The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series
Author: Ken Ono
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 226
ISBN-13: 0821833685
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Modular Web Design
Author: Nathan Curtis
Publisher: New Riders
Published: 2010-04-07
Total Pages: 495
ISBN-13: 0132104865
DOWNLOAD EBOOKUser experience design teams often suffer from a decentralized, blank canvas approach to creating and documenting a design solution for each new project. As teams repeatedly reinvent screen designs, inconsistency results, and IT teams scramble to pick up the pieces. Pattern libraries only go so far, suggesting general solutions to common problems instead of offering concrete, specific design treatments. At times, documented solutions turn into a costly mess of unclear expectations, unrealistic goals, and abandoned work. Enter components, each of which represents a chunk of a Web page. Designers can produce wireframes, mockups, or markup far more efficiently reusing components based on an established design system. Rather than limit innovation, components enable designers to render solved design frameworks quickly and to focus on the problem at hand, drastically improving the quality and rate of production. In addition, teams develop a deeper baseline for collaboration, a platform for governance, and a structure for useful and predictable documentation. This book defines the role of components and why they matter, maps out how to organize and build a component library, discusses how to use components in practice, and teaches a process for documenting and maintaining components.
Managing in the Modular Age
Author: Raghu Garud
Publisher: John Wiley & Sons
Published: 2009-02-09
Total Pages: 424
ISBN-13: 1405141948
DOWNLOAD EBOOKThis book brings together seminal articles by leading scholars of technological and organizational systems, exploring the impact of 'modularity'. Modularity refers to an ability to take apart and put together differenct products and networks, or to 'mix and match' components in order to meet different user specifications. This is of key importance today where new systems such as the World Wide Web and many areas of the computer industry depend on it. The volume pulls together and defines an exciting new area of inquiry: into how our 'modular age' is reshaping the business eco-system. Includes contributions from leading scholars of technology and organization Modularity refers to an ability to take apart and put together different products and systems, or to 'mix and match' components in order to meet different user specifications. Consolidates and defines an area of inquiry that is becoming increasingly important with the development of web-based and 'network' industries. Sensitizes readers to the complexity of issues surrounding new modular products and systems created by e-business Encourages readers to make connections among different levels and disciplines. Initiates a debate around issues of modularity. Includes a commentary co-authored by the late Nobel Laureate Herbert A. Simon to whom the book is dedicated.
Modularity
Author: Werner Callebaut
Publisher: MIT Press
Published: 2005
Total Pages: 480
ISBN-13: 9780262033268
DOWNLOAD EBOOKModularity—the attempt to understand systems as integrations of partially independent and interacting units—is today a dominant theme in the life sciences, cognitive science, and computer science. The concept goes back at least implicitly to the Scientific (or Copernican) Revolution, and can be found behind later theories of phrenology, physiology, and genetics; moreover, art, engineering, and mathematics rely on modular design principles. This collection broadens the scientific discussion of modularity by bringing together experts from a variety of disciplines, including artificial life, cognitive science, economics, evolutionary computation, developmental and evolutionary biology, linguistics, mathematics, morphology, paleontology, physics, theoretical chemistry, philosophy, and the arts. The contributors debate and compare the uses of modularity, discussing the different disciplinary contexts of "modular thinking" in general (including hierarchical organization, near-decomposability, quasi-independence, and recursion) or of more specialized concepts (including character complex, gene family, encapsulation, and mosaic evolution); what modules are, why and how they develop and evolve, and the implication for the research agenda in the disciplines involved; and how to bring about useful cross-disciplinary knowledge transfer on the topic. The book includes a foreword by the late Herbert A. Simon addressing the role of near-decomposability in understanding complex systems. Contributors: Lee Altenberg, Lauren W. Ancel-Meyers, Carl Anderson, Robert B. Brandon, Angela D. Buscalioni, Raffaele Calabretta, Werner Callebaut, Anne De Joan, Rafael Delgado-Buscalioni, Gunther J. Eble, Walter Fontana, Fernand Gobet, Alicia de la Iglesia, Slavik V. Jablan, Luigi Marengo, Daniel W. McShea, Jason Mezey, D. Kimbrough Oller, Domenico Parisi, Corrado Pasquali, Diego Rasskin-Gutman, Gerhard Schlosser, Herbert A. Simon, Roger D. K. Thomas, Marco Valente, Boris M. Velichkovsky, Gunter P. Wagner, Rasmus G. Winter Vienna Series in Theoretical Biology
Modular Forms, a Computational Approach
Author: William A. Stein
Publisher: American Mathematical Soc.
Published: 2007-02-13
Total Pages: 290
ISBN-13: 0821839608
DOWNLOAD EBOOKThis marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Economic Analysis of the Digital Economy
Author: Avi Goldfarb
Publisher: University of Chicago Press
Published: 2015-05-08
Total Pages: 510
ISBN-13: 022620684X
DOWNLOAD EBOOKThere is a small and growing literature that explores the impact of digitization in a variety of contexts, but its economic consequences, surprisingly, remain poorly understood. This volume aims to set the agenda for research in the economics of digitization, with each chapter identifying a promising area of research. "Economics of Digitization "identifies urgent topics with research already underway that warrant further exploration from economists. In addition to the growing importance of digitization itself, digital technologies have some features that suggest that many well-studied economic models may not apply and, indeed, so many aspects of the digital economy throw normal economics in a loop. "Economics of Digitization" will be one of the first to focus on the economic implications of digitization and to bring together leading scholars in the economics of digitization to explore emerging research.
Geometric Modular Forms and Elliptic Curves
Author: Haruzo Hida
Publisher: World Scientific
Published: 2012
Total Pages: 468
ISBN-13: 9814368652
DOWNLOAD EBOOK1. An algebro-geometric tool box. 1.1. Sheaves. 1.2. Schemes. 1.3. Projective schemes. 1.4. Categories and functors. 1.5. Applications of the key-lemma. 1.6. Group schemes. 1.7. Cartier duality. 1.8. Quotients by a group scheme. 1.9. Morphisms. 1.10. Cohomology of coherent sheaves. 1.11. Descent. 1.12. Barsotti-Tate groups. 1.13. Formal scheme -- 2. Elliptic curves. 2.1. Curves and divisors. 2.2. Elliptic curves. 2.3. Geometric modular forms of level 1. 2.4. Elliptic curves over C. 2.5. Elliptic curves over p-adic fields. 2.6. Level structures. 2.7. L-functions of elliptic curves. 2.8. Regularity. 2.9. p-ordinary moduli problems. 2.10. Deformation of elliptic curves -- 3. Geometric modular forms. 3.1. Integrality. 3.2. Vertical control theorem. 3.3. Action of GL(2) on modular forms -- 4. Jacobians and Galois representations. 4.1. Jacobians of stable curves. 4.2. Modular Galois representations. 4.3. Fullness of big Galois representations -- 5. Modularity problems. 5.1. Induced and extended Galois representations. 5.2. Some other solutions. 5.3. Modularity of Abelian Q-varieties
Topological Modular Forms
Author: Christopher L. Douglas
Publisher: American Mathematical Soc.
Published: 2014-12-04
Total Pages: 353
ISBN-13: 1470418843
DOWNLOAD EBOOKThe theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.
Elementary Modular Iwasawa Theory
Author: Haruzo Hida
Publisher: World Scientific
Published: 2021-10-04
Total Pages: 446
ISBN-13: 9811241384
DOWNLOAD EBOOKThis book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation.The fundamentals in the first five chapters are as follows:Many open problems are presented to stimulate young researchers pursuing their field of study.
A First Course in Modular Forms
Author: Fred Diamond
Publisher: Springer Science & Business Media
Published: 2006-03-30
Total Pages: 462
ISBN-13: 0387272267
DOWNLOAD EBOOKThis book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
