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Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 9780821886281
Category : Mathematics
Languages : en
Pages : 316
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Book Description
"In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein's equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article.
Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 9780821886281
Category : Mathematics
Languages : en
Pages : 316
Get Book
Book Description
"In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein's equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article.
Author: Michel Bilodeau
Publisher: Springer Science & Business Media
ISBN: 0387291156
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.
Author: Douglas Cenzer
Publisher: World Scientific
ISBN: 9813228245
Category : Mathematics
Languages : en
Pages : 387
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Book Description
This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.
Author: Jiří Matousek
Publisher: Springer
ISBN: 887642525X
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.
Author: Terence Tao
Publisher: American Mathematical Society
ISBN: 147047459X
Category : Mathematics
Languages : en
Pages : 296
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Book Description
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Author: Mark Fell
Publisher: MIT Press
ISBN: 1913029956
Category : Art
Languages : en
Pages : 404
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Book Description
An anthology of pioneer sound artist Mark Fell's work charting his defiantly unorthodox thinking on time, structure, technology, and the relation between academic and popular electronic music. In this extensive anthology, Mark Fell, a pioneering artist known for his sound installations and his musical work solo and as part of SND and Sensate Focus, assembles a collection of diverse materials charting his defiantly unorthodox thinking on time, structure, technology, and the relation between academic and popular electronic music. An amalgam of workbook and manifesto, featuring a collection of interleaved statements, diagrammatic scores, and instructional texts, Structure and Synthesis is a direct engagement with Fell's original thinking and his continual provocations in regard to "experimental" music. Alongside reflections on theory and practice, the volume includes exercises for dismantling musical expertise, habits, and intuitions, documenting Fell's explorations of the peripheries of rhythm, shape, and time in perception and performance. Long-term collaborator designer Joe Gilmore provides a striking graphic context for Fell's evolving thinking and the methods and structures he has developed through his solo and collaborative work.
Author: Adrian Bejan
Publisher: Cambridge University Press
ISBN: 9780521793889
Category : Science
Languages : en
Pages : 370
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Book Description
Seemingly universal geometric forms unite the flow systems of engineering and nature. For example, tree-shaped flows can be seen in computers, lungs, dendritic crystals, urban street patterns, and communication links. In this groundbreaking book, Adrian Bejan considers the design and optimization of engineered systems and discovers a deterministic principle of the generation of geometric form in natural systems. Shape and structure spring from the struggle for better performance in both engineering and nature. This idea is the basis of the new constructal theory: the objective and constraints principle used in engineering is the same mechanism from which the geometry in natural flow systems emerges. From heat exchangers to river channels, the book draws many parallels between the engineered and the natural world. Among the topics covered are mechanical structure, thermal structure, heat trees, ducts and rivers, turbulent structure, and structure in transportation and economics. The numerous illustrations, examples, and homework problems in every chapter make this an ideal text for engineering design courses. Its provocative ideas will also appeal to a broad range of readers in engineering, natural sciences, economics, and business.
Author: D.J. Daley
Publisher: Springer Science & Business Media
ISBN: 0387215646
Category : Mathematics
Languages : en
Pages : 487
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Book Description
Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 0821848836
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Focuses on ergodic theory, combinatorics, and number theory. This book discusses a variety of topics, ranging from developments in additive prime number theory to expository articles on individual mathematical topics such as the law of large numbers and the Lucas-Lehmer test for Mersenne primes.
Author: Douglas Cenzer
Publisher: World Scientific Publishing Company
ISBN: 9789813228221
Category :
Languages : en
Pages : 200
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Book Description
This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium. Contents: Limits of the Kucerea-Gacs Coding Method (George Barmpalias and Andrew Lewis-Pye);Infinitary partition properties of sums of selective ultrafilters (Andreas Blass);Semiselective Coideals and Ramsey Sets (Carlos DiPrisco and Leonardo Pacheco);Survey on Topological Ramsey Spaces Dense in Forcings (Natasha Dobrinen);Higher Computability in the Reverse Mathematics of Borel Determinacy (Sherwood Hachtman);Computability and Definability (Valentina Harizanov);A Ramsey Space of Infinite Polyhedra and the Random Polyhedron (Jose G Mijares Palacios and Gabriel Padilla);Computable Reducibility for Cantor Space (Russell G Miller);Information vs Dimension - An Algorithmic Perspective (Jan Reimann); Readership: Graduate students and researchers interested in the interface between set theory and computability.
