Critique of research methods and methodology is one of several key features of the regular dialogue between researchers. This critique takes place formally at conferences and seminars, and regularly in universities. Published critique is normally separated from the original work. This book brings together the writing of researcher and independent critique. Thus the book exposes to wider scrutiny the dialogue that exists between researchers. It will be of interest to all who are concerned to understand the nature and substance of this critique.

The volume comprises a collection of accounts of classroom studies, each complemented by the reaction of an eminent researcher. The accounts and reactions are written to expose the nature of methodology of classroom research. It argues that methodology encompasses the choice of methods and the researchers' beliefs and values.

An innovative and appealing way for the layperson to develop math skills--while actually enjoying it
Most people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in short, fun As veteran math educators Posamentier and Lehmann demonstrate, when you realize that doing math can be enjoyable, you open a door into a world of unexpected insights while learning an important skill.
The authors illustrate the point with many easily understandable examples. One of these is what mathematicians call the "Ruth-Aaron pair" (714 and 715), named after the respective career home runs of Babe Ruth and Hank Aaron. These two consecutive integers contain a host of interesting features, one of which is that their prime factors when added together have the same sum.
The authors also explore the unusual aspects of such numbers as 11 and 18, which have intriguing properties usually overlooked by standard math curriculums. And to make you a better all-around problem solver, a variety of problems is presented that appear simple but have surprisingly clever solutions.
If math has frustrated you over the years, this delightful approach will teach you many things you thought were beyond your reach, while conveying the key message that math can and should be anything but boring.

Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

In this lively volume, mathematician John Allen Paulos employs his singular wit to guide us through an unlikely mathematical jungle--the pages of the daily newspaper. From the Senate and sex to celebrities and cults, Paulos takes stories that may not seem to involve math at all and demonstrates how mathematical naivete can put readers at a distinct disadvantage. Whether he's using chaos theory to puncture economic and environmental predictions, applying logic to clarify the hazards of spin doctoring and news compression, or employing arithmetic and common sense to give us a novel perspective on greed and relationships, Paulos never fails to entertain and enlighten.

Edexcel and A Level Modular Mathematics C4 features: Student-friendly worked examples and solutions, leading up to a wealth of practice questions. Sample exam papers for thorough exam preparation. Regular review sections consolidate learning. Opportunities for stretch and challenge presented throughout the course. 'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary.

FELIX KLEIN ELEMENTARY MATHEMATICS FROM AN ADVANCED STANDPOINT- ARITHMETIi ALGEBRA -ANALYSIS. TRANSLATED FROM THE THIRD GERMAN EDlTION BY E. R. HEDRICK AND C, A. NOBLE PROFESSOR OF MATHEMATICS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF CALIFORNIA IN THE UNIVERSITY OF CALIFORNIA AT LOS ANGELES AT BERKELEY WITH 125 FIGURES MACMILLAN AND CO., LIMITED ST. MARTINS STREET, LONDON 1932 ALL RIGHTS RESERVED PRINTED IN GERMANY BY THE SPAMERSCHE BUCHDRUCKEREI LEIPZIG Preface to the First Edition. The new volume which I herewith offer to the mathematical public, and especially to the teachers of mathematics in our secondary schools, is to be looked upon as a first continuation of the lectures Uber den mathematischen Unterricht an den hoheren Schulen, in particular, of those on Die Organisation des mathematischen Unterrichts by Schimmack and me, which were published last year by Teubner. At that time our concern was with the different ways in which the problem of instruction can be presented to the mathematician. At present my concern is with deve lopments in the subject matter of instruction. I shall endeavor to put before the teacher, as well as the maturing student, from the view-point of modern science, but in a manner as simple, stimulating, and convincing as possible, both the content and the foundations of the topics of instruction, with due regard for the current methods of teaching. I shall not follow a systematically ordered presentation, as do, for example, Weber and Wellstein, but I shall allow myself free excursions as the changing stimulus of surroundings may lead me to do in the course of the actual lectures. The program thus indicated, which for the present is to be carried outonly for the fields of Arithmetic, Algebra, and Analysis, was indicated in the preface to Klein-Schimmack April 1907. I had hoped then that Mr.. Schimmack, in spite of many obstacles, would still find the time to put my lectures into form suitable for printing. But I myself, in a way, prevented his doing this by continuously claiming his time for work in another direction upon pedagogical questions that interested us both. It soon became clear that the original plan could not be carried out, particularly if the work was to be finished in a short time, which seemed desirable if it was to have any real influence upon those problems of instruction which are just now in the foreground, As in previous years, then, I had recourse to the more convenient method of lithographing my lectures, especially since my present assistant, Dr. Ernst Hellinger, showed himself especially well qualified for this work. One should not underestimate the service which Dr. Hellinger rendered. For it is a far cry from the spoken word of the teacher, influenced as it is by accidental conditions, to the subsequently polished and readable record. On the teaching of mathematics in the secondary schools. The organization of mathematical instruction. IV In precision of statement and in uniformity of explanations, the lecturer stops short of what we are accustomed to consider necessary for a printed publication. I hesitate to commit myself to still further publications on the teaching of mathematics, at least for the field of geometry. I prefer to close with the wish that the present lithographed volume may prove useful by inducing many of the teachers of our higher schools to renewed use of independent thought indetermining the best way of presenting the material of instruction. This book is designed solely as such a mental spur, not as a detailed handbook. The preparation of the latter I leave to those actively engaged in the schools. It is an error to assume, as some appear to have done, that my activity has ever had any other purpose...

This book presents, for the first time in English, the state of the art of Mathematics Education research in Brazil, a country that has the strongest community in this field in Latin America. Edited by leading researchers in the area, the volume provides the international academic community a summary of the scientific production of the thirteen working groups of the Brazilian Society of Mathematics Education (SBEM), the national scientific society that brings together researchers, teachers, students and other professionals of the area. These working groups meet every three years at the International Seminar of Mathematics Education (SIPEM) and cover the following topics: Mathematics Education in the Early Years and Primary Education (Y1-Y5); Mathematics Education in the Middle School (Y6-Y9); Mathematics Education in the High School (Y10-Y12); Mathematics Education at the University level; History of Mathematics, Culture and Mathematics Education; Digital Technologies and Distance Education; Teacher Education; Assessment and Mathematics Education; Cognitive and Linguistic Processes in Mathematics Education; Mathematical Modeling; Philosophy of Mathematics Education, Teaching Probability and Statistics; and Difference, Inclusion and Mathematics Education. Each chapter of the book presents an overview of the production of a working group and they are all preceded by an introduction by professor Ubiratan D'Ambrosio, one of the pioneers of Mathematics Education in Brazil.

This book contains the full papers presented at the MICCAI 2013 workshop Bio-Imaging and Visualization for Patient-Customized Simulations (MWBIVPCS 2013). MWBIVPCS 2013 brought together researchers representing several fields, such as Biomechanics, Engineering, Medicine, Mathematics, Physics and Statistic.

The contributions included in this book present and discuss new trends in those fields, using several methods and techniques, including the finite element method, similarity metrics, optimization processes, graphs, hidden Markov models, sensor calibration, fuzzy logic, data mining, cellular automation, active shape models, template matching and level sets. These serve as tools to address more efficiently different and timely applications involving signal and image acquisition, image processing and analysis, image segmentation, image registration and fusion, computer simulation, image based modelling, simulation and surgical planning, image guided robot assisted surgical and image based diagnosis.

This book will appeal to researchers, PhD students and graduate students with multidisciplinary interests related to the areas of medical imaging, image processing and analysis, computer vision, image segmentation, image registration and fusion, scientific data visualization and image based modeling and simulation.

"Statistical and Methodological Aspects of Oral Health Research" provides oral health researchers with an overview of the methodological aspects that are important in planning, conducting and analyzing their research projects whilst also providing biostatisticians with an idea of the statistical problems that arise when tackling oral health research questions.

This collection presents critical reflections on oral health research and offers advice on practical aspects of setting up research whilst introducing the reader to basic as well as advanced statistical methodology.

Features:

An introduction to research methodology and an exposition of the state of the art.A variety of examples from oral health research.Contributions from well-known oral health researchers, epidemiologists and biostatisticians, all of whom have rich experience in this area.Recent developments in statistical methodology prompted by a variety of dental applications.

Presenting both an introduction to research methodology and an exposition of the latest advances in oral health research, this book will appeal both beginning and experienced oral health researchers as well as biostatisticians and epidemiologists.

"Transforming Your STEM Career Through Leadership and Innovation" offers valuable information on what it means to be a leader and innovator and encourages you to discover and develop these skills for yourself. This book integrates leadership and innovation principles with personal examples and profiles of inspirational women. By providing a clear process on how to build upon your personal strengths to realize leadership and innovation goals, this book will inspire you to pick up the mantle and meet the critical need for leadership and innovation in the STEM fields. This is a must-have guide that is relevant and valuable for women in all stages of their careers.
Examines research-based leadership and innovation principles to make these critically important characteristics both real and attainableEmpowers you to build upon your own strengths and successes to discover and develop leadership and innovation skillsFeatures a companion website that highlights women s leadership success stories, innovation resources and best practicesProvides a practical guide that educates, encourages and equips you to pursue leadership and innovation opportunities
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This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.

Discover a unique and modern treatment of topology employing a cross-disciplinary approach

Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research.

Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs.

This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation.

The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology

Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.