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Oral History and Mathematics Education (History of Mathematics Education)
by Antonio Vicente Marafioti GarnicaThis book presents an innovative method to investigate the history of mathematics education using oral narratives to study different aspects related to the teaching and learning of mathematics. The application of oral history in mathematics education research was first developed as a method in Brazil in the early 2000s as a result of interdisciplinary dialogues between mathematics educators, anthropologists, sociologists, historians, psychologists, artists and philosophers. Since then, this new methodology has attracted the attention of a growing number of researchers. This contributed volume is the first book in English to bring together chapters written by different members of the research group who developed the methodology and to present a comprehensive overview of the theoretical and practical aspects of the use of oral narratives in the study of experiences in mathematics classrooms. Oral History and Mathematics Education will be a useful tool to researchers and educators looking for new methods to study the dynamics of teaching and learning mathematics in the classroom and to develop innovative mathematics teacher education programs. The volume will also be of interest to historians of education since it describes the foundations of both concepts and procedures related to the application of oral history in educational research, always giving examples of studies already conducted and, whenever possible, suggesting possible research exercises.
Ordinary Differential Equations for Engineers: Problems with MATLAB Solutions
by Ali Ümit KeskinThis monograph presents teaching material in the field of differential equations while addressing applications and topics in electrical and biomedical engineering primarily. The book contains problems with varying levels of difficulty, including Matlab simulations. The target audience comprises advanced undergraduate and graduate students as well as lecturers, but the book may also be beneficial for practicing engineers alike.
Orienteering Problems: Models and Algorithms for Vehicle Routing Problems with Profits (EURO Advanced Tutorials on Operational Research)
by Pieter Vansteenwegen Aldy GunawanThis tutorial introduces readers to several variants of routing problems with profits. In these routing problems each node has a certain profit, and not all nodes need to be visited. Since the orienteering problem (OP) is by far the most frequently studied problem in this category of routing problems, the book mainly focuses on the OP. In turn, other problems are presented as variants of the OP, focusing on the similarities and differences. The goal of the OP is to determine a subset of nodes to visit and in which order, so that the total collected profit is maximized and a given time budget is not exceeded.The book provides a comprehensive review of variants of the OP, such as the team OP, the team OP with time windows, the profitable tour problem, and the prize-collecting travelling salesperson problem. In addition, it presents mathematical models and techniques for solving these OP variants and discusses their complexity. Several simple examples and benchmark instances, together with their best-known results, are also included. Finally, the book reviews the latest applications of these problems in the fields of logistics, tourism and others.
Orlicz Spaces and Generalized Orlicz Spaces (Lecture Notes in Mathematics #2236)
by Petteri Harjulehto Peter HästöThis book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
Oxford IB Diploma Programme Ib Mathematics: Applications And Interpretation, Standard Level
by Jane Forrest Nadia Stoyanova Kennedy Paula Waldman Suzanne Doering David Harris Jennifer Chang WathallFeaturing a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: applications and interpretation SL syllabus, for first teaching in September 2019. Each Enhanced Online Course Book Pack is made up of one full-colour, print textbook and one online textbook - packed full of investigations, exercises, worksheets, worked solutions and answers, plus assessment preparation support.
Oxford Ib Diploma Programme Ib Mathematics: Analysis And Approaches, Standard Level, Print And Enhanced Online Course Book Pack
by Paul La Rondie Jennifer Chang Wathall Jill Stevens Natasha Awada Ellen Thompson Laurie Buchanan Ed KempFeaturing a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: analysis and approaches SL syllabus, for first teaching in September 2019.
Pairwise Multiple Comparisons: Theory and Computation (SpringerBriefs in Statistics)
by Taka-aki Shiraishi Shin-ichi Matsuda Hiroshi SugiuraThis book focuses on all-pairwise multiple comparisons of means in multi-sample models, introducing closed testing procedures based on maximum absolute values of some two-sample t-test statistics and on F-test statistics in homoscedastic multi-sample models. It shows that (1) the multi-step procedures are more powerful than single-step procedures and the Ryan/Einot–Gabriel/Welsh tests, and (2) the confidence regions induced by the multi-step procedures are equivalent to simultaneous confidence intervals. Next, it describes the multi-step test procedure in heteroscedastic multi-sample models, which is superior to the single-step Games–Howell procedure. In the context of simple ordered restrictions of means, the authors also discuss closed testing procedures based on maximum values of two-sample one-sided t-test statistics and based on Bartholomew's statistics. Furthermore, the book presents distribution-free procedures and describes simulation studies performed under the null hypothesis and some alternative hypotheses. Although single-step multiple comparison procedures are generally used, the closed testing procedures described are more powerful than the single-step procedures. In order to execute the multiple comparison procedures, the upper 100α percentiles of the complicated distributions are required. Classical integral formulas such as Simpson's rule and the Gaussian rule have been used for the calculation of the integral transform that appears in statistical calculations. However, these formulas are not effective for the complicated distribution. As such, the authors introduce the sinc method, which is optimal in terms of accuracy and computational cost.
The Palgrave Handbook of Economic Performance Analysis
by Thijs Ten Raa William H. GreeneThis Handbook takes an econometric approach to the foundations of economic performance analysis. The focus is on the measurement of efficiency, productivity, growth and performance. These concepts are commonly measured residually and difficult to quantify in practice. In real-life applications, efficiency and productivity estimates are often quite sensitive to the models used in the performance assessment and the methodological approaches adopted by the analysis. The Palgrave Handbook of Performance Analysis discusses the two basic techniques of performance measurement – deterministic benchmarking and stochastic benchmarking – in detail, and addresses the statistical techniques that connect them. All chapters include applications and explore topics ranging from the output/input ratio to productivity indexes and national statistics.
Panel Data Econometrics: Common Factor Analysis for Empirical Researchers
by Donggyu SulIn the last 20 years, econometric theory on panel data has developed rapidly, particularly for analyzing common behaviors among individuals over time. Meanwhile, the statistical methods employed by applied researchers have not kept up-to-date. This book attempts to fill in this gap by teaching researchers how to use the latest panel estimation methods correctly. Almost all applied economics articles use panel data or panel regressions. However, many empirical results from typical panel data analyses are not correctly executed. This book aims to help applied researchers to run panel regressions correctly and avoid common mistakes. The book explains how to model cross-sectional dependence, how to estimate a few key common variables, and how to identify them. It also provides guidance on how to separate out the long-run relationship and common dynamic and idiosyncratic dynamic relationships from a set of panel data. Aimed at applied researchers who want to learn about panel data econometrics by running statistical software, this book provides clear guidance and is supported by a full range of online teaching and learning materials. It includes practice sections on MATLAB, STATA, and GAUSS throughout, along with short and simple econometric theories on basic panel regressions for those who are unfamiliar with econometric theory on traditional panel regressions.
Parabolic Wave Equations with Applications
by Michael D. Collins William L. SiegmannThis book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Parallel Programming with Co-arrays (Chapman & Hall/CRC Computational Science)
by Robert NumrichParallel Programming with Co-Arrays describes the basic techniques used to design parallel algorithms for high-performance, scientific computing. It is intended for upper-level undergraduate students and graduate students who need to develop parallel codes with little or no previous introduction to parallel computing. It is also intended as a reference manual for researchers active in the field of scientific computing. All the algorithms in the book are based on partition operators. These operators provide a unifying principle that fits seemingly disparate techniques into an overall framework for algorithm design. The book uses the co-array programming model to illustrate how to write code for concrete examples, but it emphasizes that the important concepts for algorithm design are independent of the programming model. With these concepts in mind, the reader can write algorithms in different programming models based on personal taste and comfort.
Parameterized Complexity in the Polynomial Hierarchy: Extending Parameterized Complexity Theory to Higher Levels of the Hierarchy (Lecture Notes in Computer Science #11880)
by Ronald de HaanParameterized Complexity in the Polynomial Hierarchy was co-recipient of the E.W. Beth Dissertation Prize 2017 for outstanding dissertations in the fields of logic, language, and information. This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH). For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem. In this dissertation, a theoretical toolbox is developed that can be used to classify in which cases this is possible. The use of this toolbox is illustrated by applying it to analyze a wide range of problems from various areas of computer science and artificial intelligence.
Parkettierungen der Ebene: Von Escher Über Möbius Zu Penrose
by Ehrhard BehrendsZiel des Buches ist das Studium von Symmetrien und Parkettierungen, die Künstler und Mathematiker schon seit langer Zeit interessieren. Berühmte Beispiele sind die von den Arabern in der Alhambra geschaffenen Werke und die Bilder des holländischen Malers Maurits Escher. Die Mathematiker haben sich erst im 19. Jahrhundert des Themas intensiv angenommen. Dabei führt die Visualisierung der mathematischen Zusammenhänge zu sehr ansprechenden Bildern. Drei Ansätze werden in diesem Buch beschrieben. In Teil I wird dargestellt, dass es 17 prinzipiell verschiedene Möglichkeiten von Parkettierungen der Ebene gibt, die so genannten "Ebenen Kristallgruppen". Ergänzend dazu werden Ideen von Harald Heesch beschrieben, der zeigte, wie diese theoretischen Ergebnisse praktisch umgesetzt werden können: Er gab einen Katalog von 28 Verfahren an, die man selbst - sozusagen auf den Spuren von Escher - kreativ zur Schaffung künstlerisch anspruchsvoller Parkettierungen verwenden kann. Bei den entsprechenden Untersuchungen für die komplexe Ebene in Teil II werden Bewegungen durch bijektive holomorphe Abbildungen ersetzt. Das führt in die Theorie der Gruppen von Möbiustransformationen: Kleinsche Gruppen, Schottkygruppen usw. Dort gibt es auch interessante Verbindungen zur hyperbolischen Geometrie. Schließlich wird in Teil III noch ein dritter Aspekt des Themas behandelt, die Penroseparkettierungen. Dabei geht es um Ergebnisse aus den siebziger Jahren, als erstmals einfach zu beschreibende und beweisbar nichtperiodische Parkettierungen der Ebene angegeben wurden.
The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness (Advances in Mathematical Fluid Mechanics)
by Wojciech S. OżańskiThis monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing a clear and insightful presentation of Scheffer’s constructions showing their bound cannot be improved. A short, complete, and self-contained proof of CKN is presented in the second chapter, allowing the remainder of the book to be fully dedicated to a topic of central importance: the sharpness result of Scheffer. Chapters three and four contain a highly readable proof of this result, featuring new improvements as well. Researchers in mathematical fluid mechanics, as well as those working in partial differential equations more generally, will find this monograph invaluable.
Patentism Replacing Capitalism: A Prediction from Logical Economics
by Samuel MengBased on economic knowledge and logical reasoning, this book proposes a solution to economic recessions and offers a route for societal change to end capitalism. The author starts with a brief review of the history of economics, and then questions and rejects the trend of recent decades that has seen econometrics replace economic theory. By reviewing the different schools of economic thought and by examining the limitations of existing theories to business cycles and economic growth, the author forms a new theory to explain cyclic economic growth. According to this theory, economic recessions result from innovation scarcity, which in turn results from the flawed design of the patent system. The author suggests a new design for the patent system and envisions that the new design would bring about large economic and societal changes. Under this new patent system, the synergy of the patent and capital markets would ensure that economic recessions could be avoided and that the economy would grow at the highest speed.
Pathways to Health (SpringerBriefs in Population Studies)
by George B. Ploubidis Benedetta Pongiglione Bianca De Stavola Rhian Daniel Lenka Benova Emily Grundy Sanna ReadThis book presents a rigorous enquiry into life course processes that are thought to influence health, integrating the latest methodologies for the study of pathways that link socio-demographic circumstances to health with an emphasis on the mediating factors that lie on these pathways. Following an introductory chapter on the application of formal mediation methods within the life course framework, the book offers insights on the pathways that link early life socio-economic circumstances to physical activity in later life, the role of physical activity as a moderator and/or mediator of the association between fertility history and later life health and the evolution of self-rated health over the life course in two generations born 12 years apart in 20th century Britain. Pathways to Health presents a dynamic view on how to investigate specific hypotheses within the life course framework and enhances the ability of the social science community to investigate specific mechanisms related to public health interventions.
Pathways to Math Literacy (Second Edition)
by Dave SobeckiWe're making the process of learning useful problem-solving skills through algebra more palatable for students, which at the end of the day is a significant part of the battle.
Pathwise Estimation and Inference for Diffusion Market Models
by Nikolai Dokuchaev Lin Yee HinPathwise estimation and inference for diffusion market models discusses contemporary techniques for inferring, from options and bond prices, the market participants' aggregate view on important financial parameters such as implied volatility, discount rate, future interest rate, and their uncertainty thereof. The focus is on the pathwise inference methods that are applicable to a sole path of the observed prices and do not require the observation of an ensemble of such paths. <P><P>This book is pitched at the level of senior undergraduate students undertaking research at honors year, and postgraduate candidates undertaking Master’s or PhD degree by research. From a research perspective, this book reaches out to academic researchers from backgrounds as diverse as mathematics and probability, econometrics and statistics, and computational mathematics and optimization whose interest lie in analysis and modelling of financial market data from a multi-disciplinary approach. Additionally, this book is also aimed at financial market practitioners participating in capital market facing businesses who seek to keep abreast with and draw inspiration from novel approaches in market data analysis. <P><P>The first two chapters of the book contains introductory material on stochastic analysis and the classical diffusion stock market models. The remaining chapters discuss more special stock and bond market models and special methods of pathwise inference for market parameter for different models. The final chapter describes applications of numerical methods of inference of bond market parameters to forecasting of short rate. <P><P>Nikolai Dokuchaev is an associate professor in Mathematics and Statistics at Curtin University. His research interests include mathematical and statistical finance, stochastic analysis, PDEs, control, and signal processing. <P><P>Lin Yee Hin is a practitioner in the capital market facing industry. His research interests include econometrics, non-parametric regression, and scientific computing.
Patient Care under Uncertainty
by Charles F. ManskiHow cutting-edge economics can improve decision-making methods for doctorsAlthough uncertainty is a common element of patient care, it has largely been overlooked in research on evidence-based medicine. Patient Care under Uncertainty strives to correct this glaring omission. Applying the tools of economics to medical decision making, Charles Manski shows how uncertainty influences every stage, from risk analysis to treatment, and how this can be reasonably confronted.In the language of econometrics, uncertainty refers to the inadequacy of available evidence and knowledge to yield accurate information on outcomes. In the context of health care, a common example is a choice between periodic surveillance or aggressive treatment of patients at risk for a potential disease, such as women prone to breast cancer. While these choices make use of data analysis, Manski demonstrates how statistical imprecision and identification problems often undermine clinical research and practice. Reviewing prevailing practices in contemporary medicine, he discusses the controversy regarding whether clinicians should adhere to evidence-based guidelines or exercise their own judgment. He also critiques the wishful extrapolation of research findings from randomized trials to clinical practice. Exploring ways to make more sensible judgments with available data, to credibly use evidence, and to better train clinicians, Manski helps practitioners and patients face uncertainties honestly. He concludes by examining patient care from a public health perspective and the management of uncertainty in drug approvals.Rigorously interrogating current practices in medicine, Patient Care under Uncertainty explains why predictability in the field has been limited and furnishes criteria for more cogent steps forward.
Pattern Analysis of the Human Connectome
by Dewen Hu Ling-Li ZengThis book presents recent advances in pattern analysis of the human connectome. The human connectome, measured by magnetic resonance imaging at the macroscale, provides a comprehensive description of how brain regions are connected. Based on machine learning methods, multiviarate pattern analysis can directly decode psychological or cognitive states from brain connectivity patterns. Although there are a number of works with chapters on conventional human connectome encoding (brain-mapping), there are few resources on human connectome decoding (brain-reading). Focusing mainly on advances made over the past decade in the field of manifold learning, sparse coding, multi-task learning, and deep learning of the human connectome and applications, this book helps students and researchers gain an overall picture of pattern analysis of the human connectome. It also offers valuable insights for clinicians involved in the clinical diagnosis and treatment evaluation of neuropsychiatric disorders.
Pattern Recognition: 41st DAGM German Conference, DAGM GCPR 2019, Dortmund, Germany, September 10–13, 2019, Proceedings (Lecture Notes in Computer Science #11824)
by Gernot A. Fink Simone Frintrop Xiaoyi JiangThis book constitutes the proceedings of the 41st DAGM German Conference on Pattern Recognition, DAGM GCPR 2019, held in Dortmund, Germany, in September 2019. The 43 revised full papers presented were carefully reviewed and selected from 91 submissions. The German Conference on Pattern Recognition is the annual symposium of the German Association for Pattern Recognition (DAGM). It is the national venue for recent advances in image processing, pattern recognition, and computer vision and it follows the long tradition of the DAGM conference series.
Peer Instruction in der Mathematik: Didaktische, organisatorische und technische Grundlagen praxisnah erläutert
by Peter RieglerSie möchten Ihre Lehrveranstaltungen aktivierender und wirksamer gestalten? Sie möchten die Verständnisschwierigkeiten Ihrer Studierenden besser erkennen und verstehen? Sie möchten die studentische Beteiligung steigern, zum Nachdenken und Diskutieren anregen? Lernen Sie das Potenzial von Clickerfragen für die akademische Lehre kennen – damit es bei Ihren Studierenden klick macht! In diesem Buch werden die Grundlagen der interaktiv-dialogischen Lehrmethode praxisnah erläutert. Dabei werden auch häufige Fragen zu didaktischen, organisatorischen und technischen Aspekten beantwortet, etwa:Was ist die Grundidee von Peer Instruction?Wie wirksam ist Peer Instruction? Wie überzeuge ich meine Studierenden davon?Welche technischen Voraussetzungen gibt es?Wie stelle ich gute Clickerfragen?Was sollte ich sonst noch beachten?
Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition (Logic, Epistemology, and the Unity of Science #46)
by Mohammad Shafiei Ahti-Veikko PietarinenThis volume aims to provide the elements for a systematic exploration of certain fundamental notions of Peirce and Husserl in respect with foundations of science by means of drawing a parallelism between their works. Tackling a largely understudied comparison between these two contemporary philosophers, the authors highlight the significant similarities in some of their fundamental ideas. This volume consists of eleven chapters under four parts. The first part concerns methodologies and main principles of the two philosophers. An introductory chapter outlines central historical and systematical themes arising out of the recent scholarship on Peirce and Husserl. The second part is on logic, its Chapters dedicated to the topics from Peirce’s Existential Graphs and the philosophy of notation to Husserl’s notions of pure logic and transcendental logic. The third part includes contributions on philosophy of mathematics. Chapters in the final part deal with the theory of cognition, consciousness and intentionality. The closing chapter provides an extended glossary of central terms of Peirce’s theory of phaneroscopy, explaining them from the viewpoint of the theory of cognition.
¡Peligro! Matemática explícita
by Adrián PaenzaUn verdadero festival de problemas, paradojas, dilemas e historias extraordinarias, conducido por el mejor divulgador de matemática del mundo. Cuenta Adrián que tiene la costumbre de guardar, en el bolsillo izquierdo de la camisa, papelitos con anotaciones sobre cosas que le suceden, que observa o le comentan, y que después esos apuntes se convierten en los problemas de sus libros. Es que la matemática está mucho más presente en la vida cotidiana de lo que parece, y si aprendemos a ver con un poco de curiosidad, se encuentra en todos lados. Desafíos en torno a una hamburguesa; cámaras que registran todos los movimientos de la pelota en un partido; cómo es el sorteo de las causas en los juzgados judiciales; decisiones de la inteligencia artificial; problemas sobre la verdad, la verosimilitud y la falsedad; Lennon o McCartney; Voltaire y el FMI; cómo repartir los bienes de una herencia; historias sobre bitcoins y blockchain; tatuajes increíbles; un museo muy inquietante, cómo cambiar reglas injustas y muchos más.
Pencils of Cubics and Algebraic Curves in the Real Projective Plane
by Séverine Fiedler - Le TouzéPencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP². Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. <P><P>The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. <P><P>The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. <P><P>Features: <li>Examines how the shape of pencils depends on the corresponding configurations of points <li>Includes topology of real algebraic curves <li>Contains numerous applications and results around Hilbert’s sixteenth problem <P><P>About the Author: <P><P>Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.