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Mathematical modelling

See below for a selection of the latest books from Mathematical modelling category. Presented with a red border are the Mathematical modelling books that have been lovingly read and reviewed by the experts at Lovereading. With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Mathematical modelling books and those from many more genres to read that will keep you inspired and entertained. And it's all free!

Information Theory Meets Power Laws

Information Theory Meets Power Laws

Author: Lukasz Debowski Format: Hardback Release Date: 24/11/2020

This book introduces mathematical foundations of statistical modeling of natural language. The author attempts to explain a few statistical power laws satisfied by texts in natural language in terms of non-Markovian and non-hidden Markovian discrete stochastic processes with some sort of long-range dependence. To achieve this, he uses various concepts and technical tools from information theory and probability measures. This book begins with an introduction. The first half of the book is an introduction to probability measures, information theory, ergodic decomposition, and Kolmogorov complexity, which is provided to make the book relatively self-contained. This section also covers less standard concepts and results, such as excess entropy and generalization of conditional mutual information to -fields. The second part of the book discusses the results concerning power laws for mutual information and maximal repetition, such as theorems about facts and words. There is also a separate chapter discussing toy examples of stochastic processes, which should inspire future work in statistical language modeling.

Numerical Methods in Physics with Python

Numerical Methods in Physics with Python

Author: Alex (University of Guelph, Ontario) Gezerlis Format: Paperback / softback Release Date: 31/08/2020

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the numerical methods often used in the subject.

Numerical Methods in Physics with Python

Numerical Methods in Physics with Python

Author: Alex (University of Guelph, Ontario) Gezerlis Format: Hardback Release Date: 31/08/2020

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. Accompanying the mathematical derivations are full implementations of dozens of numerical methods in Python, as well as more than 250 end-of-chapter problems. Numerical methods and physics examples are clearly separated, allowing this introductory book to be later used as a reference; the penultimate section in each chapter is an in depth project, tackling physics problems which cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the numerical methods often used in the subject.

Advanced Problem Solving Using Maple

Advanced Problem Solving Using Maple

Author: William P (U.S. Naval Post Graduate School) Fox, William C. Bauldry Format: Hardback Release Date: 24/08/2020

The text applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. Scenarios are developed within the scope of the problem solving process. The text focuses on discrete dynamical systems, optimization techniques, single-variable unconstrained optimization and applied problems, and numerical search methods. Additional coverage includes multivariable unconstrained and constrained techniques. Linear algebra techniques to model and solve problems such as the Leontief model, advanced regression technique include nonlinear, logistics and Poisson are covered. Game Theory, the Nash equilibrium, Nash arbitration are also included.

From Fractals And Cellular Automata To Biology: Information As Order Hidden Within Chance

From Fractals And Cellular Automata To Biology: Information As Order Hidden Within Chance

The didactical level of exposition, together with many astonishing images and animations, accompanied by the related simple computer programming codes (in Python and POV-Ray languages) make this book an extremely and unique useful tool to test the power of algorithmic information in generating ordered structure models (2D and 3D) like regular geometric shapes, complex shapes like fractals and cellular automata, and biological systems as the organs of a living body. Informational biologists besides mathematicians and physicists of complexity may learn to test their own capabilities in programming and modelling ordered structures starting from random initial conditions at different scale of each system: from elementary particles, to biological systems, to galaxies and the whole universe. Moreover the philosophical comments comparing some aspects of modern information theory to the Aristotelian notion of 'form are very appealing also for the epistemologist and the philosopher involved in complexity matters.

Credit Scoring and Its Applications

Credit Scoring and Its Applications

Author: Lyn Thomas, Jonathan Crook, David Edelman Format: Paperback / softback Release Date: 01/08/2020

Credit Scoring and Its Applications is recognized as the bible of credit scoring. It contains a comprehensive review of the objectives, methods, and practical implementation of credit and behavioral scoring. The authors review principles of the statistical and operations research methods used in building scorecards, as well as the advantages and disadvantages of each approach. The book contains a description of practical problems encountered in building, using, and monitoring scorecards and examines some of the country-specific issues in bankruptcy, equal opportunities, and privacy legislation. It contains a discussion of economic theories of consumers' use of credit, and readers will gain an understanding of what lending institutions seek to achieve by using credit scoring and the changes in their objectives. New to the second edition are: lessons that can be learned for operations research model building from the global financial crisis current applications of scoring discussions on the Basel Accords and their requirements for scoring new methods for scorecard building and new expanded sections on ways of measuring scorecard performance, and survival analysis for credit scoring. Other unique features include methods of monitoring scorecards and deciding when to update them, as well as different applications of scoring, including direct marketing, profit scoring, tax inspection, prisoner release, and payment of fines.

The Water Waves Problem

The Water Waves Problem

Author: David Lannes Format: Hardback Release Date: 27/07/2020

This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models. Which model provides the best description of waves such as tsunamis or tidal waves? How can water waves equations be transformed into simpler asymptotic models for applications in, for example, coastal oceanography? This book proposes a simple and robust framework for studying these questions. The book should be of interest to graduate students and researchers looking for an introduction to water waves equations or for simple asymptotic models to describe the propagation of waves. Researchers working on the mathematical analysis of nonlinear dispersive equations may also find inspiration in the many (and sometimes new) models derived here, as well as precise information on their physical relevance.

Partition Functions and Automorphic Forms

Partition Functions and Automorphic Forms

Author: Valery A. Gritsenko Format: Hardback Release Date: 10/07/2020

This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

Mathematical and Numerical Approaches for Multi-Wave Inverse Problems

Mathematical and Numerical Approaches for Multi-Wave Inverse Problems

Author: Larisa Beilina Format: Hardback Release Date: 01/07/2020

This proceedings volume gathers peer-reviewed, selected papers presented at the Mathematical and Numerical Approaches for Multi-Wave Inverse Problems conference at the Centre Internacional de Rencontres Mathematiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems. Multi-wave inverse problems have a wide range of applications in acoustics, electromagnetics, optics, medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse problems are both nonlinear and ill-posed: two factors that pose major challenges for the development of new numerical methods for solving these problems, which are discussed in detail. These papers will be of interest to all researchers and graduate students working in the fields of nonlinear and inverse problems and its applications.

Random Summation

Random Summation

Author: Boris V. Gnedenko, Victor Yu. Korolev Format: Paperback / softback Release Date: 30/06/2020

This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.

Modellierungskompetenzen - Diagnose Und Bewertung

Modellierungskompetenzen - Diagnose Und Bewertung

Author: Gilbert Greefrath Format: Paperback / softback Release Date: 03/06/2020

Der vorliegende Band widmet sich der notwendigen Frage, wie Lernleistungen bei Modellierungsaufgaben erkannt, gemessen und bewertet werden koennen. Dazu werden in Beitragen verschiedene Tests zur Messung von Modellierungskompetenzen vorgestellt. Teilkompetenzen, die gut erfasst werden koennen, umfassen zum Beispiel Vereinfachen, Strukturieren, Erstellen von schriftliche Loesungen und Prasentationstechniken. Diskutiert wird aber auch die Bewertung komplexer Modellierungsaufgaben. Selbstredend geht es auch um lernfoerderliche Ruckmeldung im Lehr-Lern-Prozess. Die Auswirkungen der Verwendung metakognitiver Loesungsstrategien wird untersucht. Vorgestellt wird weiter ein Kompetenzstufenmodell, das zur Aufgabenstellung und Leistungsinterpretation fur die schriftliche Reifeprufung in OEsterreich dient, sowie die Konzeption von Modellierungsaufgaben im Abitur.Dieser Band zeigt, wie mathematisches Modellieren sinnvoll und gewinnbringend genutzt werden kann und liefert Materialien und Ideen fur den Einsatz in Schule und Hochschule.

Dialogues Around Models And Uncertainty: An Interdisciplinary Perspective

Dialogues Around Models And Uncertainty: An Interdisciplinary Perspective

Author: Pauline (The London Sch Of Economics & Political Science, Uk) Barrieu Format: Hardback Release Date: 21/05/2020

This book helps develop a better understanding of how researchers from different scientific backgrounds view models and uncertainty. It provides key steps in fostering and encouraging interdisciplinary research, which is vital in addressing several big issues that society faces today, such as climate change, longevity, financial and actuarial risk management. To make progress in these areas, researchers must develop an understanding of differing perspectives and methods of those working in other disciplines.This title presents the views and understandings of eminent people in their respective fields through interviews on the topic of modelling and uncertainty. Each expert was asked the same set of questions to help readers understand the similarities and differences existing between various disciplines. It also helps to bridge some of the gaps encountered by those carrying out inter- and multi-disciplinary research and suggests new approaches to modelling and uncertainty quantification.