Format: Hardback, 390 pages, height x width: 235x155 mm, 4 Illustrations, color;
9 Illustrations, black and white; XII, 390 p. 13 illus., 4 illus. in color.
Series: Infosys Science Foundation Series in Mathematical Sciences
Pub. Date: 17-Apr-2025
ISBN-13: 9789819616305
This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG). Starting with the basics of semi-Riemannian geometry, the book aims to develop the understanding of smooth 1-parameter variations of geodesics of, and correspondingly of, Jacobi fields. A few algebraic aspects required by the treatment of the Riemann?Christoffel four-tensor and sectional curvature are successively presented. Ricci curvature and Einstein manifolds are briefly discussed. The Sasaki metric on the total space of the tangent bundle over a Riemannian manifold is built, and its main properties are investigated. An important integration technique on a Riemannian manifold, related to the geometry of geodesics, is presented for further applications. The other three books of the series are
Differential Geometry 1: Manifolds, Bundle and Characteristic Classes (Book I-A)Differential Geometry 3: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C)Differential Geometry 4: Advanced Topics in Cauchy?Riemann and Pseudohermitian Geometry (Book I-D)
The four books belong to a larger book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics) by the same authors, aiming to demonstrate how certain portions of DG and the theory of partial differential equations apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG machinery yet do not constitute a comprehensive treatise on DG, but rather authors’ choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions?isometric, holomorphic, Cauchy?Riemann (CR)?and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.
Chapter 1 Riemannian Geometry.
Chapter 2 Finslerian Geometry.
Chapter 3 Isometric immersions.
Format: Hardback, 482 pages, height x width: 235x155 mm, 25 Illustrations, color; 85 Illustrations, black and white; XVIII, 482 p. 110 illus., 25 illus. in color.,
Pub. Date: 19-Apr-2025
ISBN-13: 9789819615124
This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years by F. Enriques in an attempt to extend the characterization of rational algebraic curves to the case of algebraic surfaces. The novel feature of the present exposition is that no assumption on the characteristic of the ground field is assumed.
This requirement calls for exploring the geometry of such surfaces by purely geometric and arithmetic methods that do not rely on transcendental methods such as the theory of periods of algebraic surfaces of type K3, which are close relatives of Enriques surfaces. Some of the methods use many technical tools from algebraic geometry that are discussed in Volume 1 and will be a useful source of reference for the study of algebraic surfaces over fields of positive characteristic. Volume 1 also contains a detailed exposition of the theory of elliptic surfaces over fields of arbitrary characteristic.
The second volume discusses many new topics for example, the theory of automorphisms of Enriques surfaces and the relationships with hyperbolic geometry. Together, the two volumes contain many examples and an extensive bibliography made up of more than 700 items.
6 Nodal Enriques Surfaces.- 7 Reye Congruences.- 8 Automorphisms of
Enriques Surfaces.- 9 Rational Coble Surfaces.- 10 Supersingular K3 Surfaces
and Enriques Surfaces.
Format: Paperback / softback, 270 pages, height x width: 235x155 mm, 1 Illustrations, color; 46 Illustrations,
black and white; Approx. 270 p. 47 illus., 1 illus. in color., 1 Paperback / softback
Series: Mathematics Study Resources 18
Pub. Date: 18-May-2025
ISBN-13: 9783662705629
This textbook presents the topics typically covered in a standard course on discrete structures. It is aimed at students of computer science and mathematics (teaching degree and Bachelor's/Master's) and is designed to accompany lectures, for self-study, and for exam preparation.
Through explanatory introductions to definitions, numerous examples, counterexamples, diagrams, cross-references, and outlooks, the authors manage to present the wide range of topics concisely and comprehensibly.
Numerous exercises facilitate the deepening of the material. Due to its compact presentation of all important discrete and algebraic structures and its extensive index, the book also serves as a reference for mathematicians, computer scientists, and natural scientists.
Contents: From propositional and predicate logic to sets and combinatorics, numbers, relations and mappings, graphs, to the rich spectrum of algebraic structures, and a brief introduction to category theory. Additional chapters include rings and modules as well as matroids.
This book is a translation of the second German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so the book may read stylistically differently from a conventional translation.
1. Fundamentals .-
2. Sets and Counting .-
3. Numbers and their
Representations .-
4. Relations.-
5. Mappings.-
6. Graphs.-
7. Groupoid,
Semigroup, Group.-
8. From Semirings to Fields.-
9. Act, Vector Space,
Extension.- 10 Rings and Modules. 11 Matroids.- 12 Categories.- Literature.-
Symbols.- Index.
Pages: 660
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ISBN: 978-981-98-0616-4 (hardcover)
ISBN: 978-981-98-0713-0 (softcover)
This book explores three computational formalisms for solving geometric problems. Part I introduces a trigonometric-based formalism, enabling calculations of distances, angles, and areas using basic trigonometry. Part II focuses on complex numbers, representing points in the plane to manipulate geometric properties like collinearity and concurrency, making it particularly useful for planar problems and rotations. Part III covers vector formalism, applying linear algebra to both plane and solid geometry. Vectors are effective for solving problems related to perpendicularity, collinearity, and the calculation of distances, areas, and volumes.
Each formalism has its strengths and limitations, with complex numbers excelling in the plane and vectors being more versatile in three-dimensional space. This book equips readers to choose the best approach for various geometric challenges.
This book, designed for math majors, especially future educators, is also valuable for gifted high school students and educators seeking diverse proofs and teaching inspiration.
Foundations of Geometry
Triangle Geometry
Quadrilateral Geometry
Complex Numbers in Geometry
Vectors and Their Basic Properties
Elementary Properties of Vectors
The Inner Product and Its Applications
The Cross Product
The Mixed Scalar Product
Applications to Plane Geometry
Baricentric Coordinates
Momenta and Applications
Applications to Solid Geometry
This is a textbook aimed for an undergraduate College Geometry class. The targeted students are primarily mathematics majors. Other students can be computer science or physics majors needing a minor in mathematics. The book can also be useful for math educators who are interested in diverse proofs of geometric problems and need inspiration for their classwork or Math clubs.
Pages: 396
ISBN: 978-981-98-0318-7 (hardcover)
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of "Differential Evolution Equations" emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.
This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Frechet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.
Preface
Introduction
Preliminary Background
Semilinear Evolution Equations
Semilinear Evolution Equations with State-Dependent Delay
Semilinear Differential Evolution Equations with Random Effects
Semilinear Differential Evolution Equations with Random Effects and Delay
S-Asymptotically ω-Periodic Mild Solutions for Differential Evolution Equations
Impulsive Differential Evolution Equations
Periodic Mild Solutions of Evolution Equations with Impulses and Delay
Periodic Mild Solutions of Evolution Inclusions with Impulses and Delay
Qualitative and Quantitative Analysis of Dynamical Models
Bibliography
Index
Researchers and graduate students that are interested in the study of differential equations, particularly, evolution differential equations and inclusions, and their relevant fields will find this monograph extremely useful for their future research. This book is appropriate for use in advanced graduate courses, seminars and research projects in numerous applied sciences.
Pages: 720
ISBN: 978-981-98-0351-4 (hardcover)
The main aim of this book is to provide an advanced textbook on functional analysis, focusing on the functional calculus of operators. Based on basic knowledge of functional analysis on metric spaces and linear bounded operators, this book systematically introduces the spectral theory of operators and the theory of operator semigroups, including Banach algebras, spectral theories of both bounded and unbounded linear operators, as well as semigroups of operators. They play important roles in various areas of modern mathematics such as harmonic analysis, partial differential equations, probability and statistics, engineering science, quantum physics, and statistical mechanics.
This book provides rich examples and exercises, emphasizing the combination of the theory and examples to enhance readers' ability to apply functional analysis theory to solve related problems. Compared with many other functional analysis textbooks, this book focuses on the spectral theory and the operator semigroup theory, serving as an appropriate connection for functional analysis between undergraduate and graduate levels, making it an ideal textbook for both. It will also be a good reference book for researchers who are interested in modern analysis, such as functional analysis, harmonic analysis, and partial differential equations.
Spectral Theory of Compact Operators:
Preliminary
Spectrums of Bounded Linear Operators
Compact Operators
Spectral Theory of Compact Operators
Hilbert?Schmidt Theorem
Banach Algebras:
Algebraic Preliminaries
Banach Algebras
Examples and Applications
C*-Algebras
Normal Operators on Hilbert Spaces
Hilbert?Schmidt Operators and Trace Operators
Unbounded Operators:
Closed Operators
Cayley Transform and Spectral Decomposition of Self-Adjoint Operators
Spectral Decomposition of Unbounded Normal Operators
Semigroups of Operators:
Strongly Continuous Semigroups of Bounded Linear Operators and Their Infinitesimal Generators
Examples of Infinitesimal Generators
One-Parameter Groups of Unitary Operators and Stone Theorem
Bibliography
Index
Advanced undergraduates and graduate students with a basic knowledge of functional analysis, as well as university or college teachers.
Pages: 280
ISBN: 978-981-98-0654-6 (hardcover)
Number theory could be divided into additive number theory and multiplicative number theory. In this book we raise the so-called additive and multiplicative equation, it is our new creation, and it is the collection and extension of research results by the author in the past decade. They are related with classical number theory problems. The contents consists of 7 chapters, i.e., New Waring Problem, New Fermat Problem, Euler's Conjecture, Representations of Integers as Sums of Squares, Figurate Primes and F-Perfect Numbers, abcd Equation and New Congruent Numbers, Additive and Multiplicative Congruences and Other Topics.
Preface
The New Waring Problem
The New Fermat Equation
Euler's Conjecture
Representations of Integers as Sums of Squares
Figurate Primes and F-Perfect Numbers
The abcd Equation and New Congruent Numbers
Additive and Multiplicative Congruences and Other Topics
References
Name Index
Number theorists, college mathematics teachers and students, amateur mathematicians.