The Art of Working with the Mathieu Group M24
The Leech lattice Λ, the Conway group ∙O, and the Monster group M are immensely famous structures. They each grow out of the Mathieu group M24 and its underlying combinatorial structure, and play an important role in various branches of mathematics and in theoretical physics. Written by an expert in the field, this book provides a new generation of mathematicians with the intimate knowledge of M24 needed to understand these beautiful objects, and many others. It starts by exploring Steiner systems, before introducing the Miracle Octad Generator (MOG) as a device for working with the Steiner system S(5,8,24). Emphasizing how theoretical and computational approaches complement one another, the author describes how familiarity with M24 leads to the concept of 'symmetric generation' of groups. The final chapter brings together the various strands of the book to produce a nested chain of groups culminating in the largest Conway simple group Co1.
Lectures on Lie Algebras
No detailed description available for "Lectures on Lie Algebras".
Enveloping Algebras
No detailed description available for "Enveloping Algebras".
Linear Algebra
This book is a comprehensive guide to Linear Algebra and covers all the fundamental topics such as vector spaces, linear independence, basis, linear transformations, matrices, determinants, inner products, eigenvectors, bilinear forms, and canonical forms. It also introduces concepts such as fields, rings, group homomorphism, and binary operations early on, which gives students a solid foundation to understand the rest of the material. Unlike other books on Linear Algebra that are either too theory-oriented with fewer solved examples or too problem-oriented with less good quality theory, this book strikes a balance between the two. It provides easy-to-follow theorem proofs and a considerable number of worked examples with various levels of difficulty. The fundamentals of the subject are explained in a methodical and straightforward way. This book is aimed at undergraduate and graduate students of Mathematics and Engineering Mathematics who are studying Linear Algebra. It is also a useful resource for students preparing for exams in higher education competitions such as NET, GATE, lectureships, etc. The book includes some of the most recent and challenging questions from these exams.
Quadratic Equations
Unleashing the Power of Quadratic Equations: A Comprehensive Guide to Mastery in Real-World Applications. From understanding the basics to exploring advanced techniques, this book dives into the significance of quadratic equations in various fields such as science, finance, and problem solving, offering valuable resources and support along the way.
Algebraic Number Theory
Algebraic Number Theory: Count This Shit Twice is a comprehensive and engaging guide to the foundations and advanced concepts of algebraic number theory, from basic definitions and properties to applications in cryptography and algebraic geometry.With a focus on humor, cursing, clarity and practicality, this book is a must-read for anyone interested in the fascinating world of numbers.
A First Course on Orthogonal Polynomials
A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field. Features Suitable for a graduate course in orthogonal polynomials Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the "old" classical orthogonal polynomials Includes numerous exercises for each topic Real and complex analysis are the only prerequisites
Select Topics in Signal Analysis
This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail.The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan's Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory.The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.
Algebra
Get ready to embrace the wild and badass world of algebra with Algebra Unleashed: A No-Nonsense Guide to Crushing It. This comprehensive and engaging book covers everything from basic terminology to advanced concepts, providing clear explanations, practice exercises, and mind-blowing solutions to help you master algebra. With its bold and energetic tone, this book will make you realize that algebra is not only cool as shit, but also an essential tool for problem-solving in the real world. So grab a copy and unleash your inner badass mathematician!
Spectral Theory of Operators
Are you curious about the mysteries of Spectral Theory? In this comprehensive guide, the author takes you on an entertaining journey through the fundamentals and applications of this complex mathematical concept. From its historical background to its role in quantum mechanics and everyday life, this book will enlighten and engage readers with its accessible language and practical examples. Whether youre a math enthusiast or looking to expand your knowledge in the field, Spectral Theory Made Easy is the ultimate resource that will make you give a shit about this fascinating subject.
Algebraic Structures and Homomorphisms
Discover the profound beauty and practicality of algebraic structures in The Fucking Joy of Algebra: A Comprehensive Guide to Groups, Rings, Fields, and Homomorphisms. Unveiling the power of abstraction and its applications in various areas, this book will leave you in awe of the endless possibilities of algebra.
Monoids and Semirings
Discover the power of monoids and semirings in this comprehensive guide to their definitions, properties, and applications in computer science and everyday life. From functional programming to cryptography, graph theory to art, this book explores the wide-reaching impact of these mathematical structures. Dive deep into the world of monoids and semirings and unlock their potential in various fields and industries. Get ready to expand your knowledge and embrace the fucking brilliance of monoids and semirings.
Number Systems and Algebraic Structures
Get ready to dive into the world of numbers and algebraic structures in this captivating guide. From counting and fractions to quadratic equations and group theory, this book demystifies math with its no-nonsense approach and colorful language. Discover the power and beauty of mathematics and how it can transform your life.
Linear Algebra
This book is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra.
Fundamentals of Ramsey Theory
This up-to-date book introduces the field of Ramsey theory from several different viewpoints. 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.
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).
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.
Abstract Algebra
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. This book offers a unique feature in the lists of projects at the end of each section.
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.
Algebraic Systems
No detailed description available for "Algebraic Systems".
Linear Algebra
This is the second of a two-part set of books for the undergraduate linear algebra sequence. The text is for more advanced courses taught in mathematics departments. This course is based around matrix theory and focused on the theory of linear algebra. Along with the chapters found in Elementary Linear Algebra, he offers seven additional chapters .
Normal 2-Coverings of the Finite Simple Groups and Their Generalizations
Class Field Theory and L Functions
Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, with a presentation of algebraic foundations which are usually undersized in standard algebra courses.
Functional Linear Algebra
Functional Linear Algebra is a unique text authored to address the need for a one-term linear algebra course when students have only had calculus. It does no assume students have had a proofs course.
An Invitation to Abstract Algebra
Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks. This book is offered as a manual to a new way of thinking. The author aims to instill the desire to understand the material, to encourage more discovery, and to appreciate 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.
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
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
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.
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.
