This book covers thirty years of the Leningrad Mathematical Olympiad, which was, ostensibly, the very first formally organized, open, official city-level mathematical contest in the world. Founded in 1934 by a group of dedicated Soviet mathematicians, it played an outstanding (and often underappreciated) role in creating the Leningrad (St. Petersburg) school of mathematics of the 20th century.The book begins with the extensive introduction containing two prefaces (one of them written specifically for this edition), a large historical survey of the Leningrad Mathematical Olympiad, a section describing the logistical side of the contest, and a small chapter dedicated to the very first Mathematical Olympiad held in 1934, whose problems were recently found in the Soviet-era library archives.The main text contains approximately 1,100 highly original questions for students of grades 5 through 10 (ages 11-12 through 17-18) offered at the two concluding rounds of the Leningrad City Mathematics Olympiads in the years of 1961-1991. Full solutions, hints and answers are provided for all questions with very rare exceptions.It also includes 120 additional questions, offered at the various mathematical contests held in Leningrad over the same thirty-year period — on average, their difficulty is somewhat higher than that of the regular Mathematical Olympiad problems.

From climate change forecasts and pandemic maps to Lego sets and Ancestry algorithms, models encompass our world and our lives. In her thought-provoking new book, Annabel Wharton begins with a definition drawn from the quantitative sciences and the philosophy of science but holds that history and critical cultural theory are essential to a fuller understanding of modeling. Considering changes in the medical body model and the architectural model, from the Middle Ages to the twenty-first century, Wharton demonstrates the ways in which all models are historical and political. Examining how cadavers have been described, exhibited, and visually rendered, she highlights the historical dimension of the modified body and its depictions. Analyzing the varied reworkings of the Holy Sepulchre in Jerusalem-including by monumental commanderies of the Knights Templar, Alberti's Rucellai Tomb in Florence, Franciscans' olive wood replicas, and video game renderings-she foregrounds the political force of architectural representations. And considering black boxes-instruments whose inputs we control and whose outputs we interpret, but whose inner workings are beyond our comprehension-she surveys the threats posed by such opaque computational models, warning of the dangers that models pose when humans lose control of the means by which they are generated and understood. Engaging and wide-ranging, Models and World Making conjures new ways of seeing and critically evaluating how we make and remake the world in which we live.

This book and CD-ROM compile the most widely applicable methods for solving and approximating differential equations. The CD-ROM provides convenient access to these methods through electronic search capabilities, andtogether the book and CD-ROM contain numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.

* For nearly every technique, the book and CD-ROM provide:
* The types of equations to which the method is applicable
* The idea behind the method
* The procedure for carrying out the method
* At least one simple example of the method
* Any cautions that should be exercised
* Notes for more advanced users
* References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs

Data Prefetching Techniques in Computer Systems, Volume 125 provides an in-depth review of the latest progress on data prefetching research. Topics covered in this volume include temporal prefetchers, spatial prefetchers, non-spatial-temporal prefetchers, and evaluation of prefetchers, with insights on possible future research direction. Specific chapters in this release include Introduction to Data Prefetching, Spatial Prefetching Techniques, Temporal Prefetching Techniques, Domino prefetching scheme, Bingo prefetching method, and The Champion prefetcher.

Advances in Computers, Volume 124 presents updates on innovations in computer hardware, software, theory, design and applications, with this updated volume including new chapters on Traffic-Load-Aware Virtual Channel Power-gating in Network-on-Chips, An Efficient DVS Scheme for On-chip Networks, A Power-Performance Balanced Network-on-Chip for Mixed CPU-GPU Systems, Routerless Networks-on-Chip, Routing Algorithm Design for Power- and Temperature-Aware NoCs, Approximate Communication for Energy-Efficient Network-on-Chip, Power-Efficient NoC Design by Partial Topology Reconfiguration, The Design of a Deflection-based Energy-efficient On-chip Network, and Power-Gating in Networks-on-Chip.

This book addresses the mathematical and the practical aspects of motion implied by advanced control theory. The richness and power of the theory are demonstrated by separate analyses of single-model and multi-modal repertoires, consisting of verities of estimation and control facets. Starting with purely mathematical concepts, specifically, abstract probability and information theories, model control theory is gradually revealed as a rather amazing domain. The mathematical equations, taking essentially simple forms, are exposed as powerful generators of motion. Moreover, seemingly obvious applications of the theory, such as high-performance aircraft control make room for unexpected virtual reality feedback in control of motion for the neurologically impaired.Following the presentation of some historical milestones and mathematical preliminaries, the book is divided into four parts. The first deals with minimal-order models of state estimation and control. The second addresses multi-modal estimation and control, which facilitates the operation of high-performance aircraft in large flight envelopes. The third presents the transition from naturally nonlinear control of movement in obstacle avoidance and object targeting to virtually linear control of movement in the neurologically impaired. The fourth and final part of the book addresses the application of virtual sensory feedback in walking with specific neurological impairment. While the clinical studies reported were all based on a single-model paradigm, a later reflection reveals that, given the variety of neurological symptoms associated with the relevant disorders, a multi-modal approach, as that addressed in the control of high-performance aircraft in a large flight envelope, would be similarly applicable in the treatment of neurological disorders.

This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant structure. In the first three parts of this monograph, we establish a foundation for group operads and for their higher coherent analogues called infinity group operads. Examples include planar, symmetric, braided, ribbon, and cactus operads, and their infinity analogues. For example, with the tools developed here, we observe that the coherent ribbon nerve of the universal cover of the framed little 2-disc operad is an infinity ribbon operad.In Part 4 we define general monoidal categories equipped with an action operad equivariant structure and provide a unifying treatment of coherence and strictification for them. Examples of such monoidal categories include symmetric, braided, ribbon, and coboundary monoidal categories, which naturally arise in the representation theory of quantum groups and of coboundary Hopf algebras and in the theory of crystals of finite dimensional complex reductive Lie algebras.

This book covers an introduction to convex optimization, one of the powerful and tractable optimization problems that can be efficiently solved on a computer. The goal of the book is tohelp develop a sense of what convex optimization is, and how it can be used in a widening array of practical contexts with a particular emphasis on machine learning.The first part of the book covers core concepts of convex sets, convex functions, and related basic definitions that serve understanding convex optimization and its corresponding models. The second part deals with one very useful theory, called duality, which enables us to: (1) gain algorithmic insights; and (2) obtain an approximate solution to non-convex optimization problems which are often difficult to solve. The last part focuses on modern applications in machine learning and deep learning.A defining feature of this book is that it succinctly relates the "story" of how convex optimization plays a role, via historical examples and trending machine learning applications. Another key feature is that it includes programming implementation of a variety of machine learning algorithms inspired by optimization fundamentals, together with a brief tutorial of the used programming tools. The implementation is based on Python, CVXPY, and TensorFlow. This book does not follow a traditional textbook-style organization, but is streamlined via a series of lecture notes that are intimately related, centered around coherent themes and concepts. It serves as a textbook mainly for a senior-level undergraduate course, yet is also suitable for a first-year graduate course. Readers benefit from having a good background in linear algebra, some exposure to probability, and basic familiarity with Python.

For thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. In The Art of Logic, Royal Society Science Book Prize nominee Eugenia Cheng shows how anyone can think like a mathematician - and see, argue and think better.

Learn how to simplify complex decisions without over-simplifying them. Discover the power of analogies and the dangers of false equivalences. Find out how people construct misleading arguments, and how we can argue back.

Eugenia Cheng teaches us how to find clarity without losing nuance, taking a careful scalpel to the complexities of politics, privilege, sexism and dozens of other real-world situations. Her Art of Logic is a practical and inspiring guide to decoding the modern world.

SINGLE VARIABLE CALCULUS, Metric, 9th Edition, provides you with the strongest foundation for a STEM future. James Stewart's Calculus series is the top-seller in the world because of its problem-solving focus, mathematical precision and accuracy, and outstanding examples and problem sets. Selected and mentored by Stewart, Daniel Clegg and Saleem Watson continue his legacy and their careful refinements retain Stewart's clarity of exposition and make the 9th edition an even more usable learning tool. The accompanying WebAssign includes helpful learning support and new resources like Explore It interactive learning modules. Showing that Calculus is both practical and beautiful, the Stewart approach and WebAssign resources enhance understanding and build confidence for millions of students worldwide.