A Note on the Integral Equation of the First Kind With a Cauchy Kernel
Mathematical Inequalities Volume 1
This is Volume 1 of the five-volume book Mathematical Inequalities, that introduces and develops the main types of elementary inequalities. The first three volumes are a great opportunity to look into many old and new inequalities, as well as elementary procedures for solving them: Volume 1 - Symmetric Polynomial Inequalities, Volume 2 - Symmetric Rational and Nonrational Inequalities, Volume 3 - Cyclic and Noncyclic Inequalities. As a rule, the inequalities in these volumes are increasingly ordered according to the number of variables: two, three, four, ..., n-variables. The last two volumes (Volume 4 - Extensions and Refinements of Jensen's Inequality, Volume 5 - Other Recent Methods for Creating and Solving Inequalities) present beautiful and original methods for solving inequalities, such as Half/Partial convex function method, Equal variables method, Arithmetic compensation method, Highest coefficient cancellation method, pqr method etc. The book is intended for a wide audience: advanced middle school students, high school students, college and university students, and teachers. Many problems and methods can be used as group projects for advanced high school students.
A Group Theoretic Tabu Search Approach to the Traveling Salesman Problem
A Group Theoretic Tabu Search Approach to the Traveling Salesman Problem
Mathematical Inequalities Volume 3
This is Volume 3 of the five-volume book Mathematical Inequalities, which introduces and develops the main types of elementary inequalities. The first three volumes are a great opportunity to look into many old and new inequalities, as well as elementary procedures for solving them: Volume 1 - Symmetric Polynomial Inequalities, Volume 2 - Symmetric Rational and Nonrational Inequalities, Volume 3 - Cyclic and Noncyclic Inequalities. As a rule, the inequalities in these volumes are increasingly ordered according to the number of variables: two, three, four, ..., n-variables. The last two volumes (Volume 4 - Extensions and Refinements of Jensen's Inequality, Volume 5 - Other Recent Methods for Creating and Solving Inequalities) present beautiful and original methods for solving inequalities, such as Half/Partial convex function method, Equal variables method, Arithmetic compensation method, Highest coefficient cancellation method, pqr method etc. The book is intended for a wide audience: advanced middle school students, high school students, college and university students, and teachers. Many problems and methods can be used as group projects for advanced high school students.
Functional Differential Systems
This book is a trail-blazer in robust formulations, investigations of computational feasibility and electronic implementations of mathematical results. It developed and used the core concept and computable expressions for determining matrices to establish necessary and sufficient conditions for Euclidean controllability of certain classes of functional differential systems. To actualize the applications of variation of constants formulas for initial and terminal function problems, as well as the characterization of controllability in terms of indices of control systems, this book pioneered the formulation and validation of the expressions and structures of solution and control index matrices for some classes of hereditary systems. To eliminate all computational and implementation constraints and achieve large-scale industrial applicability of the results, the book developed and provided software codes with a user guide for the implementation of results on the C++ platform. This has placed the generally neglected implementation aspect of mathematical results on the front burner, thus providing implementation paradigm shift.
Eigenfunction Expansions Associated With the Laplacian for Certain Domains With Infinite Boundaries
Application of the Bayesian Method in Statistical Modeling
Calculus
Unlock the mysteries of Calculus with a fresh approach rooted in simplicity and historical insight. This book reintroduces a nearly forgotten idea from Ren矇 Descartes (1596-1650), showing how the fundamental concepts of Calculus can be understood using just basic algebra. Starting with rational functions -- the core of early Calculus -- this method allows the reader to grasp the rules for derivatives without the intimidating concepts of limits or real numbers, making the subject more accessible than ever.But the journey doesn't stop there. While attempting to apply this algebraic approach to exponential functions, the reader will encounter the limitations of simple methods, revealing the necessity for more advanced mathematical tools. This natural progression leads to the discovery of continuity, the approximation process, and ultimately, the introduction of real numbers and limits. These deeper concepts pave the way for understanding differentiable functions, seamlessly bridging the gap between elementary algebra and the profound ideas that underpin Calculus.Whether you're a student, educator, or math enthusiast, this book offers a unique pathway to mastering Calculus. By connecting historical context with modern mathematical practice, it provides a richer, more motivating learning experience. For those looking to dive even deeper, the author's 2015 book, What is Calculus? From Simple Algebra to Deep Analysis, is the perfect next step.
Calculus
Unlock the mysteries of Calculus with a fresh approach rooted in simplicity and historical insight. This book reintroduces a nearly forgotten idea from Ren矇 Descartes (1596-1650), showing how the fundamental concepts of Calculus can be understood using just basic algebra. Starting with rational functions -- the core of early Calculus -- this method allows the reader to grasp the rules for derivatives without the intimidating concepts of limits or real numbers, making the subject more accessible than ever.But the journey doesn't stop there. While attempting to apply this algebraic approach to exponential functions, the reader will encounter the limitations of simple methods, revealing the necessity for more advanced mathematical tools. This natural progression leads to the discovery of continuity, the approximation process, and ultimately, the introduction of real numbers and limits. These deeper concepts pave the way for understanding differentiable functions, seamlessly bridging the gap between elementary algebra and the profound ideas that underpin Calculus.Whether you're a student, educator, or math enthusiast, this book offers a unique pathway to mastering Calculus. By connecting historical context with modern mathematical practice, it provides a richer, more motivating learning experience. For those looking to dive even deeper, the author's 2015 book, What is Calculus? From Simple Algebra to Deep Analysis, is the perfect next step.
Fuzzy Bi-Ideals of Gamma Near-Ring
I am very pleased to submit this book. In this book contains T -Fuzzy Bi-ideals of Gamma Near-rings, Spherical Fuzzy Bi-ideals of Gamma Near-rings, Spherical Interval-valued Fuzzy Bi-ideals ofGamma Near-rings, Spherical Cubic Bi-ideals of Gamma Near-rings, Double Framed Soft Fuzzy Bi-ideal of GammaNear-rings, Bipolar Fuzzy Bi-ideals of Gamma Near-rings, Conclusion. The concept of fuzziness as described by L.A. Zadeh in 1965 includes imprecision, uncertainty and degree of truthfulness of values. A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership function which assigns to each object a grade of membership ranging between zero and one. A fuzzy set in a universe of discourse X is a function of the form: X → [0, 1]. Membership functions characterize fuzziness (i.e., all the information in fuzzy set), whether the elements in fuzzy sets are discrete or continuous. Membership functions can be defined as a technique to solve practical problems by experience rather than knowledge. Membership functions are represented by graphical forms. Rules for defining fuzziness are fuzzy too.
Foundations of Mathematical Analysis for Statistics
Mathematical analysis forms the rigorous backbone of modern statistics, enabling a precise understanding of continuity, differentiability, integration, and convergence, all of which are central to probability theory, inference, stochastic processes, and machine learning. As the boundaries between pure mathematics and statistical applications continue to dissolve, a solid foundation in analysis becomes not just desirable but indispensable for serious students of statistics. This book, Foundations of Mathematical Analysis for Statistics, is the result of years of teaching and research, distilled into a coherent and structured resource intended for graduate and advanced undergraduate students in statistics, mathematics, and allied disciplines. It bridges classical real and complex analysis with the analytical tools used in contemporary statistical theory and modeling.
Mathematics for Machine Learning and AI
Mathematics for Machine Learning and AI provides a foundational and practical understanding of the core mathematical concepts that underpin modern artificial intelligence systems. It covers essential topics such as linear algebra, calculus, probability theory, statistics, optimization, and discrete mathematics, all tailored to their applications in machine learning and AI. This book bridges the gap between mathematical theory and practical implementation, making complex topics accessible through clear explanations, real-world examples, and hands-on problem-solving. Readers will learn how eigenvalues, gradients, probability distributions, and optimization algorithms drive intelligent systems-from neural networks and decision trees to deep learning and reinforcement learning. Designed for students, educators, and professionals, the book balances theoretical rigor with intuitive insights, offering both the mathematical depth and applied knowledge needed to excel in the evolving fields of data science, AI, and machine learning.
Advanced Engineering Mathematics
This book provides a comprehensive foundation in essential mathematical methods used in engineering and applied sciences. It bridges theory with practical applications by covering topics such as differential equations, vector calculus, Fourier analysis, and PDEs. Each chapter includes step-by-step explanations, solved problems, and practice exercises designed to build analytical thinking and problem-solving skills. Emphasis is placed on real-world engineering systems, making it an ideal guide for students, educators, and professionals.
Numerical Methods for Statistical Computation
Numerical Methods for Statistical Computation: Theory, Algorithms, and Applications bridges numerical analysis with modern statistics, offering a unified treatment of root-finding, linear systems, interpolation, integration, differential equations, and optimization all within a statistical framework. Through detailed theory, worked examples, and real applications, the book equips readers to solve complex statistical problems numerically. Designed for advanced undergraduates, graduate students, and researchers in statistics and data science, it emphasizes both algorithmic understanding and statistical insight. With a strong pedagogical structure and extensive example sets, this book serves as a comprehensive resource for statistical computation in theory and practice.
Numerical and Algorithmic Approaches for Solvable Integrals
This third volume of the Numerical and Algorithmic Approaches to Integrals series focuses on error analysis, precision, and comparison of major numerical integration methods applied to analytically solvable integrals. Combining theoretical rigor with practical Python implementation, the book offers a systematic study of absolute and relative errors, algorithm design, and guided, corrected exercises. Each method follows a consistent structure: theoretical foundations, precision estimation, algorithm development, and hands-on application. Designed for students in the sciences, as well as researchers and engineers, this volume helps consolidate numerical analysis skills through an autonomous, progressive, and comparative reading experience. It serves as a valuable resource for mastering the reliability of numerical methods in academic and professional settings that demand both precision and analytical depth.
Advanced Numerical and Algorithmic Approaches for Irresolvable Integrals
This fourth volume, Advanced Numerical and Algorithmic Approaches for Irreducible Integrals, is intended for students, researchers, and engineers dealing with integrals that cannot be solved analytically. Through a rigorous framework, it presents error bounds, estimates of maximum achievable precision, and methods for determining the optimal number of intervals required. Each numerical technique is illustrated with an algorithm, a Python implementation, and exercises grounded in diverse application domains such as biology, finance, and telecommunications. By combining mathematical theory, computational tools, and real-world case studies, the book offers a clear methodological framework for assessing and mastering the precision of numerical methods. This volume completes a four-part series dedicated to both analytical and numerical integration, delivering a structured, comprehensive, and practically oriented vision of integral calculus in the sciences and engineering.
Table of the Logarithms of the Complete -function (for Arguments 2 to 1200, i.e. Beyond Legendre's Range)
