Abstract Algebra
Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.
Linear Algebra with Applications to Economics
This textbook is intended for students of Mathematical Economics and is based on my lectures on Linear Algebra delivered at Satbayev University in Almaty, Kazakhstan. The program closely aligns with that of the London School of Economics. The textbook extensively utilizes the concept of Gauss-Jordan elimination. Every subspace of the standard coordinate space possesses a unique Gauss basis. This observation significantly clarifies many aspects of Linear Algebra. The covered topics are outlined in the table of contents.
Mathematics for Social Scientists
This book helps readers bridge the gap between school-level mathematical skills and the quantitative and analytical skills required at the professional level. It presents basic mathematical concepts in an everyday context, enabling readers to pick up skills with ease.Mathematics for Social Scientists: - Focuses on building foundational skills in reasoning, data analysis and quantitative methods that are a requisite for progressing to higher levels;- Helps readers express mathematical ideas in the form of sets, analyse arguments and their validity mathematically, interpret and handle data, and understand the concept and use of probability;- Includes a dedicated chapter on symmetry, perspective and art to encourage readers to reason, model and objectively evaluate everyday situations.The volume will be useful to students of various disciplines in Social Sciences and Liberal Arts. It will also be an invaluable companion to practitioners of social sciences, humanities and life sciences, as well as schoolteachers at the middle and higher secondary level.
Tensors For Inquiring Minds
The book takes readers on a journey to discover tensors -- powerful mathematical concepts used in many areas of modern science. Starting from familiar grounds of numbers and operations with numbers, readers will re-examine familiar concepts in a new light and then arrive at new concepts gradually, connecting the dots along the way. The goal of this book is to explain tensors by showing them in action and in relation to less complicated concepts, such as numbers and vectors. The book is accessible to anyone with solid foundations in high-school algebra and sufficient focus and curiosity. The solutions to all exercises are provided in the end
The Complete Guide to the Sagrada Familia Magic Square
The Passion (western) Facade of the Basilica de Sagrada Familia in Barcelona includes an unconventional 4 by 4 magic square with 310 unique solutions each of which sums to 33, the traditional age of Jesus at his death. In addition to background material on the square and other characteristics of it, this little book contains, for what the author believes to be the first time in print, all 310 solutions.
Commutative Algebra Methods for Coding Theory
This book aims to be a comprehensive treatise on the interactions between Coding Theory and Commutative Algebra. With the help of a multitude of examples, it expands and systematizes the known and versatile commutative algebraic framework used, since the early 90's, to study linear codes. The book provides the necessary background for the reader to advance with similar research on coding theory topics from commutative algebraic perspectives.
Linear Algebra in Data Science
This textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MATLAB. Practice projects appear as well for students to better understand the real-world applications of the material covered in a standard linear algebra course. Some topics covered include singular value decomposition, convolution, frequency filtering, and neural networks. Linear Algebra in Data Science is suitable as a supplement to a standard linear algebra course.
Advanced Linear Algebra
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics.The author begins with chapters introducing basic notation for vector spaces, permutations, polynomials, and other algebraic structures. The following chapters are designed to be mostly independent of each other so that readers with different interests can jump directly to the topic they want. This is an unusual organization compared to many abstract algebra textbooks, which require readers to follow the order of chapters.Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint, while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results.A wide array of topics is included, ranging from concrete matrix theory (basic matrix computations, determinants, normal matrices, canonical forms, matrix factorizations, and numerical algorithms) to more abstract linear algebra (modules, Hilbert spaces, dual vector spaces, bilinear forms, principal ideal domains, universal mapping properties, and multilinear algebra).The book provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra needed in many areas of pure and applied mathematics.
A Bridge to Higher Mathematics
The goal of this unique text is to provide an "experience" that would facilitate a better transition for mathematics majors to the advanced proof-based courses required for their major.If you feel like you love mathematics but hate proofs, this book is for you. The change from example-based courses such as Introductory Calculus to the proof-based courses in the major is often abrupt, and some students are left with the unpleasant feeling that a subject they loved has turned into material they find hard to understand.The book exposes students and readers to some fundamental content and essential methods of constructing mathematical proofs in the context of four main courses required for the mathematics major - probability, linear algebra, real analysis, and abstract algebra.Following an optional foundational chapter on background material, four short chapters, each focusing on a particular course, provide a slow-paced but rigorous introduction. Students get a preview of the discipline, its focus, language, mathematical objects of interest, and methods of proof commonly used in the field. The organization of the book helps to focus on the specific methods of proof and main ideas that will be emphasized in each of the courses.The text may also be used as a review tool at the end of each course and for readers who want to learn the language and scope of the broad disciplines of linear algebra, abstract algebra, real analysis, and probability, before transitioning to these courses.
Algebra II Calculator Guide
Guide to using the Texas Instruments TI-83/84+ calculators in a high school Algebra 2 class. Aligned to New York's Next Generation Regents curriculum. Includes lesser-known calculator tricks like graphing a unit circle using parametric equations, generating terms of a recursively defined sequence, and shading the area where f(x)
Algebra I Calculator Guide
Guide to using the Texas Instruments TI-83/84+ calculators in a high school Algebra 1 class. Aligned to New York's Next Generation Regents curriculum. Includes lesser-known calculator tricks like simplifying a radical, graphing a function with a restricted domain, and graphing transformations of functions.
Functional Analysis Revisited
'Functional Analysis Revisited' is not a first course in functional analysis - although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'
Algebra and Trigonometry
In this book the author covers topics in mathematics from basic algebra through trigonometry, providing definitions, properties, theorems, terminology, notation, formulas, and examples. The author has also reserved space within the book for the student to work exercises alongside the examples provided. Thus it functions as both a textbook and a workbook. It is especially well-suited to students who: wish to learn algebra or trigonometry without the aid of a teacher;are currently enrolled in a course in algebra or trigonometry at an educational institution but do not want to attend lectures or watch videos online; orhave studied algebra or trigonometry in the past but would like to review the subjects.This book does not include an ample set of additional algebraic exercises at the end of each section and may serve a student best when used in conjunction with a separate source of sets of exercises, such as Exercises in Algebra and Trigonometry by the same author. When combined with Exercises in Algebra and Trigonometry, this book will serve instructors and students well in any course in algebra or trigonometry, including those: conducted online;where the classroom is "flipped" and students complete exercises in advance of a lecture from the instructor;where not all students progress at the same pace;where the student learns independently or at home.
Elementary Linear Algebra with Applications
This text offers a unique balance of theory and a variety of standard and new applications along with solved technology-aided problems. The book includes the fundamental mathematical theory, as well as a wide range of applications, numerical methods, projects, and technology-assisted problems and solutions in Maple, Mathematica, and MATLAB. Some of the applications are new, some are unique, and some are discussed in an essay. There is a variety of exercises which include True/False questions, questions that require proofs, and questions that require computations. The goal is to provide the student with is a solid foundation of the mathematical theory and an appreciation of some of the important real-life applications. Emphasis is given on geometry, matrix transformations, orthogonality, and least-squares. Designed for maximum flexibility, it is written for a one-semester/two semester course at the sophomore or junior level for students of mathematics or science.
Asymptotic Issues for Some Partial Differential Equations (Second Edition)
The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Determinantal Ideals of Square Linear Matrices
This book explores determinantal ideals of square matrices from the perspective of commutative algebra, with a particular emphasis on linear matrices. Its content has been extensively tested in several lectures given on various occasions, typically to audiences composed of commutative algebraists, algebraic geometers, and singularity theorists.Traditionally, texts on this topic showcase determinantal rings as the main actors, emphasizing their properties as algebras. This book follows a different path, exploring the role of the ideal theory of minors in various situations-highlighting the use of Fitting ideals, for example. Topics include an introduction to the subject, explaining matrices and their ideals of minors, as well as classical and recent bounds for codimension. This is followed by examples of algebraic varieties defined by such ideals. The book also explores properties of matrices that impact their ideals of minors, such as the 1-generic property, explicitly presenting a criterion by Eisenbud. Additionally, the authors address the problem of the degeneration of generic matrices and their ideals of minors, along with applications to the dual varieties of some of the ideals.Primarily intended for graduate students and scholars in the areas of commutative algebra, algebraic geometry, and singularity theory, the book can also be used in advanced seminars and as a source of aid. It is suitable for beginner graduate students who have completed a first course in commutative algebra.
Rank 2 Amalgams and Fusion Systems
This monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups. It demonstrates a broad range of techniques from local group theory and fusion systems, several of which can be applied in more general settings. Addressing research problems that have not been treated in the past, it is the first text to explicitly use the amalgam method in this context. Fusion systems offer an enticing way to unify various p-local methods employed in group theory, representation theory and homotopy theory; but as abstract constructions they are still somewhat mysterious. This book paves the way to a broad and systematic study of these categories by applying the amalgam method, thus modernizing a methodology widely used to understand the local structure of finite groups. With this comes an introduction to several vital techniques in local group theory, a generous survey of the structure and modular representation theory of some important families of finite groups, and a demonstration of the value of combinatorial methods in finite group theory and fusion systems. Primarily aimed at researchers active in fusion systems and group amalgams, the book will also be of interest to anyone working with finite groups and their modular representations, group actions on trees, or classifying spaces. The inclusion of preliminary chapters outlining the theoretical prerequisites make it ideal for a short lecture course or as a reading group text for early career researchers and graduate students.
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.
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.
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.
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.
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.
Recent Advances in Motion Planning and Control of Autonomous Vehicles
Autonomous vehicles are increasingly prevalent, navigating both structured urban roads and challenging offroad scenes. At the core of these vehicles lie the planning and control modules, which are crucial for demonstrating the intelligence inherent in an autonomous driving system. The planning module is responsible for devising an open-loop trajectory, taking into account a variety of environmental restrictions, task-related demands, and vehicle-kinematics-related constraints, while the control module ensures adherence to this trajectory in a closed-loop manner. This adherence is vital in a range of conditions, including diverse weather scenarios, different driving situations, and in response to potential disturbances such as mechanical failures or cyber threats. In certain contexts, these modules are collectively referred to as 'control', with the planning component considered an open-loop controller. This Special Issue focuses on the latest research trends in planning and control methods for autonomous driving. It comprises 11 papers that cover a broad spectrum of applications, including occlusion-aware motion planning in warehouses, control strategies for articulated vehicles, cooperative trajectory planning for autonomous forklifts, and tracking control for underwater vehicles in the face of disturbances and uncertainties. These contributions collectively underscore the diverse and evolving nature of autonomous vehicle technology.
Activity Workbook for Understanding Linear Algebra
This is the activity workbook to supplement the Understanding Linear Algebra book by David Austin. You can find the open access version here: http: //gvsu.edu/s/0Ck
Exercises in Applied Mathematics
This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.
Abstract Algebra
Abstract Algebra: An Inquiry-Based Approach, Second Edition not only teaches abstract algebra, but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think.The second edition of this unique, flexible approach builds on the success of the first edition. The authors offer an emphasis on active learning, helping students learn algebra by gradually building both their intuition and their ability to write coherent proofs in context. The goals for this text include: Allowing the flexibility to begin the course with either groups or rings. Introducing the ideas behind definitions and theorems to help students develop intuition. Helping students understand how mathematics is done. Students will experiment through examples, make conjectures, and then refine or prove their conjectures. Assisting students in developing their abilities to effectively communicate mathematical ideas. Actively involving students in realizing each of these goals through in-class and out-of-class activities, common in-class intellectual experiences, and challenging problem sets. Changes in the Second Edition Streamlining of introductory material with a quicker transition to the material on rings and groups. New investigations on extensions of fields and Galois theory. New exercises added and some sections reworked for clarity. More online Special Topics investigations and additional Appendices, including new appendices on other methods of proof and complex roots of unity. Encouraging students to do mathematics and be more than passive learners, this text shows students the way mathematics is developed is often different than how it is presented; definitions, theorems, and proofs do not simply appear fully formed; mathematical ideas are highly interconnected; and in abstract algebra, there is a considerable amount of intuition to be found.
A Course in Linear Algebra with Applications
"There are useful discussions of two nonstandard topics which caught my eye, the method of least squares and Markov processes, consistent with the author's concern for the applications and the expected readership, which render the text useful for business, economics and social science students as well as those in physical sciences and engineering ... the book has great value for self study as well as adoption as a classroom text ... By all means adopt Robinson's text and enjoy spreading the gospel of linear algebra."Frank B CannonitoUniversity of California, Irvine"... it is very carefully written, both from the point of view of mathematical content and style, and readability ... It should therefore be very suitable as a course book as well as for self-tuition."Mathematics Abstracts, Germany
Linear Algebra Done Right
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.From the reviews of previous editions: Altogether, the text is a didactic masterpiece. -- zbMATHThe determinant-free proofs are elegant and intuitive. -- American Mathematical MonthlyThe most original linear algebra book to appear in years, it certainly belongs in every undergraduate library -- CHOICE
The Cohomology of Monoids
This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leech's original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material. It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and monoidal groupoids, including the case of monoids with operators. This cohomology is also compared to the classical Eilenberg-Mac Lane and Hochschild-Mitchell cohomologies. Connections are also established with the Lausch-Loganathan cohomology theory for inverse semigroups, the Gabriel-Zisman cohomology of simplicial sets, the Wells cohomology of small categories (also known as Baues-Wirschingcohomology), Grothendieck sheaf cohomology, and finally Beck's triple cohomology. It also establishes connections with Grillet's cohomology theory for commutative semigroups. The monograph is aimed at researchers in the theory of monoids, or even semigroups, and its interface with category theory, homological algebra, and related fields. However, it is also written to be accessible to graduate students in mathematics and mathematicians in general.
Four Famous Numbers
We delve deep into the science and interrelationships ofFour Famous mathematical constantsEuler's Number e, The Ludolphine Constant ( Pi ), Pythagoras' Constant and The Ratio of Phidias ( phi ). Along the way we assess the usefulness of diverse methodsof computing these numbers, techniques dating from theBronze Age to the twenty-first century. From the earliest days of visible life to our own times, tiny animals have plowed or burrowed the deep sea floorin systematic, geometrical paths.They often seem to have conformed to the mathematics ofour famous numbers! Can this really be true? We consider the evidence. Profusely illustrated with original research, algebraic derivations, full academic references, and acomprehensive index "Four Famous Numbers"will appeal to enthusiasts, undergraduates and teachersin higher education.
The Analysis and Solution of Cubic and Biquadratic Equations
Originally published in 1852, The Analysis and Solution of Cubic and Biquadratic Equations is a pioneering work in the field of algebra. In this book, John Radford Young provides a clear and concise introduction to the theory and solution of equations of the higher orders, building on the principles established in his earlier work, The Elements of Algebra. Young's elegant and rigorous approach to algebra has influenced generations of mathematicians and continues to be an important reference for scholars today.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Advanced Cybersecurity Services Design
This Special Issue includes 14 contributions, with 2 review contributions and 12 research contributions. The review contributions provide a survey with an overview of the state of the art in detecting and projecting cyber-attack scenarios, and the review of a specific application area, the safety of autonomous haulage systems in the mining environment related to both cybersecurity and communication. 10 research contributions are addressing the area of advanced services for intrusion detection systems: (a) the use of different machine learning models depending on the specific scenarios and datasets; (b) the use of deep learning techniques for the detection of zero-day attacks; (c) a proposal of an integrated scalable framework aimed at efficiently detecting anomalous events on large amounts of unlabeled data logs; (d) a spatiotemporal characterization of cyber-attacks for detecting such attacks; (e) a two-stage intrusion detection system for industrial control networks; (f) a chatbot for detecting online sex offenders, based on an artificial conversational entity (ACE); and (g) an open-source platform for manipulating both streaming and archived network flow data in real time. This Special Issue also contains two protection-related research contributions, including: (a) a countermeasure for on-off web defacement attacks and (b) the evaluation of multi-path routing as a protection feature against network attacks and failures.
Operator Theory - Recent Advances, New Perspectives and Applications
Operator theory is a fascinating model that includes essential theorems and diverse applications in all science. This book discusses some fundamental aspects of pure and applied operator theory and the use of the theory to solve a large array of problems. As such, it will be of interest to scholars, researchers, and undergraduate and graduate students in pure and applied mathematics, classical and modern physics, engineering, and science in general.
Optimal Mass Transport on Euclidean Spaces
Optimal mass transport has emerged in the past three decades as an active field with wide-ranging connections to the calculus of variations, PDEs, and geometric analysis. This graduate-level introduction covers the field's theoretical foundation and key ideas in applications. By focusing on optimal mass transport problems in a Euclidean setting, the book is able to introduce concepts in a gradual, accessible way with minimal prerequisites, while remaining technically and conceptually complete. Working in a familiar context will help readers build geometric intuition quickly and give them a strong foundation in the subject. This book explores the relation between the Monge and Kantorovich transport problems, solving the former for both the linear transport cost (which is important in geometric applications) and for the quadratic transport cost (which is central in PDE applications), starting from the solution of the latter for arbitrary transport costs.
Seven Lessons in Theory of Inversions of Order and Determinants
Benjamin Feland Groat's informative and accessible lessons on the theory of inversions of order and determinants are essential reading for anyone interested in mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Elementary Treatise On Algebra
A textbook on algebra, covering topics such as polynomial equations, logarithms, and inequalities.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Introduction to the Modern Theory of Equations
This classic text provides a thorough introduction to modern theory of equations. The book covers basic algebraic operations, polynomial equations, and their solutions, as well as more complex topics such as elliptic functions and transcendental equations. This is an essential text for anyone seeking a comprehensive understanding of modern algebraic theory.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Notes On the Elements of Algebra and Trigonometry With Solutions of the More Difficult Questions
This comprehensive guide to algebra and trigonometry offers readers tips and tricks to tackle even the most challenging of problems. With detailed solutions to the most difficult questions, this book is perfect for students and professionals alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Elements of Analytical Geometry; Comprehending the Doctorine of the Conic Sections and the General Theory of Curves and Surfces of the Second Order
The Elements of Analytical Geometry is a comprehensive guide to the doctrine of the conic sections and the general theory of curves and surfaces of the second order. Written by Jr Young, this book is essential reading for students and enthusiasts of mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elementary Algebra
This comprehensive guide to elementary algebra covers all the principles and fundamentals of the subject. Suitable for students and teachers alike, this book is an essential resource for anyone looking to improve their knowledge of algebra.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elementary Algebra
First published in the mid-19th century, Elementary Algebra by Charles Davies is a classic textbook on algebraic principles and techniques. Suitable for students at an introductory level, this book covers the basics of algebra, including equations, expressions, and functions. It also includes numerous examples and exercises to help students gain mastery over these concepts. Whether you are a student or an educator, Davies' Elementary Algebra remains an invaluable resource for mastering the fundamentals of algebra.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Elements of Algebra
This book provides a comprehensive introduction to algebra designed for common school students. With clear instruction and plenty of examples, students will gain a strong understanding of the fundamental principles of algebra. Written by George Roberts Perkins, this book also serves as a great introduction for more advanced algebraic concepts.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
