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.

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 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.

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

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 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.

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 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.

'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.

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. Aimed toward advanced undergraduate students and graduate students who have taken a basic course in Calculus I and Discrete Mathematics, this book serves as a core text for a course in Difference Equations and Discrete Dynamical Systems. The text contains over 200 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a first-hand introduction to patterns of periodic cycles and patterns of transient terms with exercises for most sections of the text, preparing them for significant research work in the area.

'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.

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.