Michael A. Radin – författare

Introduction to Recognition and Deciphering of Patterns is meant to acquaint STEM and non-STEM students with different patterns, as well as to where and when specific patterns arise. In addition, the book teaches students how to recognize patterns and distinguish the similarities and differences between them.Patterns, such as weather patterns, traffic patterns, behavioral patterns, geometric patterns, linguistic patterns, structural patterns, digital patterns, and the like, emerge on an everyday basis, . Recognizing patterns and studying their unique traits are essential for the development and enhancement of our intuitive skills and for strengthening our analytical skills. Mathematicians often apply patterns to get acquainted with new concepts--a technique that can be applied across many disciplines.Throughout this book we explore assorted patterns that emerge from various geometrical configurations of squares, circles, right triangles, and equilateral triangles that either repeat at the same scale or at different scales. The book also analytically examines linear patterns, geometric patterns, alternating patterns, piecewise patterns, summation-type patterns and factorial-type patterns. Deciphering the details of these distinct patterns leads to the proof by induction method, and the book will also render properties of Pascal’s triangle and provide supplemental practice in deciphering specific patterns and verifying them.This book concludes with first-order recursive relations: describing sequences as recursive relations, obtaining the general solution by solving an initial value problem, and determining the periodic traits.Features• Readily accessible to a broad audience, including those with limited mathematical background• Especially useful for students in non-STEM disciplines, such as psychology, sociology, economics and business, as well as for liberal arts disciplines and art students.

Introduction to Recognition and Deciphering of Patterns is meant to acquaint STEM and non-STEM students with different patterns, as well as to where and when specific patterns arise. In addition, the book teaches students how to recognize patterns and distinguish the similarities and differences between them.Patterns, such as weather patterns, traffic patterns, behavioral patterns, geometric patterns, linguistic patterns, structural patterns, digital patterns, and the like, emerge on an everyday basis, . Recognizing patterns and studying their unique traits are essential for the development and enhancement of our intuitive skills and for strengthening our analytical skills. Mathematicians often apply patterns to get acquainted with new concepts--a technique that can be applied across many disciplines.Throughout this book we explore assorted patterns that emerge from various geometrical configurations of squares, circles, right triangles, and equilateral triangles that either repeat at the same scale or at different scales. The book also analytically examines linear patterns, geometric patterns, alternating patterns, piecewise patterns, summation-type patterns and factorial-type patterns. Deciphering the details of these distinct patterns leads to the proof by induction method, and the book will also render properties of Pascal’s triangle and provide supplemental practice in deciphering specific patterns and verifying them.This book concludes with first-order recursive relations: describing sequences as recursive relations, obtaining the general solution by solving an initial value problem, and determining the periodic traits.Features• Readily accessible to a broad audience, including those with limited mathematical background• Especially useful for students in non-STEM disciplines, such as psychology, sociology, economics and business, as well as for liberal arts disciplines and art students.

Introduction to Math Olympiad Problems aims to introduce high school students to all the necessary topics that frequently emerge in international Math Olympiad competitions. In addition to introducing the topics, the book will also provide several repetitive-type guided problems to help develop vital techniques in solving problems correctly and efficiently. The techniques employed in the book will help prepare students for the topics they will typically face in an Olympiad-style event, but also for future college mathematics courses in Discrete Mathematics, Graph Theory, Differential Equations, Number Theory and Abstract Algebra.Features: Numerous problems designed to embed good practice in readers, and build underlying reasoning, analysis and problem-solving skills Suitable for advanced high school students preparing for Math Olympiad competitions

Introduction to Math Olympiad Problems aims to introduce high school students to all the necessary topics that frequently emerge in international Math Olympiad competitions. In addition to introducing the topics, the book will also provide several repetitive-type guided problems to help develop vital techniques in solving problems correctly and efficiently. The techniques employed in the book will help prepare students for the topics they will typically face in an Olympiad-style event, but also for future college mathematics courses in Discrete Mathematics, Graph Theory, Differential Equations, Number Theory and Abstract Algebra.Features: Numerous problems designed to embed good practice in readers, and build underlying reasoning, analysis and problem-solving skills Suitable for advanced high school students preparing for Math Olympiad competitions

Piece-wise and Max-Type Difference Equations: Periodic and Eventually Periodic Solutions is intended for lower-level undergraduate students studying discrete mathematics. The book focuses on sequences as recursive relations and then transitions to periodic recursive patterns and eventually periodic recursive patterns. In addition to this, it will also focus on determining the patterns of periodic and eventually periodic solutions inductively. The aim of the author, throughout this book, is to get students to understand the significance of pattern recognition as a mathematical tool.Key Features Can provide possible topics for undergraduate research and for bachelor’s thesis Provides supplementary practice problems and some open-ended research problems at the end of each chapter Focusses on determining the patterns of periodic and eventually periodic solutions inductively Enhances students’ algebra skills before moving forward to upper level courses Familiarize students with the topics before they start undergraduate research by providing applications.

Piece-wise and Max-Type Difference Equations: Periodic and Eventually Periodic Solutions is intended for lower-level undergraduate students studying discrete mathematics. The book focuses on sequences as recursive relations and then transitions to periodic recursive patterns and eventually periodic recursive patterns. In addition to this, it will also focus on determining the patterns of periodic and eventually periodic solutions inductively. The aim of the author, throughout this book, is to get students to understand the significance of pattern recognition as a mathematical tool.Key Features Can provide possible topics for undergraduate research and for bachelor’s thesis Provides supplementary practice problems and some open-ended research problems at the end of each chapter Focusses on determining the patterns of periodic and eventually periodic solutions inductively Enhances students’ algebra skills before moving forward to upper level courses Familiarize students with the topics before they start undergraduate research by providing applications.

This textbook on periodic character and patterns of recursive sequences focuses on discrete periodic patterns of first order, second order and higher order difference equations.

"Radlin has done a nice job in producing a textbook which provides a learner friendly introduction to difference equations. It would suit as a core text for a first year course in the topic, aimed, as the title suggests, at physical science or engineering undergraduates. The student who is prepared to work through the book will get a good grounding in basic techniques and gain a feel for the possible behaviours of standard equations. He will also be given some indication of the usefulness and potential complexity of discrete systems in modern science and engineering."London Mathematical SocietyWe introduce interdisciplinary research and get students and the audience familiarized with the difference equations; solving them explicitly, determining the long-term behavior of solutions (convergence, boundedness and periodicity). We help to develop intuition in analyzing convergence of solutions in terms of subsequences and analyzing patterns of periodic cycles. Our book helps you learn applications in biology, economics and business, computer science and engineering.

"Radlin has done a nice job in producing a textbook which provides a learner friendly introduction to difference equations. It would suit as a core text for a first year course in the topic, aimed, as the title suggests, at physical science or engineering undergraduates. The student who is prepared to work through the book will get a good grounding in basic techniques and gain a feel for the possible behaviours of standard equations. He will also be given some indication of the usefulness and potential complexity of discrete systems in modern science and engineering."London Mathematical SocietyWe introduce interdisciplinary research and get students and the audience familiarized with the difference equations; solving them explicitly, determining the long-term behavior of solutions (convergence, boundedness and periodicity). We help to develop intuition in analyzing convergence of solutions in terms of subsequences and analyzing patterns of periodic cycles. Our book helps you learn applications in biology, economics and business, computer science and engineering.

The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.

The book's primary objectives are to welcome you to the abundant and meaningful international and multidisciplinary education discovery journey. You will grow from exposure to other cultures and their practices and I daresay, become better teachers in your local as well as on-line environments. Most every local classroom is multi-cultural as well. The students have different backgrounds and different ways of internalizing information meaningfully.The book will provide practical examples how to design, promote and teach various courses and seminars abroad. Examples are those the author experienced with a specific pedagogical idea that is successful in one system, however, the same concept may face unexpected challenges or fail in another system. Most importantly, the book will focus on applying feedback as vital tools that will guide us to the designing, promoting and teaching mathematics and multidisciplinary courses and seminars. The book's most important goal is to make international and multidisciplinary education accessible to everyone.The book will compare several educational systems as well as their similarities and differences. These include different teaching and learning styles, students' preparation levels, and students' interests and value orientations. The goal is to inspire you to embark on your own innovative discovery journey, seek out multi-cultural and international teaching opportunities and to effectively reach, effectively communicate information and help students learn.

The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.

The book's primary objectives are to welcome you to the abundant and meaningful international and multidisciplinary education discovery journey. You will grow from exposure to other cultures and their practices and I daresay, become better teachers in your local as well as on-line environments. Most every local classroom is multi-cultural as well. The students have different backgrounds and different ways of internalizing information meaningfully.The book will provide practical examples how to design, promote and teach various courses and seminars abroad. Examples are those the author experienced with a specific pedagogical idea that is successful in one system, however, the same concept may face unexpected challenges or fail in another system. Most importantly, the book will focus on applying feedback as vital tools that will guide us to the designing, promoting and teaching mathematics and multidisciplinary courses and seminars. The book's most important goal is to make international and multidisciplinary education accessible to everyone.The book will compare several educational systems as well as their similarities and differences. These include different teaching and learning styles, students' preparation levels, and students' interests and value orientations. The goal is to inspire you to embark on your own innovative discovery journey, seek out multi-cultural and international teaching opportunities and to effectively reach, effectively communicate information and help students learn.

This book first presents the evolution of education, from traditional face-to-face to the current remote and online education and its various iterations. The author shares experiences and insights on the most effective teaching techniques in both environments, some recent approaches, and highlights where there is need for continued improvement. Educators are provided with practical suggestions and examples to aid them in the design, promotion, and teaching of online courses worldwide. Topics include applying student and colleague feedback to improve teaching skills in an online setting; benefits of teaching, learning, and working in an online environment; and contrasts between synchronous and asynchronous modes of online instruction, among others. The ultimate goal is to promote accessible and equitable online education for all, regardless of the pandemics or political unrest. The reader is invited on a hands-on journey to discover the potential of the online educational experience, with thought-provoking questions to encourage reflection and growth along the way.

This book first presents the evolution of education, from traditional face-to-face to the current remote and online education and its various iterations. The author shares experiences and insights on the most effective teaching techniques in both environments, some recent approaches, and highlights where there is need for continued improvement. Educators are provided with practical suggestions and examples to aid them in the design, promotion, and teaching of online courses worldwide. Topics include applying student and colleague feedback to improve teaching skills in an online setting; benefits of teaching, learning, and working in an online environment; and contrasts between synchronous and asynchronous modes of online instruction, among others. The ultimate goal is to promote accessible and equitable online education for all, regardless of the pandemics or political unrest. The reader is invited on a hands-on journey to discover the potential of the online educational experience, with thought-provoking questions to encourage reflection and growth along the way.

This comprehensive book intricately weaves together the disciplines of systems thinking, management, educational leadership, complexity science, and diversity. Unique in its approach, it bridges theoretical concepts with real-world applications providing educators, managers, and leaders with practical tools and strategies for implementing systems thinking in diverse educational and managerial contexts. This book is particularly valuable for those interested in emergent learning, future planning, and decision-making processes.Designed for a broad audience, this book is an ideal resource for those seeking to enhance their strategic thinking and decision-making skills in dynamic and diverse environments. Readers will find a thoughtful blend of theory and practice, with each chapter presenting examples and case studies that demonstrate the application of systems thinking in various scenarios.Whether you are an educator seeking innovative approaches to teaching and curriculum development, a manager looking to foster a more inclusive and systemic approach in your organization, or a leader navigating complex challenges, this book offers you valuable insights and guidance. It stands as a testament to the power of interdisciplinary thought and the importance of integrating diversity and complexity into management and educational practices.

This comprehensive book intricately weaves together the disciplines of systems thinking, management, educational leadership, complexity science, and diversity. Unique in its approach, it bridges theoretical concepts with real-world applications providing educators, managers, and leaders with practical tools and strategies for implementing systems thinking in diverse educational and managerial contexts. This book is particularly valuable for those interested in emergent learning, future planning, and decision-making processes.Designed for a broad audience, this book is an ideal resource for those seeking to enhance their strategic thinking and decision-making skills in dynamic and diverse environments. Readers will find a thoughtful blend of theory and practice, with each chapter presenting examples and case studies that demonstrate the application of systems thinking in various scenarios.Whether you are an educator seeking innovative approaches to teaching and curriculum development, a manager looking to foster a more inclusive and systemic approach in your organization, or a leader navigating complex challenges, this book offers you valuable insights and guidance. It stands as a testament to the power of interdisciplinary thought and the importance of integrating diversity and complexity into management and educational practices.

This book's primary aims is to welcome you to discover the characteristics of the international and multidisciplinary online education in Ukraine. It objective is to present the development of online teaching and learning environment in Ukraine. In particular, this book emphasizes how the online teaching and learning environment expanded during COVID-19 in 2020-2021 and has also become an essential learning environment during the ongoing Russia-Ukraine War.Many new teaching strategies, courses, and programs of study and exchange programs have been established in recent years of the online teaching and learning environment in Ukraine during COVID-19 and are still vital communications during the Russia-Ukraine War which led to the circumstances of limited internet and delayed communication.The current education environment in Ukraine presented new experiential learning opportunities and welcomed critical fundamentals and benefits of diversity, equity and inclusion to Ukrainian students and attracted foreign students as well. We invite you to learn about the unique, extended Ukrainian online international and multidisciplinary academic journey that has introduced new teaching and learning practices, innovative technologies, new courses and programs of study, and, most importantly, new assessment methods.

This book's primary aims is to welcome you to discover the characteristics of the international and multidisciplinary online education in Ukraine. It objective is to present the development of online teaching and learning environment in Ukraine. In particular, this book emphasizes how the online teaching and learning environment expanded during COVID-19 in 2020-2021 and has also become an essential learning environment during the ongoing Russia-Ukraine War.Many new teaching strategies, courses, and programs of study and exchange programs have been established in recent years of the online teaching and learning environment in Ukraine during COVID-19 and are still vital communications during the Russia-Ukraine War which led to the circumstances of limited internet and delayed communication.The current education environment in Ukraine presented new experiential learning opportunities and welcomed critical fundamentals and benefits of diversity, equity and inclusion to Ukrainian students and attracted foreign students as well. We invite you to learn about the unique, extended Ukrainian online international and multidisciplinary academic journey that has introduced new teaching and learning practices, innovative technologies, new courses and programs of study, and, most importantly, new assessment methods.

This book will reveal the essence of creative digital thinking and its significance in the new horizon of creative learning styles in the Education 1.0-7.0 Spectrum. This book asks and answers current pertinent questions such as: What new windows of opportunity does the 21st century / post- COVID New Creative Learning landscape present in online, hybrid, and blended learning environments? How can the reader design and expand the creative diversity spectrum digitally and technically? To obtain stronger learning outcomes, how does one accurately and effectively transform abstract thinking, alternative thinking, comparative thinking, divergent thinking, and creative thinking into Digital Thinking? How much adaptation from the traditional learning environment is needed for a transition to digital thinking? We will examine the intersection of creative education, digitalization, and sustainability within effective modern teaching and learning styles within our chapters. This book aims to present the significance of digital design, learning, and thinking to bridge the gaps and missing fragments that are often found between theoretical knowledge and practical implementation (of classrooms and experiential learning activities). Closing such a gap is essential for cultivating a workforce capable of harnessing digital tools to address the complex challenges facing modern education.