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The ever-growing applications and richness of approaches to the
Riordan group is captured in this comprehensive monograph, authored
by those who are among the founders and foremost world experts in
this field. Â The concept of a Riordan array has played a
unifying role in enumerative combinatorics over the last three
decades. The Riordan arrays and Riordan group is a new growth point
in mathematics that is both being influenced by, and continuing its
contributions to, other fields such as Lie groups, elliptic curves,
orthogonal polynomials, spline functions, networks, sequences and
series, Beal conjecture, Riemann hypothesis, to name several. In
recent years the Riordan group has made links to quantum field
theory and has become a useful tool for computer science and
computational chemistry. We can look forward to discovering further
applications to unexpected areas of research. Providing a baseline
and springboard to further developments and study, this book may
also serve as a text for anyone interested in discrete mathematics,
including combinatorics, number theory, matrix theory, graph
theory, and algebra.
Publisher's Note: Products purchased from Third Party sellers are
not guaranteed by the publisher for quality, authenticity, or
access to any online entitlements included with the product. Access
interactive cases on breast imaging for the best board review
possible!Part of McGraw-Hill's Radiology Case Review Series, this
unique resource challenges you to look at a group of images,
determine the diagnosis, answer related questions, and gauge your
knowledge by reviewing the answer. It all adds up to the best
interactive review of interventional radiology available--one
that's ideal for certification or recertification, or as an
incomparable clinical refresher. Distinguished by a cohesive 2-page
design, each volume in this series is filled with cases, annotated
images, questions & answers, pearls, and relevant literature
references that will efficiently prepare you for virtually any exam
topic. The book's cases are crosslinked to an online component that
includes full-resolution images, interactive image stacks,
discussions and extra teaching points that reinforce your grasp of
must-know interventional radiology topics. Radiology Case Review
Series Features 200 cases for each volume, which consist of:
Precise, state-of-the-art images accompanied by questions and
answers, descriptions of the entities, insightful clinical pearls,
and reference lists Intensive coverage of fundamental radiology
principles, the latest diagnostic imaging techniques, radiology
equipment, new technologies, and more Unique 2-page format for each
case, which features: Images with 5 questions on the right-hand
page Magnifications, annotations, and detailed answers on the verso
page--a benefit that you'll only find in this exceptional series!
Informative, bulleted comments box that provides important
additional context for each case Cases organized and coded by
difficulty level allowing you to evaluate your proficiency before
progressing to the next level Radiology-relevant scrolling and
stacking function A dedicated interactive website--accessible via
scratch-off code for each volume in the series--enables you to:
Scroll the images from each case in the text as well as stack
images (display multiple views of an image) Zoom in and out, or
scroll up and down, to highlight specific details of a subject
Access additional images for each case using the case ID number
from the text
The ever-growing applications and richness of approaches to the
Riordan group is captured in this comprehensive monograph, authored
by those who are among the founders and foremost world experts in
this field. The concept of a Riordan array has played a unifying
role in enumerative combinatorics over the last three decades. The
Riordan arrays and Riordan group is a new growth point in
mathematics that is both being influenced by, and continuing its
contributions to, other fields such as Lie groups, elliptic curves,
orthogonal polynomials, spline functions, networks, sequences and
series, Beal conjecture, Riemann hypothesis, to name several. In
recent years the Riordan group has made links to quantum field
theory and has become a useful tool for computer science and
computational chemistry. We can look forward to discovering further
applications to unexpected areas of research. Providing a baseline
and springboard to further developments and study, this book may
also serve as a text for anyone interested in discrete mathematics,
including combinatorics, number theory, matrix theory, graph
theory, and algebra.
This book is adapted from Dr. Wang's dissertation research, part of
which has been accepted by peer-reviewed journal "teacher and
teaching education." The whole picture of the research was depicted
in this book. This book is divided into five chapters. The
background of the research is described in chapter I, in which, the
readers will learn about the educationreform in China, particularly
in Shanxi Province, and the concept andcontext of 2+2 program. The
author offers the reader the opportunity to learn what have been
studies previously in terms of teacher education and Teacher
collaboration in Chapter II. The gaps in the present knowledge are
discussed in this chapter. Chapter III is the core of the study, in
which the reader will learn how the authors created the research
questions and how the study was conducted. Chapter IV lays out all
the findings followed by Chapter V with the detailed discussion on
the meanings and potential implication of the findings.
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