Fundamentals of Ramsey Theory
Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before.The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises.This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTSPrefaceList of FiguresList of TablesSymbols1. Introduction2. Integer Ramsey Theory3. Graph Ramsey Theory4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography IndexBiographyAaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
Linear Algebra
Linear Algebra: An Inquiry-based Approach is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The Inquiry-based Approach is central to this development. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra. In our approach, students begin with a problem and develop the mathematics necessary to describe, solve, and generalize it. Thus students learn a vital skill for the 21st century: the ability to create a solution to a problem. This text is offered to foster an environment that supports the creative process. The twin goals of this textbook are: -Providing opportunities to be creative, -Teaching "ways of thinking" that will make it easier for to be creative.To motivate the development of the concepts and techniques of linear algebra, we include more than two hundred activities on a wide range of problems, from purely mathematical questions, through applications in biology, computer science, cryptography, and more.Table of ContentsIntroduction and Features For the Student . . . and Teacher Prerequisites Suggested Sequences 1 Tuples and Vectors 2 Systems of Linear Equations 3 Transformations 4 Matrix Algebra5 Vector Spaces 6 Determinants 7 Eigenvalues and Eigenvectors 8 Decomposition 9 Extras Bibliography Index BibliographyJeff Suzuki is Associate Professor of Mathematics at Brooklyn College and holds a Ph.D. from Boston University. His research interests include mathematics education, history of mathematics, and the application of mathematics to society and technology. He is a two-time winner of the prestigious Carl B. Allendoerfer Award for expository writing. His publications have appeared in The College Mathematics Journals; Mathematics Magazine; Mathematics Teacher; and the American Mathematical Society's blog on teaching and learning mathematics. His YouTube channel (http: //youtube.com/jeffsuzuki1) includes videos on mathematical subjects rangingfrom elementary arithmetic to linear algebra, cryptography, and differential equations.
Non-commutative Algebras. Pseudo-BCK Algebras versus m-pseudo-BCK Algebras
This monograph is devoted mainly to the author's results in her research on non-commutative algebras related to logic started on October 17, 2022, results never published. It would not be written in so little time and with so many important results and examples without the help of the computer program Prover9-Mace4, developed by William W. McCune (1953 - 2011).There exist a frame-work of non-commutative algebras of logic, having in its `center' the pseudo-BCK algebra.In this monograph, the author mainly has generalized to the non-commutative case the m-BCK algebra and its related algebras, as particular cases of unital magmas, thus creating a new frame-work of non-commutative algebras, having in its `center' the new m-pseudo-BCK algebra. The pseudo-MV algebras are particular cases of m-pseudo-BCK algebras, the groups belong to this new frame-work. But, the goal of her research was to define and study the quantum-pseudo-MV algebra, the non-commutative generalization of quantum-MV algebra. She was able to reach her goal only because she has discovered the`principle' that governs the non-commutative algebras, called `transposition' principle (`m-transposition' principle, for magmas). She has also introduced and studied other non-commutative generalizations of quantum algebras: the bounded involutive pseudo-lattices, the pseudo-De Morgan algebras and the ortho-pseudo-lattices. The book has 18 chapters, divided into three parts: Part I (centered on pseudo-BCK algebras: Chapters 1 - 7), Part II (the core of the monograph, centered on m-pseudo-BCK algebras: Chapters 8 - 16) and Part III (`bridge' theorems: Chapters 17, 18).
Elliptic Partial Differential Equations Elementary Viewpoint
This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course.The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples.The structure of the book is flexible enough to allow different chapters to be taught independently.The book is friendly, welcoming, and written for a newcomer to the subject.It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.
Abstract Algebra
When a student of mathematics studies abstract algebra, he or she inevitably faces questions in the vein of, "What is abstract algebra" or "What makes it abstract?" Algebra, in its broadest sense, describes a way of thinking about classes of sets equipped with binary operations. In high school algebra, a student explores properties of operations (+, -, ?, and 繩) on real numbers. Abstract algebra studies properties of operations without specifying what types of number or object we work with. Any theorem established in the abstract context holds not only for real numbers but for every possible algebraic structure that has operations with the stated properties.This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups, rings, and fields; or a course that primarily emphasizes group theory. The writing style is student-centered, conscientiously motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry, number theory, cryptography and many other areas.This book offers a unique feature in the lists of projects at the end of each section. the author does not view projects as just something extra or cute, but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation.The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic, asking and to trying to answer their own questions. Expository projects invite the student to explore a topic with algebraic content or pertain to a particular mathematician's work through responsible research.The exercises challenge the student to prove new results using the theorems presented in the text. The student then becomes an active participant in the development of the field.
Semitopology. Decentralised Collaborative Action via Topology, Algebra, and Logic
We develop semitopologies, a new topological structure which gives a mathematical foundation to heterogeneous, decentralised, permissionless, computing systems. Semitopologies help to model consensus problems that commonly arise in designing cutting-edge peer-to-peer, blockchain, and other decentralised systems; especially when different such systems need to interact. Points correspond to participants in the system, and open sets correspond to the ways in which participants can cooperate.This text is aimed at mathematicians and advanced students interested in a new topology-adjacent field with strong practical applications; and at engineers working to build decentralised systems who could use a mathematical foundation for designing the relevant tools. It aims to offer pleasant surprises and new ideas for researchers; and for practitioners, it aims to help build the next generation of better, safer, more scalable decentralised systems.
Algebraic Systems
No detailed description available for "Algebraic Systems".
Linear Algebra
Linear Algebra, James R. Kirkwood and Bessie H. Kirkwood, 978-1-4987-7685-1, K29751Shelving Guide: MathematicsThis text has a major focus on demonstrating facts and techniques of linear systems that will be invaluable in higher mathematics and related fields. A linear algebra course has two major audiences that it must satisfy. It provides an important theoretical and computational tool for nearly every discipline that uses mathematics. It also provides an introduction to abstract mathematics. This book has two parts. Chapters 1-7 are written as an introduction. Two primary goals of these chapters are to enable students to become adept at computations and to develop an understanding of the theory of basic topics including linear transformations. Important applications are presented. Part two, which consists of Chapters 8-14, is at a higher level. It includes topics not usually taught in a first course, such as a detailed justification of the Jordan canonical form, properties of the determinant derived from axioms, the Perron-Frobenius theorem and bilinear and quadratic forms. Though users will want to make use of technology for many of the computations, topics are explained in the text in a way that will enable students to do these computations by hand if that is desired.Key features include: Chapters 1-7 may be used for a first course relying on applications Chapters 8-14 offer a more advanced, theoretical course Definitions are highlighted throughout MATLAB(R) and R Project tutorials in the appendices Exercises span a range from simple computations to fairly direct abstract exercises Historical notes motivate the presentation
Normal 2-Coverings of the Finite Simple Groups and Their Generalizations
Class Field Theory and L Functions
The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras. While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020). The main features of the book are: A detailed study of Pontrjagin's dualtiy theorem. A thorough presentation of the cohomology of profinite groups. A introduction to simple algebras. An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language. The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse. The study of holomorphy domains and their relevance for class field theory. Simple classical proofs of the functional equation for L functions both for number fields and function fields. A self-contained presentation of the theorems of representation theory needed for Artin L functions. Application of Artin L functions for arithmetical results.
Functional Linear Algebra
Linear algebra is an extremely versatile and useful subject. It rewards those who study it with powerful computational tools, lessons about how mathematical theory is built, examples for later study in other classes, and much more. Functional Linear Algebra is a unique text written to address the need for a one-term linear algebra course where students have taken only calculus. It does not assume students have had a proofs course. The text offers the following approaches: More emphasis is placed on the idea of a linear function, which is used to motivate the study of matrices and their operations. This should seem natural to students after the central role of functions in calculus. Row reduction is moved further back in the semester and vector spaces are moved earlier to avoid an artificial feeling of separation between the computational and theoretical aspects of the course. Chapter 0 offers applications from engineering and the sciences to motivate students by revealing how linear algebra is used. Vector spaces are developed over R, but complex vector spaces are discussed in Appendix A.1. Computational techniques are discussed both by hand and using technology. A brief introduction to Mathematica is provided in Appendix A.2. As readers work through this book, it is important to understand the basic ideas, definitions, and computational skills. Plenty of examples and problems are provided to make sure readers can practice until the material is thoroughly grasped. AuthorDr. Hannah Robbins is an associate professor of mathematics at Roanoke College, Salem, VA. Formerly a commutative algebraist, she now studies applications of linear algebra and assesses teaching practices in calculus. Outside the office, she enjoys hiking and playing bluegrass bass.
An Invitation to Abstract Algebra
Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics. To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout.The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois' achievement in understanding how we can--and cannot--represent the roots of polynomials. The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory. The presentation includes the following features: Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters. The text can be used for a one, two, or three-term course. Each new topic is motivated with a question. A collection of projects appears in Chapter 23. Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks--period. This book is offered as a manual to a new way of thinking. The author's aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.
Random Eigenvalue Problems
No detailed description available for "Random Eigenvalue Problems".
Analytic Perturbation Theory for Matrices and Operators
No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".
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.
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.
Ring Theory - Proceedings of the Biennial Ohio State-Denison Conference 1992
A Model Theoretic Oriented Approach to Partial Algebras
No detailed description available for "A Model Theoretic Oriented Approach to Partial Algebras".
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.'
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.'
Fundamentals of Abstract Algebra
Fundamentals of Abstract Algebra is a primary textbook for a one year first course in Abstract Algebra, but it has much more to offer besides this. The book is full of opportunities for further, deeper reading, including explorations of interesting applications and more advanced topics, such as Galois theory. Replete with exercises and examples, the book is geared towards careful pedagogy and accessibility, and requires only minimal prerequisites. The book includes a primer on some basic mathematical concepts that will be useful for readers to understand, and in this sense the book is self-contained.Features Self-contained treatments of all topics Everything required for a one-year first course in Abstract Algebra, and could also be used as supplementary reading for a second course Copious exercises and examples Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency, both as an applied mathematician of machine learning. He held a position as Associate Professor of Mathematics at Manhattan College in New York City, but later left to pursue research working for the US Department of Energy at Sandia National Laboratory as a Principal Data Analyst. His research interests include machine learning, statistics and computational algebra.
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.
Fractional Partial Differential Equations
This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The topics covered encompass crucial aspects of the theory, such as well-posedness, regularity, approximation, and optimal control. The book delves into the intricacies of fractional Navier-Stokes equations, fractional Rayleigh-Stokes equations, fractional Fokker-Planck equations, and fractional Schr繹dinger equations, providing a thorough exploration of these subjects. Numerous real-world applications associated with these equations are meticulously examined, enhancing the practical relevance of the presented concepts.The content in this monograph is based on the research works carried out by the author and other excellent experts during the past five years. Rooted in the latest advancements, it not only serves as a valuable resource for understanding the theoretical foundations but also lays the groundwork for delving deeper into the subject and navigating the extensive research landscape. Geared towards researchers, graduate students, and PhD scholars specializing in differential equations, applied analysis, and related research domains, this monograph facilitates a nuanced understanding of time-fractional partial differential equations and their broader implications.
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.
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.
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.
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.
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.
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
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.
