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Indiscrete Thoughts

Author: Gian-Carlo Rota
Publisher: Springer Science & Business Media
ISBN: 9780817647810
Size: 25.82 MB
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Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.

The Star And The Whole

Author: Fabrizio Palombi
Publisher: CRC Press
ISBN: 1439873526
Size: 72.81 MB
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The Star and the Whole: Gian-Carlo Rota on Mathematics and Phenomenology, authored by Fabrizio Palombi, is the first book to study Rota’s philosophical reflection. Rota (1932–1999) was a leading figure in contemporary mathematics and an outstanding philosopher, inspired by phenomenology, who made fundamental contributions to combinatorial analysis, and trained several generations of mathematicians in his long career at the Massachusetts Institute of Technology (MIT) and the Los Alamos National Laboratory. The first chapter of the book reconstructs Rota’s cultural biography and examines his philosophical style, his criticisms of analytical philosophy, and his reflection on Heidegger’s thought. The second chapter presents a general picture of Rota’s re-elaboration of phenomenology examined in the light of the Husserlian notion of Fundierung. This chapter also illustrates how the star-shape becomes a powerful instrument for understanding the properties of Husserl’s mereology and the critique of objectivism. The third chapter is a theoretical reflection on the nature of mathematical entities, and the fourth examines the complex relation of mathematical research with technological applicability and scientific progress. The foreword of the text is written by Robert Sokolowski.

Combinatorics The Rota Way

Author: Joseph P. S. Kung
Publisher: Cambridge University Press
ISBN: 052188389X
Size: 30.22 MB
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Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.

Differentiable Manifolds

Author: Lawrence Conlon
Publisher: Springer Science & Business Media
ISBN: 1475722842
Size: 38.93 MB
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This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.

An Invitation To Mathematics

Author: Dierk Schleicher
Publisher: Springer Science & Business Media
ISBN: 9783642195334
Size: 34.46 MB
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This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization. Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.

What Is Mathematics

Author: Richard Courant
Publisher: Oxford University Press, USA
ISBN: 9780195105193
Size: 55.29 MB
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

Digitized

Author: Peter J. Bentley
Publisher: OUP Oxford
ISBN: 0191633682
Size: 46.54 MB
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There's a hidden science that affects every part of your life. You are fluent in its terminology of email, WiFi, social networking, and encryption. You use its results when you make a telephone call, access the Internet, use any factory-produced product, or travel in any modern car. The discipline is so new that some prefer to call it a branch of engineering or mathematics. But it is so powerful and world-changing that you would be hard-pressed to find a single human being on the planet unaffected by its achievements. The science of computers enables the supply and creation of power, food, water, medicine, transport, money, communication, entertainment, and most goods in shops. It has transformed societies with the Internet, the digitization of information, mobile phone networks and GPS technologies. Here, Peter J. Bentley explores how this young discipline grew from its theoretical conception by pioneers such as Turing, through its growth spurts in the Internet, its difficult adolescent stage where the promises of AI were never achieved and dot-com bubble burst, to its current stage as a (semi)mature field, now capable of remarkable achievements. Charting the successes and failures of computer science through the years, Bentley discusses what innovations may change our world in the future.

Liaison Schottky Problem And Invariant Theory

Author: Maria Emilia Alonso
Publisher: Springer Science & Business Media
ISBN: 9783034602013
Size: 62.71 MB
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Federico Gaeta (1923–2007) was a Spanish algebraic geometer who was a student of Severi. He is considered to be one of the founders of linkage theory, on which he published several key papers. After many years abroad he came back to Spain in the 1980s. He spent his last period as a professor at Universidad Complutense de Madrid. In gratitude to him, some of his personal and mathematically close persons during this last station, all of whom bene?ted in one way or another by his ins- ration, have joined to edit this volume to keep his memory alive. We o?er in it surveys and original articles on the three main subjects of Gaeta’s interest through his mathematical life. The volume opens with a personal semblance by Ignacio Sols and a historical presentation by Ciro Ciliberto of Gaeta’s Italian period. Then it is divided into three parts, each of them devoted to a speci?c subject studied by Gaeta and coordinated by one of the editors. For each part, we had the advice of another colleague of Federico linked to that particular subject, who also contributed with a short survey. The ?rst part, coordinated by E. Arrondo with the advice of R.M.