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BT 34.016 514.330 Td /F1 28.5 Tf [(Graph Curves Msri)] TJ ET
BT 34.016 460.106 Td /F1 14.2 Tf [(This is likewise one of the factors by obtaining the soft documents of this )] TJ ET
BT 494.191 460.106 Td /F1 14.2 Tf [(Graph Curves Msri)] TJ ET
BT 613.748 460.106 Td /F1 14.2 Tf [( by online. You might not )] TJ ET
BT 34.016 442.707 Td /F1 14.2 Tf [(require more get older to spend to go to the book commencement as skillfully as search for them. In some cases, you )] TJ ET
BT 34.016 425.308 Td /F1 14.2 Tf [(likewise accomplish not discover the message Graph Curves Msri that you are looking for. It will utterly squander the time. )] TJ ET
BT 34.016 390.809 Td /F1 14.2 Tf [(However below, following you visit this web page, it will be thus extremely simple to acquire as without difficulty as )] TJ ET
BT 34.016 373.409 Td /F1 14.2 Tf [(download lead Graph Curves Msri )] TJ ET
BT 34.016 338.910 Td /F1 14.2 Tf [(It will not resign yourself to many become old as we run by before. You can get it even though produce a result something )] TJ ET
BT 34.016 321.511 Td /F1 14.2 Tf [(else at house and even in your workplace. for that reason easy! So, are you question? Just exercise just what we present )] TJ ET
BT 34.016 304.112 Td /F1 14.2 Tf [(below as capably as review )] TJ ET
BT 211.414 304.112 Td /F1 14.2 Tf [(Graph Curves Msri)] TJ ET
BT 330.971 304.112 Td /F1 14.2 Tf [( what you subsequent to to read!)] TJ ET
BT 34.016 241.112 Td /F1 14.2 Tf [(The Mathematics of Chip-Firing)] TJ ET
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BT 232.775 241.112 Td /F1 14.2 Tf [( Caroline J. Klivans 2018-11-15 The Mathematics of Chip-firing is a solid introduction and )] TJ ET
BT 34.016 223.713 Td /F1 14.2 Tf [(overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing )] TJ ET
BT 34.016 206.314 Td /F1 14.2 Tf [(refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple )] TJ ET
BT 34.016 188.915 Td /F1 14.2 Tf [(local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. )] TJ ET
BT 34.016 171.515 Td /F1 14.2 Tf [(The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad )] TJ ET
BT 34.016 154.116 Td /F1 14.2 Tf [(context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the )] TJ ET
BT 34.016 136.717 Td /F1 14.2 Tf [(fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and )] TJ ET
BT 34.016 119.318 Td /F1 14.2 Tf [(students will discover that this book provides a comprehensive background to approaching original sources. Features: )] TJ ET
BT 34.016 101.918 Td /F1 14.2 Tf [(Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current )] TJ ET
BT 34.016 84.519 Td /F1 14.2 Tf [(perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in )] TJ ET
BT 34.016 67.120 Td /F1 14.2 Tf [(mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(\(Institute for Computational and Experimental Research in Mathematics\). Before coming to Brown she held positions at )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.)] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(Bounded Cohomology of Discrete Groups)] TJ ET
BT 297.755 495.147 Td /F1 14.2 Tf [( Roberto Frigerio 2017-11-21 The theory of bounded cohomology, introduced by )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, self-)] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(contained introduction to the theory and its applications, making it accessible to a student who has completed a first )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(students, as a thorough introduction to the field for graduate students, and as a valuable landmark text for researchers, )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(providing both the details of the theory of bounded cohomology and links of the theory to other closely related areas. The )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(first part of the book is devoted to settling the fundamental definitions of the theory, and to proving some of the \(by now )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(classical\) results on low-dimensional bounded cohomology and on bounded cohomology of topological spaces. The )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(second part describes applications of the theory to the study of the simplicial volume of manifolds, to the classification of )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(circle actions, to the analysis of maximal representations of surface groups, and to the study of flat vector bundles with a )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(particular emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. Each chapter ends )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(with a discussion of further reading that puts the presented results in a broader context.)] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(The Shape of Inner Space)] TJ ET
BT 200.370 268.957 Td /F1 14.2 Tf [( Shing-Tung Yau 2010 Argues that geometry is fundamental to string theory--which posits that )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(we live in a 10-dimensional existence--as well as the very nature of the universe, and explains where mathematics will )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(take string theory next.)] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(Trends in Commutative Algebra)] TJ ET
BT 234.371 216.759 Td /F1 14.2 Tf [( Luchezar L. Avramov 2004-12-13 In 2002, an introductory workshop was held at the )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(Mathematical Sciences Research Institute in Berkeley to survey some of the many directions of the commutative algebra )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(field. Six principal speakers each gave three lectures, accompanied by a help session, describing the interaction of )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(commutative algebra with other areas of mathematics for a broad audience of graduate students and researchers. This )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(book is based on those lectures, together with papers from contributing researchers. David Benson and Srikanth Iyengar )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(present an introduction to the uses and concepts of commutative algebra in the cohomology of groups. Mark Haiman )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(considers the commutative algebra of n points in the plane. Ezra Miller presents an introduction to the Hilbert scheme of )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(points to complement Professor Haiman's paper. Further contributors include David Eisenbud and Jessica Sidman; Melvin )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(Hochster; Graham Leuschke; Rob Lazarsfeld and Manuel Blickle; Bernard Teissier; and Ana Bravo.)] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(Dynamics and Randomness)] TJ ET
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BT 212.198 60.166 Td /F1 14.2 Tf [( Alejandro Maass 2012-12-06 This book contains the lectures given at the Conference on )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(scientists, and graduate students interested in fields re lated to probability theory, ergodic theory, symbolic and topological )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(dynam ics. We would like to express our gratitude to all the participants of the con ference and to the people who )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(want to thank especially the authors of each chapter for their well prepared manuscripts and the stimulating conferences )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(they gave at Santiago. We are also indebted to our sponsors and supporting institutions, whose interest and help was )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(essential to organize this meeting: ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. Gladys Cavallone for their )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(different chapters of this book.)] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(Critical Issues in Mathematics Education)] TJ ET
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BT 289.803 355.953 Td /F1 14.2 Tf [( Bharath Sriraman 2009-06-01 The word "critical" in the title of this collection has )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(three meanings, all of which are relevant. One meaning, as applied to a situation or problem, is "at a point of crisis". A )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(second meaning is "expressing adverse or disapproving comments or judgments". A third is related to the verb "to )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(critique", meaning "to analyze the merits and faults of". The authors contributing to this book pose challenging questions, )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(from multiple perspectives, about the roles of mathematics in society and the implications for education. Traditional )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(reasons for teaching mathematics include: preparing a new generation of mathematics researchers and a cadre of )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(technically competent users of mathematics; training students to think logically; and because mathematics is as much part )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(of cultural heritage as literature or music. These reasons remain valid, though open to critique, but a deeper analysis is )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(required that recognizes the roles of mathematics in framing many aspects of contemporary society, that will connect )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(mathematics education to the lived experiences of students, their communities, and society in general, and that )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(acknowledges the global ethical responsibilities of mathematicians and mathematics educators. The book is organized in )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(four sections \(1\) Mathematics education: For what and why? \(2\) Globalization and cultural diversity, \(3\) Mathematics, )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(education, and society and \(4\) Social justice in, and through, mathematics education The chapters address fundamental )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(issues such as the relevance of school mathematics in people's lives; creating a sense of agency for the field of )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(mathematics education, and redefining the relationship between mathematics as discipline, mathematics as school )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(subject and mathematics as part of people's lives.)] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(Introduction to Functional Equations)] TJ ET
BT 261.346 77.565 Td /F1 14.2 Tf [( Costas Efthimiou 2011-10-13 Functions and their properties have been part of the )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(and international mathematical competitions. Yet the subject has not received equal attention by authors at an )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(which collects the relevant foundational information on functions, plus some material potentially new to the reader. The )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-)] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(as a service to young people, their parents and teachers, and the mathematics profession.)] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(Mathematical Writing)] TJ ET
BT 167.039 321.155 Td /F1 14.2 Tf [( Donald E. Knuth 1989 This book will help those wishing to teach a course in technical writing, or )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(who wish to write themselves.)] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(Tropical Algebraic Geometry)] TJ ET
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BT 214.563 286.356 Td /F1 14.2 Tf [( Ilia Itenberg 2009-05-30 These notes present a polished introduction to tropical geometry )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(in mathematics.)] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(Differential Geometry of Curves and Surfaces)] TJ ET
BT 321.495 181.961 Td /F1 14.2 Tf [( Victor Andreevich Toponogov 2006-09-10 Central topics covered include )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(and original problems \(some with hints and solutions\) Standard theoretical material is combined with more difficult )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(theorems and complex problems, while maintaining a clear distinction between the two levels)] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(Algebraic Statistics for Computational Biology)] TJ ET
BT 321.495 112.364 Td /F1 14.2 Tf [( L. Pachter 2005-08-22 This book, first published in 2005, offers an )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(introduction to the application of algebraic statistics to computational biology.)] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(Flavors of Geometry)] TJ ET
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BT 163.092 77.565 Td /F1 14.2 Tf [( Silvio Levy 1997-09-28 Lectures on hyperbolic geometry, dynamics in several complex variables, )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(convex geometry, and volume estimation.)] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(Symmetry in Graph Theory)] TJ ET
BT 205.058 529.946 Td /F1 14.2 Tf [( Jose M. Rodriguez 2019-03-14 This book contains the successful invited submissions to a )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(Special Issue of Symmetry on the subject of “Graph Theory”. Although symmetry has always played an important role in )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(of view.)] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(Combinatorial and Computational Geometry)] TJ ET
BT 311.990 425.550 Td /F1 14.2 Tf [( cob E. Goodman 2005-08-08 This 2005 book deals with interest topics in )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(Discrete and Algorithmic aspects of Geometry.)] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(Differential Geometry)] TJ ET
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BT 168.635 390.752 Td /F1 14.2 Tf [( Loring W. Tu 2017-06-01 This text presents a graduate-level introduction to differential geometry for )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(mathematics and physics students. The exposition follows the historical development of the concepts of connection and )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.)] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(Three-dimensional Geometry and Topology)] TJ ET
BT 308.827 60.166 Td /F1 14.2 Tf [( WILLIAM P AUTOR THURSTON 1997 Every mathematician should be )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-)] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(book contains a great deal of interesting mathematics.)] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(Analytic Combinatorics)] TJ ET
BT 178.924 390.752 Td /F1 14.2 Tf [( Philippe Flajolet 2009-01-15 Analytic combinatorics aims to enable precise quantitative predictions )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(graduate course, or for self-study.)] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(A Decade of the Berkeley Math Circle)] TJ ET
BT 271.606 216.759 Td /F1 14.2 Tf [( Zvezdelina Stankova 2008-11-26 Many mathematicians have been drawn to )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(mathematics through their experience with math circles: extracurricular programs exposing teenage students to advanced )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(mathematical topics and a myriad of problem solving techniques and inspiring in them a lifelong love for mathematics. )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Founded in 1998, the Berkeley Math Circle \(BMC\) is a pioneering model of a U.S. math circle, aspiring to prepare our best )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(young minds for their future roles as mathematics leaders. Over the last decade, 50 instructors--from university professors )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(to high school teachers to business tycoons--have shared their passion for mathematics by delivering more than 320 BMC )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(sessions full of mathematical challenges and wonders. Based on a dozen of these sessions, this book encompasses a )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik's )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(cube and abstract algebra; from number theory to mass point theory; from complex numbers to game theory via invariants )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(and monovariants. The treatments of these subjects encompass every significant method of proof and emphasize ways of )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(thinking and reasoning via 100 problem solving techniques. Also featured are 300 problems, ranging from beginner to )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(intermediate level, with occasional peaks of advanced problems and even some open questions. The book presents )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(possible paths to studying mathematics and inevitably falling in love with it, via teaching two important skills: thinking )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(creatively while still ``obeying the rules,'' and making connections between problems, ideas, and theories. The book )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(encourages you to apply the newly acquired knowledge to problems and guides you along the way, but rarely gives you )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(ready answers. ``Learning from our own mistakes'' often occurs through discussions of non-proofs and common problem )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(solving pitfalls. The reader has to commit to mastering the new theories and techniques by ``getting your hands dirty'' with )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(the problems, going back and reviewing necessary problem solving techniques and theory, and persistently moving )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(forward in the book. The mathematical world is huge: you'll never know everything, but you'll learn where to find things, )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(how to connect and use them. The rewards will be substantial. In the interest of fostering a greater awareness and )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(mathematics profession.)] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(Persistence Theory: From Quiver Representations to Data Analysis)] TJ ET
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BT 458.495 321.155 Td /F1 14.2 Tf [( Steve Y. Oudot 2017-05-17 Persistence theory )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(representation theory. The second part focuses on its connection to applications through a few selected topics. The third )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(topology or data analysis.)] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Introduction to Tropical Geometry)] TJ ET
BT 245.471 164.561 Td /F1 14.2 Tf [( Diane Maclagan 2021-12-13 Tropical geometry is a combinatorial shadow of algebraic )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(—Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(“Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(—Alicia Dickenstein, University of Buenos Aires, Argentina)] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(Random Surfaces)] TJ ET
BT 148.058 268.957 Td /F1 14.2 Tf [( Scott Sheffield 2005 The author develops a general theory of discrete and continuous height models )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(governed by Gibbs potentials that depend only on height differences. He characterizes the gradient phases of a given )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(slope as minimizers of specific free energy and gives large deviation principles for surface shapes and empirical )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(measures. For convex, nearest neighbor Gibbs potentials, he shows that gradient phases are characterized by their )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(slopes and, in higher dimensional discrete settings, by one additional parameter. For standard $2+1$ dimensional crystal )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(surface models, he shows that all smooth phases \(crystal facets\) lie in the dual of the lattice of translation invariance.)] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Math from Three to Seven)] TJ ET
BT 199.544 164.561 Td /F1 14.2 Tf [( Aleksandr Kalmanovich Zvonkin 2011 This book is a captivating account of a professional )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(they capable of? What should they learn first? How hard should they work? Should they even "work" at all? Should we )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(math-circle style: he doesn't ask and then answer a question, but shows us a problem--be it mathematical or pedagogical--)] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(but most important, what the kids experienced. This book does not purport to show you how to create precocious high )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(achievers. It is just one person's story about things he tried with a half-dozen young children. Mathematicians, )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(book to be an invaluable, inspiring resource. In the interest of fostering a greater awareness and appreciation of )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(profession. Titles in this series are co-published with the Mathematical Sciences Research Institute \(MSRI\).)] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(Tensor Categories)] TJ ET
BT 151.222 425.550 Td /F1 14.2 Tf [( Pavel Etingof 2016-08-05 Is there a vector space whose dimension is the golden ratio? Of course )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(algebras, low-dimensional topology \(in particular, knot theory\), homotopy theory, quantum mechanics and field theory, )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(tensor categories and fusion categories \(in particular, braided and modular ones\), and discusses the main results about )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(and references are discussed at the end of each chapter.)] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(Why Johnny Can't Add)] TJ ET
BT 178.511 216.759 Td /F1 14.2 Tf [( Morris Kline 1974 Briefly discusses the traditional mathematics formerly taught in American )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(schools and views the language and weaknesses of the modern math curriculum)] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(Mathematics of Surfaces)] TJ ET
BT 190.823 181.961 Td /F1 14.2 Tf [( England\) Ima Conference on the Mathematics of Surfaces 2003 \(Leeds 2003-09-09 This book )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(constitutes the refereed proceedings of the 10th IMA International Conference on the Mathematics of Surfaces, held in )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(Leeds, UK in September 2003. The 25 revised full papers presented were carefully reviewed and selected from numerous )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(submissions. Among the topics addressed are triangulated surface parameterization, bifurcation structures, control vertex )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(computation, polyhedral surfaces, watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(vector transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the Plateau-Bezier )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(problem, spline geometry, generative geometry, manifold representation, affine arithmetic, and PDE surfaces.)] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(Experimental Mathematics)] TJ ET
BT 201.895 60.166 Td /F1 14.2 Tf [( V. I. Arnold 2015-07-14 One of the traditional ways mathematical ideas and even new areas of )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(author's lectures, presents several new directions of mathematical research. All of these directions are based on )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(proved nor disproved. The hypotheses range from geometry and topology \(statistics of plane curves and smooth )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(functions\) to combinatorics \(combinatorial complexity and random permutations\) to algebra and number theory )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(\(continuous fractions and Galois groups\). For each subject, the author describes the problem and presents numerical )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(approach the formulated conjectures \(at least by conducting more numerical experiments\). Written in Arnold's unique )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute \(MSRI\).)] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(Exterior Differential Systems)] TJ ET
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BT 213.765 268.957 Td /F1 14.2 Tf [( Robert L. Bryant 2013-06-29 This book gives a treatment of exterior differential systems. It )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(will in clude both the general theory and various applications. An exterior differential system is a system of equations on a )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(condition are essentially the same object.)] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(Birational Geometry and Moduli Spaces)] TJ ET
BT 285.072 529.946 Td /F1 14.2 Tf [( Elisabetta Colombo 2020-02-25 This volume collects contributions from speakers )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-)] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.)] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(Image Processing and Analysis)] TJ ET
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BT 232.803 373.352 Td /F1 14.2 Tf [( Tony F. Chan 2005-09-01 This book develops the mathematical foundation of modern )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(have integrated the diversity of modern image processing approaches by revealing the few common threads that connect )] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(theoretical analysis of model building and performance with computational implementation and numerical examples.)] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(Tropical Geometry and Mirror Symmetry)] TJ ET
BT 288.179 199.360 Td /F1 14.2 Tf [( Mark Gross 2011-01-20 Tropical geometry provides an explanation for the )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.)] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(Steps in Commutative Algebra)] TJ ET
0.285 w 0 J [ ] 0 d
34.016 510.195 m 226.462 510.195 l S
BT 226.462 512.546 Td /F1 14.2 Tf [( R. Y. Sharp 2000 Introductory account of commutative algebra, aimed at students with a )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(background in basic algebra.)] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(Testimonios: Stories of Latinx and Hispanic Mathematicians)] TJ ET
BT 410.985 477.748 Td /F1 14.2 Tf [( Pamela E. Harris 2021-08-16 Testimonios brings together )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(first-person narratives from the vibrant, diverse, and complex Latinx and Hispanic mathematical community. Starting with )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(childhood and family, the authors recount their own individual stories, highlighting their upbringing, education, and career )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(paths. Their particular stories, told in their own voices, from their own perspectives, give visibility to some of the )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(experiences of Latinx/Hispanic mathematicians. Testimonios seeks to inspire the next generation of Latinx and Hispanic )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(mathematicians by featuring the stories of people like them, holding a mirror up to our own community. It also aims to )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(provide a window for mathematicians \(and aspiring mathematicians\) from all ethnicities, with the hope of inspiring a better )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(understanding of the diversity of the mathematical community.)] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(Current Developments in Algebraic Geometry)] TJ ET
BT 321.481 338.554 Td /F1 14.2 Tf [( Lucia Caporaso 2012-03-19 This volume, based on a workshop by the )] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(MSRI, offers an overview of the state of the art in many areas of algebraic geometry.)] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(Differential and Symplectic Topology of Knots and Curves)] TJ ET
BT 398.331 303.755 Td /F1 14.2 Tf [( Serge Tabachnikov 1999 This book presents a collection of )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(papers on two related topics: topology of knots and knot-like objects \(such as curves on surfaces\) and topology of )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(\(quantum knot invariants, knot invariants of finite type\), in symplectic and contact topology, and in singularity theory. The )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(objects such as wave fronts. A particularly enticing feature of the volume is its international significance. The volume )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(successfully embodies a fine collaborative effort by worldwide experts from Belgium, France, Germany, Israel, Japan, )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(Poland, Russia, Sweden, the U.K., and the U.S.)] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(Computational Topology)] TJ ET
BT 188.457 164.561 Td /F1 14.2 Tf [( Herbert Edelsbrunner 2010 Combining concepts from topology and algorithms, this book delivers )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is )] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate )] TJ ET
BT 34.016 60.166 Td /F1 14.2 Tf [(course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or )] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(computer science department.)] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(Rational Points on Modular Elliptic Curves)] TJ ET
BT 299.308 512.546 Td /F1 14.2 Tf [( Henri Darmon 2004 The book surveys some recent developments in the )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural )] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM )] TJ ET
BT 34.016 355.953 Td /F1 14.2 Tf [(field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic )] TJ ET
BT 34.016 338.554 Td /F1 14.2 Tf [(curves and leads to the so-far best evidence for the Birch and Swinnerton-Dyer conjecture.)] TJ ET
BT 34.016 321.155 Td /F1 14.2 Tf [(The Mathematics of Data)] TJ ET
0.285 w 0 J [ ] 0 d
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BT 193.202 321.155 Td /F1 14.2 Tf [( Michael W. Mahoney 2018-11-15 Nothing provided)] TJ ET
BT 34.016 303.755 Td /F1 14.2 Tf [(Lectures on Spaces of Nonpositive Curvature)] TJ ET
BT 320.726 303.755 Td /F1 14.2 Tf [( Werner Ballmann 1995-09-01 Singular spaces with upper curvature bounds )] TJ ET
BT 34.016 286.356 Td /F1 14.2 Tf [(and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric \(and )] TJ ET
BT 34.016 268.957 Td /F1 14.2 Tf [(combinatorial\) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a )] TJ ET
BT 34.016 251.558 Td /F1 14.2 Tf [(concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the )] TJ ET
BT 34.016 234.158 Td /F1 14.2 Tf [(ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative )] TJ ET
BT 34.016 216.759 Td /F1 14.2 Tf [(properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random )] TJ ET
BT 34.016 199.360 Td /F1 14.2 Tf [(walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely )] TJ ET
BT 34.016 181.961 Td /F1 14.2 Tf [(complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two \(Rank Rigidity )] TJ ET
BT 34.016 164.561 Td /F1 14.2 Tf [(conjecture\). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the )] TJ ET
BT 34.016 147.162 Td /F1 14.2 Tf [(proof of the latter theorem \(in the smooth case\) is presented in Chapter IV of the book. This chapter contains also a short )] TJ ET
BT 34.016 129.763 Td /F1 14.2 Tf [(introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic )] TJ ET
BT 34.016 112.364 Td /F1 14.2 Tf [(flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact )] TJ ET
BT 34.016 94.964 Td /F1 14.2 Tf [(Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-)] TJ ET
BT 34.016 77.565 Td /F1 14.2 Tf [(specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, )] TJ ET
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BT 34.016 547.345 Td /F1 14.2 Tf [(and the appendix can serve as an introduction into this theory.)] TJ ET
BT 34.016 529.946 Td /F1 14.2 Tf [(Computations in Algebraic Geometry with Macaulay 2)] TJ ET
BT 372.966 529.946 Td /F1 14.2 Tf [( David Eisenbud 2013-03-14 This book presents algorithmic tools )] TJ ET
BT 34.016 512.546 Td /F1 14.2 Tf [(for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system )] TJ ET
BT 34.016 495.147 Td /F1 14.2 Tf [(supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented )] TJ ET
BT 34.016 477.748 Td /F1 14.2 Tf [(here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book )] TJ ET
BT 34.016 460.349 Td /F1 14.2 Tf [(covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.)] TJ ET
BT 34.016 442.949 Td /F1 14.2 Tf [(Complex Algebraic Curves)] TJ ET
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34.016 440.598 m 202.679 440.598 l S
BT 202.679 442.949 Td /F1 14.2 Tf [( Frances Clare Kirwan 1992-02-20 This development of the theory of complex algebraic curves )] TJ ET
BT 34.016 425.550 Td /F1 14.2 Tf [(was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various )] TJ ET
BT 34.016 408.151 Td /F1 14.2 Tf [(areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the )] TJ ET
BT 34.016 390.752 Td /F1 14.2 Tf [(basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the )] TJ ET
BT 34.016 373.352 Td /F1 14.2 Tf [(algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.)] TJ ET
BT 36.266 328.458 Td /F1 8.0 Tf [(graph-curves-msri)] TJ ET
BT 512.168 328.665 Td /F1 8.0 Tf [(Downloaded from )] TJ ET
BT 577.080 328.458 Td /F1 8.0 Tf [(dev1.improvingprimarycare.org)] TJ ET
BT 687.328 328.665 Td /F1 8.0 Tf [( on September 26, 2022 by guest)] TJ ET
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