Numerical Study of Multi Parameter Boundary Layer Problems
This book aims to present, analyze, and evaluate various straightforward and effective numerical methodologies for addressing two-parameter boundary layer problems, also referred to as singularly perturbed two-parameter boundary value problems, which exhibit dual boundary layer characteristics in their solutions. The book comprises five chapters. Chapter -1 delves into elucidating the definition and rationale behind singular perturbation problems, as well as singularly perturbed two parameters boundary value problems. A fourth order computational scheme with an exponential spline, a numerical scheme using an adaptive cubic spline function, a completely exponential fitted second order finite difference method, a completely exponential fitted modified upwind finite difference method for the solution of two parameters singularly perturbed two-point boundary value problems having dual layers are proposed in the remaining four chapters. These approaches may be applied to solve differential-difference equations with several parameters, as well as higher order order singular perturbation problems. The approaches proposed are efficient for doing computations with minimal computing effort.
Intuitionistic Fuzzy Digital Spaces
This book is intended to define and analyse the geometrical and topological properties among the digital subsets of the digital images such as convexity, convex envelopes, continuity, connectedness and r-simplexes with the background of intuitionistic fuzzy logic. As an example automated detection of diabetic retinopathy using intuitionistic fuzzy digital convex envelope segmentation algorithm is propounded. As the co-extension of the above notions, some of the maps between the digital images such as continuous maps, connected maps, C-maps and enfolding maps are presented and investigated with intuitionistic fuzzy logic. Finally, intuitionistic fuzzy digital topology is framed up. Under this notion, CS - filtered spaces and Hausdorff CS - filtered spaces are instigated.
Mathematical Study of Epidemic Models
This book covers mathematical study of epidemic model and explores mathematical modeling techniques for infectious disease dynamics, focusing on stability, bifurcation analysis, stochastic influences, diffusion, and optimal control. It begins with an introductory overview of epidemiological concepts, historical modeling approaches, and methodologies. The subsequent chapters present the author's original contributions, analyzing various epidemic models under deterministic, delayed, stochastic, and controlled frameworks.
Three Body Scattering Problem
This book introduces the classical three-body problem, highlighting its complexity, non-integrability, and relevance in celestial mechanics. Discusses types of three-body systems and basic solution approaches. Applies the restricted three-body model to analyze the Moon's motion under the gravitational influence of Earth and the Sun, including effects like orbital perturbations and tidal interactions. This book explores temporary interactions among three bodies, focusing on scattering, capture, and escape phenomena. Describes chaotic behavior and energy exchanges during close encounters. Analyzes how binaries interact with a third body, leading to outcomes like binary disruption, exchange, or tightening. Crucial in stellar dynamics and compact object interactions. Examines how giant molecular clouds gravitationally perturb Oort Cloud comets, triggering inward migration and potential comet showers in the solar system.
The Statistical Methods
This book acquaints the readers with the mathematical and statistical aspects extensively used in a variety of disciplines of social, biological and engineering sciences. The statistical models find tremendous applications through their use in facilitating economic evaluation and in a number of decision-making contexts. In the present era, the applications of statistical techniques to a variety of disciplines including economics, commerce, biology, chemistry and physics are of great importance and the present book meets the requirements of these researchers.
Forced Convection Heat Transfer Inparallel Plate Channels Partially Fi
This book explains the hydrodynamic and thermal behavior of laminar Newtonian fluid flow in channels partially filled with porous material, symmetrically distributed at the walls. Using the Successive Accelerated Replacement (SAR) numerical scheme, the analysis explores the influence of porous fraction (γₚ), Darcy number (Da), Peclet number (Pe), and Brinkman number (Br) on flow and heat transfer. Results show that axial conduction significantly affects temperature profiles at low Pe (
Nonlinear Convection in Earth’s Outer Core
I worked on linear and weakly non-linear theories on magneto convection in a rotating fluid with isotropic/anisotropic diffusivities using analytical methods. In linear stability analysis, we have determined the marginal stability curves at the onset of stationary and oscillatory convection using one-term Galerkin method. In weakly nonlinear analysis, a two dimensional non-linear amplitude equation near the onset of stationary and oscillatory convection has been derived. Conditions for the occurrence of secondary instabilities such as Eckhaus and Zigzag instabilities are studied. Also, stability regions of travelling waves and standing waves are studied.
Analysis of Numerical Schemes to Singular Perturbation Problems
The primary goal of this book is to present, evaluate, and analyze efficient numerical methods for solving a specific class of singularly perturbed differential equations characterized by boundary and interior layer behaviors. Organized into six chapters, the book begins with a detailed overview of definitions, motivations, singular perturbation problems, differential-difference equations, boundary layers, and a comprehensive literature review. Subsequent chapters introduce advanced numerical methods, such as adaptive splines, numerical integration on specialized meshes, trigonometric splines, and fitted numerical schemes using the backward Euler method, to address interior layer problems, differential-difference equations, and singularly perturbed parabolic differential-difference equations. These studies underscore the significance of developing numerical techniques for singularly perturbed differential-difference equations. The research emphasizes creating simple, non-asymptotic, user-friendly, and efficient methods that are easily adaptable for computer implementation with minimal preparation.
Mathematics of Machine Learning
Build a solid foundation in the core math behind machine learning algorithms with this comprehensive guide to linear algebra, calculus, and probability, explained through practical Python examplesPurchase of the print or Kindle book includes a free PDF eBookKey Features: - Master linear algebra, calculus, and probability theory for ML- Bridge the gap between theory and real-world applications- Learn Python implementations of core mathematical conceptsBook Description: Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you'll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts.PhD mathematician turned ML engineer Tivadar Danka-known for his intuitive teaching style that has attracted 100k+ followers-guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you'll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors.By the end of this book, you'll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements.What You Will Learn: - Understand core concepts of linear algebra, including matrices, eigenvalues, and decompositions- Grasp fundamental principles of calculus, including differentiation and integration- Explore advanced topics in multivariable calculus for optimization in high dimensions- Master essential probability concepts like distributions, Bayes' theorem, and entropy- Bring mathematical ideas to life through Python-based implementationsWho this book is for: This book is for aspiring machine learning engineers, data scientists, software developers, and researchers who want to gain a deeper understanding of the mathematics that drives machine learning. A foundational understanding of algebra and Python, and basic familiarity with machine learning tools are recommended.Table of Contents- Vectors and vector spaces- The geometric structure of vector spaces- Linear algebra in practice spaces: measuring distances- Linear transformations- Matrices and equations- Eigenvalues and eigenvectors- Matrix factorizations- Matrices and graphs- Functions- Numbers, sequences, and series- Topology, limits, and continuity- Differentiation- Optimization- Integration- Multivariable functions- Derivatives and gradients- Optimization in multiple variables- What is probability?- Random variables and distributions- The expected value- The maximum likelihood estimation- It's just logic- The structure of mathematics- Basics of set theory- Complex numbers
How to talk about Mathematics. Wie man 羹ber Mathematik spricht.
In this booklet, you find the language of describing and explaining mathematical concepts, symbols, and procedures in English and German. This booklet is intended to assist people who have to learn, to teach or to apply mathematics while using English or German as a foreign language. In diesem B羹chlein findet man die Sprache der Beschreibung und Erkl瓣rung mathematischer Begriffe, Symbole und Prozeduren. Dieses B羹chlein soll Leute unterst羹tzen, die Mathematik lernen, anwenden oder lehren m羹ssen, w瓣hrend sie Englisch oder Deutsch als Fremdsprache nutzen.
Varia Mesopotamica
The central theme of the 21 essays collected here and written between 1989 and 2019 is Ancient Mesopotamian Mathematics - its techniques and concepts, but also its historical dynamics and its influence on later Greek and Arabic (and thus to later European) mathematical reasoning. In addition, the first essay deals with historical dynamics in the field of language and argues that the Sumerian as a language originated from a creole language of the slaves of the late fourth millennium and only thereafter developed into the elaborate Sumerian language attested in the late 3rd Millennium BCE.
An Introduction to String Diagrams for Computer Scientists
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
An Introduction to String Diagrams for Computer Scientists
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
Elements Of Arithmetic
Unlock the timeless wisdom of numbers with "Elements of Arithmetic" by Augustus De Morgan, a masterpiece that has been out of print for decades and is now beautifully restored by Alpha Editions. This isn't just a reprint; it's a collector's item and a cultural treasure, meticulously revived for today's and future generations. Dive into the mind of one of history's greatest mathematical thinkers as De Morgan unravels the mysteries of arithmetic with clarity and elegance. This classic work offers a unique blend of rigorous logic and engaging narrative, making complex concepts accessible to all. Whether you're a casual reader or a devoted collector of classic literature, this edition promises to enrich your understanding and appreciation of mathematics. Experience the joy of discovery as you explore the foundational principles that have shaped modern arithmetic. With its timeless insights and enduring value, "Elements of Arithmetic" is more than a book it's a journey into the heart of mathematical beauty. Don't miss the chance to own this exquisite piece of literary history, lovingly restored for you to cherish and enjoy.
Mathematics for Data Science and Artificial Intelligence
This book provides a comprehensive foundation in the mathematical tools essential for modern data science and machine learning. It blends core subjects such as linear algebra, calculus, probability, statistics, optimization, and numerical methods with real-world applications. Readers explore matrix operations, eigenvalues, and dimensionality reduction techniques like PCA and t-SNE. Optimization is covered through gradient-based methods and regularization strategies. Probability theory, Bayes' theorem, and statistical inference form the basis for modeling uncertainty. Information theory concepts like entropy, cross-entropy, and KL divergence are applied to learning and feature selection. Efficient computational methods are introduced using Python/Numpy implementations. Advanced topics include graph theory for network analysis and stochastic models such as Markov chains and ARIMA for time series forecasting. This book bridges theory and practice, offering step-by-step problem-solving, coding exercises, and a deep understanding of the mathematical backbone driving AI and data science.
Polygraphs: From Rewriting to Higher Categories
This is the first book to revisit the theory of rewriting in the context of strict higher categories, through the unified approach provided by polygraphs, and put it in the context of homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the coherence of algebraic structures. Illustrated with algorithmic computations on algebraic structures, the only prerequisite in this section is basic category theory. The theory is introduced step-by-step, with detailed proofs. The second half introduces and studies the general notion of n-polygraph, before addressing the homotopy theory of these polygraphs. It constructs the folk model structure on the category on strict higher categories and exhibits polygraphs as cofibrant objects. This allows the formulation of higher-dimensional generalizations of the coherence results developed in the first half. Graduate students and researchers in mathematics and computer science will find this work invaluable.
Handbook of Algebra and Algebraic Topology
Covering all aspects of Elementary Algebra, it will surely serve as the complete elementary textbook for studying different concepts.The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples.The content of the book is sequentially presented in the book for easy and comprehensive learning.This book forms a strong basis for students and teachers engaged in the field of mathematics especially algebra and algebraic topology.
Essentials of Nonlinearity Bifurcation and Chaos Theory
"Essentials of Nonlinearity, Bifurcation, and Chaos Theory" provides a concise yet comprehensive overview of these fundamental concepts in dynamical systems theory. This book introduces readers to the principles of nonlinear dynamics, bifurcation theory, and chaos theory, exploring their applications across various scientific disciplines. Through clear explanations and illustrative examples, readers gain insight into the behavior of nonlinear systems, including their stability, bifurcation points, and chaotic dynamics. Whether you're a student, researcher, or practitioner in fields such as physics, engineering, biology, or economics, this book serves as an essential guide to understanding the intriguing phenomena of nonlinearity, bifurcation, and chaos and their implications for modeling and analysis in complex systems.
Introduction to Modern Algebra
It covers a range of topics related to the study of algebra, from the basics of set theory to advanced topics such as Galois Theory and representation theory. The book begins with an overview of modern algebra and its importance in various fields of mathematics and also covers the history and development of ring theory, including its applications in algebraic geometry and number theory.The book covers the basics of set theory, including the axioms of set theory and cardinality and introduces module theory, which is a generalization of vector spaces, and its applications in various fields of mathematics.The book discusses the applications of commutative algebra in algebraic geometry and algebraic number theory and also includes a discussion of current research topics in group theory.The book covers the history and development of Galois Theory and discusses the importance of representation theory in various fields of mathematics, including physics and geometry.It is suitable for undergraduate and graduate students as well as researchers in mathematics and related fields.
Modern Trigonometry
"Modern Trigonometry" provides a comprehensive overview of trigonometric principles, techniques, and applications in contemporary mathematics and scientific inquiry. Through collaboration with experts, this book covers topics such as trigonometric functions, identities, equations, vectors, complex numbers, Fourier analysis, and applications in fields such as physics, engineering, computer graphics, and signal processing. With theoretical foundations and practical applications, readers gain a thorough understanding of modern trigonometry. Bridging theory and application, this book empowers readers to appreciate the beauty and utility of trigonometric concepts in the modern age.
Introduction to Finite Elements in Engineering
"Introduction to Finite Elements in Engineering" provides a comprehensive introduction to the fundamentals of finite element analysis and its application in engineering problem-solving. Through collaboration with experts, this book covers topics such as mathematical foundations, element formulations, numerical techniques, software tools, and practical applications in structural, thermal, and fluid analysis. With theoretical explanations and practical examples, readers gain insights into understanding and applying FEA concepts in engineering practice. Bridging theory and application, this book empowers readers to leverage the power of computational simulation to innovate and advance engineering design and analysis.
AP Calculus Study Guide AP 微积分 AB/BC 指导用书
本书是一部系统全面的微积分教程，涵盖了从基础概念到高级应用的完整内容。书中包括了极限与连续性、微分及其基本性质、复合函数的微分、积分及其累积变化、微分方程和积分应用等主题。内容结构清晰，循序渐进，辅以大量的例题和解析，帮助学生理解并掌握微积分的核心概念及解题技巧，特别适用于准备AP微积分的学习者。这部书为学生提供了深入的理论知识和实用的数学工具，使其能更好地理解和应用微积分于实际问题中。This book is a systematic and comprehensive calculus tutorial that covers a complete range of content from basic concepts to advanced applications. The book includes topics such as limits and continuity, differentiation and its basic properties, differentiation of composite functions, integration and its cumulative change, differential equations, and applications of integration. With a clear content structure and a step-by-step approach, it is supplemented by a large number of examples and analyses to help students understand and master the core concepts of calculus and problem-solving techniques. It is especially suitable for learners preparing for AP Calculus. This book provides students with in-depth theoretical knowledge and practical mathematical tools, enabling them to better understand and apply calculus to practical problems.
The Geometry of Equilibrium
James Clerk Maxwell is one of the giants of scientific thought, and whilst his groundbreaking contributions to electromagnetism and statistical physics are well known, his profound insights into the theory of structures are appreciated less widely. Maxwell's approach was deeply geometrical, and this richly illustrated book reveals his astute perception of the remarkable dualities that exist between the form of a structure and the forces it can carry, with understandings that will surprise contemporary readers. Early chapters introduce the background in which Maxwell was working, followed by contributions by leading researchers describing the latest applications of these ideas. Subsequent chapters introduce the many subtopics that this work embraces. The book ends with Maxwell's original papers on structural mechanics, each annotated to highlight and explain the ideas therein. This is a wonderful resource for mathematicians, scientists, engineers, and designers to enter this rich and underexplored aspect of the genius of Maxwell.
A Little History of Mathematics
A lively, accessible history of mathematics throughout the ages and across the globe Mathematics is fundamental to our daily lives. Science, computing, economics--all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from? In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers. Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad's House of Wisdom, and sangaku geometrical theorems at Japanese shrines. Lawrence goes beyond the familiar names of Newton and Pascal, exploring the prominent role women have played in the history of maths, including Emmy Noether and Maryam Mirzakhani.
HESI Math Workbook
Over 200 HESI A2(R) practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! You have arrived!Here is everything you need to pass the HESI(R) Math! We have helped thousands of students and we can help you!Complete HESI Math workbook, prepared by exam experts, with over 200 questions. Basic MathSolving Word ProblemsSolve Algebra EquationsMetric ConversionData InterpretationWhy Us?The Complete Test Preparation Team has been publishing high quality study materials since 2005, with a catalogue of over 145 titles, in English, French and Chinese, as well as ESL curriculum for all levels.You have come to the right place.If you want to spend your valuable study time where it will help you the most - we've got you covered today and tomorrow.You can pass the HESI with a great score! Here is how! You already know that Practice Makes Perfect! The more questions you see, and the more you practice - the better your HESI score! HESI A2(R) Math practice questions, easy-to-read tutorials explaining everything in plain language, exam tips and tricks, math shortcuts, and multiple choice strategies! Everything you need, complied by a dedicated team of experts with everything you need all in one place! Please note that HESI(R) is a registered trademark of the Health Education Systems Inc., which was not involved in the production of, and does not endorse, this product. Practice Really Does Make Perfect! The more questions you see, the more likely you are to pass the test. And between our study guide and practice tests, you'll have over 200 practice questions that cover every category. Our practice test questions have been developed by our dedicated team of experts. All the material in the study guide, including every practice question, are designed to engage your critical thinking skills needed to pass the test! Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Carleman Estimates in Mean Field Games
This book provides a comprehensive exploration of Mean Field Games (MFG) theory, a mathematical framework for modeling the collective behavior of rational agents in complex systems. MFG theory can govern a range of societal phenomena, including finance, sociology, machine learning, and economics. The focus is on the system of two coupled nonlinear parabolic partial differential equations (PDEs) that define the Mean Field Games System. The book covers key theoretical topics such as solution stability and uniqueness, with a particular emphasis on Carleman estimates, which are used to estimate solution errors based on noise in the input data. It also introduces the theory of Ill-Posed and Inverse Problems within MFG theory. Both theoretical and numerical aspects of forward and inverse problems are explored through Carleman estimates, offering a rigorous foundation for researchers and practitioners in applied mathematics and related fields. This book offers a rigorous approach to Carleman estimates, a key element of Mean Field Games theory, making it an essential resource for researchers, graduate students, and professionals looking to apply this powerful framework to complex, real-world systems.
Multivariable Calculus
Foundations of Multivariable Functions: Provide a comprehensive introduction to functions of multiple variables, including definitions, graphical interpretations, and basic properties. Cover topics such as partial derivatives, gradient vectors, and the concept of differentiability for functions of several variables.Multiple Integration Techniques: Explore techniques for evaluating multiple integrals, including double and triple integrals. Discuss applications of multiple integrals in calculating areas, volumes, and other physical quantities. Include methods for changing variables, such as polar, cylindrical, and spherical coordinates.Vector Calculus and Field Theory: Examine key concepts in vector calculus, including vector fields, line integrals, surface integrals, and flux. Discuss fundamental theorems such as Green's Theorem, Stokes' Theorem, and the Divergence Theorem, and their applications in physics and engineering.Optimization and Constrained Optimization: Discuss methods for optimization in multivariable settings, including finding local and global extrema of functions. Cover techniques such as Lagrange multipliers for constrained optimization problems and the use of Hessian matrices for analyzing critical points.Applications and Advanced Topics: Address various applications of multivariable calculus in fields such as physics, engineering, economics, and computer science. Include advanced topics such as differential forms, manifold theory, and the applications of multivariable calculus in differential equations and dynamical systems.
Introductory Discrete Mathematics
Fundamental Concepts: Provide an overview of foundational concepts in discrete mathematics, including sets, relations, functions, and basic logic. Explain how these concepts form the basis for more advanced topics in discrete mathematics.Combinatorics and Counting: Explore combinatorial methods and counting principles, including permutations, combinations, the pigeonhole principle, and inclusion-exclusion principles. Discuss their applications in solving counting problems and understanding discrete structures.Graph Theory: Introduce the basics of graph theory, including definitions and properties of graphs, types of graphs (e.g., directed, undirected, weighted), and key concepts such as paths, cycles, connectivity, and graph coloring.Applications of Discrete Mathematics: Explore the practical applications of discrete mathematics in computer science, including its role in cryptography, network design, coding theory, and algorithm design. Discuss how discrete mathematics provides tools for solving real-world problems in these areas.
Mathematical Modeling and Control of COVID-19 and Its Variants
In this book, we developed a new hybrid deterministic model, we do this by considering several essential properties of the pandemic COVID-19, such as the existence of individuals tested positive for COVID-19 with severe, mild, or asymptomatic symptoms, and dividing infectious compartment into two essential compartments of hospitalized individuals and those in intensive care units. The content of this book is divided into 3 chapters: In the first chapter, we study the stability properties of the solutions of a proposed nonlinear mathematical model with nine compartments, namely, susceptible-exposed infectious with severe symptoms-infectious with mild symptoms-asymptomatic infectious-hospitalized intensive care unit-dead infectious corpses-recovered to investigate the current outbreak of coronavirus disease (COVID-19) in Morocco and beyond. In the second chapter, we employed the control theory procedure to better understand the ways to maintain the progression of the COVID-19 outbreak and its variant Omicron in a case study of Morocco by designing optimal disease intervention strategies.The third chapter is devoted to expand the proposed nonlinear model into a fractional-order COVID.
Vector Calculus
It strives to present the material in a clear and accessible manner, with a focus on providing practical examples and applications to various fields such as physics, engineering, computer graphics, and more.Covers the essential concepts of vectors in three-dimensional Euclidean space and explains vector operations, including addition, subtraction, scalar multiplication, and dot product.Discusses partial derivatives, gradient vectors, directional derivatives, and tangent planes and also provides a comprehensive introduction to double and triple integrals.Demonstrates techniques for evaluating integrals using different coordinate systems and covers line integrals and their relationship to work and circulation.This book serves as a valuable resource for students studying mathematics, physics, engineering, and related disciplines. It also serves as an excellent reference for professionals seeking a concise and practical guide to vector calculus.
Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications
This Special Issue of Axioms entitled "Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking, and Their Applications" consists of a collection of ten papers written by eminent mathematicians and experts in their fields, covering numerous different areas of fuzzy MCDM, hybrid methods, ranking methods, and/or their applications. The objective of this Special Issue is to provide a platform for researchers to publish their recent work, delve deeper into various problems, and solve them mathematically.
Number Theory and Geometry Through History
Developed from a course on the history of mathematics, the book is aimed at school teachers of mathematics who need to learn more about mathematics than its history, and in a way they can communicate to middle and high school students. The author hopes to overcome, through these teachers using this book, math phobia among these students.
Number Theory and Geometry Through History
Developed from a course on the history of mathematics, the book is aimed at school teachers of mathematics who need to learn more about mathematics than its history, and in a way they can communicate to middle and high school students. The author hopes to overcome, through these teachers using this book, math phobia among these students.
Generalization of Some Inequalities for Rational Functions with Prescribed Poles
Elements of Algebraic Topology
With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for communicating complex topics and the fun nature of algebraic topology for beginners.
Game-Based Learning, Gamification in Education and Serious Games 2023
In a world where video games are more than just entertainment, Current Advances in Serious Games, Game-based Learning and Gamification in Education explores the transformative power of games in shaping learning, awareness, and engagement. This collection highlights groundbreaking research on game-based learning, digital intelligence, and adaptive gamification. Featuring insights from leading experts, it examines how serious games combat misinformation, enhance media literacy, promote cultural heritage, and personalize educational experiences. Whether you are an educator, researcher, developer, or game enthusiast, this book provides a compelling look at how games are revolutionizing education, training, and social awareness. Dive into the cutting-edge world where learning meets play!
