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Books > Science & Mathematics > Mathematics > General
This book presents a simple and original theory of distributions,
both real and vector, adapted to the study of partial differential
equations. It deals with value distributions in a Neumann space,
that is, in which any Cauchy suite converges, which encompasses the
Banach and Frechet spaces and the same "weak" spaces. Alongside the
usual operations - derivation, product, variable change, variable
separation, restriction, extension and regularization -
Distributions presents a new operation: weighting. This operation
produces properties similar to those of convolution for
distributions defined in any open space. Emphasis is placed on the
extraction of convergent sub-sequences, the existence and study of
primitives and the representation by gradient or by derivatives of
continuous functions. Constructive methods are used to make these
tools accessible to students and engineers.
The relationship between research and practice has long been an
area of interest for researchers, policy makers, and practitioners
alike. One obvious arena where mathematics education research can
contribute to practice is the design and implementation of school
mathematics curricula. This observation holds whether we are
talking about curriculum as a set of broad, measurable competencies
(i.e., standards) or as a comprehensive set of resources for
teaching and learning mathematics. Impacting practice in this way
requires fine-grained research that is focused on individual
student learning trajectories and intimate analyses of classroom
pedagogical practices as well as large-scale research that explores
how student populations typically engage with the big ideas of
mathematics over time. Both types of research provide an empirical
basis for identifying what aspects of mathematics are important and
how they develop over time. This book has its origins in
independent but parallel work in Australia and the United States
over the last 10 to 15 years. It was prompted by a research seminar
at the 2017 PME Conference in Singapore that brought the
contributors to this volume together to consider the development
and use of evidence-based learning progressions/trajectories in
mathematics education, their basis in theory, their focus and
scale, and the methods used to identify and validate them. In this
volume they elaborate on their work to consider what is meant by
learning progressions/trajectories and explore a range of issues
associated with their development, implementation, evaluation, and
on-going review. Implications for curriculum design and future
research in this field are also considered. Contributors are:
Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary
Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret
Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates,
Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne
Siemon, Max Stephens, Ron Tzur, and Jane Watson.
This book introduces the specifics of mathematics lesson study with
regard to regional/national particularities, discussing the
methodological and theoretical tools that can be used to pursue
research on lesson study (its forms, contents, effects etc.) from
an international perspective. Lesson study and learning study (LS)
are becoming increasingly important in teacher education, mostly in
continuous professional development, but also in prospective
teachers' education, and this interest is accompanied by a demand
for more solid theorization of the lesson study process. A number
of social, cultural, cognitive and affective issues are reflected
in the way LS develops, and the book examines the latest results of
these developments.
This book is a blue print on the steps that must be taken to
make America great again.
It addresses America's problems from war to health care; from
energy and nuclear power to global warming; from illegal immigrants
to reinstitution of the draft of all young Americans; from a
national registration system for all Americans to a practical
solution to the financial difficulties of Social Security. The
views and solutions to these problems are expressed through the
eyes of Richard Michael White, a seventy-one year old man who holds
advanced degrees in both engineering and mathematics. As Richard's
life progresses from being a student in high school, to serving as
an Army Officer on active duty, to a thirty year professional
career, to his eventual, early retirement at the age of
fifty-seven, his view of America's most pressing problems changes
and solidifies into a coherent and detailed plan on solving these
problems.
The book begins as Richard describes the differences in the
current world from 1957 when he graduated from high school to the
present. He discusses Christianity and concludes that he might, or
might not, be a Christian depending or your definition what it
takes to be a Christian. He deals with the topics of love, sex,
marriage, and divorce, and shows that although they are all
related, they are all different. He believes that the most pressing
problem facing the world is population growth.
Richard addresses the subject of America's energy dependence and
pushes for an expansion of nuclear power. He also presses for the
development of nuclear power from the element Thorium. He lays out
a detailed blueprint to address Thorium's usage in power generation
as well as using government owned Thorium nuclear reactors for coal
gasification, shale oil extraction, and seawater desalination.
Exam Board: Pearson Edexcel Academic Level: A level Subject:
Mathematics First teaching: September 2017 First Exams: Summer 2018
This Revision Guide is suitable for classroom and independent
study, and is the smart choice for those revising for A level
Mathematics. Organise their revision with the one topic-per-page
format Speed up their revision with summary notes in short,
memorable chunks Track their revision progress with at-a-glance
check boxes Check their understanding with worked examples Develop
their exam technique with exam-style practice questions and answers
This book shows how the practice of script writing can be used both
as a pedagogical approach and as a research tool in mathematics
education. It provides an opportunity for script-writers to
articulate their mathematical arguments and/or their pedagogical
approaches. It further provides researchers with a corpus of
narratives that can be analyzed using a variety of theoretical
perspectives.Various chapters argue for the use of dialogical
method and highlight its benefits and special features. The
chapters examine both "low tech" implementations as well as the use
of a technological platform, LessonSketch. The chapters present
results of and insights from several recent studies, which utilized
scripting in mathematics education research and practice.
The three volumes of this series of books, of which this is the
second, put forward the mathematical elements that make up the
foundations of a number of contemporary scientific methods: modern
theory on systems, physics and engineering. Whereas the first
volume focused on the formal conditions for systems of linear
equations (in particular of linear differential equations) to have
solutions, this book presents the approaches to finding solutions
to polynomial equations and to systems of linear differential
equations with varying coefficients. Fundamentals of Advanced
Mathematics, Volume 2: Field Extensions, Topology and Topological
Vector Spaces, Functional Spaces, and Sheaves begins with the
classical Galois theory and the theory of transcendental field
extensions. Next, the differential side of these theories is
treated, including the differential Galois theory (Picard-Vessiot
theory of systems of linear differential equations with
time-varying coefficients) and differentially transcendental field
extensions. The treatment of analysis includes topology (using both
filters and nets), topological vector spaces (using the notion of
disked space, which simplifies the theory of duality), and the
radon measure (assuming that the usual theory of measure and
integration is known). In addition, the theory of sheaves is
developed with application to the theory of distributions and the
theory of hyperfunctions (assuming that the usual theory of
functions of the complex variable is known). This volume is the
prerequisite to the study of linear systems with time-varying
coefficients from the point-of-view of algebraic analysis and the
algebraic theory of nonlinear systems.
The relationship between research and practice has long been an
area of interest for researchers, policy makers, and practitioners
alike. One obvious arena where mathematics education research can
contribute to practice is the design and implementation of school
mathematics curricula. This observation holds whether we are
talking about curriculum as a set of broad, measurable competencies
(i.e., standards) or as a comprehensive set of resources for
teaching and learning mathematics. Impacting practice in this way
requires fine-grained research that is focused on individual
student learning trajectories and intimate analyses of classroom
pedagogical practices as well as large-scale research that explores
how student populations typically engage with the big ideas of
mathematics over time. Both types of research provide an empirical
basis for identifying what aspects of mathematics are important and
how they develop over time. This book has its origins in
independent but parallel work in Australia and the United States
over the last 10 to 15 years. It was prompted by a research seminar
at the 2017 PME Conference in Singapore that brought the
contributors to this volume together to consider the development
and use of evidence-based learning progressions/trajectories in
mathematics education, their basis in theory, their focus and
scale, and the methods used to identify and validate them. In this
volume they elaborate on their work to consider what is meant by
learning progressions/trajectories and explore a range of issues
associated with their development, implementation, evaluation, and
on-going review. Implications for curriculum design and future
research in this field are also considered. Contributors are:
Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary
Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret
Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates,
Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne
Siemon, Max Stephens, Ron Tzur, and Jane Watson.
The UK's most trusted A level Mathematics resources With over
900,000 copies sold (plus 1.3 million copies sold of the previous
edition), Pearson's own resources for Pearson Edexcel are the
market-leading and most trusted for AS and A level Mathematics.
This book covers all the content needed for the optional Edexcel AS
and A level Further Pure Mathematics 1 exams Enhanced focus on
problem-solving and modelling, as well as supporting the large data
set and calculators Packed with worked examples with guidance, lots
of exam-style questions, practice papers, and plenty of mixed and
review exercises Full worked solutions to every question available
free and online for quick and easy access. Plus free additional
online content with GeoGebra interactives and Casio calculator
tutorials Practice books also available offering the most
comprehensive and flexible AS/A level Maths practice with over 2000
extra questions Includes access to an online digital edition (valid
for 3 years once activated) Pearson Edexcel AS and A level Further
Mathematics Further Pure Mathematics 1 Textbook + e-book matches
the Pearson Edexcel exam structure and is fully integrated with
Pearson Edexcel's interactive scheme of work. All of the books in
this series focus on problem-solving and modelling, as well as
supporting the large data set and calculators. They are packed with
worked examples with guidance, lots of exam-style questions,
practice papers, and plenty of mixed and review exercises. There
are full worked solutions to every question available free and
online for quick and easy access. You will also have access to lots
of free additional online content with GeoGebra interactives and
Casio calculator tutorials. There are separate Pure and Applied
textbooks for AS and A level Maths, and a textbook per option for
AS and A level Further Maths. Practice books are also available
offering the most comprehensive and flexible AS/A level Maths
practice with over 2000 extra questions. Pearson's revision
resources are the smart choice for those revising for Pearson
Edexcel AS and A level Mathematics - there is a Revision Workbook
for exam practice and a Revision Guide for classroom and
independent study. Practice Papers Plus+ books contain additional
full length practice papers, so you can practice answering
questions by writing straight into the book and perfect your
responses with targeted hints, guidance and support for every
question, including fully worked solutions.
Mathematics teacher education includes the mathematics content
teachers need to understand, ways that pedagogical approaches are
developed, messages about the nature of mathematics teaching and
learning, and interfaces between tertiary preparation and school
contexts. Scholars from Sweden, France, Malawi, Singapore, New
Zealand, Brazil, the USA, and Canada provide insights for the
mathematics education community's understanding of how teacher
educators structure, develop, and implement their respective
mathematics teacher education programs. Several themes emerged
across the chapters, including: varied approaches to developing
culturally responsive pedagogies and/or Indigenous perspectives;
issues and challenges in fostering partnerships and collaborations;
strategies for developing mathematics knowledge for teaching; and
preparing flexible and resourceful teachers
A volume in Research on Women and Education (RWE) Series Editors
Beverly Irby, Sam Houston State University and Janice Koch, Hofstra
University Encouraging the participation of girls and women in
science, technology, engineering and mathematics (STEM) remains as
vital today as it was in the 1970s. ... hence, the sub-title: "A
Never Ending Story." This volume is about ongoing advocacy on
behalf of the future workforce in fields that lie on the cutting
edge of society's future. Acknowledging that deeply embedded
beliefs about social and academic entitlement take generations to
overcome, the editors of this volume forge forward in the knowledge
that these chapters will resonate with readers and that those in
positions of access will learn more about how to provide
opportunities for girls and women that propel them into STEM
fields. This volume will give the reader insight into what works
and what does not work for providing the message to girls and women
that indeed STEM fields are for them in this second decade of the
21st century. Contributions to this volume will connect to readers
at all levels of STEM education and workforce participation.
Courses that address teaching and learning in STEM fields as well
as courses in women's studies and the sociology of education will
be enhanced by accessing this volume. Further, students and
scholars in STEM fields will identify with the success stories
related in some of these chapters and find inspiration in the ways
their own journeys are reflected by this volume.
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