Ancilla to the Pre-Socratic Philosophers
Dive into the intellectual origins of Western philosophy with "Ancilla to the Pre-Socratic Philosophers." This comprehensive translation brings to life the fragments of wisdom left by the ancient Greek thinkers, spanning from the enigmatic Orpheus to the brilliant minds of Thales, Pythagoras, Heracleitus, Zeno, and Democritus. Delve into the essence of their philosophies through meticulously translated quotations, discovering the lost books they authored and gaining insight into the perspectives of contemporaneous authors on their beliefs.This invaluable reference provides a window into the foundations of philosophical thought, offering not only the known but also the obscure and debated fragments. From brief biographies to spurious quotes, this book paints a vivid picture of the Pre-Socratic era, making it an essential companion for scholars and a captivating read for anyone intrigued by the roots of Western philosophical inquiry.
The Mathematics of Machine Learning
This book is an introduction to machine learning, with a strong focus on the mathematics behind the standard algorithms and techniques in the field, aimed at senior undergraduates and early graduate students of Mathematics. There is a focus on well-known supervised machine learning algorithms, detailing the existing theory to provide some theoretical guarantees, featuring intuitive proofs and exposition of the material in a concise and precise manner. A broad set of topics is covered, giving an overview of the field. A summary of the topics covered is: statistical learning theory, approximation theory, linear models, kernel methods, Gaussian processes, deep neural networks, ensemble methods and unsupervised learning techniques, such as clustering and dimensionality reduction. This book is suited for students who are interested in entering the field, by preparing them to master the standard tools in Machine Learning. The reader will be equipped to understand the main theoretical questions of the current research and to engage with the field.
The World Through the Lens of Mathematics
This amazing book aims to shatter the barrier between students and mathematics. By encouraging students to look at mathematics from a different perspective, build a bridge between their surroundings and mathematics and, at the same time, enrich them with the culture, history, customs, and geography of different parts of the world.
Synthetic Aperture Radar (Sar) Data Applications
This carefully curated volume presents an in-depth, state-of-the-art discussion on many applications of Synthetic Aperture Radar (SAR). Integrating interdisciplinary sciences, the book features novel ideas, quantitative methods, and research results, promising to advance computational practices and technologies within the academic and industrial communities. SAR applications employ diverse and often complex computational methods rooted in machine learning, estimation, statistical learning, inversion models, and empirical models. Current and emerging applications of SAR data for earth observation, object detection and recognition, change detection, navigation, and interference mitigation are highlighted. Cutting edge methods, with particular emphasis on machine learning, are included. Contemporary deep learning models in object detection and recognition in SAR imagery with corresponding feature extraction and training schemes are considered. State-of-the-art neural network architectures in SAR-aided navigation are compared and discussed further. Advanced empirical and machine learning models in retrieving land and ocean information -- wind, wave, soil conditions, among others, are also included.
Analysis of Categorical Data with R
Analysis of Categorical Data with R, Second Edition presents a modern account of categorical data analysis using the R software environment. It covers recent techniques of model building and assessment for binary, multicategory, and count response variables and discusses fundamentals, such as odds ratio and probability estimation. The authors give detailed advice and guidelines on which procedures to use and why to use them.The second edition is a substantial update of the first based on the authors' experiences of teaching from the book for nearly a decade. The book is organized as before, but with new content throughout, and there are two new substantive topics in the advanced topics chapter--group testing and splines. The computing has been completely updated, with the "emmeans" package now integrated into the book. The examples have also been updated, notably to include new examples based on COVID-19, and there are more than 90 new exercises in the book. The solutions manual and teaching videos have also been updated.Features: Requires no prior experience with R, and offers an introduction to the essential features and functions of R Includes numerous examples from medicine, psychology, sports, ecology, and many other areas Integrates extensive R code and output Graphically demonstrates many of the features and properties of various analysis methods Offers a substantial number of exercises in all chapters, enabling use as a course text or for self-study Supplemented by a website with data sets, code, and teaching videos Analysis of Categorical Data with R, Second Edition is primarily designed for a course on categorical data analysis taught at the advanced undergraduate or graduate level. Such a course could be taught in a statistics or biostatistics department, or within mathematics, psychology, social science, ecology, or another quantitative discipline. It could also be used by a self-learner and would make an ideal reference for a researcher from any discipline where categorical data arise.
Fractional Integrals and Derivatives
This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like "What are the fractional integrals and derivatives?", "What are their decisive mathematical properties?", "What fractional operators make sense in applications and why?'', etc. In particular, the "new fractional derivatives and integrals" and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.
Smart Algebra 1
Smart Algebra 1, helps the students to grasp the math that they need to develop critical thinking skills. That includes problem solving, logic, patterns and reasoning to succeed in a High School math class. In this Smart Algebra 1 book, you will find: * Foundation of Algebra * Solving and graphing linear equations * Relation and function * Solving and graphing linear and absolute value inequalities * Simultaneous equations * Exponents and exponential functions * Sets * Polynomial functions * Algorithm for simplifying and solving equations * Evaluating radical expressions * Quadratic equations and functions * Ratio, proportion, rates and percentage * Graph of square root function * Statistic and probability * Solved word problems * Practice equations and so on.
Elementary School Test Materials 2022-2023
This book contains one year of mathleague.org elementary school tests and answer keys: 7 qualifying-level test sets, one district-level test set, one state-level test set, one national-level test set, and one international-level test set. Each test set contains a Sprint, Target, Team, and Number Sense test.
Logos and Alogon
This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book's title, an alogon in the logos of mathematics. The outcomeof this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.
Algebra, Analysis, and Associated Topics
The chapters in this contributed volume explore new results and existing problems in algebra, analysis, and related topics. This broad coverage will help generate new ideas to solve various challenges that face researchers in pure mathematics. Specific topics covered include maximal rotational hypersurfaces, k-Horadam sequences, quantum dynamical semigroups, and more. Additionally, several applications of algebraic number theory and analysis are presented. Algebra, Analysis, and Associated Topics will appeal to researchers, graduate students, and engineers interested in learning more about the impact pure mathematics has on various fields.
2022-2023 High School Contest Materials
This book contains one year of mathleague.org high school tests and answer keys: 7 qualifying-level test sets, one state-level test set, one national-level test set, and one international-level test set. Each test set contains a Sprint, Target, Team, and Relay test; three of the sets contain a Power Question.
A Compact Capstone Course in Classical Calculus
This textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The author's enthusiastic and engaging style makes this material, which typically requires a substantial amount of study, accessible to students with minimal prerequisites. Readers will gain a broad knowledge of the area, with approaches based on those found in recent literature, as well as historical remarks that deepen the exposition. Specific topics covered include the binomial theorem, the harmonic series, Euler's constant, geometric probability, and much more. Over the fifteen chapters, readers will discover the elegance of calculus and the pivotal role it plays within mathematics. A Compact Capstone Course in Classical Calculus is ideal for exploring interesting topics in mathematics beyond the standard calculus sequence, particularly for undergraduates who may not be taking more advanced math courses. It would also serve as a useful supplement for a calculus course and a valuable resource for self-study. Readers are expected to have completed two one-semester college calculus courses.
An Introduction to Traffic Flow Theory
This second edition of An Introduction to Traffic Flow Theory adds new material in several chapters related to advanced technologies including autonomy, the use of sensors and communications, and particularly congestion mitigation solutions that leverage connected and autonomous vehicles (CAVs). It also includes a new chapter that briefly outlines several mathematical analysis techniques commonly used in traffic flow theory, aiming to introduce students to some of the most frequently used tools available for traffic operational-related analysis. This new edition also includes several updates related to the most recent versions of the Highway Capacity Manual and the Green Book. This textbook is meant for use in advanced undergraduate/graduate level courses in traffic flow theory with prerequisites including two semesters of calculus, statistics, and an introductory course in transportation. The text would also be of interest to transportation professionals as a refresherin traffic flow theory or as a reference. Students and engineers of diverse backgrounds will find this text accessible and applicable to today's traffic issues.This text provides a comprehensive and concise treatment of the topic of traffic flow theory and includes several topics relevant to today's highway transportation system. It provides the fundamental principles of traffic flow theory as well as applications of those principles for evaluating specific types of facilities (freeways, intersections, etc.). Newer concepts of Intelligent transportation systems (ITS) and their potential impact on traffic flow are discussed. State-of-the-art traffic flow research, microscopic traffic analysis, and traffic simulation have significantly advanced and are also discussed in this text. Real-world examples and useful problem sets complement each chapter.
Elliptic Equations: An Introductory Course
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and complicated refinements. Apart from the basic theory of equations in divergence form, it includes subjects as singular perturbations, homogenization, computations, asymptotic behavior of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes systems, p-Laplace type operators, large solutions, and mountain pass techniques. Just a minimum on Sobolev spaces has been introduced and work on integration on the boundary has been carefully avoided to keep the reader attention focused on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original, and have not been published elsewhere. The book will be of interest to graduate students and researchers specializing in partial differential equations.
The Logica Yearbook 2022
This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2022, Tepl獺, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
Math Mammoth Grade 8 Answer Keys
Math Mammoth Grade 8 Answer Keys includes answer keys to: Math Mammoth Grade 8-A worktext;Math Mammoth Grade 8-B worktext;End-of-chapter tests;End-of-year test;Cumulative reviews.
Introductory Differential Equations
**2025 Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner** Introductory Differential Equations, Sixth Edition provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. The book's accessible explanations and many robust sample problems are appropriate for a first semester course in introductory ordinary differential equations (including Laplace transforms), for a second course in Fourier series and boundary value problems, and for students with no background on the subject.
Tidy Finance with Python
This textbook shows how to bring theoretical concepts from finance and econometrics to the data. Focusing on coding and data analysis with Python, we show how to conduct research in empirical finance from scratch.
Confidence Intervals for Discrete Data in Clinical Research
There is only one published book on confidence interval for clinical research. This book has a cookbook style with several examples and codes so that methods presented in the book can be implemented. The primary audience will be statisticians.
Partial Clones of Terms
Words are strings of letters from a fixed alphabet. Sets of words are said to be formal languages. Natural languages, but also programming languages, are examples of such formal languages. On the set of all words the concatenation is a binary associative operation which produces a new word from any two given words. Therefore, there is a semigroup defined on the set of all words on an alphabet. This semigroup is an algebra of type (2), i.e., it has one binary operation satisfying the associative identity. Many properties of words and formal languages can be described by the algebraic properties of the word semigroup. To get languages of more expressive power, words can be generalized to terms using one more alphabet consisting of operation symbols. The combination of n+1 terms to a new term can be described by an (n+1)-ary superposition operation. This superposition operation satisfies the superassociative identity, a generalization of the associative identity. A clone is a multi-based algebraic structure with (n+1)-ary superposition operations as fundamental operations and satisfying the superassociative itentity. Clones of terms take over the role of word semigroups and describe the properties of terms and sets of terms which are also called tree languages. In this book we generalize the superposition operations to partial many-sorted operations. If the superassociative law is satisfied as a weak identity we obtain partial clones. The properties of several important kinds of terms such as linear terms and linear tree languages can be described by partial clones.
Advanced Electromagnetic Wave Propagation Methods
This textbook provides a solid foundation into the approaches used in the analysis of complex electromagnetic problems and wave propagation. The techniques discussed are essential to obtain closed-form solutions or asymptotic solutions and meet an existing need for instructors and students in electromagnetic theory.
Documentary review of the Pythagorean Theorem throughout history
Geometry has two great treasures: one is the theorem of Pythagoras; the other is the division of a line into an extreme and an average proportion. We may compare the first to a measure of gold; the second we may call a precious jewel. Jonannes Kepler (1596)The Pythagorean theorem, as Kepler (1596) says, is one of the greatest treasures of Geometry, it states that "in every right triangle the measure of the hypotenuse squared is equal to the sum of the measures of the squares of the legs". Anyone who has attended high school has been in contact with this theorem, whether they remember it or not. The general objective of this work is to analyze the proofs and demonstrations of the Pythagorean Theorem throughout the History of Mathematics, with the purpose of creating didactic sequences for its teaching at the Middle Level.
Human and Artificial Intelligence
Although tremendous advances have been made in recent years, many real-world problems still cannot be solved by machines alone. Hence, the integration of Human Intelligence and Artificial Intelligence is needed. However, several challenges make this integration complex. The aim of this Special Issue was to provide a large and varied collection of high-level contributions presenting novel approaches and solutions to address the above issues. This Special Issue contains 14 papers (13 research papers and 1 review paper) that deal with various topics related to human-machine interactions and cooperation. Most of these works concern different aspects of recommender systems, which are among the most widespread decision support systems. The domains covered range from healthcare to movies and from biometrics to cultural heritage. However, there are also contributions on vocal assistants and smart interactive technologies. In summary, each paper included in this Special Issue represents a step towards a future with human-machine interactions and cooperation. We hope the readers enjoy reading these articles and may find inspiration for their research activities.
The Big Book of Real Analysis
This book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus. Beginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the studyof measures and how one can construct the Lebesgue integral as an extension of the Riemann integral. This textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.
Introduction to Quantum Groups
This book introduces the reader to quantum groups, focusing on the simplest ones, namely the closed subgroups of the free unitary group.Although such quantum groups are quite easy to understand mathematically, interesting examples abound, including all classical Lie groups, their free versions, half-liberations, other intermediate liberations, anticommutation twists, the duals of finitely generated discrete groups, quantum permutation groups, quantum reflection groups, quantum symmetry groups of finite graphs, and more.The book is written in textbook style, with its contents roughly covering a one-year graduate course. Besides exercises, the author has included many remarks, comments and pieces of advice with the lone reader in mind. The prerequisites are basic algebra, analysis and probability, and a certain familiarity with complex analysis and measure theory. Organized in four parts, the book begins with the foundations of the theory, due to Woronowicz, comprising axioms, Haar measure, Peter-Weyl theory, Tannakian duality and basic Brauer theorems. The core of the book, its second and third parts, focus on the main examples, first in the continuous case, and then in the discrete case. The fourth and last part is an introduction to selected research topics, such as toral subgroups, homogeneous spaces and matrix models.Introduction to Quantum Groups offers a compelling introduction to quantum groups, from the simplest examples to research level topics.
Proven Impossible
In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand.
Proven Impossible
In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand.
Generating Functions in Engineering and the Applied Sciences
Generating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc. This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems. Specifically, the book discusses probability GFs (PGF), moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs. Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.
The Bertrand Russell Collection
Embark on an intellectual journey with "The Bertrand Russell Collection," a comprehensive anthology spanning the influential philosopher's groundbreaking works. From "The Analysis of Mind" to insightful essays on humanism, ethics, and society, this collection encapsulates Russell's brilliance and offers timeless reflections on reason, knowledge, and the complexities of the human experience. Explore the mind of one of the 20th century's greatest thinkers through his diverse and impactful writings.
Journal of Applied Logics, Volume 10, Number 6, December 2023. Special Issue
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Fractal Patterns with MATLAB
This book presents the iterative beauty of fractals and fractal functions graphically with the aid of MATLAB programming. The fractal images generated using the MATLAB codes provide visual delight and highly encourage the fractal lovers for creative thinking. The book compiles five cutting-edge research chapters, each with state-of-the art fractal illustrations. It starts with the fundamental theory for the construction of fractal sets via the deterministic iteration algorithm. Incorporating the theoretical base, fractal illustrations of elementary fractal sets are provided with the explicit MATLAB code. The book gives examples of MATLAB codes to present the fractal surfaces. This book is contributed to all the research beginners as well as the professionals on the field of fractal analysis. As it covers basic fractals like Sierpinski triangle to advanced fractal functions with explicit MATLAB code, the presented fractal illustrations hopefully benefit even the non-field readers. The book is a useful course to all the research beginners on the fractal and fractal-related fields.
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.
Instability and Non-Uniqueness for the 2D Euler Equations, After M. Vishik
An essential companion to M. Vishik's groundbreaking work in fluid mechanics The incompressible Euler equations are a system of partial differential equations introduced by Leonhard Euler more than 250 years ago to describe the motion of an inviscid incompressible fluid. These equations can be derived from the classical conservations laws of mass and momentum under some very idealized assumptions. While they look simple compared to many other equations of mathematical physics, several fundamental mathematical questions about them are still unanswered. One is under which assumptions it can be rigorously proved that they determine the evolution of the fluid once we know its initial state and the forces acting on it. This book addresses a well-known case of this question in two space dimensions. Following the pioneering ideas of M. Vishik, the authors explain in detail the optimality of a celebrated theorem of V. Yudovich from the 1960s, which states that, in the vorticity formulation, the solution is unique if the initial vorticity and the acting force are bounded. In particular, the authors show that Yudovich's theorem cannot be generalized to the L^p setting.
Problem Posing and Problem Solving in Mathematics Education
This book presents both theoretical and empirical contributions from a global perspective on problem solving and posing (PS/PP) and their application, in relation to the teaching and learning of mathematics in schools. The chapters are derived from selected presentations in the PS/PP Topical Study Group in ICME14. Although mathematical problem posing is a much younger field of inquiry in mathematics education, this topic has grown rapidly. The mathematics curriculum frameworks in many parts of the world have incorporated problem posing as an instructional focus, building on problem solving as its foundation. The juxtaposition of problem solving and problem posing in mathematics presented in this book addresses the needs of the mathematics education research and practice communities at the present day. In particular, this book aims to address the three key points: to present an overview of research and development regarding students' mathematical problem solving and posing; to discuss new trends and developments in research and practice on these topics; and to provide insight into the future trends of mathematical problem solving and posing.
Groups and Graphs, Designs and Dynamics
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Analytical Properties of Nonlinear Partial Differential Equations
Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
The Cartoon Guide to Geometry
A comprehensive new illustrated guide to geometry--from New York Times bestselling cartoonist Larry GonickWhat's the point of points? Where do we draw the line? If there are two sides to everything, then what's up with triangles, squares, and polygons?Once again, mathematician-turned-cartoonist Larry Gonick uses his unique gift for witty, lively, and clear exposition to demystify another complex subject: geometry.Moving from the most basic geometrical concepts--planes, lines, and points--through elementary postulates and to elaborate proofs, The Cartoon Guide to Geometry is a comprehensive primer on all the essentials of plane geometry: angles, triangles, area, similarity, and, yes, the Pythagorean theorem. Carefully tailored to the curriculum standards and standardized testing guidelines of the subject, the book provides innovative visuals that develop proofs and constructions with sequential graphics rather than single illustrations. The reader emerges with a deep grasp of key ideas--and has fun getting there.
Math Mammoth Grade 8-A Worktext
Math Mammoth Grade 8-A Worktext is the first student book for eighth grade mathematics, and part of the Math Mammoth Grade 8 complete curriculum.This book starts with a study of exponent laws, using both numerical and algebraic expressions. The first chapter also covers scientific notation (both with large and small numbers), significant digits, and calculations with numbers given in scientific notations. In chapter 2, students learn about geometric transformations (translations, reflections, rotations, dilations), common angle relationships, and volume of prisms, cylinders, spheres, and cones. Next, in chapter 3, our focus is on linear equations. Students both review and learn more about solving linear equations, including equations whose solutions require the usage of the distributive property and equations where the variable is on both sides. Chapter 4 presents an introduction to functions. Students construct functions to model linear relationships, learn to use the rate of change and initial value of the function, and they describe functions qualitatively based on their graphs. Features Math Mammoth focuses on conceptual understanding. It explains the "WHY", so students can understand the math, not just learn "HOW" to do it.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.It requires very little teacher preparation.: )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.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.
Modern FORTRAN Explained
Fortran remains one of the principal programming languages used in high-performance scientific, numerical, and engineering computing. A series of significant revisions to the standard versions of the language have progressively enhanced its capabilities, and the current standard - Fortran 2023 - brings with it further additions and improvements. The language as defined by its most recent standards, with their introduction of object-oriented programming and of coarrays, is often referred to generically as 'Modern Fortran', and this term is increasingly used in the literature. Thus, we see that Fortran's particular advantages as a high-end numerical language, especially where arrays are the main form of data object and/or where complex arithmetic is involved, are still to the fore. It is able to attain the highest achievable optimization, mainly because multi-dimensional arrays are 'natural' objects and because its pointers are highly constrained. There is every sign that Modern Fortran will continue to be used to tackle major scientific computing problems in the next decade and beyond and will long remain a living tribute to its early pioneers. This third edition of Modern Fortran Explained expands on the second. The material contained in the four final chapters of the second edition have been merged into the main text, thereby offering, in 20 chapters, a comprehensive and uniform description of Fortran 2018. The additional features now brought by the 2023 standard, which are mostly relatively minor in nature, are described in two final chapters, the first on generic programming and the second on the other features. This structure enables the reader to distinguish clearly between what is old and what is new. This new edition, written by experts in the field, three of whom have actively contributed to Fortran 2023, is thus a complete and authoritative description of Fortran in its latest form, with the intention that it remain the main reference work in the field.
The Bertrand Russell Collection
Embark on an intellectual journey with "The Bertrand Russell Collection," a comprehensive anthology spanning the influential philosopher's groundbreaking works. From "The Analysis of Mind" to insightful essays on humanism, ethics, and society, this collection encapsulates Russell's brilliance and offers timeless reflections on reason, knowledge, and the complexities of the human experience. Explore the mind of one of the 20th century's greatest thinkers through his diverse and impactful writings.
Math Mammoth Grade 8-B Worktext
Math Mammoth Grade 8-B Worktext is the second student book for eighth grade mathematics, and part of the Math Mammoth Grade 8 complete curriculum. Please note: The book does not include the answer key. All answer keys for grade 8 are sold in a separate book. The book starts with chapter 5, graphing linear equations. Students study slope, and graph and write linear equations in slope-intercept and standard forms. They also learn about parallel and perpendicular lines.In chapter 6, students delve into square roots, cube roots, and irrational numbers and solve equations involving square and cube roots. The rest of the chapter is spent studying the Pythagorean Theorem and its applications.Next, in chapter 7, we focus on systems of linear equations. Students learn the three basic techniques for solving these and also solve a variety of problems that are solved with a pair of linear equations. The last chapter covers statistical topics: scatter plots and two-way tables.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so students can understand the math, not just learn "HOW" to do it.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.It requires very little teacher preparation.: )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.Each chapter introduction also includes a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Advances in Fuzzy Decision Theory and Applications
In the realm of complex decision making, characterized by inherent incompleteness and uncertainty, the foundational work of Lotfi A. Zadeh on fuzzy set theory has been instrumental. The efficacy of classical fuzzy sets in addressing vagueness has prompted an exploration of various extensions, each catering to the intricacies of real-world decision-making problems. This reprint delves into an array of advanced fuzzy theories, including type-2 fuzzy sets, hesitant fuzzy sets, multivalued fuzzy sets, cubic sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, spherical fuzzy sets, neutrosophic sets, and more. The richness of these extensions reflects the dynamism of fuzzy theories in diverse decision-making applications.
Viscoelasticity
This Special Issue brings together the latest advancements across various facets of viscous and viscoelastic fluid flows. Encompassing a spectrum of contributions, the topics span from innovative numerical methods and sophisticated mathematical modeling to cutting-edge experimental research. In addition to providing insights into the current state of research in these domains, the issue aims to foster a comprehensive understanding of the intricate dynamics and behaviors exhibited by viscous and viscoelastic fluids.
Math Mammoth Grade 8 Tests and Cumulative Reviews
Math Mammoth Grade 8 Tests & Cumulative Reviews contains the end-of-chapter tests, the comprehensive end-of-year test, and optional cumulative review lessons for Math Mammoth grade 8 complete curriculum.
Understanding Linear Algebra
Understanding Linear Algebra is an open textbook designed to support a two-course undergraduate linear algebra sequence. Topics include systems of equations, vector and matrix algebra, span, linear independence, bases, eigenvectors and eigenvalues, orthogonality, least squares, and singular value decompositions.There are a few features that distinguish it from other linear algebra textbooks. First, it will always be freely available at http: //gvsu.edu/s/0Ck in a number of formats, including accessible HTML, PDF, and even braille.Until recently, linear algebra has mainly lived in the long shadow of calculus with many university linear algebra courses requiring several semesters of calculus as a prerequisite. Given the increasing prominence of linear algebra, Understanding Linear Algebra assumes no familiarity with calculus and, as such, can provide an alternative introduction into university-level mathematics.Learners are supported as they develop a deep understanding of linear algebraic concepts and their ability to reason mathematically using those concepts. While not intended as an introduction to proofs, the text helps learners to express their thinking clearly and with precision. Following best pedagogical practices, numerous activities are interwoven with exposition to facilitate active learning and can be easily adapted for small group collaboration in a classroom. Each section begins with a preview activity to support a flipped class environment and concludes with numerous exercises of varying depth. In addition, learners develop computational proficiency through the use of Sage, an open source computer algebra system. The online version of the text contains many embedded "Sage cells" that enable readers to perform computations directly in the book as they are reading. Readers first perform basic algorithms, such as Gaussian elimination and matrix multiplication, by hand but later automate them using Sage. In this way, learners can focus on higher-level linear algebraic thinking and develop their ability to deploy it in more realistic situations.By introducing many in-depth applications, Understanding Linear Algebra also aims to develop an appreciation for the many significant ways in which linear algebra impacts our society. Examples include the JPEG image compression and Google's PageRank algorithms as well as important data science topics such as k-means clustering, linear regression, principal component analysis, and singular value decompositions. These applications give concrete meaning to many of the abstract algebraic concepts on which they rely, and the use of Sage enables learners to authentically explore them.Besides the text itself, there is an accompanying workbook that contains the activities and is suitable for in-class use. There are also solution manuals for both the activities and the homework exercises that are available upon request of the author and a community of instructors who share their experiences and resources with one another through a Google Group.
