Pages: 450
ISBN: 978-981-121-502-5 (hardcover)
ISBN: 978-981-121-596-4 (softcover)
The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space R^n, orthogonality in R^n, determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices.
In the first nine chapters everything is formulated in terms of R^n. This makes the ideas of linear algebra easier to understand. The general vector spaces are introduced in Chapter 10. The last chapter presents problems solved with a computer algebra system. At the end of the book we have results or solutions for odd numbered exercises.
Matrices
The Vector Space R^n
Orthogonality in R^n
Determinants
Eigenvalues and Eigenvectors
Linear Transformations
Jordan Forms by Examples
Singular Value Decomposition
Quadratic Forms and Positive Definite Matrices
Vector Spaces
Problems for a Computer Algebra System
Answers to Selected Exercises
Undergraduate students taking a first course in linear algebra.
May 2020
Pages: 190
ISBN: 978-981-121-684-8 (hardcover)
ISBN: 978-981-121-624-4 (softcover)
The ancient Roman orator Horace (65 B.C.?8 B.C.) wrote, "Control your mind or it will control you." In today's society we are faced with more information, and more complex information, than ever. Faced with making decisions, we can feel overwhelmed and helpless. One way to become less helpless ? to gain control over our lives ? is to gain control over our own thinking. We can feel helpless when faced with this barrage of information, opinions, data, and conflicting arguments if we lack the skills to quickly grasp and critically evaluate them. This book is designed to impart these kinds of skills.
Any course in a university should do more than teach information ? in nearly every field, 'facts' become obsolete quickly. The goals of Thinking Matters are to help you:
to be more creative, fluid, and perceptive in solving problems;
to identify the implicit premises, fallacies, or moral principles that are presupposed in the arguments of others;
to be able to advocate for what you believe by effectively refuting opposing arguments and presenting persuasive arguments of your own;
to understand the logic of scientific testing to distinguish between science and pseudo-science;
to develop your own style and intuitive powers of logical deduction, probabilistic reasoning, and computational thinking.
The text is punctuated with exercises or 'personal experiments' to challenge and stimulate your curiosity. These exercises may take the form of an inventory to be taken, a puzzle to be solved, or some thoughts to ponder.
The first module Thinking Matters: Critical Thinking as Creative Problem Solving introduces the student to all the above topics ? logic, probability, argument forms and fallacies, ethical reasoning, algorithms, and computational thinking ? through logic puzzles and games and mathematical magic tricks.
Preface to Teachers, Preface to Students
The Thinking Reed
"Eureka!" Problem Solving Heuristics
Bridges to Problem Solving
Puzzles, Paradoxes, and Previews
Computational Magic
Cultivating Creativity
References
Index
Undergraduates in Logical and Critical Thinking courses, general public with interests in Logical Puzzles. Mathematical Magic, Logic Games, Creative Problem Solving, Computational Thinking.
June 2020
Pages: 450
ISBN: 978-981-121-520-9 (hardcover)
Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments.
In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell?Weil groups, which are originally introduced for elliptic fibrations.
This is the first book which explains the phenomena arising from purely inseparable coverings and Artin?Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces.
Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characterisitcs, but also understand what are crucial in computations. This type of experience will lead to finding of unsolved problems by the readers themselves.
Forms of the Affine Line:
Picard Scheme and Jacobian Variety
Forms of the Affine Line
Groups of Russell Type
Hyper-Elliptic Forms of the Affine Line
Automorphisms
Divisor Class Groups
Purely Inseparable and Artin?Schreier Coverings:
Vector Fields and Infinitesimal Group Schemes
Zariski Surfaces
Quasi-Elliptic Fibrations
Mordell?Weil Group
Artin?Schreier Coverings
Higher Derivations
Unified p-Group Scheme
Rational Double Points:
Basics on Rational Double Points
Deformation of Rational Double Points
Open Questions on Rational Double Points in Positive Characteristics
Graduate students and researchers in the fields of Algebraic Geometry, Fields and Rings, and Commutative Algebra.
June 2020
Pages: 260
ISBN: 978-981-120-978-9 (hardcover)
Description
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.
The topics presented in this volume are:
dynamics of stochastic reaction-diffusion equations;
stochastic Ito-Volterra backward equations in Banach spaces;
stochastic equations of Schrodinger type;
optimal control of stochastic Navier-Stokes equations;
quantum Hamilton equations from stochastic optimal control theory.
This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Contents:
Preface
Dynamics of Stochastic Reaction-Diffusion Equations (Chr Kuhn, A Neamtu)
Stochastic Ito-Volterra Backward Equations in Banach Spaces (M Azimi, W Grecksch)
Stochastic Equations of Schrodinger Type (W Grecksch, H Lisei)
Optimal Control of Stochastic Navier-Stokes Equations (Chr Trautwein, P Benner)
Quantum Hamilton Equations from Stochastic Optimal Control Theory (J Koppe, M Patzold, M Beyer, W Grecksch and W Paul)
Readership:
Graduate students in mathematics or physics, mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
February 2021
Pages: 350
ISBN: 978-981-3234-79-6 (hardcover)
This book is an introductory text to the field of Continuous Variable Quantum Computing and Quantum Information. Continuous variables (CVs) offer an extremely important alternative to the usual qubit substrate, as it involves easy to analyze Gaussian statistics, off-the-shelf experimental components and near universal deterministic quantum gates and operations. For communications, CVs can be easily adapted to the current telecommunication infrastructures and components, offering much higher communication rates. The contents intend to cover the most exciting topics in this field.
Introduction
Quantum Physics using Continuous Variables
Quantum Communication using Continuous Variables
Quantum Cryptography using Continuous Variables
Quantum Computing
Quantum Error Correction
Quantum Sensing
Experimental Continuous Variables
Advanced undergraduate and graduate students as well as researchers working in the field of quantum computing and quantum information.
September 2020
Pages: 600
ISBN: 978-981-121-177-5 (hardcover)
This book describes recent theoretical and experimental developments in the study of static and dynamic properties of atomic nuclei, many-body systems of strongly interacting neutrons and protons. The theoretical approach is based on the concept of the mean field, describing the motion of a nucleon in terms of a self-consistent single-particle potential well which approximates the interactions of a nucleon with all the other nucleons. The theoretical approaches also go beyond the mean-field approximation by including the effects of two-body collisions.
The self-consistent mean-field approximation is derived using the effective nucleon?nucleon Skyrme-type interaction. The many-body problem is described next in terms of the Wigner phase space of the one-body density, which provides a basis for semi-classical approximations and leads to kinetic equations. Results of static properties of nuclei and properties associated with small amplitude dynamics are also presented. Relaxation processes, due to nucleon?nucleon collisions, are discussed next, followed by instability and large amplitude motion of excited nuclei. Lastly, the book ends with the dynamics of hot nuclei. The concepts and methods developed in this book can be used for describing properties of other many-body systems.
Preface
Introduction
Self-Consistent Mean-Field Approximations
Many-Body Problem in Phase Space
Fluid Dynamic Approach
Static Properties of Nuclei
Direct Variational Method
Small Amplitude Dynamics: Quantum Approach
Small Amplitude Dynamics in Phase Space
Relaxation Processes
Instability and Large Amplitude Motion
Dynamics of Hot Nuclei
Appendices
Bibliography
Index
Students with basic knowledge of quantum mechanics and nuclear physics, as well as researchers and students interested in advanced topics in the study of properties of many-body systems.
October 2020
Pages: 400
Quantum Chromodynamics is the theory of strong interactions: a quantum field theory of colored gluons (Yang?Mills gauge fields) coupled to quarks (Dirac fermion fields). Lattice gauge theory is defined by discretizing spacetime into a four-dimensional lattice ? and entails defining gauge fields and Dirac fermions on a lattice. The applications of lattice gauge theory are vast, from the study of high-energy theory and phenomenology to the numerical studies of quantum fields.
Lattice Quantum Field Theory of the Dirac and Gauge Fields: Selected Topics examines the mathematical foundations of lattice gauge theory from first principles. It is indispensable for the study of Dirac and lattice gauge fields and lays the foundation for more advanced and specialized studies.
Synopsis
Fermion Calculus
Lattice Dirac Quantum Field
Dirac Hamiltonian: Fermionic Variables
Review of Compact Lie Groups
SU(N) Path Integrals
Lattice Gauge Field Lagrangian
Lattice Gauge Field Mass Renormalization
Lattice Gauge Field Hamiltonian
Hamiltonian, Wilson Fermions and Action
Gauge Field Block-Spin Renormalization
Epilogue
Researchers in theoretical particle physics.