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Heart of Mathematics: An Invitation to Effective Thinking (Third Edition)
by Edward B. Burger Michael StarbirdMake mathematics fun and satisfying for everyone Math can be a living source of powerful ideas that transcend mathematics; a window into mind-opening philosophical concepts such as infinity, fourth dimensions, chaos, and fractals; and a practical training ground for developing skills in analysis, reasoning, and thought if you have the right approach and the right guide. The Heart of Mathematics: An Invitation to Effective Thinking, now in its third edition, transforms mathematics into an engaging, relevant experience even for the most math-phobic student. Infusing this book with humor and enthusiasm, Edward B. Burger and Michael Starbird both recipients of the Mathematical Association of America's foremost national teaching award and countless state, regional, and campus-wide teaching honors introduce students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking. Richer and more rewarding than ever, this new edition features: An emphasis on mathematical methods of investigation Visualization techniques that make key concepts easier to understand Accessible, friendly writing style that encourages critical thinking "Life Lessons"-effective methods of thinking that students will retain and apply beyond the classroom End of section Mindscape activities for the development of application, problem-solving, and argumentation skills.
The Heart of Mathematics (4th Edition): An Invitation to Effective Thinking
by Edward B. Burger Michael StarbirdTransform your mathematics course into an engaging and mind-opening experience for even your most math-phobic students. Now in its Fourth Edition, The Heart of Mathematics: An Invitation to Effective Thinking succeeds at reaching non-math, non-science-oriented majors, encouraging them to discover the mathematics inherent in the world around them. Infused with the authors' humor and enthusiasm throughout, The Heart of Mathematics introduces students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.
Heart Rate Variability Analysis with the R package RHRV (Use R!)
by Constantino Antonio García Martínez Abraham Otero Quintana Xosé A. Vila María José Lado Touriño Leandro Rodríguez-Liñares Jesús María Rodríguez Presedo Arturo José Méndez PenínThis book introduces readers to the fundamental concepts of Heart Rate Variability (HRV) and its most important analysis algorithms using a hands-on approach based on the open-source RHRV software. HRV refers to the variation over time of the intervals between consecutive heartbeats. Despite its apparent simplicity, HRV is one of the most important markers of autonomic nervous system activity and it has been recognized as a useful predictor of several pathologies. The book discusses all the basic HRV topics, including the physiological contributions to HRV, clinical applications, HRV data acquisition, HRV data manipulation and HRV analysis using time-domain, frequency-domain, time-frequency, nonlinear and fractal techniques. Detailed examples based on real data sets are provided throughout the book to illustrate the algorithms and discuss the physiological implications of the results. Offering a comprehensive guide to analyzing beat information with RHRV, the book is intended for masters and Ph.D. students in various disciplines such as biomedical engineering, human and veterinary medicine, biology, and pharmacy, as well as researchers conducting heart rate variability analyses on both human and animal data. The second edition of the book has been updated to RHRV version 5.0. This version introduces a functionality to perform heart rate variability analysis on entire populations. This functionality automates and streamlines both the calculation of HRV indices in the time, frequency, and nonlinear domains, as well as the subsequent statistical analysis.
Heat Carriers in Liquids: An Introduction (SpringerBriefs in Physics)
by Jaeyun MoonThis book provides a succinct overview of recent progress in characterization of heat carriers describing atomic motion in liquids. Unlike solids and gases where heat carriers are typically described by phonons and real atomic particles, the nature of effective heat carriers in liquids is still elusive. The emphasis is on two widely used spectral methods to describe heat carriers: instantaneous normal modes and velocity autocorrelation functions. Various bulk materials properties from a bottom-up perspective using these spectra are presented in detail. This book is an ideal introduction to the field for graduate students and young researchers.
The Heat Kernel and Theta Inversion on SL2(C)
by Jay Jorgenson Serge LangThe worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform.</
Heat Kernel on Lie Groups and Maximally Symmetric Spaces (Frontiers in Mathematics)
by Ivan G. AvramidiThis monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form – and derives them – for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics – such as global analysis, spectral geometry, stochastic processes, and financial mathematics – as well in areas of mathematical and theoretical physics – including quantum field theory, quantum gravity, string theory, and statistical physics.
Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry
by Glen Van BrummelenAn unparalleled illustrated history of spherical trigonometry from antiquity to todayHeavenly Mathematics traces the rich history of spherical trigonometry, revealing how the cultures of classical Greece, medieval Islam, and the modern West used this forgotten art to chart the heavens and the Earth. Once at the heart of astronomy and ocean-going navigation for two millennia, the discipline was also a mainstay of mathematics education for centuries and taught widely until the 1950s. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation of its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams. This unique compendium also features easy-to-use appendixes as well as exercises that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
Heavy-Tailed Distributions and Robustness in Economics and Finance
by Marat Ibragimov Rustam Ibragimov Johan WaldenThis book focuses on general frameworks for modeling heavy-tailed distributions in economics, finance, econometrics, statistics, risk management and insurance. A central theme is that of (non-)robustness, i. e. , the fact that the presence of heavy tails can either reinforce or reverse the implications of a number of models in these fields, depending on the degree of heavy-tailed ness. These results motivate the development and applications of robust inference approaches under heavy tails, heterogeneity and dependence in observations. Several recently developed robust inference approaches are discussed and illustrated, together with applications.
Heavy-Tailed Distributions in Disaster Analysis
by M. Rodkin V. PisarenkoMathematically, natural disasters of all types are characterized by heavy tailed distributions. The analysis of such distributions with common methods, such as averages and dispersions, can therefore lead to erroneous conclusions. The statistical methods described in this book avoid such pitfalls. Seismic disasters are studied, primarily thanks to the availability of an ample statistical database. New approaches are presented to seismic risk estimation and forecasting the damage caused by earthquakes, ranging from typical, moderate events to very rare, extreme disasters. Analysis of these latter events is based on the limit theorems of probability and the duality of the generalized Pareto distribution and generalized extreme value distribution. It is shown that the parameter most widely used to estimate seismic risk - Mmax, the maximum possible earthquake value - is potentially non-robust. Robust analogues of this parameter are suggested and calculated for some seismic catalogues. Trends in the costs inferred by damage from natural disasters as related to changing social and economic situations are examined for different regions. The results obtained argue for sustainable development, whereas entirely different, incorrect conclusions can be drawn if the specific properties of the heavy-tailed distribution and change in completeness of data on natural hazards are neglected. This pioneering work is directed at risk assessment specialists in general, seismologists, administrators and all those interested in natural disasters and their impact on society.
Heavy-Tailed Time Series (Springer Series in Operations Research and Financial Engineering)
by Rafal Kulik Philippe SoulierThis book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology. Appropriate for graduate coursework or professional reference, the book requires a background in extreme value theory for i.i.d. data and basics of time series. Following a brief review of foundational concepts, it progresses linearly through topics in limit theorems and time series models while including historical insights at each chapter’s conclusion. Additionally, the book incorporates complete proofs and exercises with solutions as well as substantive reference lists and appendices, featuring a novel commentary on the theory of vague convergence.
Hecke’s L-functions: Spring, 1964 (SpringerBriefs in Mathematics)
by Kenkichi IwasawaThis volume contains the notes originally made by Kenkichi Iwasawa in his own handwriting for his lecture course at Princeton University in 1964. These notes give a beautiful and completely detailed account of the adelic approach to Hecke’s L-functions attached to any number field, including the proof of analytic continuation, the functional equation of these L-functions, and the class number formula arising from the Dedekind zeta function for a general number field. This adelic approach was discovered independently by Iwasawa and Tate around 1950 and marked the beginning of the whole modern adelic approach to automorphic forms and L-series. While Tate’s thesis at Princeton in 1950 was finally published in 1967 in the volume Algebraic Number Theory, edited by Cassels and Frohlich, no detailed account of Iwasawa’s work has been published until now, and this volume is intended to fill the gap in the literature of one of the key areas of modern number theory. In the final chapter, Iwasawa elegantly explains some important classical results, such as the distribution of prime ideals and the class number formulae for cyclotomic fields.
Heisenberg’s 1958 Weltformel and the Roots of Post-Empirical Physics (SpringerBriefs in History of Science and Technology)
by Alexander S. BlumThis book presents the first detailed account of Werner Heisenberg’s failed attempt to find a theory of everything in the autumn of his career. It further investigates what we can learn from his failure in relation to the search for a final theory of physics, an endeavour that continues to define research in fundamental physics to this day. Thereby it provides the first historically informed contribution to the current debate on post-empirical physics and the state of particle physics.
Heisenberg’s Uncertainty Principle and the Electron Statistics in Quantized Structures
by Kamakhya Prasad Ghatak Madhuchhanda Mitra Arindam BiswasThis book highlights the importance of Electron Statistics (ES), which occupies a singular position in the arena of solid state sciences, in heavily doped (HD) nanostructures by applying Heisenberg’s Uncertainty Principle directly without using the complicated Density-of-States function approach as given in the literature. The materials considered are HD quantum confined nonlinear optical, III-V, II-VI, IV-VI, GaP, Ge, PtSb2, stressed materials, GaSb, Te, II-V, Bi2Te3, lead germanium telluride, zinc and cadmium diphosphides, and quantum confined III-V, IV-VI, II-VI and HgTe/CdTe super-lattices with graded interfaces and effective mass super-lattices. The presence of intense light waves in optoelectronics and strong electric field in nano-devices change the band structure of materials in fundamental ways, which have also been incorporated in the study of ES in HD quantized structures of optoelectronic compounds that control the studies of the HD quantum effect devices under strong fields. The influence of magnetic quantization, magneto size quantization, quantum wells, wires and dots, crossed electric and quantizing fields, intense electric field, and light waves on the ES in HD quantized structures and superlattices are discussed. The content of this book finds six different applications in the arena of nano-science and nanotechnology and the various ES dependent electronic quantities, namely the effective mass, the screening length, the Einstein relation and the elastic constants have been investigated. This book is useful for researchers, engineers and professionals in the fields of Applied Sciences, solid state and materials science, nano-science and technology, condensed matter physics, and allied fields, including courses in semiconductor nanostructures.
Helix Structures in Quantum Cohomology of Fano Varieties (Lecture Notes in Mathematics #2356)
by Giordano Cotti Boris A. Dubrovin Davide GuzzettiThis research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM). This conjecture asserts the equivalence, for a Fano variety, between the semisimplicity condition of its quantum cohomology and the existence of full exceptional collections in its derived category of coherent sheaves. Additionally, in its quantitative form, the conjecture specifies an explicit relation between the monodromy data of the quantum cohomology, characteristic classes, and exceptional collections. A refined version of the conjecture is introduced, with a particular focus on the central connection matrix, and a precise link is established between this refined conjecture and Γ-conjecture II, as proposed by S. Galkin, V. Golyshev, and H. Iritani. By performing explicit calculations of the monodromy data, the validity of the refined conjecture for all complex Grassmannians G(r,k) is demonstrated. Intended for students and researchers, the book serves as an introduction to quantum cohomology and its isomonodromic approach, along with its algebraic counterpart in the derived category of coherent sheaves.
Hello Numbers! What Can You Do?: An Adventure Beyond Counting
by Edmund Harriss Houston HughesLearning meets wonder when you invite numbers to come play in your imagination! <P><P> First think of One peeking out from the night Like a point, or a dot, or a shimmering light. But when One finds a friend to run from or run to, Then we can’t call both “One”—that new One must be Two! And should you want something to go in between, You’ll need a new number, a number like Three. Four makes a square when it’s standing around, But what would you see if it flies off the ground? And then when another new One comes to mind, Yell out its name if you know it . . . it’s Five! Do you like the way that these numbers are sounding? Then join our adventure to count beyond counting! Hello Numbers! What Can You Do? is not like any other counting book. As each “new One” appears on the scene, the numbers’ antics hint at ever-deeper math. Young readers ages 3 to 6 will not only count along, but begin to wonder about symmetry, angles, shapes, and more. Written by the mathematician-and-poet team Edmund Harriss and Houston Hughes, and illustrated by longstanding New York Times artist Brian Rea, this rollicking, rhyming book will take you to a whole new world of numbers.
Hello World: Being Human in the Age of Algorithms
by Hannah FryShortlisted for the 2018 Royal Society Investment Science Book Prize A look inside the algorithms that are shaping our lives and the dilemmas they bring with them. If you were accused of a crime, who would you rather decide your sentence—a mathematically consistent algorithm incapable of empathy or a compassionate human judge prone to bias and error? What if you want to buy a driverless car and must choose between one programmed to save as many lives as possible and another that prioritizes the lives of its own passengers? And would you agree to share your family’s full medical history if you were told that it would help researchers find a cure for cancer? These are just some of the dilemmas that we are beginning to face as we approach the age of the algorithm, when it feels as if the machines reign supreme. Already, these lines of code are telling us what to watch, where to go, whom to date, and even whom to send to jail. But as we rely on algorithms to automate big, important decisions—in crime, justice, healthcare, transportation, and money—they raise questions about what we want our world to look like. What matters most: Helping doctors with diagnosis or preserving privacy? Protecting victims of crime or preventing innocent people being falsely accused? Hello World takes us on a tour through the good, the bad, and the downright ugly of the algorithms that surround us on a daily basis. Mathematician Hannah Fry reveals their inner workings, showing us how algorithms are written and implemented, and demonstrates the ways in which human bias can literally be written into the code. By weaving in relatable, real world stories with accessible explanations of the underlying mathematics that power algorithms, Hello World helps us to determine their power, expose their limitations, and examine whether they really are improvement on the human systems they replace.
The Helmholtz Equation Least Squares Method
by Sean F. WuThis book represents the HELS (Helmholtz equation least squares) theory and its applications for visualizing acoustic radiation from an arbitrarily shaped vibrating structure in free or confined space. yIt culminates the most updated research work of the author and his graduate students since 1997. yThe book contains six chapters. yThe first serves as a review of the fundamentals in acoustics and the rest cover five specific topics on the HELS theory. "
Help Your Kids with Math: A Unique Step-by-Step Visual Guide (DK Help Your Kids)
by Barry LewisIf you and your child find math mindboggling, then you can count on this ultimate home-study guide to get all the answers you need. This visual reference book gets you ready to help your children tackle the trickiest of subjects. From algebra and angles to sequences and statistics – and everything in between – Carol Vorderman's unique study companion sums it all up. Help Your Kids with Math encourages parents and children to work together as a team to solve even the most challenging problems on the school syllabus. Made with home learning in mind, this book uses a clear mix of pictures, diagrams, and instructions help to build knowledge, boost confidence, and gain understanding. With your support, children can overcome the challenges of math, leaving them calm, confident, and exam ready.Series Overview: DK's bestselling Help Your Kids With series contains crystal-clear visual breakdowns of important subjects. Simple graphics and jargon-free text are key to making this series a user-friendly resource for frustrated parents who want to help their children get the most out of school.
Helping Children Who are Anxious or Obsessional: A Guidebook (Helping Children with Feelings)
by Margot SunderlandThis is a guidebook to help children who: are insecure or worry too much; suffer from phobias or nightmares; find it difficult to concentrate to let go and have fun; have suffered a trauma; are worryingly good or seem like little adults; use order and routine as a way of coping with 'messy' feelings; retreat into dullness as a way of managing their being in the world; and, develop obsessive-compulsive behaviour in order to ward off their too-powerful feelings.
Helping Students Become Powerful Mathematics Thinkers: Case Studies of Teaching for Robust Understanding (Studies in Mathematical Thinking and Learning Series)
by Alan Schoenfeld Heather Fink Sandra Zuñiga-Ruiz Siqi Huang Xinyu Wei Brantina ChirindaThis book supports teacher educators, teachers, coaches, administrators, math-ed faculty, and researchers in understanding and using the Teaching for Robust Understanding (TRU) Framework to improve instruction. Detailed case studies take readers on deep dives into five essential dimensions of classroom practice: The Mathematics; Cognitive Demand; Equitable Access; Agency, Ownership, and Identity; and Formative Assessment. Three case studies form the core of the book. Each case uses the TRU framework to pose conversational questions to the reader on different aspects of the lessons, focusing on the ways that students are led to engage with mathematics and how they make sense of it. These include “What’s important in this classroom episode?,” “What might students be experiencing?,” or “What might the impact of alternative teaching decisions have been in this situation?”. The book concludes with guides for planning, observation, and reflection that readers can use in their own work, continuing the journey toward the ambitious and equitable instruction that each case study describes. This book will support all mathematics educators in developing deeper understandings of mathematics classrooms and in problematizing their own mathematics instruction. By exploring the challenges students face, the decisions teachers make, and the ways that students learn, readers will experience TRU as a powerful way of thinking about instruction – one that can shape lesson planning and reflection and make teaching more impactful and equitable.
Helping Students Make Sense of the World Using Next Generation Science and Engineering Practices
by Christina Schwarz Cynthia Passmore Brian ReiserWhen it’s time for a game change, you need a guide to the new rules. Helping Students Make Sense of the World Using Next Generation Science and Engineering Practices provides a play-by-play understanding of the practices strand of A Framework for K–12 Science Education (Framework) and the Next Generation Science Standards (NGSS). Written in clear, nontechnical language, this book provides a wealth of real-world examples to show you what’s different about practice-centered teaching and learning at all grade levels. The book addresses three important questions: <P><P>1. How will engaging students in science and engineering practices help improve science education? 2. What do the eight practices look like in the classroom? 3. How can educators engage students in practices to bring the NGSS to life? <P><P>Helping Students Make Sense of the World Using Next Generation Science and Engineering Practices was developed for K–12 science teachers, curriculum developers, teacher educators, and administrators. Many of its authors contributed to the Framework’s initial vision and tested their ideas in actual science classrooms. If you want a fresh game plan to help students work together to generate and revise knowledge—not just receive and repeat information—this book is for you.
Henke's Med-Math: Dosage Calculation, Preparation and Administration (Seventh Edition)
by Susan BuchholzThis best-selling text features a highly visual, hands-on approach to learning dosage calculations and principles of drug administration. It presents step-by-step approaches to solving problems and includes dosage problems that simulate actual clinical experience. Each chapter includes numerous examples, self-tests, and proficiency tests.
Henri Poincaré: Translation of Selected Papers and Discussion
by Bruce D PoppProduced by an award-winning translator of Henri Poincaré, this book contains translations of several seminal articles by Poincaré and discusses the experimental and theoretical investigations of electrons that form their context. In the 1950s, a dispute ignited about the origin of the theory of special relativity and thrust considerable notoriety on a paper written by Henri Poincaré in 1905. Accordingly, Part I presents the relevant translations of Poincaré’s work showing that radiation carries momentum and the covariance of the equations of electrodynamics, the continuity equation for charge, and the spacetime interval. Part II then discusses investigations by Thomson, Becquerel, and Kaufmann of electrons in diverse contexts; contributions of Abraham, Lorentz and Poincaré to a theory of electrons that includes Lorentz transformations and explains the dependence of mass on velocity; and finally, Poincaré’s exploration of the relativity principle, electron stability, and gravitation while rejecting absolute motion (ether) and an electromagnetic origin of mass. Part III contains the 1904 article by H. A. Lorentz presenting his transformations.This book will be a fascinating read to graduate-level students, physicists, and science historians who are interested in the development of electrodynamics and the classical, relativistic theory of electrons at the beginning of the 20th century.
Henry P. McKean Jr. Selecta
by F. Alberto Grünbaum Pierre Van Moerbeke Victor H. MollThis volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics. Each paper represents a contribution by Prof. McKean, either alone or together with other researchers, that has had a profound influence in the respective area.
Herausforderung Mathematik im ersten Semester der Ingenieurwissenschaften: Eine exemplarische Untersuchung von Studienbeginn bis zur ersten Klausur zum mathematischen Basiswissen (BestMasters)
by Julian PlackDieses Buch widmet sich dem verfügbaren mathematischen Basiswissen der Studierenden zu Beginn eines Studiums in ingenieurwissenschaftlichen Studiengängen. Der große Stellenwert solcher Berufe für die Gesellschaft in der Zukunft und die hohen Abbruchquoten, die sich seit langer Zeit in mathematiklastigen Studiengängen verzeichnen lassen, bieten Anlass für das Forschungsinteresse. Zum quantitativen Forschungsdesign gehört ein Fragebogen, der an die Studierenden gerichtet ist und persönliche sowie schulische Eingangsparameter abfragt sowie eine Lernstandserhebung bestehend aus Aufgaben der Schulmathematik. Dabei stellt sich die Frage, ob sich Zusammenhänge zwischen den erhobenen Eingangsparametern der Erstsemesterstudierenden, den mathematischen Grundkenntnissen zu Studienbeginn sowie dem Klausurerfolg gemessen an der Klausurnote am Ende des ersten Semesters erkennen lassen. Das Ziel der Studie ist es, Bedingungen zu formulieren, die den Klausurerfolg beeinflussen.