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› Find signed collectible books: 'Combinatorics: The Rota Way (Cambridge Mathematical Library)'
Written by two of Gian-Carlo Rota's former students, this book is based on notes from his courses and on personal discussions with him. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. This book should be on the shelf of all students and researchers in combinatorics and related areas.
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› Find signed collectible books: 'Discrete Thoughts: Essays on Mathematics, Science and Philosophy'
This is a volume of essays and reviews that delightfully explores mathematics in all its moods from the light and the witty, and humorous to serious, rational, and cerebral. These beautifully written articles from three great modern mathematicians will provide a source for supplemental reading for almost any math class. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and broad applications of mathematics. Readers will also find coverage of history and philosophy, including discussion of the work of Ulam, Kant, and Heidegger, among others.
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› Find signed collectible books: 'Essays on the Future: In Honor of Nick Metropolis'
This collection represents a unique undertaking in scientific publishing to honor Nick Metropolis, the last survivor of the World War II Manhattan Project in Los Alamos. In this volume, some of the leading scientists and humanists of our time have contributed essays related to their respective disciplines, exploring various aspects of future developments in science and society, philosophy, national security, nuclear power, pure and applied mathematics, physics and biology, particle physics, computing, and information science.
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› Find signed collectible books: 'Finite Operator Calculus'
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› Find signed collectible books: 'Gian-Carlo Rota on Analysis and Probability: Selected Papers and Commentaries (Contemporary Mathematicians)'
Gian-Carlo Rota was born in Vigevano, Italy, in 1932. He died in Cambridge, Mas sachusetts, in 1999. He had several careers, most notably as a mathematician, but also as a philosopher and a consultant to the United States government. His mathe matical career was equally varied. His early mathematical studies were at Princeton (1950 to 1953) and Yale (1953 to 1956). In 1956, he completed his doctoral thesis under the direction of Jacob T. Schwartz. This thesis was published as the pa per "Extension theory of differential operators I", the first paper reprinted in this volume. Rota's early work was in analysis, more specifically, in operator theory, differ ential equations, ergodic theory, and probability theory. In the 1960's, Rota was motivated by problems in fluctuation theory to study some operator identities of Glen Baxter (see [7]). Together with other problems in probability theory, this led Rota to study combinatorics. His series of papers, "On the foundations of combi natorial theory", led to a fundamental re-evaluation of the subject. Later, in the 1990's, Rota returned to some of the problems in analysis and probability theory which motivated his work in combinatorics. This was his intention all along, and his early death robbed mathematics of his unique perspective on linkages between the discrete and the continuous. Glimpses of his new research programs can be found in [2,3,6,9,10].
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› Find signed collectible books: 'Indiscrete Thoughts (Modern Birkhäuser Classics)'
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 as well as 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 Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.
Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come.
"Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer
"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offendbut everywhere readable and entertaining."--The American Mathematical Monthly
"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews
› Find signed collectible books: 'Introduction to Geometric Probability (Lezioni Lincee)'
Here is the first modern introduction to geometric probability, also known as integral geometry, presented at an elementary level, requiring little more than first-year graduate mathematics. Klein and Rota present the theory of intrinsic volumes due to Hadwiger, McMullen, Santaló and others, along with a complete and elementary proof of Hadwiger's characterization theorem of invariant measures in Euclidean n-space. They develop the theory of the Euler characteristic from an integral-geometric point of view. The authors then prove the fundamental theorem of integral geometry, namely, the kinematic formula. Finally, the analogies between invariant measures on polyconvex sets and measures on order ideals of finite partially ordered sets are investigated. The relationship between convex geometry and enumerative combinatorics motivates much of the presentation. Every chapter concludes with a list of unsolved problems.
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› Find signed collectible books: 'On The Foundations of Combinatorial Theory: Combinatorial Geometries'
It has been clear within the last ten years that combinatorial geometry, together with its order-theoretic counterpart, the geometric lattice, can serve to catalyze the whole field of combinatorial theory, and a major aim of this book, now available in a preliminary edition, is to present the theory in a form accessible to mathematicians working in disparate subjects.
Earlier studies have been one-sided or restricted in their point of view; they were motivated primarily by the desire to extend the classical theory of graphs, or were lattice-theoretic approaches confined to axiomatics and algebraic dependence. These approaches largely ignored the original geometric motivations.
The present work brings all these aspects together in order to emphasize the many-sidedness of combinatorial geometry, and to point up the unifying role it may well play in current developments in combinatorics and its applications.
The book defines the axiomatics of combinatorial geometry, describes a variety of geometrical examples, and discusses the notion of a strong map between geometries. In addition, there is a brief presentation of coordinatization theory and a sketch of two important lines of future work, the "critical problem" and matching theory. The full chapter titles are given below.
Contents: 1. Introduction. 2. Geometrics and Geometric Lattices. 3. Six Classical Examples. 4. Span, Bases, Bonds, Dependence, and Circuits. 5. Cryptomorphic Versions of Geometry. 6. Simplicial Geometries. 7. Semimodular Functions. 8. A Glimpse of Matching Theory. 9. Maps. 10. The Extension Theorem. 11. Orthogonality. 12. Factorization of Relatively Complemented Lattices. 13. Factorization of Geometries. 14. Connected Sets. 15. Representation. 16. The Critical Problem. 17. Bibliography.
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› Find signed collectible books: 'Ordinary Differential Equations'
A carefully revised edition of the well-respected ODE text, whose unique treatment provides a smooth transition to critical understanding of proofs of basic theorems. First chapters present a rigorous treatment of background material; middle chapters deal in detail with systems of nonlinear differential equations; final chapters are devoted to the study of second-order linear differential equations. The power of the theory of ODE is illustrated throughout by deriving the properties of important special functions, such as Bessel functions, hypergeometric functions, and the more common orthogonal polynomials, from their defining differential equations and boundary conditions. Contains several hundred exercises. Prerequisite is a first course in ODE.
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› Find signed collectible books: 'phenomenologie discrete'
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