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The Problem of Catalan
by Yann Bugeaud Yuri F. Bilu Maurice MignotteIn 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda MihÄfilescu. In other words, 32 - 23 = 1 is the only solution of the equation xp - yq = 1 in integers x, y, p, q with xy ≠ 0 and p, q ≥ 2. In this book we give a complete and (almost) self-contained exposition of MihÄfilescu's work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.
The Problem of Coronal Heating: A Rosetta Stone for Electrodynamic Coupling in Cosmic Plasmas (Astrophysics and Space Science Library #470)
by Philip Judge James A. IonsonThis book reflects on 8 decades of research on one of the longest-standing unsolved problems in modern astrophysics: why does the Sun form a hot corona? The authors give a critical overview of the field and offer suggestions on how to bridge the chasm between what we can measure, and what we can calculate. They go back to basics to explain why the problem is difficult, where we have made progress and where we have not, to help the next generation of scientists devise novel techniques to crack such a long-lasting problem. A way forward is formulated centered around refutation, using Bayesian methods to propose and to try to reject hypotheses and models, and avoiding seduction by ``confirmation bias’’.This book is aimed at physicists, students and researchers interested in understanding, learning from and solving the coronal heating problem, in an era of new dedicated facilities such as the Parker Solar Probe and the Daniel K. Inouye Solar Telescope. Thebook will appeal to those interested in understanding research methods and how they are changing in the modern academic environment, particular in astrophysics and Earth sciences where remote sensing is essential.
The Problem with Math Is English: A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics
by Concepcion MolinaTeaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. <P><P>Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property. Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism.
The Proceedings of the 12th International Congress on Mathematical Education
by Sung Je ChoThis book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.
The Proceedings of the 2023 Conference on Systems Engineering Research: Systems Engineering Towards a Smart and Sustainable World (Conference on Systems Engineering Research Series)
by Azad M. Madni Dinesh Verma Lu Xiao Steven HoffensonThe 20th International Conference on Systems Engineering Research (CSER 2023) pushes the boundaries of systems engineering research and responds to new challenges for systems engineering. CSER 2023 invited researchers and practitioners to submit their work in alignment with the thematic focus on a smart and sustainable world. CSER was founded in 2003 by Stevens Institute of Technology and the University of Southern California, and in 2023 the conference returned to the Stevens campus in Hoboken, New Jersey.
The Proceedings of the 2024 Conference on Systems Engineering Research (Conference on Systems Engineering Research Series)
by Rick Steiner Ricardo Valerdi Alejandro Salado Larry HeadThe 22nd International Conference on Systems Engineering Research (CSER 2024) pushes the boundaries of systems engineering research and responds to new challenges for systems engineering. CSER was founded in 2003 by Stevens Institute of Technology and the University of Southern California. In 2024 the conference was hosted by the University of Arizona, home to the first-ever established Department of Systems Engineering. The following foundational research topics are included: • Scientific Foundations of Systems Engineering • Digital Engineering, Digital Twins • Digital Transformation • Advances in Model-Based Systems Engineering (MBSE) • Value-based and Agile Systems Engineering • Artificial Intelligence for Systems and Software Engineering (AI4SE) • Systems and Software Engineering for Artificial Intelligence (SE4AI) • Cybersecurity and System Security Engineering • Uncertainty and Complexity Management • Trust and Autonomous Systems • Human-Systems Integration • Systems of Systems • Social Systems Engineering • Systems Thinking • Advances in requirements engineering, systems architecture, systems integration, and verification and validation. The 21st Annual Conference on Systems Engineering Research (CSER 2024) was poised to push the boundaries of systems engineering, embracing a wide array of themes from its scientific underpinnings to the forefront of digital engineering transformation and the seamless integration of artificial intelligence within systems and software engineering. Delving into cutting-edge topics such as Model-Based Systems Engineering (MBSE), cybersecurity, and the management of uncertainty and complexity, CSER 2024 tackled the varied challenges and seize the opportunities emerging in the field. The conference's commitment to blending theoretical insights with practical innovations makes it a pivotal event for the systems engineering community.
The Process of Psychotherapy: Causation and Chance
by Hermann Haken Wolfgang TschacherThis book describes an encompassing modeling approach to psychotherapy, created with the most recent research in the field. Therapeutic interventions are staged within a therapist-client relationship ('alliance'), and become effective by the interplay of deterministic ('causation') and stochastic ('chance') forces. The authors use a Fokker-Planck approach complemented by a structural-mathematical framework from complexity theory. Chapters present statistical tools, which can be applied to analyze the differing time series that depict therapeutic processes. Chapters include examples of how to use these tools within research. The approach adopted in the book – contemporary psychotherapy terminology combined with a systems-theoretical model and algorithms for quantitative psychotherapy research – has the potential to become the new benchmark in psychotherapy. The Process of Psychotherapy is an informative and sophisticated resource for all levels of students, from undergraduate through post-doctoral studies, in the fields of psychology, cognitive psychology, and psychotherapy.
The Process of Statistical Analysis in Psychology: Mcbride: The Process Of Statistical Analysis In Psychology (paperback) + Mcbride: The Process Of Statistical Analysis In Psychology (paperback)
by Dawn M. McBrideThis new introductory statistics text from Dawn M. McBride, best-selling author of The Process of Research in Psychology, covers the background and process of statistical analysis, along with how to use essential tools for working with data from the field. Research studies are included throughout from both the perspective of a student conducting their own research study and of someone encountering research in their daily life. McBride helps readers gain the knowledge they need to become better consumers of research and statistics used in everyday decision-making and connects the process of research design with the tools employed in statistical analysis. Instructors and students alike will appreciate the extra opportunities for practice with the accompanying Lab Manual for Statistical Analysis, also written by McBride and her frequent collaborator, J. Cooper Cutting.
The Process of Statistical Analysis in Psychology: The Process of Statistical Analysis in Psychology
by Dawn M. McBrideThis new introductory statistics text from Dawn M. McBride, best-selling author of The Process of Research in Psychology, covers the background and process of statistical analysis, along with how to use essential tools for working with data from the field. Research studies are included throughout from both the perspective of a student conducting their own research study and of someone encountering research in their daily life. McBride helps readers gain the knowledge they need to become better consumers of research and statistics used in everyday decision-making and connects the process of research design with the tools employed in statistical analysis. Instructors and students alike will appreciate the extra opportunities for practice with the accompanying Lab Manual for Statistical Analysis, also written by McBride and her frequent collaborator, J. Cooper Cutting.
The Projected Subgradient Algorithm in Convex Optimization (SpringerBriefs in Optimization)
by Alexander J. ZaslavskiThis focused monograph presents a study of subgradient algorithms for constrained minimization problems in a Hilbert space. The book is of interest for experts in applications of optimization to engineering and economics. The goal is to obtain a good approximate solution of the problem in the presence of computational errors. The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for different steps are different, in general. The book is especially useful for the reader because it contains solutions to a number of difficult and interesting problems in the numerical optimization. The subgradient projection algorithm is one of the most important tools in optimization theory and its applications. An optimization problem is described by an objective function and a set of feasible points. For this algorithm each iteration consists of two steps. The first step requires a calculation of a subgradient of the objective function; the second requires a calculation of a projection on the feasible set. The computational errors in each of these two steps are different. This book shows that the algorithm discussed, generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if computational errors for the two steps of the algorithm are known, one discovers an approximate solution and how many iterations one needs for this. In addition to their mathematical interest, the generalizations considered in this book have a significant practical meaning.
The Proof Stage: How Theater Reveals the Human Truth of Mathematics
by Stephen AbbottHow playwrights from Alfred Jarry and Samuel Beckett to Tom Stoppard and Simon McBurney brought the power of abstract mathematics to the human stageThe discovery of alternate geometries, paradoxes of the infinite, incompleteness, and chaos theory revealed that, despite its reputation for certainty, mathematical truth is not immutable, perfect, or even perfectible. Beginning in the last century, a handful of adventurous playwrights took inspiration from the fractures of modern mathematics to expand their own artistic boundaries. Originating in the early avant-garde, mathematics-infused theater reached a popular apex in Tom Stoppard’s 1993 play Arcadia. In The Proof Stage, mathematician Stephen Abbott explores this unlikely collaboration of theater and mathematics. He probes the impact of mathematics on such influential writers as Alfred Jarry, Samuel Beckett, Bertolt Brecht, and Stoppard, and delves into the life and mathematics of Alan Turing as they are rendered onstage. The result is an unexpected story about the mutually illuminating relationship between proofs and plays—from Euclid and Euripides to Gödel and Godot.Theater is uniquely poised to discover the soulful, human truths embedded in the austere theorems of mathematics, but this is a difficult feat. It took Stoppard twenty-five years of experimenting with the creative possibilities of mathematics before he succeeded in making fractal geometry and chaos theory integral to Arcadia’s emotional arc. In addition to charting Stoppard’s journey, Abbott examines the post-Arcadia wave of ambitious works by Michael Frayn, David Auburn, Simon McBurney, Snoo Wilson, John Mighton, and others. Collectively, these gifted playwrights transform the great philosophical upheavals of mathematics into profound and sometimes poignant revelations about the human journey.
The Proof and the Pudding
by Jim HenleTie on your apron and step into Jim Henle's kitchen as he demonstrates how two equally savory pursuits--cooking and mathematics--have more in common than you realize. A tasty dish for gourmets of popular math, The Proof and the Pudding offers a witty and flavorful blend of mathematical treats and gastronomic delights that reveal how life in the mathematical world is tantalizingly similar to life in the kitchen.Take a tricky Sudoku puzzle and a cake that fell. Henle shows you that the best way to deal with cooking disasters is also the best way to solve math problems. Or take an L-shaped billiard table and a sudden desire for Italian potstickers. He explains how preferring geometry over algebra (or algebra over geometry) is just like preferring a California roll to chicken tikka masala. Do you want to know why playfulness is rampant in math and cooking? Or how to turn stinky cheese into an awesome ice cream treat? It's all here: original math and original recipes plus the mathematical equivalents of vegetarianism, Asian fusion, and celebrity chefs.Pleasurable and lighthearted, The Proof and the Pudding is a feast for the intellect as well as the palate.
The Proper Generalized Decomposition for Advanced Numerical Simulations
by Francisco Chinesta Roland Keunings Adrien LeygueMany problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab© software used to generate these examples.
The Psychology Behind Design: A Marketing Perspective
by Chris Baumann Jeongmin Lee Wujin ChuThis book explains the psychology theory behind design using plain language. The inspiration came from the "democratic design" philosophy of IKEA. This book attempts to help people enjoy designs more, by explaining consumer psychology that lurks behind designs of everyday things. Another purpose of the book is to aid designers and marketers in understanding consumer behavior and to help them leverage this knowledge in their respective fields. Marketers and designers often find it hard to communicate effectively due to their disparate fields. However, this book aims to bridge this gap by showing that activities in both design and marketing can be better understood through the lens of design psychology, promoting better communication and collaboration. Although the book contains more than a hundred psychology theories that can affect design, it is structured in a reader-friendly manner, and chapters are segmented such that each chapter contains about 7~15 theories. Despite the large amount of academic research behind the theories, the application of these theories comes from commonplace consumer behaviors and daily design examples, promising an easy, relatable read.
The Psychology Student’s Career Survival Guide: Here Be Dragons
by Alex ForsytheThe Psychology Student’s Career Survival Guide is designed to aid students in identifying their ideal career pathway and imbue them with the right tools and skills to not only achieve their desired job but to progress and thrive within the workplace. The first half of the book focuses on how to find and get a suitable job. The remaining chapters explore gaining success in the workplace in terms of personal growth, navigating criticism, workplace relations and the critical job assignments that every graduate should pursue. Forsythe, an experienced organisational psychologist, helps students recognise and apply the acquired psychological skill set to develop a personal brand, increase personal visibility and develop professional networks. This smooths the transition from university into the world of work by developing effective working practices that will support personal performance and that of the workplace. This book can also serve as a practical guide for academics looking to bridge the gap between the developing student at university and demands of their future employers. It explicitly calls for vocational elements such as communication, team-working, goal setting and planning within the curriculum. This engaging book comes with an abundance of resources to support students' individual development and to help academics run workshops. These resources include tool kits which include self-diagnostic tools and strengths finders, networking skill development, job search strategies, difficult interview questions, personal branding and so on. This is an essential text for psychology students at all levels looking for employability guidance and for psychology academics who are seeking supportive resources and guidance on helping students achieve their career ambitions.
The Psychology of Global Mobility
by Stuart C. CarrHuman mobility has been a defining feature of human social evolution. In a global community, the term "mobility" captures the full gamut of types, directions, and patterns of human movement. The psychology of mobility is important because movement is inherently behavioral. Much of the behavioral study of mobility has focused on the negative - examining the trauma of forced migration, or the health consequences of the lack of adaptation - but this work looks into the benefits of mobility, such as its impact on career capital and well-being. Recent years have witnessed a phenomenal increase in efforts to understand human mobility, by social scientists, think-tanks, and policymakers alike. The book focuses on the transformational potential of mobility for human development. The book details the historical, methodological, and theoretical trajectory of human mobility (Context), followed by sections on pre-departure incentives and predispositions (Motivation), influences on acculturation, health and community fit (Adjustment), and changes in career capital, overcoming bias, and diaspora networks (Performance).
The Psychology of Learning Mathematics: Expanded American Edition (Pelican Ser.)
by Richard R. SkempThis classic text presents problems of learning and teaching mathematics from both a psychological and mathematical perspective. The Psychology of Learning Mathematics, already translated into six languages (including Chinese and Japanese), has been revised for this American Edition to include the author's most recent findings on the formation of mathematical concepts, different kinds of imagery, interpersonal and emotional factors, and a new model of intelligence. The author contends that progress in the areas of learning and teaching mathematics can only be made when such factors as the abstract and hierarchical nature of mathematics, the relation to mathematical symbolism and the distinction between intelligent learning and rote memorization are taken into account and instituted in the classroom.
The Psychology of Mathematics: A Journey of Personal Mathematical Empowerment for Educators and Curious Minds
by Anderson NortonThis book offers an innovative introduction to the psychological basis of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. Through accessible and engaging writing, award-winning mathematician and educator Anderson Norton reframes mathematics as something that exists first in the minds of students, rather than something that exists first in a textbook. By exploring the psychological basis for mathematics at every level—including geometry, algebra, calculus, complex analysis, and more—Norton unlocks students’ personal power to construct mathematical objects based on their own mental activity and illustrates the power of mathematics in organizing the world as we know it. Including reflections and activities designed to inspire awareness of the mental actions and processes coordinated in practicing mathematics, the book is geared toward current and future secondary and elementary mathematics teachers who will empower the next generation of mathematicians and STEM majors. Those interested in the history and philosophy that underpins mathematics will also benefit from this book, as well as those informed and curious minds attentive to the human experience more generally.
The Pure Theory of International Trade and Distortions (Routledge Revivals)
by Bharat HazariFirst published in 1978. This book provides a simple, systematic, yet rigorous treatment of the key aspects of the pure theory of international trade and distortions. The opening chapter presents the standard two-factor, two-commodity barter model of international trade and a comprehensive treatment of the important properties and relationships. The rest of the book consists of four sections: parts One and Two are devoted to an analysis of factor market imperfections, and Parts Three and Four consider the trade-theoretical consequences of product market imperfections. A concluding chapter presents some generalised theorems. This book would be of interest to students of economics.
The Pursuit of Perfect Packing
by Tomaso Aste Denis WeaireCoauthored by one of the creators of the most efficient space packing solution, the Weaire-Phelan structure, The Pursuit of Perfect Packing, Second Edition explores a problem of importance in physics, mathematics, chemistry, biology, and engineering: the packing of structures. Maintaining its mathematical core, this edition continues and rev
The Pursuit of Reality: Narrative History of the Quantum and the Great Minds That Made it
by Selçuk Ş. BayınIn a highly accessible style, this book presents a narrative history of the quantum theory with the new developments that intrigue all inquisitive minds. Quantum theory is counter-intuitive and sometimes downright weird. Even Nobel Laureate physicists like Richard Feynman admit that they do not understand it. Yet, so far, there is not a shred of experimental data that conflicts with its predictions. Its effect on our lives is bound to increase with the quantum information era ushered in by the great Bohr–Einstein debate. Tantalizing applications of quantum information like teleportation, spy-proof communication, super-fast quantum computers, and more are going to influence our lives and change our beliefs about the nature of physical reality. This book takes the reader on an exhilarating journey through the intellectual history of quantum that is turning out to be more surprising every day.
The Puzzler's Dilemma: From the Lighthouse of Alexandria to Monty Hall, a Fresh Look at Classic Conundrums of Logic, Mathematics, and Life
by Derrick NiedermanCalling all puzzlers. . . From mathematics to word puzzles, from logic to lateral thinking, veteran puzzle maker Derrick Niederman delights in tackling the trickiest brainteasers in a new way. Among the old chestnuts he cracks wide open are the following classics: Knights and knaves The monk and the mountain The dominoes and the chessboard The unexpected hanging The Tower of Hanoi Using real-world analogies, infectious humor, and a fresh approach, this deceptively simple volume will challenge, amuse, enlighten, and surprise even the most experienced puzzle solver.
The Pythagorean World
by Jane McdonnellThis book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that "everything is number". However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.
The Python Book
by Rob MastrodomenicoThe Python Book Discover the power of one of the fastest growing programming languages in the world with this insightful new resource The Python Book delivers an essential introductory guide to learning Python for anyone who works with data but does not have experience in programming. The author, an experienced data scientist and Python programmer, shows readers how to use Python for data analysis, exploration, cleaning, and wrangling. Readers will learn what in the Python language is important for data analysis, and why. The Python Book offers readers a thorough and comprehensive introduction to Python that is both simple enough to be ideal for a novice programmer, yet robust to be useful for those more experienced in the language. The book assists budding programmers to gradually increase their skills as they move through the book, always with an understanding of what they are covering and why it is useful. Used by major companies like Google, Facebook, Instagram, Spotify, and more, Python promises to remain central to the programming landscape for years to come. Containing a thorough discussion of Python programming topics like variables, equalities and comparisons, tuple and dictionary data types, while and for loops, and if statements, readers will also learn: How to use highly useful Python programming libraries, including Pandas and Matplotlib How to write Python functions and classes How to write and use Python scripts To deal with different data types within Python Perfect for statisticians, computer scientists, software programmers, and practitioners working in private industry and medicine, The Python Book will also be of interest to students in any of the aforementioned fields. As it assumes no programming experience or knowledge, the book is ideal for those who work with data and want to learn to use Python to enhance their work. <P><P><i>Advisory: Bookshare has learned that this book offers only partial accessibility. We have kept it in the collection because it is useful for some of our members. Benetech is actively working on projects to improve accessibility issues such as these.</i>
The Quadratic Reciprocity Law
by Oswald BaumgartThis book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law ("Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise"), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart's comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.