Approximation & Regular Methods Operator-Function Equations
This book presents an overview of the most recent research and results in the field of approximation and regularisation methods for operator-functional equations, and explores their applications in electrical and power engineering. It presents the state of the art in building operator theory, regularised numerical methods, and in the verification of mathematical models for dynamical models based on integral and differential equations. Special attention is paid to Volterra models, a powerful tool for modelling hereditary dynamics.This book begins by exploring the solvability of singular integral equations, and moves on to study approximation methods for linear operator equations and nonlinear integral equations. Following this, it examines loaded equations and bifurcation analysis, before concluding with an investigation of the applications of the contents of the book in electrical engineering and automation. Each chapter provides an overview and analysis of the relevant problem statements, outlines current methods within the field, and identifies future directions for research.With an interdisciplinary approach, this book is essential reading for anyone interested in operator-functional equations. Graduate students and professors in the fields of applied mathematics, physics, material science, and numerical analysis will find this work insightful and valuable, as will industry professionals in related fields.
Amusements in Mathematics
Unlock the Enigma of Numbers with a Timeless Classic! Dive into the captivating world of ""Amusements in Mathematics"" by the legendary Henry Ernest Dudeney, a masterpiece that has enchanted puzzle enthusiasts for generations. This extraordinary collection of mathematical puzzles and brainteasers, once out of print for decades, is now beautifully republished by Alpha Editions, making it a must-have collector's edition for both the curious minds of today and the inquisitive thinkers of tomorrow. From mind-bending riddles to ingenious conundrums, Dudeney's brilliance shines through every page, offering a delightful challenge to both novice and seasoned puzzle solvers. Whether you're looking to sharpen your problem-solving skills or simply seeking an entertaining escape into the world of numbers, this book promises hours of intellectual amusement. Don't miss your chance to own a piece of mathematical history that has stood the test of time. Rediscover the joy of puzzles with ""Amusements in Mathematics"" and let your imagination soar!
Lectures on Advanced Engineering Mathematics (With Worked Examples)
Applied Nonparametric Statistical Methods
A comprehensive course text in nonparametric techniques suitable for undergraduate mathematics students. Assumes only basic experience of statistics with algebra kept to a minimum. Ideal for quantitative methods modules delivered to undergraduate or postgrad students in science, business, and health service training.
Random Number Generators for Computer Simulation and Cyber Security
This book discusses the theory and practice of random number generators that are useful for computer simulation and computer security applications. Random numbers are ubiquitous in computation. They are used in randomized algorithms to perform sampling or choose randomly initialized parameters or perform Markov Chain Monte Carlo (MCMC). They are also used in computer security applications for various purposes such as cryptographic nuances or in authenticators. In practice, the random numbers used by any of these applications are from a pseudo-random sequence. These pseudo-random sequences are generated by RNGs (random number generators). This book discusses the theory underlying such RNGs, which are used by all programmers. However, few try to understand the theory behind them. This topic is an active area of research, particularly when the generators are used for cryptographic applications. The authors introduce readers to RNGs, how they are judged for quality, the mathematical and statistical theory behind them, as well as provide details on how these can be implemented in any programming language. The book discusses non-linear transformations that use classical linear generators for cryptographic applications and how to optimize to make such generators more efficient. In addition, the book provides up-to-date research on RNGs including a modern class of efficient RNGs and shows how to search for new RNGs with good quality and how to parallelize these RNGs.
Derivatives Pricing
This is a masters-level overview of the mathematical concepts needed to fully grasp the art of derivatives pricing, and a must-have for anyone considering a career in quantitative finance in industry or academia. Starting from the foundations of probability, this textbook allows students with limited technical background to build a solid knowledge of the most important principles. It offers a unique compromise between intuition and mathematics, even when discussing abstract ideas such as change of measure. Mathematical concepts are introduced initially using toy examples, before moving on to examples of finance cases, both in discrete and continuous time. Throughout, numerical applications and simulations illuminate the analytical results. The end-of-chapter exercises test students' understanding, with solved exercises at the end of each part to aid self-study. Additional resources are available online, including slides, code and an interactive app.
Math Mammoth Grade 3-A Worktext, International Version
Math Mammoth Grade 3-A Worktext (International Version, 2025 edition) is the student book for the first half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers addition, subtraction, rounding, word problems, the concept of multiplication, multiplication tables, time, and money. Please note: The worktext does not include the answer key. The answer keys for grade 3 are sold as a separate book. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching.The curriculum meets and exceeds the Common Core standards. Please note this is a student worktext and does not contain the answers. The answer key book is available separately.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 3-B Worktext, International Version
Math Mammoth Grade 3-B Worktext (International Version, 2025 edition) is the student book for the latter half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers four-digit numbers, division, measurement, geometry, and fractions. Please note: The worktext does not include the answer key. The answer keys for grade 3 are sold as a separate book. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. The curriculum meets and exceeds the Common Core standards. Please note this is a student worktext and does not contain the answers. The answer key book is available separately.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.For multiplication tables and division facts, you can use our online practice program (free).
Math Mammoth Grade 3 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 3 Tests and Cumulative Revisions (International Version) includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 3 curriculum. This is the 2025 edition. Please note: The book does not include the answer key. The answer keys for grade 3 are sold as a separate book.
Intelligent Systems and Pattern Recognition
This Three-volume set CCIS 2303-2305 constitutes the proceedings of the 4th International Conference on Intelligent Systems and Pattern Recognition, ISPR 2024, held in Istanbul, Turkey, in June 26-28, 2024. The 77 full papers presented were thoroughly reviewed and selected from the 210 submissions. The conference provided an interdisciplinary forum for the exchange of innovative advancements in the fields of artificial intelligence and pattern recognition.
The Siml Filtering Method for Noisy Non-Stationary Economic Time Series
Geometry and Analysis on Finsler Spaces
Finsler geometry is just Riemannian geometry without a quadratic restriction. It has applications in many fields of natural sciences, including physics, psychology, and ecology. The book is intended to provide basic materials on Finsler geometry for readers and to bring them to the frontiers of active research on related topics.This book is comprised of three parts. In Part I (Chapters 1-4), the author introduces the basics, such as Finsler metrics, the Chern connection, geometric invariant quantities, etc., and gives some rigidity results on Finsler manifolds with certain curvature properties. Part II (Chapters 5-6) covers the theory of geodesics, using which the author establishes some comparison theorems, which are fundamental tools to study global Finsler geometry. In Part III (Chapters 7-9), the author presents recent developments in nonlinear geometric analysis on Finsler spaces, partly based on the author's recent works on Finsler harmonic functions, the eigenvalue problem, and heat flow. The author has made efforts to ensure that the contents are accessible to advanced undergraduates, graduate students, and researchers who are interested in Finsler geometry.
Course in Ordinary Differential Equations with Applications
This book was written for advanced undergraduate math or science majors. Its initial purpose was to illustrate the elementary mathematical theory of ordinary differential equations and their diverse and powerful applications. Historically these have been decisive in many physical problems, some of which have philosophically challenged and indeed altered our civilization's concepts. Because of the importance of the subject, the book is also suitable for a one-semester course for graduate students. The book consists of 12 chapters and six appendices.
Bayesian Statistics
Bayesian Statistics: The Basics provides a comprehensive yet accessible introduction to Bayesian statistics, specifically tailored for any researcher with an interest in statistical methods. It covers the theoretical foundations of Bayesian inference, contrasting it with classical statistical methods like null hypothesis significance testing. The book emphasizes key concepts such as prior and posterior distributions, Bayes' theorem, and the Bayes factor, making them understandable even for readers with minimal mathematical backgrounds.Methodologically, the book offers practical, step-by-step guides on how to conduct Bayesian analyses using the free software package JASP. Each chapter focuses on applying Bayesian methods to common research designs with real-world data. Readers will benefit from the clear examples, visualizations, and JASP screenshots that ensure the learning experience is interactive and easy to follow.Full of practical content, the book emphasizes the advantages of Bayesian model comparison over traditional approaches, especially in quantifying evidence for competing hypotheses. Readers will also learn how to perform sensitivity analyses to assess the impact of different prior assumptions on their results.By the end of the book, readers will get both the theoretical understanding and practical skills to implement Bayesian methods in their own research, making it an invaluable resource for both novice and experienced researchers studying Bayesian Statistics.
Game Theory Explained
This book provides an introduction to the mathematical theory of games using both classical methods and optimization theory. Employing a theorem-proof-example approach, the book emphasizes not only results in game theory, but also how to prove them.Part 1 of the book focuses on classical results in games, beginning with an introduction to probability theory by studying casino games and ending with Nash's proof of the existence of mixed strategy equilibria in general sum games. On the way, utility theory, game trees and the minimax theorem are covered with several examples. Part 2 introduces optimization theory and the Karush-Kuhn-Tucker conditions and illustrates how games can be rephrased as optimization problems, thus allowing Nash equilibria to be computed. Part 3 focuses on cooperative games. In this unique presentation, Nash bargaining is recast as a multi-criteria optimization problem and the results from linear programming and duality are revived to prove the classic Bondareva-Shapley theorem. Two appendices covering prerequisite materials are provided, and a 'bonus' appendix with an introduction to evolutionary games allows an instructor to swap out some classical material for a modern, self-contained discussion of the replicator dynamics, the author's particular area of study.
Higher Recursion Theory and Set Theory
This volume celebrates the research contributions of Professors Theodore A Slaman and W Hugh Woodin, marking their distinguished careers in higher recursion theory and set theory as they approached the milestone of their 65th birthdays in 2019. It originates from the Institute for Mathematical Sciences program, Higher Recursion Theory and Set Theory, held at the National University of Singapore (May 20-June 14, 2019).The program explored cutting-edge developments in higher recursion theory, set theory, and their intricate interconnections. Topics discussed during the workshop included Martin's conjecture, higher randomness, the HOD conjecture, descriptive inner model theory, and the Ultimate-L program.This volume presents 15 peer-reviewed contributions by leading experts in the field, offering a comprehensive overview of recent advances in higher recursion theory and set theory, with a focus on their dynamic interactions.
Mathematical Theory of Compressible Fluids on Moving Domains
Geometric Gems (V3)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.
Geometric Gems (V3)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.
The Art of Uncertainty
How dangerous is our diet? How much of sports falls into the realm of luck? When authorities categorize a given event as "highly likely"--how likely is that, really? Whether we're trying to decide if the benefits of a new medication are worth the chance of side effects or if artificial intelligence truly threatens humanity, our lives are riddled with uncertainties both everyday and existential--yet it can be difficult to know how to properly weigh all those unknowns. Luckily for us, renowned statistician David Spiegelhalter has spent his career dissecting data to resolve the apparently random and decode the many decisions we face with imperfect information. In The Art of Uncertainty, he shows how we can become better at dealing with what we don't know to make smarter choices in a world so full of puzzling variablesIn lucid, lively prose, Spiegelhalter guides us through the principles of probability, illustrating how they can help us think more analytically about everything from medical advice to sports to climate change forecasts. He demonstrates how taking a mathematical approach to phenomena we might otherwise attribute to fate or luck can help us sort hidden patterns from mere coincidences, better evaluate cause and effect, and predict what's likely to happen in the future. Along the way, we learn how a misinterpretation of a probability contributed to the infamous Bay of Pigs fiasco, why a ship twice the size of the Titanic sank without a trace, and why we can be so confident that no two properly shuffled decks of cards have ever been in the same orderSparkling with wit and fascinating real-world examples, this is an essential guide to navigating uncertainty while also retaining the humility to admit what we don't, or simply cannot, know.
Fuzzy Mathematics
This book aims to introduce readers without a strong mathematical background to the basic ideas of fuzzy set theory and logic. Fuzzy mathematics is the mathematics of vagueness, a universal property of this world. There are many objects that are called vague because they cannot be precisely defined. Since vagueness is so common, a tool is needed to describe it and to effectively deal with it. Fuzzy mathematics is such a tool, and it is used by most researchers and scholars. As such, this book provides a short overview of the field written for non-specialists. This book allows readers to delve into the theory of fuzzy sets and introduces core mathematical ideas without using the usual formalities of books in mathematics, i.e. theorems, proofs, etc.
Deep Learning in Time Series Analysis
The concept of deep machine learning is easier to understand by paying attention to the cyclic stochastic time series and a time series whose content is non-stationary not only within the cycles, but also over the cycles as the cycle-to-cycle variations.
Space-Time Algebra of Sedeons
This book is a comprehensive guide to the space-time algebra of sixteen-component values "sedeons". This algebra is designed to provide a compact representation of equations that describe various physical systems. The book considers the symmetry of physical quantities concerning the operations of spatial and temporal inversion. This approach allows the formulation of a wide class of mathematical physics equations within a unified framework and enables the generalization of these equations for essential problems in electrodynamics, hydrodynamics, plasma physics, field theory, and quantum mechanics. In particular, it is shown that the broken symmetry between electricity and magnetism in electrodynamics equations is a result of choosing an asymmetric representation of these phenomena. The sedeonic algebra enables the formulation of Maxwell-like equations for the fields with a nonzero mass of quantum, which facilitates the calculation of energy for baryon-baryon interaction and the semi-classical interpretation of this interaction. It also allows one to generalize the hydrodynamics equations for the case of vortex turbulent flows and for a hydrodynamic two-fluid model of electron-ion plasma.
State-of-the-Art of Mathematical Modeling, Dynamics, and Control of Wind Turbines Engineering
Lectures on the H-Cobordism Theorem
Important lectures on differential topology by acclaimed mathematician John Milnor These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.
Hands-On Mathematical Optimization with Python
This practical guide to optimization combines mathematical theory with hands-on coding examples to explore how Python can be used to model problems and obtain the best possible solutions. Presenting a balance of theory and practical applications, it is the ideal resource for upper-undergraduate and graduate students in applied mathematics, data science, business, industrial engineering and operations research, as well as practitioners in related fields. Beginning with an introduction to the concept of optimization, this text presents the key ingredients of an optimization problem and the choices one needs to make when modeling a real-life problem mathematically. Topics covered range from linear and network optimization to convex optimization and optimizations under uncertainty. The book's Python code snippets, alongside more than 50 Jupyter notebooks on the author's GitHub, allow students to put the theory into practice and solve problems inspired by real-life challenges, while numerous exercises sharpen students' understanding of the methods discussed.
