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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.
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