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Advanced Common Core Math Explorations: Measurement & Polygons (Grades 5-8)
by Jerry BurkhartStudents become mathematical adventurers in these challenging and engaging activities designed to deepen and extend their understanding of concepts from the Common Core State Standards in Mathematics. The investigations in this book stretch students' mathematical imaginations to their limits as they create and manipulate geometric figures, draw and analyze complex designs, and develop and apply measurement strategies to solve challenging real-world and mathematical problems. Each activity comes with extensive support for classroom implementation including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigation. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.Grades 5-8
Advanced Common Core Math Explorations: Fractions (Grades 5-8)
by Jerry BurkhartStudents become mathematical adventurers in these challenging and engaging activities designed to deepen and extend their understanding of concepts from the Common Core State Standards in Mathematics. The investigations in this book stretch students' mathematical imaginations to their limits as they solve puzzles, create stories, and explore fraction-related concepts that take them from the mathematics of ancient Greece to the outer reaches of infinity. Each activity comes with detailed support for classroom implementation including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigation. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.Grades 5-8
Advanced Functional Evolution Equations and Inclusions (Developments in Mathematics #39)
by Saïd Abbas Mouffak BenchohraThis book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.
Advanced Linear Algebra (Textbooks in Mathematics)
by Bruce CoopersteinThis book discusses structure theory of an operator, topics on inner product spaces, and trace and determinant functions of a linear operator. It addresses bilinear forms with a full treatment of symplectic spaces and orthogonal spaces, as well as explains construction of tensor, symmetric, and exterior algebras. Featuring several new exercises, the second edition adds coverage of sesquilinear forms, linear groups, matrices, normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebras. A solutions manual is available upon qualifying course adoption.
Advanced Methodologies for Bayesian Networks: Second International Workshop, AMBN 2015, Yokohama, Japan, November 16-18, 2015. Proceedings (Lecture Notes in Computer Science #9505)
by Joe Suzuki Maomi UenoThis volume constitutes the refereed proceedings of the Second International Workshop on Advanced Methodologies for Bayesian Networks, AMBN 2015, held in Yokohama, Japan, in November 2015. The 18 revised full papers and 6 invited abstracts presented were carefully reviewed and selected from numerous submissions. In the International Workshop on Advanced Methodologies for Bayesian Networks (AMBN), the researchers explore methodologies for enhancing the effectiveness of graphical models including modeling, reasoning, model selection, logic-probability relations, and causality. The exploration of methodologies is complemented discussions of practical considerations for applying graphical models in real world settings, covering concerns like scalability, incremental learning, parallelization, and so on.
Advanced Methods in the Fractional Calculus of Variations (SpringerBriefs in Applied Sciences and Technology)
by Agnieszka B. Malinowska Tatiana Odzijewicz Delfim F.M. TorresThis brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler-Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler-Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm-Liouville problems. Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.
Advanced Quantitative Reasoning: Mathematics for the World Around Us (Texas Edition)
by Gregory D. Foley Thomas R. Butts Stephen W. Phelps Daniel A. ShowalterAdvanced Quantitative Reasoning provides a balanced approach to relevant mathematics for students entering higher education or the workforce. It balances traditional high school mathematics with statistics and modeling; quantitative literacy with financial and overall literacy; and technology-enhanced mathematics with mental and paper-and-pencil mathematics.
Advanced State Space Methods for Neural and Clinical Data
by Zhe ChenThis authoritative work provides an in-depth treatment of state space methods, with a range of applications in neural and clinical data. Advanced and state-of-the-art research topics are detailed, including topics in state space analyses, maximum likelihood methods, variational Bayes, sequential Monte Carlo, Markov chain Monte Carlo, nonparametric Bayesian, and deep learning methods. Details are provided on practical applications in neural and clinical data, whether this is characterising time series data from neural spike trains recorded from the rat hippocampus, the primate motor cortex, or the human EEG, MEG or fMRI, or physiological measurements of heartbeats or blood pressures. With real-world case studies of neuroscience experiments and clinical data sets, and written by expert authors from across the field, this is an ideal resource for anyone working in neuroscience and physiological data analysis.
Advances in Architectural Geometry 2014
by Philippe Block Jan Knippers Niloy J. Mitra Wenping WangThis book contains 24 technical papers presented at the fourth edition of the Advances in Architectural Geometry conference, AAG 2014, held in London, England, September 2014. It offers engineers, mathematicians, designers, and contractors insight into the efficient design, analysis, and manufacture of complex shapes, which will help open up new horizons for architecture. The book examines geometric aspects involved in architectural design, ranging from initial conception to final fabrication. It focuses on four key topics: applied geometry, architecture, computational design, and also practice in the form of case studies. In addition, the book also features algorithms, proposed implementation, experimental results, and illustrations. Overall, the book presents both theoretical and practical work linked to new geometrical developments in architecture. It gathers the diverse components of the contemporary architectural tendencies that push the building envelope towards free form in order to respond to multiple current design challenges. With its introduction of novel computational algorithms and tools, this book will prove an ideal resource to both newcomers to the field as well as advanced practitioners.
Advances in Artificial Economics (Lecture Notes in Economics and Mathematical Systems #676)
by Benoit Gaudou Frédéric Amblard Francisco J. Miguel Adrien BlanchetThe book presents a peer-reviewed collection of papers presented during the 10th issue of the Artificial Economics conference, addressing a variety of issues related to macroeconomics, industrial organization, networks, management and finance, as well as purely methodological issues. The field of artificial economics covers a broad range of methodologies relying on computer simulations in order to model and study the complexity of economic and social phenomena. The grounding principle of artificial economics is the analysis of aggregate properties of simulated systems populated by interacting adaptive agents that are equipped with heterogeneous individual behavioral rules. These macroscopic properties are neither foreseen nor intended by the artificial agents but generated collectively by them. They are emerging characteristics of such artificially simulated systems.
Advances in Complex Data Modeling and Computational Methods in Statistics (Contributions to Statistics)
by Anna Maria Paganoni Piercesare SecchiThe book is addressed to statisticians working at the forefront of the statistical analysis of complex and high dimensional data and offers a wide variety of statistical models, computer intensive methods and applications: network inference from the analysis of high dimensional data; new developments for bootstrapping complex data; regression analysis for measuring the downsize reputational risk; statistical methods for research on the human genome dynamics; inference in non-euclidean settings and for shape data; Bayesian methods for reliability and the analysis of complex data; methodological issues in using administrative data for clinical and epidemiological research; regression models with differential regularization; geostatistical methods for mobility analysis through mobile phone data exploration. This volume is the result of a careful selection among the contributions presented at the conference "S. Co. 2013: Complex data modeling and computationally intensive methods for estimation and prediction" held at the Politecnico di Milano, 2013. All the papers published here have been rigorously peer-reviewed.
Advances in Global Optimization: In Honor Of Gilbert Strang (Springer Proceedings in Mathematics & Statistics #95)
by David Gao Ning Ruan Wenxun XingThis proceedings volume addresses advances in global optimization--a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.
Advances in Heavy Tailed Risk Modeling
by Pavel V. Shevchenko Gareth W. PetersA cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes in high consequence low frequency loss modeling. With a companion, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the book provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distributional approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modelling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The book is also a useful handbook for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Advances in Intelligent Data Analysis XIV: 14th International Symposium, IDA 2015, Saint Etienne. France, October 22 -24, 2015. Proceedings (Lecture Notes in Computer Science #9385)
by Elisa Fromont Tijl De Bie Matthijs Van LeeuwenThis book constitutes the refereed conference proceedings of the 14th International Conference on Intelligent Data Analysis, which was held in October 2015 in Saint Étienne. France. The 29 revised full papers were carefully reviewed and selected from 65 submissions. The traditional focus of the IDA symposium series is on end-to-end intelligent support for data analysis. The symposium aims to provide a forum for inspiring research contributions that might be considered preliminary in other leading conferences and journals, but that have a potentially dramatic impact. To facilitate this, IDA 2015 will feature two tracks: a regular "Proceedings" track, as well as a "Horizon" track for early-stage research of potentially ground-breaking nature.
Advances in Latent Variables: Methods, Models and Applications (Studies in Theoretical and Applied Statistics)
by Maurizio Carpita Eugenio Brentari El Mostafa QannariThe book, belonging to the series "Studies in Theoretical and Applied Statistics- Selected Papers from the Statistical Societies", presents a peer-reviewed selection of contributions on relevant topics organized by the editors on the occasion of the SIS 2013 Statistical Conference "Advances in Latent Variables. Methods, Models and Applications", held at the Department of Economics and Management of the University of Brescia from June 19 to 21, 2013. The focus of the book is on advances in statistical methods for analyses with latent variables. In fact, in recent years, there has been increasing interest in this broad research area from both a theoretical and an applied point of view, as the statistical latent variable approach allows the effective modeling of complex real-life phenomena in a wide range of research fields. A major goal of the volume is to bring together articles written by statisticians from different research fields, which present different approaches and experiences related to the analysis of unobservable variables and the study of the relationships between them.
Advances in Robust Fractional Control
by Antonio Visioli Fabrizio PadulaThis monograph presents design methodologies for (robust) fractional control systems. It shows the reader how to take advantage of the superior flexibility of fractional control systems compared with integer-order systems in achieving more challenging control requirements. There is a high degree of current interest in fractional systems and fractional control arising from both academia and industry and readers from both milieux are catered to in the text. Different design approaches having in common a trade-off between robustness and performance of the control system are considered explicitly. The text generalizes methodologies, techniques and theoretical results that have been successfully applied in classical (integer) control to the fractional case. The first part of Advances in Robust Fractional Control is the more industrially oriented. It focuses on the design of fractional controllers for integer processes. In particular, it considers fractional-order proportional-integral-derivative controllers, because integer-order PID regulators are, undoubtedly, the controllers most frequently adopted in industry. The second part of the book deals with a more general approach to fractional control systems, extending techniques (such as H-infinity optimal control and optimal inputoutput inversion based control) originally devised for classical integer-order control. Advances in Robust Fractional Control will be a useful reference for the large number of academic researchers in fractional control, for their industrial counterparts and for graduate students who want to learn more about this subject.
Advances in the Theory of Numbers: Proceedings of the Thirteenth Conference of the Canadian Number Theory Association (Fields Institute Communications #77)
by Kenneth S. Williams Ayşe Alaca Şaban AlacaThe theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as discrete mathematics, cryptography, and coding theory. The proof by Andrew Wiles (with Richard Taylor) of Fermat's last theorem published in 1995 illustrates the high level of difficulty of problems encountered in number-theoretic research as well as the usefulness of the new ideas arising from its proof. The thirteenth conference of the Canadian Number Theory Association was held at Carleton University, Ottawa, Ontario, Canada from June 16 to 20, 2014. Ninety-nine talks were presented at the conference on the theme of advances in the theory of numbers. Topics of the talks reflected the diversity of current trends and activities in modern number theory. These topics included modular forms, hypergeometric functions, elliptic curves, distribution of prime numbers, diophantine equations, L-functions, Diophantine approximation, and many more. This volume contains some of the papers presented at the conference. All papers were refereed. The high quality of the articles and their contribution to current research directions make this volume a must for any mathematics library and is particularly relevant to researchers and graduate students with an interest in number theory. The editors hope that this volume will serve as both a resource and an inspiration to future generations of researchers in the theory of numbers.
Advances in Variational and Hemivariational Inequalities: Theory, Numerical Analysis, and Applications (Advances in Mechanics and Mathematics #33)
by Mircea Sofonea Stanisław Migórski Weimin HanThis volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities.
Affine Diffusions and Related Processes: Simulation, Theory and Applications (Bocconi & Springer Series #6)
by Aurélien AlfonsiThis book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments. The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.
Africa's Demographic Transition
by Abdo S. Yazbeck David Canning Sangeeta RajaAfrica is poised on the edge of a potential takeoff to sustained economic growth. This takeoff can be abetted by a demographic dividend from the changes in population age structure. Declines in child mortality, followed by declines in fertility, produce a 'bulge' generation and a large number of working age people, giving a boost to the economy. In the short run lower fertility leads to lower youth dependency rates and greater female labor force participation outside the home. Smaller family sizes also mean more resources to invest in the health and education per child boosting worker productivity. In the long run increased life spans from health improvements mean that this large, high-earning cohort will also want to save for retirement, creating higher savings and investments, leading to further productivity gains. Two things are required for the demographic dividend to generate an African economic takeoff. The first is to speed up the fertility decline that is currently slow or stalled in many countries. The second is economic policies that take advantage of the opportunity offered by demography. While demographic change can produce more, and high quality, workers, this potential workforce needs to be productively employed if Africa is to reap the dividend. However, once underway, the relationship between demographic change and human development works in both directions, creating a virtuous cycle that can accelerate fertility decline, social development, and economic growth. Empirical evidence points to three key factors for speeding the fertility transition: child health, female education, and women's empowerment, particularly through access to family planning. Harnessing the dividend requires job creation for the large youth cohorts entering working age, and encouraging foreign investment until domestic savings and investment increase. The appropriate mix of policies in each country depends on their stage of the demographic transition.
Agent-Based Modelling in Economics
by Lynne Hamill Nigel GilbertAgent-based modelling in economics Lynne Hamill and Nigel Gilbert, Centre for Research in Social Simulation (CRESS), University of Surrey, UK New methods of economic modelling have been sought as a result of the global economic downturn in 2008.This unique book highlights the benefits of an agent-based modelling (ABM) approach. It demonstrates how ABM can easily handle complexity: heterogeneous people, households and firms interacting dynamically. Unlike traditional methods, ABM does not require people or firms to optimise or economic systems to reach equilibrium. ABM offers a way to link micro foundations directly to the macro situation. Key features: Introduces the concept of agent-based modelling and shows how it differs from existing approaches. Provides a theoretical and methodological rationale for using ABM in economics, along with practical advice on how to design and create the models. Each chapter starts with a short summary of the relevant economic theory and then shows how to apply ABM. Explores both topics covered in basic economics textbooks and current important policy themes; unemployment, exchange rates, banking and environmental issues. Describes the models in pseudocode, enabling the reader to develop programs in their chosen language. Supported by a website featuring the NetLogo models described in the book. Agent-based Modelling in Economics provides students and researchers with the skills to design, implement, and analyze agent-based models. Third year undergraduate, master and doctoral students, faculty and professional economists will find this book an invaluable resource.
Alan Turing: The Book That Inspired the Film The Imitation Game - Updated Edition
by Andrew HodgesA NEW YORK TIMES BESTSELLERThe official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira KnightleyIt is only a slight exaggeration to say that the British mathematician Alan Turing (1912–1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades—all before his suicide at age forty-one. This New York Times bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing&’s royal pardon in 2013, is the definitive account of an extraordinary mind and life.Capturing both the inner and outer drama of Turing&’s life, Andrew Hodges tells how Turing&’s revolutionary idea of 1936—the concept of a universal machine—laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design. The book also tells how this work was directly related to Turing&’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. At the same time, this is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program—all for trying to live honestly in a society that defined homosexuality as a crime.The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley, Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.
Algebra: Form and Function (Second Edition)
by William G. Mccallum Elliot J. Marks Aysegul Sahin Ellen Schmierer Pat Shure Adam H. Spiegler Carl Swenson Eric Connally Deborah Hughes-Hallett Philip Cheifetz Ann Davidian Selin Kalaycýoðlu Brigitte Lahme Patti Frazer Lock David LovelockAlgebra: Form and Function offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. Meant for a College Algebra course, Algebra: Form and Function is an introduction to one of the fundamental aspects of modern society. Algebraic equations describe the laws of science, the principles of engineering, and the rules of business. The power of algebra lies in the efficient symbolic representation of complex ideas, which also presents the main difficulty in learning it. It is easy to forget the underlying structure of algebra and rely instead on a surface knowledge of algebraic manipulations. Most students rely on surface knowledge of algebraic manipulations without understanding the underlying structure of algebra that allows them to see patterns and apply it to multiple situations: McCallum focuses on the structure from the start.
Algebra: A Teaching and Source Book
by Ernest Shult David SurowskiThis book presents a graduate-level course on modern algebra. It can be used as a teaching book - owing to the copious exercises - and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan-Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.
