by E. Artin Papers by Emil Artin: Axiomatic characterization of fields by the product formula for valuations by E. Artin and G. Whaples A note on axiomatic characterization of fields by E. Artin and G. Whaples A characterization of the field of real algebraic numbers by E. Artin The algebraic construction of real fields by E. Artin and O. Schreier A characterization of real closed fields by E. Artin and O. Schreier The theory of braids by E. Artin Theory of braids by E. Artin On the theory of complex functions by E. Artin A proof of the Krein-Milman theorem by E. Artin The influence of J. H. M. Wedderbum on the development of modern algebra by E. Artin.
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Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. He also discovered and proved the Artin reciprocity law, the culmination of over a century and a half of progress in algebraic number theory. Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching and expository writing. In this volume we gather together in one place a selection of his writings wherein the reader can learn some beautiful mathematics as seen through the eyes of a true master. The volume's Introduction provides a short biographical sketch of Emil Artin, followed by an introduction to the books and papers included in the volume. The reader will first find three of Artin's short books, titled The Gamma Function, Galois Theory, and Theory of Algebraic Numbers, respectively. These are followed by papers on algebra, algebraic number theory, real fields, braid groups, and complex and functional analysis. The three papers on real fields have been translated into English for the first time. The flavor of these works is best captured by the following quote of Richard Brauer. "There are a number of books and sets of lecture notes by Emil Artin. Each of them presents a novel approach. There are always new ideas and new results. It was a compulsion for him to present each argument in its purest form, to replace computation by conceptual arguments, to strip the theory of unnecessary ballast. What was the decisive point for him was to show the beauty of the subject to the reader." Information for our distributors: Copublished with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
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• Encounters with mathematicians by A. P. Yushkevich The Moscow school of the theory of functions in the 1930s by S. S. Demidov About mathematics at Moscow State University in the late 1940s and early 1950s by E. M. Landis Reminiscences of Soviet mathematicians by B. A. Rosenfeld A. N. Kolmogorov by V. M. Tikhomirov On A. N. Kolmogorov by V. I. Arnold Pages of a mathematical autobiography (1942-1953) by M. M. Postnikov Markov and Bishop: An essay in memory of A. A. Markov (1903-1979) and E. Bishop (1928-1983) by B. A. Kushner Etude on life and automorphic forms in the Soviet Union by I. Piatetski-Shapiro On Soviet mathematics of the 1950s and 1960s by D. B. Fuchs In the other direction by A. B. Sossinsky A brief survey of the literature on the development of mathematics in the USSR by S. S. Demidov Russian bibliography by S. S. Demidov Moscow mathematics--Then and now by V. M. Tikhomirov Errata Index of names.
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This volume contains articles on the history of Soviet mathematics, many of which are personal accounts by mathematicians who witnessed and contributed to the turbulent and glorious years of Moscow mathematics. The articles in the book focus on mathematical developments in that era, the personal lives of Russian mathematicians, and political events that shaped the course of scientific work in the Soviet Union. Important contributions include an article about Luzin and his school, based in part on documents that were released only after perestroika, and two articles on Kolmogorov. The volume concludes with annotated bibliographies in English and Russian for further reading. The revised edition is appended by an article of Tikhomirov, which provides an update and general overview of 20th-century Moscow mathematics, and it also includes an Index of Names. This book should appeal to mathematicians, historians, and anyone else interested in Soviet mathematical history. Information for our distributors: Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
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• Early youth and abitur 1928-1938 -- Weimar Republic and National Socialism in peace. From the beginning of studies to the extension of the unscheduled assistantship for another year with effect from 1 October 1938 1939-1942 -- From the beginning of the war to dismissal from the Wehrmacht and the wartime habilitation under Helmut Hasse The fight over "German logic" from 1940 to 1945: A battle between amateurs Recovery and docent position 1942 to 1944 Arrest, imprisonment, death and Nachlass Conclusion Tables of the life of Gerhard Gentzen Appendix A. Gentzen and geometry, by C. Smoryński Appendix B. Hilbert's programme, by C. Smoryński Appendix C. Three lectures, by Gerhard Gentzen Appendix D. From Hilbert's programme to Gentzen's programme, by Jan von Plato

• "The Jewish mathematician" "A new era is dawning, " 1860 "This, above all, I promise, " 1863-1870 "That damned passion, " 1874-1877 "Long live the republic, " 1878-1882 "Professor by deed, " 1880-1883 "Our professor of small intervals, " 1883-1893 "The life I live, " 1887-1895 "Demonstrations of their resentment, " 1893-1900 "God liberate us from his symbols" "It is the greatest desire of my life, " 1900 "Most important for our fatherland" "Will they create a new world?" "A political man" "A professor in America" "Empires die" Epilogue Sir Edmund Whittaker, "Vito Volterra, 1860-1940" On the attempts to apply mathematics to the biological and social sciences Science at the present moment and the new Italian society for the progress of science Acknowledgments Selected bibliography Notes Index.
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The life of Vito Volterra, one of the finest scientists and mathematicians Italy ever produced, spans the period from the unification of the Italian peninsula in 1860 to the onset of the Second World War--an era of unparalleled progress and unprecedented turmoil in the history of Europe. Born into an Italian Jewish family in the year of the liberation of Italy's Jewish ghettos, Volterra was barely in his twenties when he made his name as a mathematician and took his place as a leading light in Italy's modern scientific renaissance. By his early forties, he was a world-renowned mathematician, a sought-after figure in European intellectual and social circles, the undisputed head of Italy's mathematics and physics school--and still living with his mother, who decided the time was ripe to arrange his marriage. When Italy entered World War I in 1915, the fifty-five-year-old Volterra served with distinction and verve as a lieutenant and did not put on civilian clothes again until the Armistice of 1918. By This book, based in part on unpublished personal letters and interviews, traces the extraordinary life and times of one of Europe's foremost scientists and mathematicians, from his teenage struggles to avoid the stifling life of a "respectable" bank clerk in Florence, to his seminal mathematical work--which today influences fields as diverse as economics, physics, and ecology--and from his spirited support of Italy's scientific and democratic institutions during his years as an Italian Senator, to his steadfast defiance of the Fascists and Mussolini. In recounting the life of this outstanding scientist, European Jewish intellectual, committed Italian patriot, and devoted if frequently distracted family man, The Volterra Chronicles depicts a remarkable individual in a prodigious age and takes the reader on a vivid and splendidly detailed historical journey. Information for our distributors: Copublished with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
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• Selected Hausdorff bibliography by J. M. Plotkin Introduction to "About a certain kind of ordered sets" by J. M. Plotkin About a certain kind of ordered sets [H 1901b] by F. Hausdorff Introduction to "The concept of power in set theory" by J. M. Plotkin The concept of power in set theory [H 1904a] by F. Hausdorff Introduction to "Investigations into order types, I, II, III" by J. M. Plotkin Investigations into order types [H 1906b] by F. Hausdorff Introduction to "Investigations into order types IV, V" by J. M. Plotkin Investigations into order types [H 1907a] by F. Hausdorff Introduction to "About dense order types" by J. M. Plotkin About dense order types [H 1907b] by F. Hausdorff Introduction to "The fundamentals of a theory of ordered sets" by J. M. Plotkin The fundamentals of a theory of ordered sets [H 1908] by F. Hausdorff Introduction to "Graduation by final behavior" by J. M. Plotkin Graduation by final behavior [H 1909a] by F. Hausdorff Appendix. Sums of $\aleph_1$ sets [H 1936b] by F. Hausdorff.
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Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the International Congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem.It was time for the second generation of Cantorians to emerge. Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian. Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets.This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra. This book is suitable for graduate students and researchers interested in set theory and the history of mathematics. Also available from the AMS by Felix Hausdorff are the classic works, Grundzuge der Mengenlehre (Volume 61) and Set Theory (Volume 119), in the AMS Chelsea Publishing series.
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• Introduction Olinde Rodrigues and his times Towards a better understanding of Olinde Rodrigues and his circle: Family and faith in his life and career Euphrasie and Olinde Rodrigues: The 'woman question' within Saint-Simonism Rodrigues's early work in mathematics, 1813-1816 The 1839 paper on permutations: Its relation to the Rodrigues formula and further developments Olinde Rodrigues and combinatorics Olinde Rodrigues's paper of 1840 on a group of transformations After Rodrigues: From rotations to quaternions

• The evolution of an international mathematical research community, 1800
• -1945: An overview and an agenda by K. H. Parshall and A. C. Rice The end of dominance: The diffusion of French mathematics elsewhere, 1820-1870 by I. Grattan-Guinness Spanish initiatives to bring mathematics in Spain into the international mainstream by E. Ausejo and M. Hormigon International mathematical contributions to British scientific journals, 1800-1900 by S. E. Despeaux International participation in Liouville's \textit{Journal de mathematiques pures et appliquees} by J. Lutzen The effects of war on France's international role in mathematics, 1870-1914 by H. Gispert Charles Hermite and German mathematics in France by T. Archibald Gosta Mittag-Leffler and the foundation and administration of \textit{Acta Mathematica} by J. E. Barrow-Green An episode in the evolution of a mathematical community: The case of Cesare Arzela at Bologna by L. Martini The first international mathematical community: The \textit{Circolo matematico di Palermo} by A. Brigaglia Languages for mathematics and the language of mathematics in a world of nations by J. J. Gray The emergence of the Japanese mathematical community in the modern western style, 1855-1945 by C. Sasaki Internationalizing mathematics east and west: Individuals and institutions in the emergence of a modern mathematical community in China by J. W. Dauben Chinese-U. S. mathematical relations, 1859-1949 by Y. Xu American initiatives toward internationalization: The case of Leonard Dickson by D. D. Fenster The effects of Nazi rule on the international participation of German mathematicians: An overview and two case studies by R. Siegmund-Schultze War, refugees, and the creation of an international mathematical community by S. L. Segal The formation of the international mathematical union by O. Lehto Index.
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Although today's mathematical research community takes its international character very much for granted, this 'global nature' is relatively recent, having evolved over a period of roughly 150 years - from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries.Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues. The resulting volume is essential reading for anyone interested in the history of modern mathematics. It will be of interest to mathematicians, historians of mathematics, and historians of science in general.
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• Overview Full reducibility and invariants for $\mathbf{SL}_2(\mathbb C)$ Hermann Weyl and Lie groups Elie Cartan, symmetric spaces and Lie groups Linear algebraic groups in the 19th century Linear algebraic groups in the 20th century The work of Chevalley in Lie groups and algebraic groups Algebraic groups and Galois theory in the work of Ellis R. Kolchin Name index Subject index Photo section.
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Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passage from local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large. The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groups and algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields. The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.
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• Commentary (by R. A. R.) by R. A. Rankin The life of Ramanujan: The four photographs of Ramanujan The books studied by Ramanujan in India The influence of Carr's synopsis on Ramanujan The notebooks of Srinivasa Ramanujan A recently discovered letter giving Ramanujan's examination scores On Ramanujan The Ramanujan family record Ramanujan's illness: Ramanujan as a patient Ramanujan's illness An incident in the life of S. Ramanujan, F.R.S.: Conversations with G. H. Hardy, F.R.S. and J. E. Littlewood, F.R.S. and their sequel S. Janaki: S. Janaki Ammal (Mrs. Ramanujan) Conversation "I didn't understand his work, but I knew his worth" S. Narayana Iyer: A short biography of S. Narayana Iyer The distribution of primes Some theorems in summation E. H. Neville: Srinivasa Ramanujan University lectures in Madras Ramanujan's manuscripts and notebooks: Ramanujan's manuscripts and notebooks Ramanujan's manuscripts and notebooks, II An overview of Ramanujan's notebooks An introduction to Ramanujan's "lost" notebook Nontechnical articles on Ramanujan's work: Ramanujan and pi $\pi$ related developments since 1988 Reflections around the Ramanujan centenary The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society Somewhat more technical articles on Ramanujan's work: A walk through Ramanujan's garden Ramanujan and hypergeometric and basic hypergeometric series The final problem: An account of the mock theta functions.
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This book contains essays on Ramanujan and his work that were written especially for this volume. It also includes important survey articles in areas influenced by Ramanujan's mathematics. Most of the articles in the book are nontechnical, but even those that are more technical contain substantial sections that will engage the general reader. The book opens with the only four existing photographs of Ramanujan, presenting historical accounts of them and information about other people in the photos. This section includes an account of a cryptic family history written by his younger brother, S. Lakshmi Narasimhan. Following are articles on Ramanujan's illness by R. A. Rankin, the British physician D. A. B. Young, and Nobel laureate S. Chandrasekhar. They present a study of his symptoms, a convincing diagnosis of the cause of his death, and a thorough exposition of Ramanujan's life as a patient in English sanitariums and nursing homes.Following this are biographies of S. Janaki (Mrs. Ramanujan) and S. Narayana Iyer, Chief Accountant of the Madras Port Trust Office, who first communicated Ramanujan's work to the "Journal of the Indian Mathematical Society". The last half of the book begins with a section on 'Ramanujan's Manuscripts and Notebooks'. Included is an important article by G. E. Andrews on Ramanujan's lost notebook. The final two sections feature both nontechnical articles, such as Jonathan and Peter Borwein's 'Ramanujan and pi', and more technical articles by Freeman Dyson, Atle Selberg, Richard Askey, and G. N. Watson. This volume complements the book "Ramanujan: Letters and Commentary, Volume 9", in the AMS series, "History of Mathematics". For more on Ramanujan, see these AMS publications, "Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Volume 136", "H, and Collected Papers of Srinivasa Ramanujan, Volume 159", "H", in the AMS Chelsea Publishing series.
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The editorial board for the History of Mathematics series has selected for this volume a series of translations from two Russian publications, Kolmogorov in Remembrance and Mathematics and its Historical Development. This book, Kolmogorov in Perspective, includes articles written by Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. Specifically, the article, "Andrei? Nikolaevich Kolmogorov. A Biographical Sketch of His Life and Creative Paths" by A. N. Shiryaev, gives an excellent personal and scientific biography of Kolmogorov. The volume also includes the following articles: "On A. N. Kolmogorov" by V. I. Arnol'd, "In Memory of A. N. Kolmogorov" by S. M. Nikol'skii?, "Remembrances of A. N. Kolmogorov" by Ya. G. Sinai?, "The Influence of Andrei? Nikolaevich Kolmogorov on My Life" by P. L. Ul'yanov, "A Few Words on A. N. Kolmogorov" by P. S. Aleksandrov, "Memories of P. S. Aleksandrov" by A. N. Kolmogorov, "Newton and Contemporary Mathematical Thought" by A. N. Kolmogorov, and an extensive bibliography with the complete list of Kolmogorov's works-including the articles written for encyclopedias and newspapers. The book is illustrated with photographs and includes quotations from Kolmogorov's letters and conversations, uniquely reflecting his mathematical tastes and opinions. Co-published with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price.
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• Introduction Catalog of the West Point collection Catalog of 1803 Inventory of books, maps and charts, belonging to the Military Academy at West Point Photographs Portraits in the collection Frontispieces in the collection.
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This book reveals the rich collection of mathematical works located at the nation's first military school, the U.S. Military Academy at West Point. It outlines the relevant history of the Academy, discusses the mathematics department and curriculum, and describes the development of the library during the nineteenth century. A major part of this book is an annotated catalog of the more than 1300 works published between 1496 and 1915 found in the West Point library. Mathematics and its instruction greatly influenced the development of the Academy, the technological growth of America's army, and the standards of the military profession. These events, in turn, were crucial to the overall development of mathematics, mechanics, and engineering during the nineteenth century in the United States.Three individuals played a prominent role in this chronicle: Sylvanus Thayer, Charles Davies, and Albert Church. Listed are rare and historically valuable works in a broad range of mathematical subjects. The collection clearly shows the strong European influence on the early Academy. Also listed are numerous textbooks by West Point faculty and graduates; significant contributions were made by these writers to algebra, geometry, calculus, descriptive geometry, mechanics, surveying, and mathematics education. This book provides an important resource for the general audience as well as for those in pursuit of more scholarly information. It contains many interesting photographs and valuable details about the West Point collection. It is a must-have for anyone interested in mathematical books and collections.
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• On the divisibility of numbers On the congruence of numbers On quadratic residues On quadratic forms Determination of the class number of binary quadratic forms Some theorems from Gauss's theory of circle division On the limiting value of an infinite series A geometric theorem Genera of quadratic forms Power residues for composite moduli Primes in arithmetic progressions Some theorems from the theory of circle division On the Pell equation Convergence and continuity of some infinite series Index.
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This volume is a translation of Dirichlet's "Vorlesungen uber Zahlentheorie" which includes nine supplements by Dedekind and an introduction by John Stillwell, who translated the volume. "Lectures on Number Theory" is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions. The book is suitable as a textbook, yet it also offers a fascinating historical perspective that links Gauss with modern number theory. The legendary story is told how Dirichlet kept a copy of Gauss' "Disquisitiones Arithmeticae" with him at all times and how Dirichlet strove to clarify and simplify Gauss' results.Dedekind's footnotes document what material Dirichlet took from Gauss, allowing insight into how Dirichlet transformed the ideas into essentially modern form. Also shown is how Gauss built on a long tradition in number theory - going back to Diophantus - and how it set the agenda for Dirichlet's work. This important book combines historical perspective with transcendent mathematical insight. The material is still fresh and presented in a very readable fashion. This volume is one of an informal sequence of works within the "History of Mathematics" series. Volumes in this subset, 'Sources', are classical mathematical works that served as cornerstones for modern mathematical thought. (For another historical translation by Professor Stillwell, see "Sources of Hyperbolic Geometry, Volume 10" in the "History of Mathematics" series.).
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• Historical introduction A brief history of automorphic function theory, 1880-1930 The group of motions of the hyperbolic plane and its properly discontinuous subgroups Discontinuous groups in three geometries. Fuchsian functions Fuchsian functions Kleinian groups and functions Algebraic functions and linear algebraic differential equations Fuchsian groups and geodesics References Additional references.
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This is the English translation of a volume originally published only in Russian and now out of print. The book was written by Jacques Hadamard on the work of Poincare. Poincare's creation of a theory of automorphic functions in the early 1880s was one of the most significant mathematical achievements of the nineteenth century. It directly inspired the uniformization theorem, led to a class of functions adequate to solve all linear ordinary differential equations, and focused attention on a large new class of discrete groups. It was the first significant application of non-Euclidean geometry. The implications of these discoveries continue to be important to this day in numerous different areas of mathematics. Hadamard begins with hyperbolic geometry, which he compares with plane and spherical geometry. He discusses the corresponding isometry groups, introduces the idea of discrete subgroups, and shows that the corresponding quotient spaces are manifolds.In Chapter 2 he presents the appropriate automorphic functions, in particular, Fuchsian functions. He shows how to represent Fuchsian functions as quotients, and how Fuchsian functions invariant under the same group are related, and indicates how these functions can be used to solve differential equations. Chapter 4 is devoted to the outlines of the more complicated Kleinian case. Chapter 5 discusses algebraic functions and linear algebraic differential equations, and the last chapter sketches the theory of Fuchsian groups and geodesics. This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts. This volume is one of an informal sequence of works within the "History of Mathematics" series. Volumes in this subset, "Sources", are classical mathematical works that served as cornerstones for modern mathematical thought.
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• Some 19th-century algebra and number theory. Frobenius and the invention of character theory. Burnside: Representations and structure of finite groups. Schur: A new beginning. Polynomial representations of GL_n(\Bbb{C}). Richard Brauer and Emmy Noether: 1926
• -1933. Modular representation theory. Bibliography. Index.
• (source: Nielsen Book Data)

The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849-1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852-1927). Burnside soon developed his own approach to representations of finite groups. In the next few years, working independently, Frobenius and Burnside explored the new subject and its applications to finite group theory. They were soon joined in this enterprise by Issai Schur (1875-1941) and some years later, by Richard Brauer (1901-1977). These mathematicians' pioneering research is the subject of this book. It presents an account of the early history of representation theory through an analysis of the published work of the principals and others with whom the principals' work was interwoven. Also included are biographical sketches and enough mathematics to enable readers to follow the development of the subject. An introductory chapter contains some of the results involving characters of finite abelian groups by Lagrange, Gauss, and Dirichlet, which were part of the mathematical tradition from which Frobenius drew his inspiration. This book presents the early history of an active branch of mathematics. It includes enough detail to enable readers to learn the mathematics along with the history. The volume would be a suitable text for a course on representations of finite groups, particularly one emphasizing an historical point of view.
(source: Nielsen Book Data)