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BT 34.016 765.881 Td /F1 25.5 Tf [(Graph Curves Msri)] TJ ET
BT 34.016 717.365 Td /F1 12.8 Tf [(Yeah, reviewing a books )] TJ ET
BT 176.459 717.365 Td /F1 12.8 Tf [(Graph Curves Msri)] TJ ET
BT 283.431 717.365 Td /F1 12.8 Tf [( could increase your close connections listings. )] TJ ET
BT 34.016 701.797 Td /F1 12.8 Tf [(This is just one of the solutions for you to be successful. As understood, attainment does not )] TJ ET
BT 34.016 686.229 Td /F1 12.8 Tf [(recommend that you have extraordinary points. )] TJ ET
BT 34.016 655.361 Td /F1 12.8 Tf [(Comprehending as well as deal even more than new will have enough money each )] TJ ET
BT 505.982 655.361 Td /F1 12.8 Tf [(success. )] TJ ET
BT 34.016 639.794 Td /F1 12.8 Tf [(adjacent to, the publication as skillfully as perspicacity of this Graph Curves Msri can be )] TJ ET
BT 34.016 624.226 Td /F1 12.8 Tf [(taken as skillfully as picked to act.)] TJ ET
BT 34.016 567.858 Td /F1 12.8 Tf [(Mathematics of Surfaces)] TJ ET
BT 174.317 567.858 Td /F1 12.8 Tf [( England\) Ima Conference on the Mathematics of Surfaces 2003 )] TJ ET
BT 34.016 552.290 Td /F1 12.8 Tf [(\(Leeds 2003-09-09 This book constitutes the refereed proceedings of the 10th IMA )] TJ ET
BT 34.016 536.723 Td /F1 12.8 Tf [(International Conference on the Mathematics of Surfaces, held in Leeds, UK in September )] TJ ET
BT 34.016 521.155 Td /F1 12.8 Tf [(2003. The 25 revised full papers presented were carefully reviewed and selected from )] TJ ET
BT 34.016 505.587 Td /F1 12.8 Tf [(numerous submissions. Among the topics addressed are triangulated surface )] TJ ET
BT 34.016 490.019 Td /F1 12.8 Tf [(parameterization, bifurcation structures, control vertex computation, polyhedral surfaces, )] TJ ET
BT 34.016 474.452 Td /F1 12.8 Tf [(watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, vector )] TJ ET
BT 34.016 458.884 Td /F1 12.8 Tf [(transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the )] TJ ET
BT 34.016 443.316 Td /F1 12.8 Tf [(Plateau-Bezier problem, spline geometry, generative geometry, manifold representation, )] TJ ET
BT 34.016 427.748 Td /F1 12.8 Tf [(affine arithmetic, and PDE surfaces.)] TJ ET
BT 34.016 412.181 Td /F1 12.8 Tf [(Symmetry in Graph Theory)] TJ ET
BT 187.054 412.181 Td /F1 12.8 Tf [( Jose M. Rodriguez 2019-03-14 This book contains the )] TJ ET
BT 34.016 396.613 Td /F1 12.8 Tf [(successful invited submissions to a Special Issue of Symmetry on the subject of “Graph )] TJ ET
BT 34.016 381.045 Td /F1 12.8 Tf [(Theory”. Although symmetry has always played an important role in Graph Theory, in recent )] TJ ET
BT 34.016 365.477 Td /F1 12.8 Tf [(years, this role has increased significantly in several branches of this field, including but not )] TJ ET
BT 34.016 349.910 Td /F1 12.8 Tf [(limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and )] TJ ET
BT 34.016 334.342 Td /F1 12.8 Tf [(topological indices. This Special Issue includes contributions addressing new results on )] TJ ET
BT 34.016 318.774 Td /F1 12.8 Tf [(these topics, both from a theoretical and an applied point of view.)] TJ ET
BT 34.016 303.206 Td /F1 12.8 Tf [(Computational Topology)] TJ ET
BT 172.200 303.206 Td /F1 12.8 Tf [( Herbert Edelsbrunner 2010 Combining concepts from topology and )] TJ ET
BT 34.016 287.639 Td /F1 12.8 Tf [(algorithms, this book delivers what its title promises: an introduction to the field of )] TJ ET
BT 34.016 272.071 Td /F1 12.8 Tf [(computational topology. Starting with motivating problems in both mathematics and )] TJ ET
BT 34.016 256.503 Td /F1 12.8 Tf [(computer science and building up from classic topics in geometric and algebraic topology, )] TJ ET
BT 34.016 240.935 Td /F1 12.8 Tf [(the third part of the text advances to persistent homology. This point of view is critically )] TJ ET
BT 34.016 225.368 Td /F1 12.8 Tf [(important in turning a mostly theoretical field of mathematics into one that is relevant to a )] TJ ET
BT 34.016 209.800 Td /F1 12.8 Tf [(multitude of disciplines in the sciences and engineering. The main approach is the discovery )] TJ ET
BT 34.016 194.232 Td /F1 12.8 Tf [(of topology through algorithms. The book is ideal for teaching a graduate or advanced )] TJ ET
BT 34.016 178.664 Td /F1 12.8 Tf [(undergraduate course in computational topology, as it develops all the background of both )] TJ ET
BT 34.016 163.097 Td /F1 12.8 Tf [(the mathematical and algorithmic aspects of the subject from first principles. Thus the text )] TJ ET
BT 34.016 147.529 Td /F1 12.8 Tf [(could serve equally well in a course taught in a mathematics department or computer )] TJ ET
BT 34.016 131.961 Td /F1 12.8 Tf [(science department.)] TJ ET
BT 34.016 116.393 Td /F1 12.8 Tf [(Introduction to Functional Equations)] TJ ET
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BT 237.416 116.393 Td /F1 12.8 Tf [( Costas Efthimiou 2011-10-13 Functions and their )] TJ ET
BT 34.016 100.826 Td /F1 12.8 Tf [(properties have been part of the rigorous precollege curriculum for decades. And functional )] TJ ET
BT 34.016 85.258 Td /F1 12.8 Tf [(equations have been a favorite topic of the leading national and international mathematical )] TJ ET
BT 34.016 69.690 Td /F1 12.8 Tf [(competitions. Yet the subject has not received equal attention by authors at an introductory )] TJ ET
BT 34.016 54.122 Td /F1 12.8 Tf [(level. The majority of the books on the topic remain unreachable to the curious and )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(intelligent precollege student. The present book is an attempt to eliminate this disparity. The )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(book opens with a review chapter on functions, which collects the relevant foundational )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(information on functions, plus some material potentially new to the reader. The next chapter )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(presents a working definition of functional equations and explains the difficulties in trying to )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(systematize the theory. With each new chapter, the author presents methods for the solution )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(of a particular group of equations. Each chapter is complemented with many solved )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(examples, the majority of which are taken from mathematical competitions and professional )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(journals. The book ends with a chapter of unsolved problems and some other auxiliary )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(material. The book is an invaluable resource for precollege and college students who want to )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(deepen their knowledge of functions and their properties, for teachers and instructors who )] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(In the interest of fostering a greater awareness and appreciation of mathematics and its )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(connections to other disciplines and everyday life, MSRI and the AMS are publishing books )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(in the Mathematical Circles Library series as a service to young people, their parents and )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(teachers, and the mathematics profession.)] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(Trends in Commutative Algebra)] TJ ET
BT 213.281 561.904 Td /F1 12.8 Tf [( Luchezar L. Avramov 2004-12-13 In 2002, an introductory )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(workshop was held at the Mathematical Sciences Research Institute in Berkeley to survey )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(some of the many directions of the commutative algebra field. Six principal speakers each )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(gave three lectures, accompanied by a help session, describing the interaction of )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(commutative algebra with other areas of mathematics for a broad audience of graduate )] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(students and researchers. This book is based on those lectures, together with papers from )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(contributing researchers. David Benson and Srikanth Iyengar present an introduction to the )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(uses and concepts of commutative algebra in the cohomology of groups. Mark Haiman )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(considers the commutative algebra of n points in the plane. Ezra Miller presents an )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(introduction to the Hilbert scheme of points to complement Professor Haiman's paper. )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(Further contributors include David Eisenbud and Jessica Sidman; Melvin Hochster; Graham )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(Leuschke; Rob Lazarsfeld and Manuel Blickle; Bernard Teissier; and Ana Bravo.)] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(Lectures on Spaces of Nonpositive Curvature)] TJ ET
BT 290.546 375.091 Td /F1 12.8 Tf [( Werner Ballmann 1995-09-01 Singular spaces )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(of interest in many fields, including geometric \(and combinatorial\) group theory, topology, )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(dynamical systems and probability theory. In the first two chapters of the book, a concise )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(discussion of the ideal boundary at infinity for simply connected complete spaces of )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on )] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(geodesically complete spaces of nonpositive curvature are discussed, as are random walks )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(on groups of isometries of nonpositively curved spaces. The main class of spaces )] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(considered should be precisely complementary to symmetric spaces of higher rank and )] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(Euclidean buildings of dimension at least two \(Rank Rigidity conjecture\). In the smooth case, )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(this is known and is the content of the Rank Rigidity theorem. An updated version of the )] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(proof of the latter theorem \(in the smooth case\) is presented in Chapter IV of the book. This )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(chapter contains also a short introduction into the geometry of the unit tangent bundle of a )] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(Riemannian manifold of negative curvature is given. The proof is elementary and should be )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(accessible to the non-specialist. Some of the essential features and problems of the ergodic )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(theory of smooth dynamical systems are discussed, and the appendix can serve as an )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(introduction into this theory.)] TJ ET
BT 34.016 63.736 Td /F1 12.8 Tf [(Tensor Categories)] TJ ET
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BT 138.884 63.736 Td /F1 12.8 Tf [( Pavel Etingof 2016-08-05 Is there a vector space whose dimension is the )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(golden ratio? Of course not—the golden ratio is not an integer! But this can happen for )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(generalizations of vector spaces—objects of a tensor category. The theory of tensor )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(categories is a relatively new field of mathematics that generalizes the theory of group )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(representations. It has deep connections with many other fields, including representation )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(theory, Hopf algebras, operator algebras, low-dimensional topology \(in particular, knot )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(theory\), homotopy theory, quantum mechanics and field theory, quantum computation, )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(theory of motives, etc. This book gives a systematic introduction to this theory and a review )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(of its applications. While giving a detailed overview of general tensor categories, it focuses )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(especially on the theory of finite tensor categories and fusion categories \(in particular, )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(braided and modular ones\), and discusses the main results about them with proofs. In )] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(particular, it shows how the main properties of finite-dimensional Hopf algebras may be )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(derived from the theory of tensor categories. Many important results are presented as a )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(sequence of exercises, which makes the book valuable for students and suitable for )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(graduate courses. Many applications, connections to other areas, additional results, and )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(references are discussed at the end of each chapter.)] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(A Decade of the Berkeley Math Circle)] TJ ET
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34.016 559.800 m 246.596 559.800 l S
BT 246.596 561.904 Td /F1 12.8 Tf [( Zvezdelina Stankova 2008-11-26 Many )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(mathematicians have been drawn to mathematics through their experience with math circles: )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(extracurricular programs exposing teenage students to advanced mathematical topics and a )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(myriad of problem solving techniques and inspiring in them a lifelong love for mathematics. )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(Founded in 1998, the Berkeley Math Circle \(BMC\) is a pioneering model of a U.S. math )] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(circle, aspiring to prepare our best young minds for their future roles as mathematics )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(leaders. Over the last decade, 50 instructors--from university professors to high school )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(teachers to business tycoons--have shared their passion for mathematics by delivering more )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(than 320 BMC sessions full of mathematical challenges and wonders. Based on a dozen of )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(these sessions, this book encompasses a wide variety of enticing mathematical topics: from )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(inversion in the plane to circle geometry; from combinatorics to Rubik's cube and abstract )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(algebra; from number theory to mass point theory; from complex numbers to game theory )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(via invariants and monovariants. The treatments of these subjects encompass every )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(significant method of proof and emphasize ways of thinking and reasoning via 100 problem )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(solving techniques. Also featured are 300 problems, ranging from beginner to intermediate )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(level, with occasional peaks of advanced problems and even some open questions. The )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(book presents possible paths to studying mathematics and inevitably falling in love with it, )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(via teaching two important skills: thinking creatively while still ``obeying the rules,'' and )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(making connections between problems, ideas, and theories. The book encourages you to )] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(apply the newly acquired knowledge to problems and guides you along the way, but rarely )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(gives you ready answers. ``Learning from our own mistakes'' often occurs through )] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(discussions of non-proofs and common problem solving pitfalls. The reader has to commit to )] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(mastering the new theories and techniques by ``getting your hands dirty'' with the problems, )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(going back and reviewing necessary problem solving techniques and theory, and persistently )] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(moving forward in the book. The mathematical world is huge: you'll never know everything, )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(but you'll learn where to find things, how to connect and use them. The rewards will be )] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(substantial. In the interest of fostering a greater awareness and appreciation of mathematics )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(and its connections to other disciplines and everyday life, MSRI and the AMS are publishing )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(books in the Mathematical Circles Library series as a service to young people, their parents )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(and teachers, and the mathematics profession.)] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(Algebraic Statistics for Computational Biology)] TJ ET
BT 291.234 94.871 Td /F1 12.8 Tf [( L. Pachter 2005-08-22 This book, first )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(published in 2005, offers an introduction to the application of algebraic statistics to )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(computational biology.)] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(Introduction to Tropical Geometry)] TJ ET
0.255 w 0 J [ ] 0 d
34.016 777.749 m 223.213 777.749 l S
BT 223.213 779.852 Td /F1 12.8 Tf [( Diane Maclagan 2021-12-13 Tropical geometry is a )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(invariants of algebraic varieties. It is based on tropical algebra, where the sum of two )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(numbers is their minimum and the product is their sum. This turns polynomials into )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(varieties retain a surprising amount of information about their classical counterparts. Tropical )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(geometry is a young subject that has undergone a rapid development since the beginning of )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(the 21st century. While establishing itself as an area in its own right, deep connections have )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(been made to many branches of pure and applied mathematics. This book offers a self-)] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(contained introduction to tropical geometry, suitable as a course text for beginning graduate )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(students. Proofs are provided for the main results, such as the Fundamental Theorem and )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(the Structure Theorem. Numerous examples and explicit computations illustrate the main )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(concepts. Each of the six chapters concludes with problems that will help the readers to )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(practice their tropical skills, and to gain access to the research literature. This wonderful )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(book will appeal to students and researchers of all stripes: it begins at an undergraduate )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(level and ends with deep connections to toric varieties, compactifications, and )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(degenerations. In between, the authors provide the first complete proofs in book form of )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(many fundamental results in the subject. The pages are sprinkled with illuminating examples, )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare )] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(kind of book which will be used equally as an introductory text by students and as a )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(exciting new field, which requires tools from various parts of mathematics and has )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(connections with many areas. A short definition is given by Maclagan and Sturmfels: )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(“Tropical geometry is a marriage between algebraic and polyhedral geometry”. This )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(wonderful book is a pleasant and rewarding journey through different landscapes, inviting )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(the readers from a day at a beach to the hills of modern algebraic geometry. The authors )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(present building blocks, examples and exercises as well as recent results in tropical )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(geometry and algebraic geometry. The volume will appeal both to beginning graduate )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(University of Buenos Aires, Argentina)] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(Computations in Algebraic Geometry with Macaulay 2)] TJ ET
BT 337.287 297.252 Td /F1 12.8 Tf [( David Eisenbud 2013-03-14 This book )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(presents algorithmic tools for algebraic geometry, with experimental applications. It also )] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(introduces Macaulay 2, a computer algebra system supporting research in algebraic )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(geometry, commutative algebra, and their applications. The algorithmic tools presented here )] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(are designed to serve readers wishing to bring such tools to bear on their own problems. The )] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(first part of the book covers Macaulay 2 using concrete applications; the second emphasizes )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(details of the mathematics.)] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(Rational Points on Modular Elliptic Curves)] TJ ET
BT 271.382 188.278 Td /F1 12.8 Tf [( Henri Darmon 2004 The book surveys some )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(recent developments in the arithmetic of modular elliptic curves. It places a special emphasis )] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(conjecture, and the crucial role played by modularity in shedding light on these two closely )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(related issues. The main theme of the book is the theory of complex multiplication, Heegner )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(points, and some conjectural variants. The first three chapters introduce the background and )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(complex multiplication and the Heegner point construction. The next three chapters )] TJ ET
BT 34.016 63.736 Td /F1 12.8 Tf [(introduce variants of modular parametrizations in which modular curves are replaced by )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(Shimura curves attached to certain indefinite quaternion algebras. The main new )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(contributions are found in Chapters 7-9, which survey the author's attempts to extend the )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(theory of Heegner points and complex multiplication to situations where the base field is not )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(points to the arithmetic of elliptic curves and leads to the so-far best evidence for the Birch )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(and Swinnerton-Dyer conjecture.)] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(The Mathematics of Data)] TJ ET
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34.016 699.910 m 176.446 699.910 l S
BT 176.446 702.014 Td /F1 12.8 Tf [( Michael W. Mahoney 2018-11-15 Nothing provided)] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(Current Developments in Algebraic Geometry)] TJ ET
BT 291.221 686.446 Td /F1 12.8 Tf [( Lucia Caporaso 2012-03-19 This volume, )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(based on a workshop by the MSRI, offers an overview of the state of the art in many areas )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(of algebraic geometry.)] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(Tropical Geometry and Mirror Symmetry)] TJ ET
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34.016 637.639 m 261.425 637.639 l S
BT 261.425 639.743 Td /F1 12.8 Tf [( Mark Gross 2011-01-20 Tropical geometry provides )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(an explanation for the remarkable power of mirror symmetry to connect complex and )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(symplectic geometry. The main theme of this book is the interplay between tropical geometry )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(and mirror symmetry, culminating in a description of the recent work of Gross and Siebert )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(using log geometry to understand how the tropical world relates the A- and B-models in )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(and manifolds, and then gives a thorough description of both sides of mirror symmetry for )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(projective space, bringing together material which so far can only be found scattered )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting )] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(mirror, B-model side, giving recent results of the author showing how tropical geometry can )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(be used to evaluate the oscillatory integrals appearing. The final chapter surveys )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(version of the argument is given in two dimensions.)] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(Birational Geometry and Moduli Spaces)] TJ ET
BT 258.645 406.226 Td /F1 12.8 Tf [( Elisabetta Colombo 2020-02-25 This volume )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(collects contributions from speakers at the INdAM Workshop “Birational Geometry and )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(to the interplay between birational geometry and moduli spaces and the contributions of the )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(volume reflect the same idea, focusing on both these areas and their interaction. In )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(particular, the book includes both surveys and original papers on irreducible holomorphic )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(principle, birational transformations, and deformations of diagrams of algebras. The intention )] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(is to disseminate the knowledge of advanced results and key techniques used to solve open )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(problems. The book is intended for all advanced graduate students and researchers )] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(interested in the new research frontiers of birational geometry and moduli spaces.)] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(Flavors of Geometry)] TJ ET
BT 149.505 219.413 Td /F1 12.8 Tf [( Silvio Levy 1997-09-28 Lectures on hyperbolic geometry, dynamics in )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(several complex variables, convex geometry, and volume estimation.)] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(Math from Three to Seven)] TJ ET
BT 182.120 188.278 Td /F1 12.8 Tf [( Aleksandr Kalmanovich Zvonkin 2011 This book is a captivating )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(account of a professional mathematician's experiences conducting a math circle for )] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(young children knows, mathematical education for little kids is a real mystery. What are they )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(capable of? What should they learn first? How hard should they work? Should they even )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [("work" at all? Should we push them, or just let them be? There are no correct answers to )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(these questions, and the author deals with them in classic math-circle style: he doesn't ask )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(and then answer a question, but shows us a problem--be it mathematical or pedagogical--)] TJ ET
BT 34.016 63.736 Td /F1 12.8 Tf [(and describes to us what happened. His book is a narrative about what he did, what he tried, )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(what worked, what failed, but most important, what the kids experienced. This book does not )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(purport to show you how to create precocious high achievers. It is just one person's story )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(about things he tried with a half-dozen young children. Mathematicians, psychologists, )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(educators, parents, and everybody interested in the intellectual development in young )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(children will find this book to be an invaluable, inspiring resource. In the interest of fostering )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(a greater awareness and appreciation of mathematics and its connections to other )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(Circles Library series as a service to young people, their parents and teachers, and the )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(mathematics profession. Titles in this series are co-published with the Mathematical )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(Sciences Research Institute \(MSRI\).)] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(Differential and Symplectic Topology of Knots and Curves)] TJ ET
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34.016 637.639 m 359.982 637.639 l S
BT 359.982 639.743 Td /F1 12.8 Tf [( Serge Tabachnikov 1999 This )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(book presents a collection of papers on two related topics: topology of knots and knot-like )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(objects \(such as curves on surfaces\) and topology of Legendrian knots and links in 3-)] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(dimensional contact manifolds. Featured is the work of international experts in knot theory )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(\(quantum knot invariants, knot invariants of finite type\), in symplectic and contact topology, )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(and in singularity theory. The interplay of diverse methods from these fields makes this )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(particularly enticing feature of the volume is its international significance. The volume )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(successfully embodies a fine collaborative effort by worldwide experts from Belgium, France, )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(Germany, Israel, Japan, Poland, Russia, Sweden, the U.K., and the U.S.)] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(Critical Issues in Mathematics Education)] TJ ET
BT 262.878 484.065 Td /F1 12.8 Tf [( Bharath Sriraman 2009-06-01 The word "critical" in )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(the title of this collection has three meanings, all of which are relevant. One meaning, as )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(applied to a situation or problem, is "at a point of crisis". A second meaning is "expressing )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(adverse or disapproving comments or judgments". A third is related to the verb "to critique", )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(meaning "to analyze the merits and faults of". The authors contributing to this book pose )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(challenging questions, from multiple perspectives, about the roles of mathematics in society )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(and the implications for education. Traditional reasons for teaching mathematics include: )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(preparing a new generation of mathematics researchers and a cadre of technically )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(competent users of mathematics; training students to think logically; and because )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(mathematics is as much part of cultural heritage as literature or music. These reasons )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(remain valid, though open to critique, but a deeper analysis is required that recognizes the )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(roles of mathematics in framing many aspects of contemporary society, that will connect )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(mathematics education to the lived experiences of students, their communities, and society )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(in general, and that acknowledges the global ethical responsibilities of mathematicians and )] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(mathematics educators. The book is organized in four sections \(1\) Mathematics education: )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(For what and why? \(2\) Globalization and cultural diversity, \(3\) Mathematics, education, and )] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(society and \(4\) Social justice in, and through, mathematics education The chapters address )] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(fundamental issues such as the relevance of school mathematics in people's lives; creating )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(a sense of agency for the field of mathematics education, and redefining the relationship )] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(between mathematics as discipline, mathematics as school subject and mathematics as part )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(of people's lives.)] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(Experimental Mathematics)] TJ ET
BT 184.223 157.142 Td /F1 12.8 Tf [( V. I. Arnold 2015-07-14 One of the traditional ways mathematical )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(ideas and even new areas of mathematics are created is from experiments. One of the best-)] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(creation of a whole field of knowledge, but it was proved only after several hundred years. )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(This book, based on the author's lectures, presents several new directions of mathematical )] TJ ET
BT 34.016 63.736 Td /F1 12.8 Tf [(research. All of these directions are based on numerical experiments conducted by the )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(author, which led to new hypotheses that currently remain open, i.e., are neither proved nor )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(disproved. The hypotheses range from geometry and topology \(statistics of plane curves and )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(smooth functions\) to combinatorics \(combinatorial complexity and random permutations\) to )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(algebra and number theory \(continuous fractions and Galois groups\). For each subject, the )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(author describes the problem and presents numerical results that led him to a particular )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(conjecture. In the majority of cases there is an indication of how the readers can approach )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(the formulated conjectures \(at least by conducting more numerical experiments\). Written in )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(Arnold's unique style, the book is intended for a wide range of mathematicians, from high )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(school students interested in exploring unusual areas of mathematics on their own, to )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(college and graduate students, to researchers interested in gaining a new, somewhat )] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(nontraditional perspective on doing mathematics. In the interest of fostering a greater )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(awareness and appreciation of mathematics and its connections to other disciplines and )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(series as a service to young people, their parents and teachers, and the mathematics )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(profession. Titles in this series are co-published with the Mathematical Sciences Research )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(Institute \(MSRI\).)] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(Three-dimensional Geometry and Topology)] TJ ET
BT 279.899 546.336 Td /F1 12.8 Tf [( WILLIAM P AUTOR THURSTON 1997 Every )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(mathematician should be acquainted with the basic facts about the geometry of surfaces, of )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(and still only partly understood, although there is ample evidence that the theory of three-)] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(dimensional manifolds is one of the most beautiful in the whole of mathematics. This )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(excellent introductory work makes this mathematical wonderland remained rather )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(inaccessible to non-specialists. The author is both a leading researcher, with a formidable )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(appeals to intuition, but his enthusiasm is infectious and should make many converts for this )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(kind of mathematics. There are good pictures, plenty of exercises and problems, and the )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(reader will find a selection of topics which are not found in the standard repertoire. This book )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(contains a great deal of interesting mathematics.)] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(Complex Algebraic Curves)] TJ ET
BT 184.925 343.955 Td /F1 12.8 Tf [( Frances Clare Kirwan 1992-02-20 This development of the )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(They have many fascinating properties and arise in various areas of mathematics, from )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(number theory to theoretical physics, and are the subject of much research. By using only )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan )] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(introduces the theory, observes the algebraic and topological properties of complex )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(algebraic curves, and shows how they are related to complex analysis.)] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(The Mathematics of Chip-Firing)] TJ ET
BT 211.853 234.981 Td /F1 12.8 Tf [( Caroline J. Klivans 2018-11-15 The Mathematics of Chip-)] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(firing is a solid introduction and overview of the growing field of chip-firing. It offers an )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete )] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(dynamical system — a commodity is exchanged between sites of a network according to )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(very simple local rules. Although governed by local rules, the long-term global behavior of )] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(the system reveals fascinating properties. The Fundamental properties of chip-firing are )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(covered from a variety of perspectives. This gives the reader both a broad context of the )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(field and concrete entry points from different backgrounds. Broken into two sections, the first )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(examines the fundamentals of chip-firing, while the second half presents more general )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(frameworks for chip-firing. Instructors and students will discover that this book provides a )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(comprehensive background to approaching original sources. Features: Provides a broad )] TJ ET
BT 34.016 63.736 Td /F1 12.8 Tf [(introduction for researchers interested in the subject of chip-firing The text includes historical )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(and current perspectives Exercises included at the end of each chapter About the Author: )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(Applied Mathematics at Brown University. She is also an Associate Director of ICERM )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(\(Institute for Computational and Experimental Research in Mathematics\). Before coming to )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(algebraic, geometric and topological combinatorics.)] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(Why Johnny Can't Add)] TJ ET
BT 163.301 686.446 Td /F1 12.8 Tf [( Morris Kline 1974 Briefly discusses the traditional mathematics )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(formerly taught in American schools and views the language and weaknesses of the modern )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(math curriculum)] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(Real Analysis and Foundations, Fourth Edition)] TJ ET
BT 296.219 639.743 Td /F1 12.8 Tf [( Steven G. Krantz 2016-12-12 A Readable yet )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(Rigorous Approach to an Essential Part of Mathematical Thinking Back by popular demand, )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(texts and less rigorous ones, providing a smooth transition from logic and proofs to real )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(analysis, metric spaces and applications, and differential equations. New to the Third Edition )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(Offering a more streamlined presentation, this edition moves elementary number systems )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(and set theory and logic to appendices and removes the material on wavelet theory, )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(measure theory, differential forms, and the method of characteristics. It also adds a chapter )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(on normed linear spaces and includes more examples and varying levels of exercises. )] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding This )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(best-selling book continues to give students a solid foundation in mathematical analysis and )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(its applications. It prepares them for further exploration of measure theory, functional )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(analysis, harmonic analysis, and beyond.)] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(Testimonios: Stories of Latinx and Hispanic Mathematicians)] TJ ET
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BT 371.304 421.794 Td /F1 12.8 Tf [( Pamela E. Harris 2021-08-16 )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(Testimonios brings together first-person narratives from the vibrant, diverse, and complex )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(Latinx and Hispanic mathematical community. Starting with childhood and family, the authors )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(recount their own individual stories, highlighting their upbringing, education, and career )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(paths. Their particular stories, told in their own voices, from their own perspectives, give )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(visibility to some of the experiences of Latinx/Hispanic mathematicians. Testimonios seeks )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(to inspire the next generation of Latinx and Hispanic mathematicians by featuring the stories )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(of people like them, holding a mirror up to our own community. It also aims to provide a )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(window for mathematicians \(and aspiring mathematicians\) from all ethnicities, with the hope )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(of inspiring a better understanding of the diversity of the mathematical community.)] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(Evolution Equations)] TJ ET
BT 146.700 266.117 Td /F1 12.8 Tf [( David Ellwood 2013-06-26 This volume is a collection of notes from )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, )] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(Switzerland. The lectures were designed for graduate students and mathematicians within )] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(five years of the Ph.D., and the main focus of the program was on recent progress in the )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(theory of evolution equations. Such equations lie at the heart of many areas of mathematical )] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(physics and arise not only in situations with a manifest time evolution \(such as linear and )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(nonlinear wave and Schrödinger equations\) but also in the high energy or semi-classical )] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(limits of elliptic problems. The three main courses focused primarily on microlocal analysis )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(equations, and evolution problems in general relativity. These major topics were )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(supplemented by several mini-courses reporting on the derivation of effective evolution )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(equations from microscopic quantum dynamics; on wave maps with and without symmetries; )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear )] TJ ET
BT 34.016 63.736 Td /F1 12.8 Tf [(Schrödinger equations at critical regularity. Although highly detailed treatments of some of )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(these topics are now available in the published literature, in this collection the reader can )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(treatment in this volume emphasizes common themes and techniques in the field, including )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(exact and approximate conservation laws, energy methods, and positive commutator )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(arguments. Titles in this series are co-published with the Clay Mathematics Institute )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(\(Cambridge, MA\).)] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(The Shape of Inner Space)] TJ ET
BT 182.859 702.014 Td /F1 12.8 Tf [( Shing-Tung Yau 2010 Argues that geometry is fundamental to )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(string theory--which posits that we live in a 10-dimensional existence--as well as the very )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(nature of the universe, and explains where mathematics will take string theory next.)] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(Persistence Theory: From Quiver Representations to Data Analysis)] TJ ET
BT 413.813 655.310 Td /F1 12.8 Tf [( Steve Y. Oudot 2017-05-)] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(17 Persistence theory emerged in the early 2000s as a new theory in the area of applied and )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(computational topology. This book provides a broad and modern view of the subject, )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(including its algebraic, topological, and algorithmic aspects. It also elaborates on applications )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(in data analysis. The level of detail of the exposition has been set so as to keep a survey )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(style, while providing sufficient insights into the proofs so the reader can understand the )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(mechanisms at work. The book is organized into three parts. The first part is dedicated to the )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(foundations of persistence and emphasizes its connection to quiver representation theory. )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(The second part focuses on its connection to applications through a few selected topics. The )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(third part provides perspectives for both the theory and its applications. The book can be )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(used as a text for a course on applied topology or data analysis.)] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(Dynamics and Randomness)] TJ ET
BT 193.442 484.065 Td /F1 12.8 Tf [( Alejandro Maass 2012-12-06 This book contains the lectures )] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(brought together mathematicians, theoretical physicists and theoretical computer scientists, )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(and graduate students interested in fields re lated to probability theory, ergodic theory, )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(symbolic and topological dynam ics. We would like to express our gratitude to all the )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(participants of the con ference and to the people who contributed to its organization. In )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(to thank especially the authors of each chapter for their well prepared manuscripts and the )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(stimulating conferences they gave at Santiago. We are also indebted to our sponsors and )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(supporting institutions, whose interest and help was essential to organize this meeting: )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(Gladys Cavallone for their excellent work during the preparation of the meeting as well as for )] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(the considerable task of unifying the typography of the different chapters of this book.)] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(Mathematical Writing)] TJ ET
BT 153.037 250.549 Td /F1 12.8 Tf [( Donald E. Knuth 1989 This book will help those wishing to teach a )] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(course in technical writing, or who wish to write themselves.)] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(Combinatorial and Computational Geometry)] TJ ET
BT 282.730 219.413 Td /F1 12.8 Tf [( cob E. Goodman 2005-08-08 This 2005 book )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(deals with interest topics in Discrete and Algorithmic aspects of Geometry.)] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(A Guide to Real Variables)] TJ ET
BT 180.704 188.278 Td /F1 12.8 Tf [( Steven G. Krantz 2009-08-13 The purpose of A Guide to Real )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(Variables is to provide an aid and conceptual support for the student studying for the )] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(qualifying exam in real variables. Beginning with the foundations of the subject, the text )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(moves rapidly but thoroughly through basic topics like completeness, convergence, )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(sequences, series, compactness, topology and the like. All the basic examples like the )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated.The book )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(contains over 100 examples, and most of the basic proofs. It illustrates both the theory and )] TJ ET
BT 34.016 63.736 Td /F1 12.8 Tf [(the practice of this sophisticated subject. Graduate students studying for the qualifying )] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(exams will find this book to be a concise, focused and informative resource. Professional )] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(mathematicians who need a quick review of the subject, or need a place to look up a key )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(fact, will find this book to be a useful resource too.)] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(Exterior Differential Systems)] TJ ET
BT 194.844 748.717 Td /F1 12.8 Tf [( Robert L. Bryant 2013-06-29 This book gives a treatment of )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(exterior differential systems. It will in clude both the general theory and various applications. )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(An exterior differential system is a system of equations on a manifold defined by equating to )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(zero a number of exterior differential forms. When all the forms are linear, it is called a )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(the equations of the system. A fundamental fact is that every equation implies the one )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(obtained by exterior differentiation, so that the complete set of equations associated to an )] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(exterior differential system constitutes a differential ideal in the algebra of all smooth forms. )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(Thus the theory is coordinate-free and computations typically have an algebraic character; )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(however, even when coordinates are used in intermediate steps, the use of exterior algebra )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(helps to efficiently guide the computations, and as a consequence the treatment adapts well )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(to geometrical and physical problems. A system of partial differential equations, with any )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(number of inde pendent and dependent variables and involving partial derivatives of any )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(order, can be written as an exterior differential system. In this case we are interested in )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(integral manifolds on which certain coordinates remain independent. The corresponding )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(notion in exterior differential systems is the independence condition: certain pfaffian forms )] TJ ET
BT 34.016 499.633 Td /F1 12.8 Tf [(remain linearly indepen dent. Partial differential equations and exterior differential systems )] TJ ET
BT 34.016 484.065 Td /F1 12.8 Tf [(with an independence condition are essentially the same object.)] TJ ET
BT 34.016 468.497 Td /F1 12.8 Tf [(Analytic Combinatorics)] TJ ET
BT 163.670 468.497 Td /F1 12.8 Tf [( Philippe Flajolet 2009-01-15 Analytic combinatorics aims to enable )] TJ ET
BT 34.016 452.930 Td /F1 12.8 Tf [(precise quantitative predictions of the properties of large combinatorial structures. The theory )] TJ ET
BT 34.016 437.362 Td /F1 12.8 Tf [(has emerged over recent decades as essential both for the analysis of algorithms and for the )] TJ ET
BT 34.016 421.794 Td /F1 12.8 Tf [(study of scientific models in many disciplines, including probability theory, statistical physics, )] TJ ET
BT 34.016 406.226 Td /F1 12.8 Tf [(computational biology, and information theory. With a careful combination of symbolic )] TJ ET
BT 34.016 390.659 Td /F1 12.8 Tf [(enumeration methods and complex analysis, drawing heavily on generating functions, )] TJ ET
BT 34.016 375.091 Td /F1 12.8 Tf [(results of sweeping generality emerge that can be applied in particular to fundamental )] TJ ET
BT 34.016 359.523 Td /F1 12.8 Tf [(structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. )] TJ ET
BT 34.016 343.955 Td /F1 12.8 Tf [(This account is the definitive treatment of the topic. The authors give full coverage of the )] TJ ET
BT 34.016 328.388 Td /F1 12.8 Tf [(underlying mathematics and a thorough treatment of both classical and modern applications )] TJ ET
BT 34.016 312.820 Td /F1 12.8 Tf [(of the theory. The text is complemented with exercises, examples, appendices and notes to )] TJ ET
BT 34.016 297.252 Td /F1 12.8 Tf [(aid understanding. The book can be used for an advanced undergraduate or a graduate )] TJ ET
BT 34.016 281.684 Td /F1 12.8 Tf [(course, or for self-study.)] TJ ET
BT 34.016 266.117 Td /F1 12.8 Tf [(Steps in Commutative Algebra)] TJ ET
BT 206.204 266.117 Td /F1 12.8 Tf [( R. Y. Sharp 2000 Introductory account of commutative )] TJ ET
BT 34.016 250.549 Td /F1 12.8 Tf [(algebra, aimed at students with a background in basic algebra.)] TJ ET
BT 34.016 234.981 Td /F1 12.8 Tf [(Differential Geometry of Curves and Surfaces)] TJ ET
BT 291.234 234.981 Td /F1 12.8 Tf [( Victor Andreevich Toponogov 2006-09-10 )] TJ ET
BT 34.016 219.413 Td /F1 12.8 Tf [(Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the )] TJ ET
BT 34.016 203.846 Td /F1 12.8 Tf [(Alexandrov global angle comparision theorem Many nontrivial and original problems \(some )] TJ ET
BT 34.016 188.278 Td /F1 12.8 Tf [(with hints and solutions\) Standard theoretical material is combined with more difficult )] TJ ET
BT 34.016 172.710 Td /F1 12.8 Tf [(theorems and complex problems, while maintaining a clear distinction between the two levels)] TJ ET
BT 34.016 157.142 Td /F1 12.8 Tf [(Tropical Algebraic Geometry)] TJ ET
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BT 195.558 157.142 Td /F1 12.8 Tf [( Ilia Itenberg 2009-05-30 These notes present a polished )] TJ ET
BT 34.016 141.575 Td /F1 12.8 Tf [(introduction to tropical geometry and contain some applications of this rapidly developing )] TJ ET
BT 34.016 126.007 Td /F1 12.8 Tf [(and attractive subject. It consists of three chapters which complete each other and give a )] TJ ET
BT 34.016 110.439 Td /F1 12.8 Tf [(possibility for non-specialists to make the first steps in the subject which is not yet well )] TJ ET
BT 34.016 94.871 Td /F1 12.8 Tf [(represented in the literature. The notes are based on a seminar at the Mathematical )] TJ ET
BT 34.016 79.304 Td /F1 12.8 Tf [(Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-)] TJ ET
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BT 34.016 795.420 Td /F1 12.8 Tf [(graduate, and Ph.D. students as well as established researchers in mathematics.)] TJ ET
BT 34.016 779.852 Td /F1 12.8 Tf [(Bounded Cohomology of Discrete Groups)] TJ ET
BT 269.993 779.852 Td /F1 12.8 Tf [( Roberto Frigerio 2017-11-21 The theory of )] TJ ET
BT 34.016 764.285 Td /F1 12.8 Tf [(bounded cohomology, introduced by Gromov in the late 1980s, has had powerful )] TJ ET
BT 34.016 748.717 Td /F1 12.8 Tf [(applications in geometric group theory and the geometry and topology of manifolds, and has )] TJ ET
BT 34.016 733.149 Td /F1 12.8 Tf [(been the topic of active research continuing to this day. This monograph provides a unified, )] TJ ET
BT 34.016 717.581 Td /F1 12.8 Tf [(self-contained introduction to the theory and its applications, making it accessible to a )] TJ ET
BT 34.016 702.014 Td /F1 12.8 Tf [(student who has completed a first course in algebraic topology and manifold theory. The )] TJ ET
BT 34.016 686.446 Td /F1 12.8 Tf [(book can be used as a source for research projects for master's students, as a thorough )] TJ ET
BT 34.016 670.878 Td /F1 12.8 Tf [(introduction to the field for graduate students, and as a valuable landmark text for )] TJ ET
BT 34.016 655.310 Td /F1 12.8 Tf [(researchers, providing both the details of the theory of bounded cohomology and links of the )] TJ ET
BT 34.016 639.743 Td /F1 12.8 Tf [(theory to other closely related areas. The first part of the book is devoted to settling the )] TJ ET
BT 34.016 624.175 Td /F1 12.8 Tf [(fundamental definitions of the theory, and to proving some of the \(by now classical\) results )] TJ ET
BT 34.016 608.607 Td /F1 12.8 Tf [(on low-dimensional bounded cohomology and on bounded cohomology of topological )] TJ ET
BT 34.016 593.039 Td /F1 12.8 Tf [(spaces. The second part describes applications of the theory to the study of the simplicial )] TJ ET
BT 34.016 577.472 Td /F1 12.8 Tf [(volume of manifolds, to the classification of circle actions, to the analysis of maximal )] TJ ET
BT 34.016 561.904 Td /F1 12.8 Tf [(representations of surface groups, and to the study of flat vector bundles with a particular )] TJ ET
BT 34.016 546.336 Td /F1 12.8 Tf [(emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. )] TJ ET
BT 34.016 530.768 Td /F1 12.8 Tf [(Each chapter ends with a discussion of further reading that puts the presented results in a )] TJ ET
BT 34.016 515.201 Td /F1 12.8 Tf [(broader context.)] TJ ET
BT 36.266 473.973 Td /F1 8.0 Tf [(graph-curves-msri)] TJ ET
BT 336.686 474.180 Td /F1 8.0 Tf [(Downloaded from )] TJ ET
BT 401.598 473.973 Td /F1 8.0 Tf [(tunaipsum.com)] TJ ET
BT 455.838 474.180 Td /F1 8.0 Tf [( on October 3, 2022 by guest)] TJ ET
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