front cover of Adjoint Sensitivity Analysis of High Frequency Structures with MATLAB®
Adjoint Sensitivity Analysis of High Frequency Structures with MATLAB®
Mohamed H. Bakr
The Institution of Engineering and Technology, 2017
This book presents the theory of adjoint sensitivity analysis for high frequency applications through time-domain electromagnetic simulations in MATLAB®. This theory enables the efficient estimation of the sensitivities of an arbitrary response with respect to all parameters in the considered problem. These sensitivities are required in many applications including gradient-based optimization, surrogate-based modeling, statistical analysis, and yield analysis.

front cover of Advances in Modal Logic, Volume 1
Advances in Modal Logic, Volume 1
Edited by Marcus Kracht, Maarten de Rijke, Heinrich Wansing, and Michael Zakhary
CSLI, 1998
Modal logic originated in philosophy as the logic of necessity and possibility. Nowadays it has reached a high level of mathematical sophistication and found many applications in a variety of disciplines, including theoretical and applied computer science, artificial intelligence, the foundations of mathematics, and natural language syntax and semantics. This volume represents the proceedings of the first international workshop on Advances in Modal Logic, held in Berlin, Germany, October 8-10, 1996. It offers an up-to-date perspective on the field, with contributions covering its proof theory, its applications in knowledge representation, computing and mathematics, as well as its theoretical underpinnings. "This collection is a useful resource for anyone working in modal logic. It contains both interesting surveys and cutting-edge technical results" --Edwin D. Mares The Bulletin of Symbolic Logic, March 2002

front cover of African Fractals
African Fractals
Modern Computing and Indigenous Design
Eglash, Ron
Rutgers University Press, 1999
Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences.

Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems.

Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

front cover of After Euclid
After Euclid
Jesse Norman
CSLI, 2006
What does it mean to have visual intuition? Can we gain geometrical knowledge by using visual reasoning? And if we can, is it because we have a faculty of intuition? In After Euclid, Jesse Norman reexamines the ancient and long-disregarded concept of visual reasoning and reasserts its potential as a formidable tool in our ability to grasp various kinds of geometrical knowledge. The first detailed philosophical case study of its kind, this text is essential reading for scholars in the fields of mathematics and philosophy.

front cover of Algebras, Diagrams and Decisions in Language, Logic and Computation
Algebras, Diagrams and Decisions in Language, Logic and Computation
Edited by Kees Vermeulen and Ann Copestake
CSLI, 2002
This exemplary volume shows how the shared interests of three different research areas can lead to significant and fruitful exchanges: six papers each very accessibly present an exciting contribution to the study and uses of algebras, diagrams, and decisions, ranging from indispensable overview papers about shared formal members to inspirational applications of formal tools to specific problems. Contributors include Pieter Adriaans, Sergei Artemov, Steven Givant, Edward Keenan, Almerindo Ojeda, Patrick Scotto di Luzio, and Edward Stabler.

front cover of Algorithmes
Donald E. Knuth
CSLI, 2011

This book is a French translation of seventeen papers by Donald Knuth on algorithms both in the field of analysis of algorithms and in the design of new algorithms. They cover fundamental concepts and techniques and numerous discrete problems such as sorting, searching, data compression, theorem-proving, and cryptography, as well as methods for controlling errors in numerical computations.


front cover of The American and Japanese Auto Industries in Transition
The American and Japanese Auto Industries in Transition
Report of the Joint U.S.–Japan Automotive Study
Robert E. Cole and Taizo Yakushiji, Editors
University of Michigan Press, 1984
This report was prepared for the Policy Board by the U.S. and Japanese research staffs of the Joint U.S.–Japan Automotive Study under the general direction of Professors Paul W. McCracken and Keichi Oshima, with research operations organized and coordinated by Robert E. Cole on the U.S. side, in close communication with the Taizo Yakushiji on the Japanese side. [preface]
In view of the importance of stable, long-term economic relationships between Japan and the United States, automotive issues have to be dealt with in ways consistent with the joint prosperity of both countries. Furthermore, the current economic friction has the potential to adversely affect future political relationships. Indeed, under conditions of economic stagnation, major economic issues inevitably become political issues.
With these considerations in mind, the Joint U.S.–Japan Automotive Study project was started in September 1981 to determine the conditions that will allow for the prosperous coexistence of the respective automobile industries. During this two-year study, we have identified four driving forces that will play a major role in determining the future course of the automotive industry of both countries. These are: (1) consumers’ demands and aspirations vis-à-vis automobiles; (2) flexible manufacturing systems (FMS); (3) rapidly evolving technology; and (4) the internationalization of the automotive industry. [exec. summary]

front cover of The Applicability of Mathematics as a Philosophical Problem
The Applicability of Mathematics as a Philosophical Problem
Mark Steiner
Harvard University Press, 1998

This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos.

Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions.

The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.


front cover of Architecture and Geometry in the Age of the Baroque
Architecture and Geometry in the Age of the Baroque
George L. Hersey
University of Chicago Press, 2001
The age of the Baroque—a time when great strides were made in science and mathematics—witnessed the construction of some of the world's most magnificent buildings. What did the work of great architects such as Bernini, Blondel, Guarini, and Wren have to do with Descartes, Galileo, Kepler, Desargues, and Newton? Here, George Hersey explores the ways in which Baroque architecture, with its dramatic shapes and playful experimentation with classical forms, reflects the scientific thinking of the time. He introduces us to a concept of geometry that encompassed much more than the science we know today, one that included geometrics (number and shape games), as well as the art of geomancy, or magic and prophecy using shapes and numbers.

Hersey first concentrates on specific problems in geometry and architectural design. He then explores the affinities between musical chords and several types of architectural form. He turns to advances in optics, such as artificial lenses and magic lanterns, to show how architects incorporated light, a heavenly emanation, into their impressive domes. With ample illustrations and lucid, witty language, Hersey shows how abstract ideas were transformed into visual, tactile form—the epicycles of the cosmos, the sexual mystique surrounding the cube, and the imperfections of heavenly bodies. Some two centuries later, he finds that the geometric principles of the Baroque resonate, often unexpectedly, in the work of architects such as Frank Lloyd Wright and Le Corbusier. A discussion of these surprising links to the past rounds out this brilliant reexamination of some of the long-forgotten beliefs and practices that helped produce some of Europe's greatest masterpieces.

front cover of Are Changing Constituencies Driving Rising Polarization in the U.S. House of Representatives?
Are Changing Constituencies Driving Rising Polarization in the U.S. House of Representatives?
Jesse Sussell
RAND Corporation, 2015
This report addresses two questions: first, whether the spatial distribution of the American electorate has become more geographically clustered over the last 40 years with respect to party voting and socioeconomic attributes; and second, whether this clustering process has contributed to rising polarization in the U.S. House of Representatives.

front cover of Arithmetic
Paul Lockhart
Harvard University Press, 2017

“Inspiring and informative…deserves to be widely read.”
Wall Street Journal

“This fun book offers a philosophical take on number systems and revels in the beauty of math.”
Science News

Because we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.

Paul Lockhart presents arithmetic not as rote manipulation of numbers—a practical if mundane branch of knowledge best suited for filling out tax forms—but as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher.

“A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education…Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting.”
—Jonathon Keats, New Scientist

“What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind’s most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story…A wonderful book.”
—Keith Devlin, author of Finding Fibonacci


front cover of Arrow Logic and Multi-Modal Logic
Arrow Logic and Multi-Modal Logic
Edited by Maarten Marx, László Pólos, and Michael Masuch
CSLI, 1996
Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, their logic, arrow logic can be studied from two different perspectives, and by two (complementary) methodologies: modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tags. They show what the prices of desirable properties, such as decidability, (finite) axiomatisability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The research program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. The content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalised research program.

front cover of Asset Prices and Monetary Policy
Asset Prices and Monetary Policy
Edited by John Y. Campbell
University of Chicago Press, 2008
Economic growth, low inflation, and financial stability are among the most important goals of policy makers, and central banks such as the Federal Reserve are key institutions for achieving these goals.  In Asset Prices and Monetary Policy, leading scholars and practitioners probe the interaction of central banks, asset markets, and the general economy to forge a new understanding of the challenges facing policy makers as they manage an increasingly complex economic system.

The contributors examine how central bankers determine their policy prescriptions with reference to the fluctuating housing market, the balance of debt and credit, changing beliefs of investors, the level of commodity prices, and other factors. At a time when the public has never been more involved in stocks, retirement funds, and real estate investment, this insightful book will be useful to all those concerned with the current state of the economy.

front cover of The Asymptotic Developments of Functions Defined by Maclaurin Series
The Asymptotic Developments of Functions Defined by Maclaurin Series
By Walter B. Ford
University of Michigan Press, 1936
A publication of the University of Michigan’s Science Series, The Asymptotic Developments of Functions Defined by Maclaurin Series by Walter Burton Ford is an inquiry into the problem of functions defined by Maclaurin series. Here, Ford introduces his own theorem of asymptotic developments, as well as other mathematical theorems, and applies them to mathematical problems. This book was published with the hope of stimulating further research in the field.

front cover of Axiomatics
Mathematical Thought and High Modernism
Alma Steingart
University of Chicago Press, 2023
The first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century.

Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. 

For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. 

Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart’s history ably demonstrates, mathematics is the social activity in which styles of truth—here, abstraction—become synonymous with ways of knowing. 

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