Copyright Year 2022
ISBN 9781032277592
June 2, 2022 Forthcoming by CRC Press
234 Pages 35 B/W Illustrations
Format Hardback
This book contains a number of elementary ideas on numbers, their representations, interesting arithmetical problems and their analytical solutions, fundamentals of computers and programming plus programming solutions as an alternative to the analytical solutions and much more.
Spanning seven chapters, this book, while keeping its lucid storytelling verve, describes integers, real numbers and numerous interesting properties and historical references; followed by a good collection of arithmetic problems and their analytical solutions.
1. Introduction 2. Integers 3. Real Numbers 4. Problems 5. Solutions 6. Computer and programming fundamentals 7. Programming Solutions A. Brahmagupta’s Equation B. Bernoulli Numbers C. Unit Fractions D. Pattern in Decimal Representation E. Platonic Solids F. Conversion table, Boolean Algebra rules, Floating Point Format etc. G. Your own Library, command line parameters and dealing with big numbers
Copyright Year 2022
ISBN 9781032289397
July 5, 2022 Forthcoming by Chapman and Hall/CRC
569 Pages 47 B/W Illustrations
Format Hardback
When a student of mathematics studies abstract algebra, he or she inevitably faces questions in the vein of, "What is abstract algebra" or "What makes it abstract?"
Algebra, in its broadest sense, describes a way of thinking about classes of sets equipped with binary operations. In high school algebra, a student explores properties of operations (+, ?, ×, and ÷) on real numbers.
Abstract algebra studies properties of operations without specifying what types of number or object we work with. Any theorem established in the abstract context holds not only for real numbers but for every possible algebraic structure that has operations with the stated properties.
This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups, rings, and fields; or a course that primarily emphasizes group theory.
The writing style is student-centered, conscientiously motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry, number theory, cryptography and many other areas.
This book offers a unique feature in the lists of projects at the end of each section. the author does not view projects as just something extra or cute, but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation.
The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic, asking and to trying to answer their own questions.
Expository projects invite the student to explore a topic with algebraic content or pertain to a particular mathematician’s work through responsible research.
The exercises challenge the student to prove new results using the theorems presented in the text. The student then becomes an active participant in the development of the field.
1. Groups.
2. Quotient Groups.
3. Rings.
4. Divisibility in Integral Domains.
5. Field Extensions.
6. Topics in Group Theory.
A. Appendix.
Copyright Year 2022
ISBN 9781032211244
June 20, 2022 Forthcoming by Chapman and Hall/CRC
268 Pages 87 Color Illustrations
Format Hardback
Handbook of Graphs and Networks in People Analytics: With Examples in R and Python covers the theory and practical implementation of graph methods in R and Python for the analysis of people and organizational networks. Starting with an overview of the origins of graph theory and its current applications in the social sciences, the book proceeds to give in-depth technical instruction on how to construct and store graphs from data, how to visualize those graphs compellingly and how to convert common data structures into graph-friendly form.
The book explores critical elements of network analysis in detail, including the measurement of distance and centrality, the detection of communities and cliques, and the analysis of assortativity and similarity. An extension chapter offers an introduction to graph database technologies. Real data sets from various research contexts are used for both instruction and for end of chapter practice exercises and a final chapter contains data sets and exercises ideal for larger personal or group projects of varying difficulty level.
Immediately implementable code, with extensive and varied illustrations of graph variants and layouts.
Examples and exercises across a variety of real-life contexts including business, politics, education, social media and crime investigation.
Dedicated chapter on graph visualization methods.
Practical walkthroughs of common methodological uses: finding influential actors in groups, discovering hidden community structures, facilitating diverse interaction in organizations, detecting political alignment, determining what influences connection and attachment.
Various downloadable data sets for use both in class and individual learning projects.
Final chapter dedicated to individual or group project examples.
1 Graphs Everywhere! 2 Working With Graphs 3 Visualizing Graphs 4 Restructuring Data For Use in Graphs 5 Paths and Distance 6 Vertex Importance and Centrality 7 Components, Communities and Cliques 8 Assortativity and Similarity 9 Graphs as Databases 10 Further Exercises for Practice
Copyright Year 2023
ISBN 9781032013251
July 20, 2022 Forthcoming by Chapman and Hall/CRC
310 Pages 10 B/W Illustrations
Format Hardback
The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications.
Discusses the Fibonacci and vector valued difference sequence spaces
Presents the solution of Volterra integral equation in Banach algebra
Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix
Presents the Tauberian theorems of double sequences
Discusses the paranormed Riesz difference sequence space of fractional order
Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces
The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces.
1. Hahn-Banach and Duality Type Theorems for Vector Lattice- Valued Operators and Applications to Subdifferential Calculus and Optimization
Antonio Boccuto
2. Application of Measure of Noncompactness on Infinite Sys- tem of Functional Integro-differential Equations with Integral Initial Conditions
Anupam Das
3. λ-Statistical Convergence of Interval Numbers of Order α
Ayhan Esi and Ayten Esi
4. Necessary and Sufficient Tauberian Conditions under which Convergence follows from (Ar,δ, p, q; 1, 1), (Ar,?, p, ?; 1, 0) and (A?,δ, ?, q; 0, 1) Summability Methods of Double Sequences
Cagla Kambak and Ibrahim Canak
5. On New Sequence Spaces Related to Domain of the Jordan Totient Matrix
Emrah Evren Kara, Necip Simsek, and Merve Ilkhan Kara
6. A Study of Fibonacci Difference I?Convergent Sequence Spaces
Vakeel A. Khan, Kamal M. A. S. Alshlool, and Sameera A. A. Abdullah
7. Theory of Approximation for Operators in Intuitionistic Fuzzy Normed Linear Spaces
Nabanita Konwar and Pradip Debnath
8. Solution of Volterra Integral Equations in Banach Algebras using Measure of Noncompactness
Hemant Kumar Nashine and Anupam Das
9. Solution of a pair of Nonlinear Matrix Equation using Fixed Point Theory
Hemant Kumar Nashine and Sourav Shil
10. Sequence Spaces and Matrix Transformations
Ekrem Savas
11. Carath´eodory Theory of Dynamic Equations on Time Scales
Sanket Tikare
12. Vector Valued Ideal Convergent Generalized Difference Se- quence Spaces Associated with Multiplier Sequences
Binod Chandra Tripathy
13. Domain of Generalized Riesz Difference Operator of Frac- tional Order in Maddox’s Space f(p) and Certain Geometric Properties
Taja Yaying, Bipan Hazarika, and S. A. Mohiuddine
Copyright Year 2022
ISBN 9781032287812
June 27, 2022 Forthcoming by Chapman and Hall/CRC
328 Pages 22 B/W Illustrations
Format Hardback
Linear Algebra is intended primarily as an undergraduate textbook but is written in such a way that it can be also a valuable resource for independent learning. The narrative of the book takes a matrix approach: the exposition is intertwined with matrices either as the main subject or as tools to explore the theory. Each chapter contains a description of its aims, a summary at the end of the chapter, exercises and solutions. The reader is carefully guided through the theory and techniques presented which are outlined throughout in "How to…" text boxes. Common mistakes and pitfalls are also pointed out as one goes along.
Written to be self-contained.
Ideal as a primary textbook for an undergraduate course in linear algebra.
Applications of the general theory which are of interest to disciplines outside of mathematics, such as engineering.
1. Matrices. 1.1. Real and Complex Matrices. 1.2. Matrix Calculus. 1.3. Matrix Inverses. 1.4. Elementary Matrices. 1.5. Exercises. 1.6. At a Glance. 2. Determinant. 2.1. Axiomatic Definition. 2.2. Leibniz's Formula. 2.3. Laplace's Formula. 2.4. Exercises. 2.5. At a Glance. 3. Vector Spaces. 3.1. Vector Spaces. 3.2. Linear Independence. 3.3. Bases and Dimension. 3.4. Null Space, Row Space and Column Space. 3.5. Sum and intersection of Subspaces. 3.6. Change of Basis. 3.7. Exercises. 3.8. At a Glance. 4. Eigenvalues and Eigenvectors. 4.1. Spectrum of a Matrix. 4.2. Spectral Properties. 4.3. Similarity and Diagonalisation. 4.4. Jordan Canonical Form. 4.5. Exercises. 4.6. At a Glance. 5. Linear Transformations. 5.1. Linear Transformations. 5.2. Matrix Representations. 5.3. Null Space and Image. 5.4. Isomorphisms and Rank-Nullity Theorem. 5.5. Composition and Invertibility. 5.6. Change of Basis. 5.7. Spectrum and Diagonalisation. 5.8. Exercises. 5.9. At a Glance. 6. Inner Product Spaces. 6.1. Real Inner Product Spaces. 6.2. Complex Inner Product Spaces. 6.3. Orthogonal Sets. 6.4. Orthogonal and Unitary Diagonalisation. 6.5. Singular Value decomposition. 6.6. Affine Subspaces of Rn. 6.7. Exercises. 6.8. At a Glance. 7 Special Matrices by Example. 7.1. Least Squares Solutions. 7.2. Markov Chains. 7.3. Population Dynamics. 7.4. Graphs. 7.5. Differential Equations. 7.6. Exercises. 7.7. At a Glance. 8. Appendix. 8.1. Uniqueness of Reduced Row Echelon Form. 8.2. Uniqueness of determinant. 8.3. Direct sum of Subspaces. 9. Solutions.
Copyright Year 2022
ISBN 9781032199016
July 4, 2022 Forthcoming by Chapman and Hall/CRC
200 Pages
Banach-Space Operators On C*-Probability Spaces Generated by Multi Semicircular Elements introduces new areas in operator theory and operator algebra, in connection with free probability theory. In particular, the book considers projections and partial isometries distorting original free-distributional data on the C?-probability spaces.
Suitable for graduate students and professional researchers in operator theory and/or analysis.
Numerous applications in related scientific fields and areas.
1. Introduction. 2. Preliminaries. 3. Joint Free Distributions of Multi Semicircular Elements. 4. A C*-Probability Space of |?|-Many Semicircular Elements. 5. C*-Probability Spaces (ЖN ; ?N). 6. Adjointable Banach-Space Operators Acting on ЖN. 7. Free-Probabilistic Information on ЖN Affected by Partial Isometries. 8. Application I. Shift Operators Acting on Ж∞. 9. Application II. The Circular Law. 10. Application III. Free Poisson Distributions. 11. Examples. 12. The Group Dynamical System ?. 13. On the ?-Semicircular *-Probability Space X. 14. Operator-Theoretic Properties on X. Free Probability on ЖN = (ЖN ?C ^N; TN). 16. Operator-Theoretic Properties on ЖN.