Pletser, Vladimir, Chinese Academy of Sciences, Beijing, China

Lagrangian and Hamiltonian Analytical Mechanics:
Forty Exercises Resolved and Explained

1st ed. 2018, IX, 128 p. 23 illus.
Hardcover
ISBN 978-981-13-3025-4
Series : UNITEXT for Physics
Physics : Classical Mechanics

Explains how to analytically solve classical problems and exercises
Covers classical, celestial and quantum mechanics

Provides theoretical reviews before the problems and exercises

Presents a solution to Einsteinfs problem of the advance of Mercury perihelion

This textbook introduces readers to the detailed and methodical resolution of classical and
more recent problems in analytical mechanics. This valuable learning tool includes worked
examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in
classical, celestial and quantum mechanics. The collection comprises six chapters, offering
essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral
and Variational Principle; (4) Canonical Transformations; (5) Hamilton ? Jacobi Equations; and
(6) Phase Integral and Angular Frequencies Each chapter begins with a brief theoretical review
before presenting the clearly solved exercises. The last two chapters are of particular interest,
because of the importance and flexibility of the Hamilton-Jacobi method in solving many
mechanical problems in classical mechanics, as well as quantum and celestial mechanics.
Above all, the book provides students and teachers alike with detailed, point-by-point and stepby-
step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to
most problems in classical physics, astronomy, celestial mechanics and quantum physics.


Dalla Chiara, M.L., Giuntini, R., Leporini, R., Sergioli, G., University of Florence, Florence, Italy

Quantum Computation and Logic

Due 2019-01-29
1st ed. 2018, XVI, 178 p. 18
illus., 3 illus. in color.
Hardcover
ISBN 978-3-030-04470-1
Series : Trends in Logic
Philosophy : Logic

How Quantum Computers Have Inspired Logical Investigations
Presents new approach to quantum logic inspired by quantum computation
Offers a logical discussion of the question gcan quantum computers be
modelled by classical Turing machines?h

Shows how the logics suggested by quantum computation can be naturally
applied to the semantics of natural and artistic languages

Illustrates problems in intuitive and formally rigorous language

This book provides a general survey of the main concepts, questions and results that have
been developed in the recent interactions between quantum information, quantum computation
and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts
of the quantum-theoretic formalism used in quantum information. It then gives a synthetic
presentation of the main gmathematical charactersh of the quantum computational game:
qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates
the puzzling entanglement-phenomena and logically analyses the Einstein?Podolsky?Rosen
paradox and introduces the reader to quantum computational logics, and new forms of
quantum logic. The middle chapters investigate the possibility of a quantum computational
semantics for a language that can express sentences like gAlice knows that everybody knows
that she is prettyh, explore the mathematical concept of quantum Turing machine, and illustrate
some characteristic examples that arise in the framework of musical languages. The book
concludes with an analysis of recent discussions, and contains a Mathematical Appendix which
is a survey of the definitions of all main mathematical concepts used in the book.

Alexander, S., Kapovitch, V., Petrunin, A., University of Illinois Department of
Mathematics, Urbana, IL, USA

An Invitation to Alexandrov Geometry

Due 2019-02-18
1st ed. 2018, XII, 88 p. 38 illus.
Softcover
ISBN 978-3-030-05311-6
Series : SpringerBriefs in Mathematics
Mathematics : Differential Geometry

CAT(0) Spaces

Explains the importance of CAT(0) geometry in geometric group theory

Demonstrates Alexandrov geometry through applications and theorems

Discusses Reshetnyak gluing theorem and Hadamard-Cartan globilization
theorem

Aimed toward graduate students and research mathematicians, with minimal prerequisites this
book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0)
geometry in geometric group theory. Beginning with an overview of fundamentals, definitions,
and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem
and applies it to the billiards problems. The Hadamard?Cartan globalization theorem is
explored and applied to construct exotic aspherical manifolds.


Uehara, Ryuhei, Japan Advanced Institute of Science and Technology, Nomi, Japan

First Course in Algorithms Through Puzzles

Due 2019-02-04
1st ed. 2019, XI, 175 p. 68
illus., 3 illus. in color.
Hardcover
ISBN 978-981-13-3187-9
Undergraduate textbook
Computer Science : Algorithm Analysis and Problem Complexity

Provides an introduction to algorithms in a self-contained way

Contains more than 40 exercises and their solutions

Includes famous puzzles to explain basic techniques of algorithms

This textbook introduces basic algorithms and explains their analytical methods. All algorithms
and methods introduced in this book are well known and frequently used in real programs.
Intended to be self-contained, the contents start with the basic models, and no prerequisite
knowledge is required. This book is appropriate for undergraduate students in computer
science, mathematics, and engineering as a textbook, and is also appropriate for self-study by
beginners who are interested in the fascinating field of algorithms. More than 40 exercises are
distributed throughout the text, and their difficulty levels are indicated. Solutions and
comments for all the exercises are provided in the last chapter. These detailed solutions will
enable readers to follow the authorfs steps to solve problems and to gain a better
understanding of the contents. Although details of the proofs and the analyses of algorithms
are also provided, the mathematical descriptions in this book are not beyond the range of high
school mathematics. Some famous real puzzles are also used to describe the algorithms.
These puzzles are quite suitable for explaining the basic techniques of algorithms, which show
how to solve these puzzles.


Younes, Laurent, Johns Hopkins University, Baltimore, MD, USA

Shapes and Diffeomorphisms

Due 2019-02-18
2nd ed. 2019, XX, 548 p. 46 illus., 14 illus. in color.
Hardcover
ISBN 978-3-662-58495-8
Series :Applied Mathematical Sciences
Mathematics : Mathematical Applications in Computer Science

Suitable for an advanced undergraduate course in the differential geometry
of curves and surfaces, featuring applications that are rarely treated in
standard texts

Provides a graduate-level theoretical background in shape analysis and
connects it with algorithms and statistical methods

Offers a unique presentation of diffeomorphic registration methods, which
has no equivalent in the current literature

This book covers mathematical foundations and methods for the computerized analysis of
shapes, providing the requisite background in geometry and functional analysis and introducing
various algorithms and approaches to shape modeling, with a special focus on the interesting
connections between shapes and their transformations by diffeomorphisms. A direct application
is to computational anatomy, for which techniques such as largedeformation diffeomorphic
metric mapping and metamorphosis, among others, are presented. The appendices detail a
series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal
control).The intended audience is applied mathematicians and mathematically inclined
engineers interested in the topic of shape analysis and its possible applications in computer
vision or medical imaging. The first part can be used for an advanced undergraduate course on
differential geometry with a focus on applications while the later chapters are suitable for a
graduate course on shape analysis through the action of diffeomorphisms. Several significant
additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a
discussion of optimal control theory in an infinite-dimensional framework, which is then used
to enrich the presentation of diffeomorphic matching.