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Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete mathematics curriculum initiatives in several countries, and presents ongoing research, especially in the areas of combinatorial reasoning and the affective dimension of learning discrete mathematics. Discrete mathematics is the math of our time.' So declared the immediate past president of the National Council of Teachers of Mathematics, John Dossey, in 1991. Nearly 30 years later that statement is still true, although the news has not yet fully reached school mathematics curricula. Nevertheless, much valuable work has been done, and continues to be done. This volume reports on some of that work. It provides a glimpse of the state of the art in learning and teaching discrete mathematics around the world, and it makes the case once again that discrete mathematics is indeed mathematics for our time, even more so today in our digital age, and it should be included in the core curricula of all countries for all students.

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness.

Probabilistic Methods for Algorithmic Discrete Mathematics

Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact.

Discrete Mathematics

Elementary and Beyond

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics.

Religion in the Media: A Linguistic Analysis

This ground-breaking book takes an interdisciplinary approach to language, religion and media using an audience-response study. In this book, the author investigates how the three Abrahamic faiths - Christianity, Judaism and Islam - are represented in mainstream British media and analyses how members of each religious group and those with no religion receive those representations. Employing Critical Discourse Analysis, Al-Azami considers the way the media use their power of language to influence the audience’s perceptions of the three religions through newspaper articles, television documentaries and television dramas. Chapter 3 presents the results of an original investigation into the responses of members of the three religious groups and those with no religion when exposed to those same media materials. The author applies the encoding/decoding model and also considers people’s views in face-to-face interactions compared to comments on online newspapers. Comprehensive in its analysis, this book will be of interest to students of Linguistics, Media Studies, Religious Studies, and Journalism.

Comprehensive in its analysis, this book will be of interest to students of Linguistics, Media Studies, Religious Studies, and Journalism. Salman Al-Azami is Senior Lecturer in English Language at Liverpool Hope University.

Tumors of the Brain and Spine

Tumors of the Brain and Spine focuses primarily on approaches to the treatment of benign, primary low-grade to high-grade, and metastatic tumors in the brain and spine, as practiced by surgeons and clinicians at the University of Texas M. D. Anderson Cancer Center. The book is written mainly for the primary care oncologist, general neurologist, and general neurosurgeon. Discussion of treatment coverage focuses on neurosurgery, chemotherapy, and radiation therapy, singly and in combination. Also included are chapters on symptom management, molecular genetics and neuropathology of intracranial tumors, leptomeningeal dissemination of systemic cancer, epidemiology of brain tumors, and innovative treatment strategies.

... xanthoastrocytomas, and subependymal giant cell astrocytomas). Diffusely
infiltrating low-grade. Low-grade gliomas consist of the diffusely infiltrating low-
grade gliomas (astrocytomas, oligodendrogliomas, and mixed gliomas) and the
more circumscribed “astroglial variants” (pilocytic astrocytomas, gangliogliomas,
Figure 5–3. The use of intraoperative MRI, such as the. 5 LOW-GRADE GLIOMAS
: Chapter 5 Low-Grade Gliomas: Evidence-Based Treatment Options Frederick F
Lang.

Atlas of Brain and Spine Oncology Imaging

Atlas of Brain and Spine Oncology Imaging presents a comprehensive visual review of pathologic disease variations of cancers of the brain and spine through extensive radiologic images. The focus of the book is on algorithmic strategies for identifying neoplastic pathologies commonly found in brain and spinal tumors through a visual representation of the variety of appearances that each neoplasm takes, within both benign and malignant manifestations. With contributions from radiologists on staff at a National Cancer Institute-designated comprehensive cancer center, who draw from an extensive collection of diagnostic images across all imaging modalities, this book will be valuable to practicing radiologists, radiation oncologists, surgeons and other practitioners involved in the diagnosis and treatment of brain and spinal neoplasms in all patient populations.

exterior to the pial membrane that covers the brain, spinal cord, and proximal
nerve roots. Meningioma Meningiomas are tumors that arise from arachnoidal
cap cells. Meningiomas are the most common primary intracranial neoplasm in
adults [Q]. Meningiomas have an incidence of around six cases per 100,000
person-years [m]. This tumor type peaks in the middle-aged population and has a
slight predominance in women [Q]. Meningiomas have a geographic predilection
for the ...

Epigenetics, Brain and Behavior

What lies at the heart of neuronal plasticity? Accumulating evidence points to epigenetics. This word originally indicated potentially heritable modifications in gene expression that do not involve changes in DNA sequence. Today this definition is much less strict, and epigenetic control is thought to include DNA methylation, histone modifications, histone variants, microRNA metabolic pathways and non-histone proteins modifications. Thus, while neuronal plasticity is rightly thought to be intimately associated to genomic control, it is critical to appreciate that there is much more to the genome than DNA sequence. Recent years have seen spectacular advances in the field of epigenetics. These have attracted the interest of researchers in many fields and evidence connecting epigenetic regulation to brain functions has been accumulating. Neurons daily convert a variety of external stimuli into rapid or long-lasting changes in gene expression. A variety of studies have centered on the molecular mechanisms implicated in epigenetic control and how these may operate in concert. It will be critical to unravel how specificity is achieved. Importantly, specific modifications seem to mediate both developmental processes and adult brain functions, such as synaptic plasticity and memory. Many aspects of the research in neurosciences and endocrinology during the upcoming decade will be dominated by the deciphering of epigenetic control. This book constitutes a compendium of the most updated views in the field.

Thomas Bourgeron Abstract Autism spectrum disorders (ASD) are characterized
by impairments in reciprocal social communication and stereotyped behaviors.
Genetic and epigenetic studies have identified a relatively large number of genes
and biological processes that constitute a comprehensive framework to better
understand this heterogeneous syndrome. Based on the most robust findings,
three observations can be made. First, genetic and epigenetic contributions to
ASD are ...

Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques

This book outlines the core theory and practice of data mining and knowledge discovery (DM & KD) examining theoretical foundations for various methods, and presenting an array of examples, many drawn from real-life applications. Most theoretical developments are accompanied by extensive empirical analysis, offering a deep insight into both theoretical and practical aspects of the subject. The book presents the combined research experiences of 40 expert contributors of world renown.

METHODS. Andrew Kusiak Intelligent Systems Laboratory Mechanical and
Industrial Engineering 2139 Seamans Center The University of Iowa Iowa City,
Iowa 52242 - 1527 Email andrew-kusiak (du iowa . edu Web: http://www. iCaen.
uiowa. edu/~ank usiak Abstract: Key Words: A typical data mining project uses
data collected for various purposes, ranging from routinely gathered data, to
process improvement projects, and to data required for archival purposes. In
some cases, the ...

Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory

This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop. The pro ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: Math ematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. The tutorial and the workshop are integral parts of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BI OLOGY. " I would like to thank Carlos Castillo-Chavez (Director of the Math ematical and Theoretical Biology Institute and a member of the Depart ments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University), Sally M. Blower (Biomathematics, UCLA School of Medicine), Pauline van den Driessche (Mathematics and Statistics, Uni versity of Victoria), and Denise Kirschner (Microbiology and Immunology, University of Michigan Medical School) for their superb roles as organizers of the meetings and editors of the proceedings. Carlos Castillo-Chavez, es pecially, made a major contribution by spearheading the editing process. I am also grateful to Kenneth L. Cooke (Mathematics, Pomona College), for being one of the workshop organizers and to Abdul-Aziz Yakubu (Mathe matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton Uni versity) for providing an introduction.

New Approaches in Modeling Multiphase Flows and Dispersion in Turbulence, Fractal Methods and Synthetic Turbulence

This book contains a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42. It is intended as an illustration of the sig’s activities and of the latest developments in the field. This volume investigates the use of Kinematic Simulation (KS) and other synthetic turbulence models for the particular application to environmental flows. This volume offers the best syntheses on the research status in KS, which is widely used in various domains, including Lagrangian aspects in turbulence mixing/stirring, particle dispersion/clustering, and last but not least, aeroacoustics. Flow realizations with complete spatial, and sometime spatio-temporal, dependency, are generated via superposition of random modes (mostly spatial, and sometime spatial and temporal, Fourier modes), with prescribed constraints such as: strict incompressibility (divergence-free velocity field at each point), high Reynolds energy spectrum. Recent improvements consisted in incorporating linear dynamics, for instance in rotating and/or stably-stratified flows, with possible easy generalization to MHD flows, and perhaps to plasmas. KS for channel flows have also been validated. However, the absence of "sweeping effects" in present conventional KS versions is identified as a major drawback in very different applications: inertial particle clustering as well as in aeroacoustics. Nevertheless, this issue was addressed in some reference papers, and merits to be revisited in the light of new studies in progress.

of. State. H.W. Zheng, C. Shu, Y.T. Chew, and N. Qin Abstract In many situations,
the equations of state (EOS) found in the literature have only a limited range of
validity. Besides, different types of EOS are required for different fluids of
compressible multi-fluid flows. These inspire us to investigate compressible multi-
fluid flows with different types of equation of state (EOS). In this paper, the
oscillation-free adaptive method for compressible two-fluid flows with different
types of equation of ...