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Books > Science & Mathematics > Mathematics
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.
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