The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.

Mathematical modeling is a powerful craft that requires practice. The more practice the better one will become in executing the art. The authors wrote this book to develop the craft of mathematical modeling and to foster a desire for lifelong learning, habits of mind and develop competent and confident problem solvers and decision makers for the 21st century. This book offers a problem-solving approach. The authors introduce a problem to help motivate the learning of a particular mathematical modeling topic. The problem provides the issue or what is needed to solve using an appropriate modeling technique. Then principles are applied to the problem and present the steps in obtaining an appropriate model to solve the problem. Modeling Change and Uncertainty: Covers both linear and nonlinear models of discrete dynamical systems. Introduces statistics and probability modeling. Introduces critical statistical concepts to handle univariate and multivariate data. Establishes a foundation in probability modeling. Uses ordinary differential equations (ODEs) to develop a more robust solution to problems. Uses linear programming and machine learning to support decision making. Introduces the reality of uncertainty and randomness that is all around us. Discusses the use of linear programing to solve common problems in modern industry. Discusses he power and limitations of simulations. Introduces the methods and formulas used in businesses and financial organizations. Introduces valuable techniques using Excel, MAPLE, and R. Mathematical modeling offers a framework for decision makers in all fields. This framework consists of four key components: the formulation process, the solution process, interpretation of the solution in the context of the actual problem, and sensitivity analysis. Modeling Change and Uncertainty will be of interest to mathematics departments offering advanced mathematical modeling courses focused on decision making or discrete mathematical modeling and by undergraduate, graduate students and practitioners looking for an opportunity to develop, practice, and apply the craft of mathematical modeling. Table of Contents 1. Perfect Partners: Combining Models of Change and Uncertainty with Technology 2. Modeling Change: Discrete Dynamical Systems (DDS) and Modeling Systems of DDS 3. Statistical and Probabilistic Models 4. Modeling with Probability 5. Differential Equations 6. Forecasting with Linear Programming and Machine Learning 7. Stochastic Models and Markov Chains 8. Linear Programming 9. Simulation of Queueing Models 10. Modeling of Financial Analysis 11. Reliability Models 12. Machine Learning and Unconstrained Optimal Process Dr. William P. Fox is currently a visiting professor of Computational Operations Research at the College of William and Mary. He is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School and teaches a three-course sequence in mathematical modeling for decision making. He received his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy for twelve years until retiring and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including twenty plus books and one hundred and fifty journal articles. Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor in the Defense Analysis Department of the Naval Postgraduate School (NPS) and the Director of the NPS' Wargaming Center. He holds a Ph.D. in Operations Research from the Air Force Institute of Technology. He is a retired logistics Army Colonel with more than thirty years of military experience in leadership, advanced analytics, decision modeling, and logistics operations who served as an Army Operations Research analyst at the Naval Postgraduate School, TRADOC Analysis Center, United States Military Academy, and the United States Army Recruiting Command. Other book by William P. Fox and Robert E. Burks: Advanced Mathematical Modeling with Technology, 2021, CRC Press. Other books by William P. Fox from CRC Press: Mathematical Modeling in the Age of the Pandemic, 2021, CRC Press. Advanced Problem Solving Using Maple: Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis (w/William Bauldry), 2020, CRC Press. Mathematical Modeling with Excel (w/Brian Albright), 2020, CRC Press. Nonlinear Optimization: Models and Applications, 2020, CRC Press. Advanced Problem Solving with Maple: A First Course (w/William Bauldry), 2019. CRC Press. Mathematical Modeling for Business Analytics, 2018, CRC Press.

;This book is intended to be a text for either a first or a second course in numerical methods for students in all engineering disciplines. Difficult concepts which usually pose problems to students are explained in detail and illustrated with solved examples. Enough elementary material that could be covered in the first-level course is included such as methods for solving linear and nonlinear algebraic equations, interpolation, differentiation, integration, and simple techniques for integrating ODEs and PDEs (ordinary and partial differential equations). Advanced techniques and concepts that could form part of a second-level course include Gear's method for solving ODE-IVPs (initial value problems), stiffness of ODE-IVPs, multiplicity of solutions, convergence characteristics, the orthogonal collocation method for solving ODEBVPs (boundary value problems) and finite element techniques. An extensive set of graded problems, often with hints, has been included. Some involve simple applications of the concepts and can be solved using a calculator, while several are from real-life situations and require writing computer programs or use of library subroutines. Practice on these is expected to build up the reader's confidence in developing large computer codes.

An Introduction to Numerical Methods: A MATLAB® Approach, Fifth Edition continues to offer readers an accessible and practical introduction to numerical analysis. It presents a wide range of useful and important algorithms for scientific and engineering applications, using MATLAB to illustrate each numerical method with full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes new chapters on Approximation of Continuous Functions and Dealing with Large Sets of Data. Features: Covers the most common numerical methods encountered in science and engineering Illustrates the methods using MATLAB Ideal as an undergraduate textbook for numerical analysis Presents numerous examples and exercises, with selected answers provided at the back of the book Accompanied by downloadable MATLAB code hosted at https/www.routledge.com/ 9781032406824

Describes the outbreak of compartment fires, and the mechanisms for best controlling them Derives simple analytical relationships from first principles and shows how to compare the derived equations with experimental data Provides the calculational procedures and computer models needed to design a building for safety Cites the most up to date standards and references throughout Includes numerous chapter problems to test student readers' understanding of fire behavior

COVID Transmission Modeling: An Insight into Infectious Diseases Mechanism provides an interdisciplinary overview of the COVID-19 pandemic crisis and covers various aspects of newer modeling techniques and practical solutions for health emergencies. This book aims to formulate various innovative and pragmatic mathematical, statistical, and epidemiological models using COVID-19 real data sets. It emphasizes interdisciplinary theoretical postulates derived from practical insights and knowledge of public health. Each of the book's 12 chapters provides invaluable and exploratory tools to enable explicit assumptions, highlights key health indicators, and determines the geometric progression and control measures of the disease. The present developed models will allow readers to extrapolate the exact reason for the outbreak and pave the way for scientific information on vaccine trials and socioeconomic, psychological, and disease burden worldwide. These advanced techniques of modeling and their applications are in greater need than ever for effective connection between mathematicians, statisticians, epidemiologists, researchers, clinicians, and policymakers for making appropriate decisions at the right time. With the advent of emerging health science, all models are demonstrated with real-life data sets and provided with illustrations and eye-catching graphs and diagrams so that the readers can easily understand the concept of COVID-19 pandemic interventions and their control measures, and their impact. Features Addresses all aspects of mitigation/control measures, estimation of transmission rate, economic impact assessment, genetic complexity of COVID-19, herd immunity, and various methods, including newer mathematical, statistical, and epidemiological models in the analysis of COVID-19 pandemic outbreak Covers the application of innovative, advanced statistical and epidemiological models and demonstrates possible solutions toward supportive treatment aspects of COVID-19 and its control measures Includes models that can easily be followed in formulating the mathematical derivations and key points Supplemented with ample illustrations, images, diagrams, and figures This book is aimed at postgraduate students studying medicine and healthcare, mathematics, and statistical information. Researchers will also find this book very helpful.

With easily accessible oil reserves dwindling, petroleum engineers must have a sound understanding of how to access technically challenging resources, especially in the deepwater environment. These technically challenging resources bring with them complexities around fluid flow not normally associated with conventional production systems, and engineers must be knowledgeable about navigating these complexities. Practical Aspects of Flow Assurance in the Petroleum Industry aims to provide practical guidance on all aspects of flow assurance to offer readers a ready reference on how to ensure uninterrupted transport of processed fluids throughout the flow infrastructure by covering all practical aspects of flow assurance, being written in such a way that any engineer dealing with the oil and gas industry will be able to understand the material, containing solved examples on most topics, placing equal emphasis on experimental techniques and modeling methods, and devoting an entire chapter to the analysis and interpretation of published case studies. With its balance of theory and practical applications, this work provides petroleum engineers from a variety of backgrounds with the information needed to maintain and enhance productivity.

Features Suitable for graduate students and professional researchers in operator theory and/or analysis Numerous applications in related scientific fields and areas.

This book addresses the functioning of financial markets, in particular the financial market model, and modelling. More specifically, the book provides a model of adaptive preference in the financial market, rather than the model of the adaptive financial market, which is mostly based on Popper's objective propensity for the singular, i.e., unrepeatable, event. As a result, the concept of preference, following Simon's theory of satisficing, is developed in a logical way with the goal of supplying a foundation for a robust theory of adaptive preference in financial market behavior. The book offers new insights into financial market logic, and psychology: 1) advocating for the priority of behavior over information - in opposition to traditional financial market theories; 2) constructing the processes of (co)evolution adaptive preference-financial market using the concept of fetal reaction norms - between financial market and adaptive preference; 3) presenting a new typology of information in the financial market, aimed at proving point (1) above, as well as edifying an explicative mechanism of the evolutionary nature and behavior of the (real) financial market; 4) presenting sufficient, and necessary, principles or assumptions for developing a theory of adaptive preference in the financial market; and 5) proposing a new interpretation of the pair genotype-phenotype in the financial market model. The book's distinguishing feature is its research method, which is mainly logically rather than historically or empirically based. As a result, the book is targeted at generating debate about the best and most scientifically beneficial method of approaching, analyzing, and modelling financial markets.

Applies concepts and theorems from real and complex analysis (e.g. Fourier series; implicit function theorem) and topology in the framework of this key theorem from mathematical physics. Covers all aspects of Arnold's proof, including those often left out in more general or simplified presentations. Discusses, in detail, the ideas used in the proof of the KAM theorem and puts them in historical context (e.g. mapping degree from algebraic topology).

An Image Processing Tour of College Mathematics aims to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies. The topics covered include a library of elementary functions, basic concepts of descriptive statistics, probability distributions of functions of random variables, definitions and concepts behind first- and second-order derivatives, most concepts and techniques of traditional linear algebra courses, an introduction to Fourier analysis, and a variety of discrete wavelet transforms - all of that in the context of digital image processing. Features Pre-calculus material and basic concepts of descriptive statistics are reviewed in the context of image processing in the spatial domain. Key concepts of linear algebra are reviewed both in the context of fundamental operations with digital images and in the more advanced context of discrete wavelet transforms. Some of the key concepts of probability theory are reviewed in the context of image equalization and histogram matching. The convolution operation is introduced painlessly and naturally in the context of naive filtering for denoising and is subsequently used for edge detection and image restoration. An accessible elementary introduction to Fourier analysis is provided in the context of image restoration. Discrete wavelet transforms are introduced in the context of image compression, and the readers become more aware of some of the recent developments in applied mathematics. This text helps students of mathematics ease their way into mastering the basics of scientific computer programming.

A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically Additional end-of-chapter problems with different ranges of difficulty This exemplary text shows students how cutting-edge theoretical topics are applied to a variety of areas, from elementary atomic physics and mathematics to angular momentum and time dependence to relativity and quantum computing. Many examples and exercises illustrate the principles and test students understanding.

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc.

Solid-Liquid Thermal Energy Storage: Modeling and Applications provides a comprehensive overview of solid-liquid phase change thermal storage. Chapters are written by specialists from both academia and industry. Using recent studies on the improvement, modeling, and new applications of these systems, the book discusses innovative solutions for any potential drawbacks. This book: Discusses experimental studies in the field of solid-liquid phase change thermal storage Reviews recent research on phase change materials Covers various innovative applications of phase change materials (PCM) on the use of sustainable and renewable energy sources Presents recent developments on the theoretical modeling of these systems Explains advanced methods for enhancement of heat transfer in PCM This book is a reference for engineers and industry professionals involved in the use of renewable energy systems, energy storage, heating systems for buildings, sustainability design, etc. It can also benefit graduate students taking courses in heat transfer, energy engineering, advanced materials, and heating systems.

Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in n, Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions as well as functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's covering theorem, Rademacher's theorem (on the differentiability a.e. of Lipschitz functions), area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrov's theorem (on the twice differentiability a.e. of convex functions). This revised edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the - theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated. Topics are carefully selected and the proofs are succinct, but complete. This book provides ideal reading for mathematicians and graduate students in pure and applied mathematics.

During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing applications. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential end users often get the impression that jump and Lévy processes are beyond their reach.

Financial Modelling with Jump Processes demonstrates that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects of using jump processes in financial modeling, and does so in terms well within the grasp of nonspecialists. With clear-sighted explanations, the authors motivate the use of the various mathematical tools used in the modelling process, and while giving an intuitive understanding of proofs, provide precise mathematical statements of the results. They illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms.

This book clearly shows that the concepts and tools necessary for understanding and implementing these models can be much more accessible and intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.

The author has shown that practically all our laws, principles, and theories are not physically realizable, since they were derived from an empty space paradigm. From which this book is started with the origin of our temporal (t > 0) universe, it shows that temporal subspace is a physically realizable space within our universe. As in contrasted with generally accepted paradigm where time is an independent variable. From which the author has shown that it is not how rigorous mathematics is, but it is the temporal (t > 0) space paradigm determines the physically realizable solution. Although Einstein's relativity and Schroedinger's principle had revolutionized the modern science, this book has shown that both theory and principle are physically non-realizable since they were developed from an empty space paradigm. One of the most important contribution of this book must be the revolutionary idea of our temporal (t > 0) space, for which the author has shown that absolute certainty exists only at the present (t = 0) moment. Where past-time information has no physical substance and future-time represents a physically realizable yet uncertainty. From which the author has shown that all the existent laws, principles, and theories were based on past-time certainties to predict the future, but science is supposed to be approximated. The author has also shown that this is precisely our theoretical science was developed. But time independent laws and principles are not existed within our temporal universe, in view of the author's temporal exclusive principle. By which the author has noted that timeless science has already created a worldwide conspiracy for examples such as superposition principle, qubit information, relativity theory, wormhole travelling and many others. This book has also shown that Heisenberg's uncertainty is an observational principle independent with time, yet within our universe everything changes with time. In this book the author has also noted that micro space behaviors the same as macro space regardless of the particle size. Finally, one of interesting feature is that, that big bang creation was ignited by a self-induced gravitational force instead by time as commonly believed. Nevertheless, everything has a price to pay; a section of time t and an amount of energy E and it is not free. The author has also shown that time is the only variable that cannot be changed. Although we can squeeze a section of time t as small as we wish but we can never able to squeeze t to zero even we have all the needed energy. Nevertheless, this revolutionary book closer to the truth is highly recommended to every scientist and engineer, otherwise we will forever be trapped within the timeless fantasyland of science. This book is intended for cosmologists, particle physicists, astrophysicists, quantum physicists, computer scientists, optical scientists, communication engineers, professors, and students as a reference or a research-oriented book.

Gives basics of Fortran and Numerical Calculation. The book includes Fortran codes and also gives access to author's website. Summarizes history of Quantum Mechanics through the most important papers. Presents detailed mathematical basis of Quantum Mechanics and Quantum Chemistry. Includes proposed exercises and do-it-yourself activities.

A concise and practical guide to financial modeling in Excel In The Essentials of Financial Modeling in Excel: A Concise Guide to Concepts and Methods, veteran quantitative modeling and business analysis expert Dr. Michael Rees delivers a practical and hands-on introduction to financial modeling in Excel. The author offers readers a well-structured and strategic toolkit to learn modeling from scratch, focusing on the core economic concepts and the structures commonly required within Excel models. Divided into six parts, the book discusses the use of models and the factors to consider when designing and building models so that they can be as powerful as possible, yet simple. . Readers will also find: The foundational structures and calculations most frequently used in modeling, including growth- and ratio-based methods, corkscrews, and waterfall analysis Walkthroughs of economic modeling, measurement, and evaluation, and the linking of these to the decision criteria. These include breakeven and payback analysis, compounding, discounting, calculation of returns, loan calculations, and others Structured approaches for modeling in corporate finance, including financial statement modeling, cash flow valuation, cost of capital, and ratio analysis Techniques to implement sensitivity and scenario analysis Core aspects of statistical analysis, including data preparation, manipulation, and integration The use of approximately 100 Excel functions within example modeling contexts Further Topics Sections, which introduce advanced aspects of many areas, in order to provide further benefit to more advance readers, whilst presenting the truly essential topics separately. Examples of these include introductions to PowerQuery and PowerPivot, as well as advanced waterfall structures An invaluable, all-in-one blueprint for learning financial modeling in Excel, this book is ideal for beginning and intermediate financial professionals and students seeking to build and reinforce essential topics in financial modeling.

Rotary Drum: Fluid Dynamics, Dimensioning Criteria, and Industrial Applications provides in-depth analysis of fluid dynamics in rotary drums. In addition, it provides analysis on the different configurations, including nonconventional ones, diverse industrial applications, and comparison with competing dryer types, as well as the modeling of these devices. Covering important aspects of fluid dynamics in rotary drums, which directly influence the drying performance, the book also considers the significant cost of conventional rotary dryers. It takes into account the scale-up of rotary dryers and the control of product quality during processing, which can leave the final product overdried and overheated, wasting thermal energy. The book serves as a useful reference for researchers, graduate students, and engineers in the field of drying technology.

*This book balances the development, implementation, application and analysis of computational ideas and methods. *Problems are designed toward computer projects so that students can test and apply numerical method. *The book is written with motivation examples and real-world application problems to catch students' interest. *Short Matlab and Python tutorials to quickly start programming in scientific computing.

Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials, making it accessible for those unfamiliar with graduate-level mathematics. Topics include topology, vector spaces, tensor spaces, Lebesgue integrals, and operators, to name a few. Each chapter explains, concisely, the purpose of the specific topic and the benefit of understanding it. Researchers and graduate students in physics, mechanical engineering, and information science will benefit from this view of functional analysis.

Applied Mathematics with Open-source Software: Operational Research Problems with Python and R is aimed at a broad segment of readers who wish to learn how to use open-source software to solve problems in applied mathematics. The book has an innovative structure with 4 sections of two chapters covering a large range of applied mathematical techniques: probabilistic modelling, dynamical systems, emergent behaviour and optimisation. The pairs of chapters in each section demonstrate different families of solution approaches. Each chapter starts with a problem, gives an overview of the relevant theory, shows a solution approach in R and in Python, and finally gives wider context by including a number of published references. This structure will allow for maximum accessibility, with minimal prerequisites in mathematics or programming as well as giving the right opportunities for a reader wanting to delve deeper into a particular topic. Features An excellent resource for scholars of applied mathematics and operational research, and indeed any academics who want to learn how to use open-source software. Offers more general and accessible treatment of the subject than other texts, both in terms of programming language but also in terms of the subjects considered. The R and Python sections purposefully mirror each other so that a reader can read only the section that interests them. An accompanying open-source repository with source files and further examples is posted online at https://bit.ly/3kpoKSd.