Equations of Motion for Incompressible Viscous Fluids
This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena. The authors' approach carefully walks readers through the development of fluid equations at the cutting edge of research, and the applications of a variety of boundary conditions to real-world problems. Special attention is paid to the equivalence between partial differential equations with a mixture of various boundary conditions and their corresponding variational problems, especially variational inequalities with one unknown. A self-contained approach is maintained throughout by first covering introductory topics, and then moving on to mixtures of boundary conditions, a thorough outline of the Navier-Stokes equations, an analysis of both the steady and non-steady Boussinesq system, and more. Equations of Motion for Incompressible Viscous Fluids is ideal for postgraduate students and researchers in the fields of fluid equations, numerical analysis, and mathematical modelling.
A Guide to Spectral Theory
Foreword.- Prolegomena.- Chapter 1: A First Look at Spectral Theory.- Chapter 2: Unbounded Operators.- Chapter 3: Spectrum .- Chapter 4: Compact Operators.- Chapter 5: Fredholm Theory.- Chapter 6: Spectrum of Self-Adjoint Operators.- Chapter 7: Hille-Yosida and Stone's Theorems.- Chapter 8: About the Spectral Measure.- Chapter 9: Trace-class and Hilbert-Schmidt Operators.- Chapter 10: Selected Applications of the Functional Calculus.- Appendix A: Reminders of Functional Analysis.- Bibliography.- Index.
Casual Calculus: A Friendly Student Companion - Volume 2
Yes, this is another Calculus book. However, I think it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one -- it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide -- because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between these two extremes. It is best used as a companion to a traditional text or as a refresher -- with its conversational tone, its 'get right to it' content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.Exercises are structured in three sets to force multiple encounters with each topic. Solved examples in the text are accompanied by 'You Try It' problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are 'Practice Problems': more problems similar to the You Try It problems, but given all at once. Finally, each section has Challenge Problems -- these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.My goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. Because we have large engineering and meteorology programs at my institution, and they make up the largest portion of our Calculus students; naturally, then, these sorts of STEM students are the target audience.
Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics
This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.
Casual Calculus: A Friendly Student Companion - Volume 2
Yes, this is another Calculus book. However, it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one - it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide - because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between these two extremes. It is best used as a companion to a traditional text or as a refresher - with its conversational tone, its "get right to it" content structure, and its inclusion of complete solutions to many problems, it is a friendly partner for students who are learning Calculus, either in class or via self-study.Exercises are structured in three sets to force multiple encounters with each topic. Solved examples in the text are accompanied by "You Try It" problems, which are similar to the solved examples; the students use these to see if they're ready to move forward. Then at the end of the section, there are "Practice Problems" more problems similar to the "You Try It" problems, but given all at once. Finally, each section has Challenge Problems - these lean to being equally or a bit more difficult than the others, and they allow students to check on what they've mastered.The goal is to keep the students engaged with the text, and so the writing style is very informal, with attempts at humor along the way. The target audience is STEM students including those in engineering and meteorology programs.
An Invitation to Representation Theory
Preface Introduction Chapter 1. First Steps Chapter 2. Polynomials, Subspaces, and Subrepresentations Chapter 3. Intertwining Maps, Complete Reducibility, and Invariant Inner Products Chapter 4. The Structure of the Symmetric Group Chapter 5. Sn Decomposition of Polynomial Spaces for n= 1,2,3. Chapter 6. The Group Algebra Chapter 7. The Irreducible Representations of Sn: Characters Chapter 8. The Irreducible Representations of Sn: Young Symmetrizers Chapter 9. Cosets, Restricted and Induced Representations Chapter 10. Direct Products of Groups, Young Subgroups and Permutation Modules Chapter 11. Specht Modules Chapter 12. Decomposition of Young Permutation Modules Chapter 13. Branching Relations Bibliography Index
The Rise and Fall of the German Combinatorial Analysis
This text presents the ideas of a particular group of mathematicians of the late 18th century known as "the German combinatorial school" and its influence. The book tackles several questions concerning the emergence and historical development of the German combinatorial analysis, which was the unfinished scientific research project of that group of mathematicians. The historical survey covers the three main episodes in the evolution of that research project: its theoretical antecedents (which go back to the innovative ideas on mathematical analysis of the late 17th century) and first formulation, its consolidation as a foundationalist project of mathematical analysis, and its dissolution at the beginning of the 19th century. In addition, the book analyzes the influence of the ideas of the combinatorial school on German mathematics throughout the 19th century.
Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics
This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.
A Brief History of Analysis
This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstra?, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.
Mathematical Olympiad in China (2017-2018): Problems and Solutions
In China, lots of excellent maths students take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results - they won the first place almost every year.The authors of this book are coaches of the China national team. They are Xiong Bin, Yao Yijun, Qu Zhenhua, et al. Those who took part in the translation work are Wang Shanping and Chen Haoran.The materials of this book come from a series of two books (in Chinese) on Forward to IMO: A Collection of Mathematical Olympiad Problems (2017-2018). It is a collection of problems and solutions of the major mathematical competitions in China. It provides a glimpse of how the China national team is selected and formed.
Advances in Metric Fixed Point Theory and Applications
This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed point property and almost fixed point property in digital spaces, nonexpansive semigroups over CAT(κ) spaces, measures of noncompactness, integral equations, the study of fixed points that are zeros of a given function, best proximity point theory, monotone mappings in modular function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic programming and Picard operators.This book addresses the mathematical community working with methods and tools of nonlinear analysis. It also serves as a reference, source for examples and new approaches associated with fixed point theory and its applications for a wide audience including graduate students and researchers.
Mathematical Olympiad in China (2017-2018): Problems and Solutions
In China, lots of excellent maths students take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results -- they won the first place almost every year.The authors of this book are coaches of the China national team. They are Xiong Bin, Yao Yijun, Qu Zhenhua, et al. Those who took part in the translation work are Wang Shanping and Chen Haoran.The materials of this book come from a series of two books (in Chinese) on Forward to IMO: A Collection of Mathematical Olympiad Problems (2017-2018). It is a collection of problems and solutions of the major mathematical competitions in China. It provides a glimpse of how the China national team is selected and formed.
Computational Linear Algebra
Courses on linear algebra and numerical analysis need each other. Often NA courses have some linear algebra topics, and LA courses mention some topics from numerical analysis/scientific computing. This text merges these two areas into one introductory undergraduate course. It assumes students have had multivariable calculus.
Mathematical Surprises
This is open access book provides plenty of pleasant mathematical surprises. There are many fascinating results that do not appear in textbooks although they are accessible with a good knowledge of secondary-school mathematics. This book presents a selection of these topics including the mathematical formalization of origami, construction with straightedge and compass (and other instruments), the five- and six-color theorems, a taste of Ramsey theory and little-known theorems proved by induction. Among the most surprising theorems are the Mohr-Mascheroni theorem that a compass alone can perform all the classical constructions with straightedge and compass, and Steiner's theorem that a straightedge alone is sufficient provided that a single circle is given. The highlight of the book is a detailed presentation of Gauss'spurely algebraic proof that a regular heptadecagon (a regular polygon with seventeen sides) can be constructed with straightedge and compass. Although the mathematics used in the book is elementary (Euclidean and analytic geometry, algebra, trigonometry), students in secondary schools and colleges, teachers, and other interested readers will relish the opportunity to confront the challenge of understanding these surprising theorems. Supplementary material to the book can be found at https: //github.com/motib/surprises.
Kurt G繹del
Preface.- Prologue.- La Belle ?poque in Br羹nn. Beginnings.- School Days. A New Nation.- Moving to the Capital. Student Life in 1920's Vienna.- The Wiener Kreis and the Mathematical Colloquium. Graduate work.- Private Life in Vienna.- G繹del's Doctoral Thesis. The Incompleteness Theorems.- The Mathematician in Vienna. Habilitation.- Matters of Health.- A Sojourn Abroad: 1933/34 - Princeton.- Back to Vienna. The First Breakdown.- 'Commuting' between Vienna and Princeton - The Late 1930's. Marriage.- The Continuum Hypothesis.- Professional Uncertainty. A Long Journey Eastwards.- Princeton and the IAS - Philosophy, Einstein and von Neumann. A Bizarre Birthday Present: G繹del's Universe.- Reception, Recognition, Honors. Einstein's Loss. The Professor at Princeton.- The 1960's: Fame and Seclusion.- Later Years. Philosophy, Cosmology, Logic, Computability.- G繹del's Legacy - The Lessons of an Unusual Life.- Epilogue.
Research in Pdes and Related Fields
This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields" held at the University of Sidi Bel Abb癡s, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as: Sobolev spaces and elliptic boundary value problemsLocal energy solutions of the nonlinear wave equationGeometric control of eigenfunctions of Schr繹dinger operatorsResearch in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.
Introduction to Modern Analysis
This textbook provides an introduction to modern analysis aimed at advanced undergraduate and graduate-level students of mathematics. Professional academics will also find this to be a useful reference work. It covers measure theory, basic functional analysis, single operator theory, spectral theory of bounded and unbounded operators, semigroups of operators, and Banach algebras. Further, this new edition of the textbook also delves deeper into C*-algebras and their standard constructions, von Neumann algebras, probability and mathematical statistics, and partial differential equations. Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills.
Spatial Sampling with R
Scientific research often starts with data collection. However, many researchers pay insufficient attention to this first step in their research. The author, researcher at Wageningen University and Research, often had to conclude that the data collected by fellow researchers were suboptimal, or in some cases even unsuitable for their aim.
Interpretability for Industry 4.0: Statistical and Machine Learning Approaches
- 1. Different Views of Interpretability. - 2. Model Interpretability, Explainability and Trust for Manufacturing 4.0. - 3. Interpretability via Random Forests. - 4. Interpretability in Generalized Additive Models.
Statistical Foundations of Actuarial Learning and Its Applications
This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus.
Classically Semisimple Rings
Classically Semisimple Rings is a textbook on rings, modules and categories, aimed at advanced undergraduate and beginning graduate students.The book presents the classical theory of semisimple rings from a modern, category-theoretic point of view. Examples from algebra are used to motivate the abstract language of category theory, which then provides a framework for the study of rings and modules, culminating in the Wedderburn-Artin classification of semisimple rings. In the last part of the book, readers are gently introduced to related topics such as tensor products, exchange modules and C*-algebras. As a final flourish, Rickart's theorem on group rings ties a number of these topics together. Each chapter ends with a selection of exercises of varying difficulty, and readers interested in the history of mathematics will find biographical sketches of important figures scattered throughout the text.Assuming previous knowledge in linear and basic abstract algebra, this book can serve as a textbook for a course in algebra, providing students with valuable early exposure to category theory.
Approximation Theory, Sequence Spaces and Applications
Chapter 1. Topology on Geometric Sequence Spaces.- Chapter 2. Composition Operators on Second Order Ces`aro Function Spaces.- Chapter 3. Generalized Deferred Statistical Convergence.- Chapter 4. Approximation By Generalized Lupas, -P ˇaltˇanea Operators.- Chapter 5. Zachary spaces Z p[R ] and separable Banach spaces.- Chapter 6. New generalization of the power summability methods for Dunkl generalization of Sz織asz operators via q-calculus.- Chapter 7. Approximation by generalized Sz織asz-Jakimovski-Leviatan type operators.- Chapter 8. On Approximation of Signals.- Chapter 9. Numerical Solution for nonlinear problems.- Chapter 10. Sz織asz-type operators involving q-Appell polynomials.- Chapter 11. Commutants of the infinite Hilbert operators.- Chapter 12. On complex uncertain sequences defined by Orlicz function.- Chapter 13. Ulam-Hyers stability of mixed type functional equation deriving from additive and quadratic mappings in intuitionistic random normed spaces.- Chapter 14. A Study On Q-Euler Difference Sequence Spaces.
Statistical Foundations of Actuarial Learning and Its Applications
Mathematical Principles of Natural Philosophy
"I have presented principles of philosophy that are not, however, philosophical but strictly mathematicalthat is, those on which the study of philosophy can be based."Translated from the classic text Philosophi疆 Naturalis Principia Mathematica, which was originally published in Latin in 1687. Such is its influence, the book is often referred to simply as the Principia.The text alongside its numerous, historically important diagrams formed the foundation of classical mechanics, Newton's law of universal gravitation and a derivation of Kepler's laws of planetary motion.The French mathematical physicist Alexis Clairaut summed up the influence of the book in 1747 by saying that Principia was: "The epoch of a great revolution in physics. The method followed by its illustrious author... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses."
Effective Kan Fibrations in Simplicial Sets
1. Introduction2. Preliminaries3. Dominances4. AWFS from Moore structure5. The Frobenius construction6. Mould squares and effective Kan fibrations7. Pi-types8. Effective trivial Kan fibrations in simplicial sets9. Simplicial sets as a Moore category10. Hyperdeformation retracts in simplicial sets11. Mould squares in simplicial sets12. Horn squares13. Conclusion
Parametric Geometry of Curves and Surfaces
This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides control over the construction. This book relates the classical mathematical theory of parametrized curves and surfaces to multiple applications in architecture. The presentation is mathematically complete with numerous figures and animations illustrating the theory, and special attention is given to some of the recent trends in the field. Solved exercises are provided to see the theory in practice.Intended as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically-inclined students in engineering, architecture and related fields, and can also serve as a textbook for traditional differential geometry courses to mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will also value its combination of precise mathematics and architectural examples.
On Extended Hardy-Hilbert Integral Inequalities and Applications
Hilbert-type inequalities, including Hilbert's inequalities proved in 1908, Hardy-Hilbert-type inequalities proved in 1934, and Yang-Hilbert-type inequalities first proved around 1998, play an important role in analysis and its applications. These inequalities are mainly divided in three classes: integral, discrete and half-discrete. During the last twenty years, there have been many research advances on Hilbert-type inequalities, and especially on Yang-Hilbert-type inequalities.In the present monograph, applying weight functions, the idea of parametrization as well as techniques of real analysis and functional analysis, we prove some new Hilbert-type integral inequalities as well as their reverses with parameters. These inequalities constitute extensions of the well-known Hardy-Hilbert integral inequality. The equivalent forms and some equivalent statements of the best possible constant factors associated with several parameters are considered. Furthermore, we also obtain the operator expressions with the norm and some particular inequalities involving the Riemann-zeta function and the Hurwitz-zeta function. In the form of applications, by means of the beta function and the gamma function, we use the extended Hardy-Hilbert integral inequalities to consider several Hilbert-type integral inequalities involving derivative functions and upper limit functions. In the last chapter, we consider the case of Hardy-type integral inequalities. The lemmas and theorems within provide an extensive account of these kinds of integral inequalities and operators.Efforts have been made for this monograph hopefully to be useful, especially to graduate students of mathematics, physics and engineering, as well as researchers in these domains.
Continued Fractions and Signal Processing
Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony's problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.
Approximation and Online Algorithms
This book constitutes revised selected papers from the thoroughly refereed workshop proceedings of the 20th International Workshop on Approximation and Online Algorithms, WAOA 2022, which was colocated with ALGO 2022 and took place in Potsdam, Germany, in September 2022.The 12 papers included in these proceedings were carefully reviewed and selected from21 submissions. They focus on topics such as graph algorithms, network design, algorithmic game theory, approximation and online algorithms, etc.
Research Trends in Graph Theory and Applications
The Workshop for Women in Graph Theory and Applications was held at the Institute for Mathematics and Its Applications (University of Minnesota, Minneapolis) on August 19-23, 2019. During this five-day workshop, 42 participants performed collaborative research, in six teams, each focused on open problems in different areas of graph theory and its applications. The research work of each team was led by two experts in the corresponding area, who prior to the workshop, carefully selected relevant and meaningful open problems that would yield high-quality research and results of strong impact. As a result, all six teams have made significant contributions to several open problems in their respective areas. The workshop led to the creation of the Women in Graph Theory and Applications Research Collaboration Network, which provided the framework to continue collaborating and to produce this volume.This book contains six chapters, each of them on one of the different areas of research at the Workshop for Women in Graph Theory and Applications, and written by participants of each team.
Stochastic Transport in Upper Ocean Dynamics
This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20-23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea.All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity;Large scale numerical simulations;Data-based stochastic equations for upper ocean dynamics that quantify simulation error;Stochastic data assimilation to reduce uncertainty.These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation andoceanography.
Mathematical Foundation of Fuzzy Sets
Mathematical Foundations of Fuzzy Sets Introduce yourself to the foundations of fuzzy logic with this easy-to-use guide Many fields studied are defined by imprecise information or high degrees of uncertainty. When this uncertainty derives from randomness, traditional probabilistic statistical methods are adequate to address it; more everyday forms of vagueness and imprecision, however, require the toolkit associated with 'fuzzy sets' and 'fuzzy logic'. Engineering and mathematical fields related to artificial intelligence, operations research and decision theory are now strongly driven by fuzzy set theory. Mathematical Foundations of Fuzzy Sets introduces readers to the theoretical background and practical techniques required to apply fuzzy logic to engineering and mathematical problems. It introduces the mathematical foundations of fuzzy sets as well as the current cutting edge of fuzzy-set operations and arithmetic, offering a rounded introduction to this essential field of applied mathematics. The result can be used either as a textbook or as an invaluable reference for working researchers and professionals. Mathematical Foundations of Fuzzy Sets offers thereader: Detailed coverage of set operations, fuzzification of crisp operations, and more Logical structure in which each chapter builds carefully on previous results Intuitive structure, divided into 'basic' and 'advanced' sections, to facilitate use in one- or two-semester courses Mathematical Foundations of Fuzzy Sets is essential for graduate students and academics in engineering and applied mathematics, particularly those doing work in artificial intelligence, decision theory, operations research, and related fields.
Quaternions for Computer Graphics
If you have ever wondered what quaternions are - then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions. John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, disappeared, and reemerged to be adopted by the flight simulation industry and computer graphics. This book will give you the confidence to use quaternions within your every-day mathematics, and explore more advanced texts.
How to succeed in EPSO numerical reasoning tests
This book will help you to prepare numerical reasoning tests for any competition or selection procedure, especially to work in the EU institutions - EPSO Administrators (AD), Assistants (AST), and calls for contract agents (CAST). It includes the tools that you need to face a numerical reasoning test, many tips, recommendations, and shortcuts, as well as an explanation about the particular conditions of EPSO tests. We will also analyse in detail a series of sample exercises, very similar to the ones that you are going to find in the real exam, guiding you step-by-step along the process -mental and technical- that will allow you to get to the right answer of every question. The author is an economist and successful candidate in the reasoning tests of the highly competitive EPSO AD cycle, several EPSO CAST profiles, and other tests and interviews at the assessment centre, being also an official at the public administration in Spain and having held various positions as a head of unit from 2009 to the present. He has also worked as a national expert at the European Commission, provided training to civil servants, coached many candidates for open competitions and temporary/contract agents' positions, and written books for this purpose.=========== Author's note: I would like to clarify to all my potential readers that this book is structured as a clear training guide, easy to read (by using font 12 and spacing 1.5), to facilitate making your own notes on the pages themselves and solving the practices presented throughout the book.
Stochastic Elasticity
Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains.Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.
A Ludic Journey Into Geometric Topology
Preface.- Mathematical Models.- The Big Bang Theory of Ancient Greece.- Geometry: From disorder to order.- Topology.- Fourth dimension.- Non-orientable surfaces.- Hypersurfaces.
Invertible Fuzzy Topological Spaces
Motivation and Preliminaries.- H-fuzzy topological spaces.- Invertible fuzzy topological spaces.- Types of invertible fuzzy topological spaces.- Properties of invertible fuzzy topological spaces.- Invertibility of the related spaces.- Invertible R-topological spaces.
Data Science for Public Policy
This textbook presents the essential tools and core concepts of data science to public officials, policy analysts, and economists among others in order to further their application in the public sector. An expansion of the quantitative economics frameworks presented in policy and business schools, this book emphasizes the process of asking relevant questions to inform public policy. Its techniques and approaches emphasize data-driven practices, beginning with the basic programming paradigms that occupy the majority of an analyst's time and advancing to the practical applications of statistical learning and machine learning. The text considers two divergent, competing perspectives to support its applications, incorporating techniques from both causal inference and prediction. Additionally, the book includes open-sourced data as well as live code, written in R and presented in notebook form, which readers can use and modify to practice working with data.
The Language of Symmetry
This book is a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University. This book aims to open up the scope of interdisciplinary work in the study of symmetry and is intended for scholars of any background.
The Language of Symmetry
This book is a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University. This book aims to open up the scope of interdisciplinary work in the study of symmetry and is intended for scholars of any background.
Statistics Is Easy
Computational analysis of natural science experiments often confronts noisy data due to natural variability in environment or measurement. Drawing conclusions in the face of such noise entails a statistical analysis. Parametric statistical methods assume that the data is a sample from a population that can be characterized by a specific distribution (e.g., a normal distribution). When the assumption is true, parametric approaches can lead to high confidence predictions. However, in many cases particular distribution assumptions do not hold. In that case, assuming a distribution may yield false conclusions. The companion book Statistics is Easy, gave a (nearly) equation-free introduction to nonparametric (i.e., no distribution assumption) statistical methods. The present book applies data preparation, machine learning, and nonparametric statistics to three quite different life science datasets. We provide the code as applied to each dataset in both R and Python 3. We also include exercises for self-study or classroom use.
Time Series Models
Preface.- 1 Time Series and Stationary Processes.- 2 Prediction.- 3 Spectral Representation.- 4 Filter.- 5 Autoregressive Processes.- 6 ARMA Systems and ARMA Processes.- 7 State-Space Systems.- 8 Models with Exogenous Variables.- 9 Granger Causality.- 10 Dynamic Factor Models.- 10 ARCH and GARCH Models.- Index.
Mathematical and Computational Models of Flows and Waves in Geophysics
- Geostrophic Turbulence and the Formation of Large Scale Structure. - Ocean Surface Waves and Ocean-Atmosphere Interactions. - A 3D Two-Phase Conservative Level-Set Method Using an Unstructured Finite-Volume Formulation. - The Physics of Granular Natural Flows in Volcanic Environments. - Cooperative Gravity and Full Wave form Inversion: Elastic Case. - Modelling the 3D Electromagnetic Wave Equation: Negative Apparent Conductivities and Phase Changes.
Introduction to Combinatorial Optimization
Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.
Partial Differential Equations
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple(TM) completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The Black-Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
Economic Policy of the People's Republic of China
This book deals with the current economic policy of the People's Republic of China. In addition to a brief overview of economic history since its founding and discussions of economic models, an overview of both the forms of business and the Chinese labor market is provided. The book pays particular attention to the development of China's e-commerce sector. Equally significant are China's environmental issues against the backdrop of the climate crisis. Without innovations, for example in energy production and waste management, the Chinese economy will hardly be able to continue growing. Therefore, one focus of the book is on economic policy in the environmental sector. Finally, foreign policy, including the Silk Road Initiative, is examined. The aim of this book is to highlight the above developments. It is aimed at laypersons involved in the business of China as well as first-year students who want an overview of economic policy institutions and current developments.
Mathematical Stories II - Recursion, Divisibility and Proofs
Using field-tested, carefully crafted units of study, the authors in this essential teach fundamental mathematical techniques that are relevant well beyond the elementary school years. In this Volume II, the Gaussian summation formula and a recursion formula are derived and applied. Tasks on divisibility, prime factors and divisors follow. For calculating with remainders, the modulo calculation is introduced and applied. Students learn to perform proofs in a variety of contexts. As in Volume I, "Graphs, Games, and Proofs," the tasks encourage mathematical thinking skills, imagination, and creativity. The detailed sample solutions are designed for non-mathematicians.This book is a translation of the original German 1st edition Mathematische Geschichten II - Rekursion, Teilbarkeit und Beweise by Susanne Schindler-Tschirner and Werner Schindler, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
