An Introduction to Module Theory
Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, written by two experienced teachers and researchers in the area, is based on courses given in their respective universities over the last thirty years. It is an accessible and modern account of module theory, meant as a textbook for graduate or advanced undergraduate students, though it can also be used for self-study. It is aimed at students in algebra, or students who need algebraic tools in their work. Following the recent trends in the area, the general approach stresses from the start the use of categorical and homological techniques. The book includes self-contained introductions to category theory and homological algebra with applications to Module theory, and also contains an introduction to representations of quivers. It includes a very large number of examples of all kinds worked out in detail, mostly of abelian groups, modules over matrix algebras, polynomial algebras, or algebras given by bound quivers. In order to help visualise and analyse examples, it includes many figures. Each section is followed by exercises of all levels of difficulty, both computational and theoretical, with hints provided to some of them.
Completely Regular Semigroup Varieties
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Pol獺k's theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands is a complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Pol獺k's theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
Algebra Part 2
Over 1 million sold to college and high school students supporting better test scores, grades, and improved skills - a best-selling reference for over 25 years. As a college student or being college bound, the importance of algebra in a student's academic career is so large it can determine your future path. Whether math is second nature or a challenge, this guide is your go-to for answers at your fingertips covering the need-to-know facts you normally have to search hundreds of pages of a textbook or website to find. 6-pages and durably laminated it is filled with clear and concise rules, terminology, example equations and explanations for review, study, or to quickly look up that concept you just can't remember. Author and math expert Sandy Kizlik and the developers at ExpoLog who write and edit for textbook publishing companies target content that is the backbone of support you need which we offer at a price lower than any college level study tool you will find anywhere, making it easy to add it to your college success toolbox. A good grade could be critical for a higher grade point average for some students or Algebra could be the gateway to a person's career. This best-selling guide combined with QuickStudy's Algebra Part 1 has helped many accomplish both. 6 page laminated guide includes: Graphing Real Number Line Symbol & Graphic Notation Rectangular Coordinate System Lines Slope of a Line Linear Equations Graphing Finding the Equation of a Line Graphing Linear Inequalities Finding the Intersection of Lines Functions Notation Basic Concepts Types of Functions Polynomial Functions Exponential Functions Logarithmic Functions Rational Functions To Graph Asymptotes Symmetry Sequences & Series Definitions Properties of Sums, Sequences & Series Conic Sections Line - Equation - Graph Example Horizontal Line - Equation - Graph Example Vertical Line - Equation - Graph Example Parabola - Equation - Standard Form - Graph Example Parabola - Equation - Standard Form - Graph Example Circle - Equation - Graph Example Ellipse - Equation - Graph Example Hyperbola - Equation - Graph Example Hyperbola - Equation - Graph Example Problem Solving - Includes Notations, Formulas Directions Multiples of Numbers Rectangles Triangles Circle Pythagorean Theorem Money, Coins, Bills & Purchases Mixture Work Distance Simple Interest Compound Interest Proportion & Variation
Algebra Part 1
Over 1 million sold to college and high school students supporting better test scores, grades, and improved skills - a best-selling reference for over 25 years. As a college student or being college bound, the importance of algebra in a student's academic career is so large it can determine your future path. Whether math is second nature or a challenge, this guide is your go-to for answers at your fingertips covering the need-to-know facts you normally have to search hundreds of pages of a textbook or website to find. 6-pages and durably laminated it is filled with clear and concise rules, terminology, example equations and explanations for review, study, or to quickly look up that concept you just can't remember. Author and math expert Sandy Kizlik and the developers at ExpoLog who write and edit for textbook publishing companies target content that is the backbone of support you need which we offer at a price lower than any college level study tool you will find anywhere, making it easy to add it to your college success toolbox. A good grade could be critical for a higher grade point average for some students or Algebra could be the gateway to a person's career. This best-selling guide combined with QuickStudy's Algebra Part 1 has helped many accomplish both. 6 page laminated guide includes: Set Theory Notation Operations Properties Properties of Real Numbers Operations with Real Numbers Algebraic Terms Combining Like Terms Multiplying Dividing Steps for Solving a First-Degree Equation with One Variable Steps for Solving a First-Degree Inequality with One Variable Order of Operations Factoring First Step - GCF Second Step - Categorize & Factor Special Factoring Hints Trinomials Binomials Perfect Cubes Rational Expressions Definition & Basics Operations Complex Fractions Synthetic Division Roots & Radicals Basics Rules Simplifying Radical Expressions Rational Expressions in Equations Radical Operations Radical Expressions in Equations Quadratic Equations Complex Numbers
Geometric Gems (V2)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating quadrilateral properties.
Geometric Gems (V2)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating quadrilateral properties.
Fast Track to a 5: AP Test Preparation Workbook
Students benefit from this workbook that provides full test-prep support to help them study quickly, efficiently, and effectively. It features diagnostic tests, quizzes, and more.
Fast Track to a 5 AP Test Preparation Workbook
Students benefit from this workbook that provides full test-prep support to help them study quickly, efficiently, and effectively.
Fast Track to a 5 Test Prep for Calculus (AP Edition)
Fast Track to a 5 helps prepare students for the AP Calculus Examination. This workbook is closley corrlated to the textbook program and includes a diagnostic test, test-taking strategies, course content review, and two full-length practice exams.
Linear Algebra with its Applications
This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a subject that has found the broadest range of applications in all branches of mathematics, physical and social sciences, and engineering.
Exploring Linear Algebra
This text focuses on the primary topics in a first course in Linear Algebra including additional advanced topics related to data analysis, singular value decomposition and connections to differential equations. This is a lab text that would lead a class through Linear Algebra using Mathematica demonstrations and Mathematica coding
Quadratic Ideal Numbers
This book introduces quadratic ideal numbers as objects of study with applications to binary quadratic forms and other topics. The text requires only minimal background in number theory, much of which is reviewed as needed. Computational methods are emphasized throughout, making this subject appropriate for individual study or research at the undergraduate level or above.
Groups St Andrews 2022 in Newcastle
Every four years leading researchers gather to survey the latest developments in all aspects of group theory. Since 1981, the proceedings of these meetings have provided a regular snapshot of the state of the art in group theory and helped to shape the direction of research in the field. This volume contains selected papers from the 2022 meeting held in Newcastle. It includes substantial survey articles from the invited speakers, namely the mini course presenters Michel Brion, Fanny Kassel and Pham Huu Tiep; and the invited one-hour speakers Bettina Eick, Scott Harper and Simon Smith. It features these alongside contributed survey articles, including some new results, to provide an outstanding resource for graduate students and researchers.
Vectorization
Enables readers to develop foundational and advanced vectorization skills for scalable data science and machine learning and address real-world problems Offering insights across various domains such as computer vision and natural language processing, Vectorization covers the fundamental topics of vectorization including array and tensor operations, data wrangling, and batch processing. This book illustrates how the principles discussed lead to successful outcomes in machine learning projects, serving as concrete examples for the theories explained, with each chapter including practical case studies and code implementations using NumPy, TensorFlow, and PyTorch. Each chapter has one or two types of contents: either an introduction/comparison of the specific operations in the numerical libraries (illustrated as tables) and/or case study examples that apply the concepts introduced to solve a practical problem (as code blocks and figures). Readers can approach the knowledge presented by reading the text description, running the code blocks, or examining the figures. Written by the developer of the first recommendation system on the Peacock streaming platform, Vectorization explores sample topics including: Basic tensor operations and the art of tensor indexing, elucidating how to access individual or subsets of tensor elements Vectorization in tensor multiplications and common linear algebraic routines, which form the backbone of many machine learning algorithms Masking and padding, concepts which come into play when handling data of non-uniform sizes, and string processing techniques for natural language processing (NLP) Sparse matrices and their data structures and integral operations, and ragged or jagged tensors and the nuances of processing them From the essentials of vectorization to the subtleties of advanced data structures, Vectorization is an ideal one-stop resource for both beginners and experienced practitioners, including researchers, data scientists, statisticians, and other professionals in industry, who seek academic success and career advancement.
Algebra I for Starters
ALGEBRA I FOR BEGINNERSThe Ultimate Step-by-Step Guide to Acing Algebra IUnlock the secrets of Algebra I with the ultimate guide designed to make math simple and achievable for everyone! Whether you're a student tackling algebra for the first time or someone seeking to refresh your skills, Algebra I for Beginners provides the tools and confidence you need to excel.This comprehensive guide includes: Clear and easy-to-understand lessons on essential topics like equations, inequalities, functions, and graphing.Step-by-step examples and explanations that break down complex problems into manageable steps.Practice exercises with detailed solutions to reinforce learning and build problem-solving skills.Tips and strategies to help you tackle exams and overcome common math challenges.Real-world applications to show how algebra is used in everyday life and future careers.Written with beginners in mind, this book simplifies algebraic concepts, making them accessible and engaging for learners of all levels. From mastering linear equations to understanding quadratic functions, you'll gain the skills you need to succeed in class and beyond.Take the stress out of Algebra I and achieve your academic goals with Algebra I for Beginners! Your journey to math success starts here
Elementary Galois Theory
Why is the squaring of the circle, why is the division of angles with compass and ruler impossible? Why are there general solution formulas for polynomial equations of degree 2, 3 and 4, but not for degree 5 or higher? This textbook deals with such classical questions in an elementary way in the context of Galois theory. It thus provides a classical introduction and at the same time deals with applications. The point of view of a constructive mathematician is consistently adopted: To prove the existence of a mathematical object, an algorithmic construction of that object is always given. Some statements are therefore formulated somewhat more cautiously than is classically customary; some proofs are more elaborately conducted, but are clearer and more comprehensible. Abstract theories and definitions are derived from concrete problems and solutions and can thus be better understood and appreciated. The material in this volume can be covered in a one-semester lecture on algebra right at the beginning of mathematics studies and is equally suitable for first-year students at the Bachelor's level and for teachers. The central statements are already summarised and concisely presented within the text, so the reader is encouraged to pause and reflect and can repeat content in a targeted manner. In addition, there is a short summary at the end of each chapter, with which the essential arguments can be comprehended step by step, as well as numerous exercises with an increasing degree of difficulty. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Standard and Non-Standard Methods for Solving Elementary Algebra Problems
Solving elementary algebra lies at the heart of this basic textbook. Some of the topics addressed include inequalities with rational functions, equations and inequalities with modules, exponential, irrational, and logarithmic equations and inequalities, and problems with trigonometric functions. Special attention is paid to methods for solving problems containing parameters.The book takes care to introduce topics with a description of the basic properties of the functions under study, as well as simple, typical tasks necessary for the initial study of the subject. Each topic concludes with problems for readers to solve, some of which may require serious effort and solutions are provided in all cases. Many of these problems were specifically created for this book and are set at university entrance exam or mathematical Olympiad level.The authors both have extensive experience in conducting and compiling tasks for exams and Olympiads. They seek to continue and share the traditions of Russian mathematical schools with schoolchildren, math teachers, and everyone who loves to solve problems.
Standard and Non-Standard Methods for Solving Elementary Algebra Problems
Solving elementary algebra lies at the heart of this basic textbook. Some of the topics addressed include inequalities with rational functions, equations and inequalities with modules, exponential, irrational, and logarithmic equations and inequalities, and problems with trigonometric functions. Special attention is paid to methods for solving problems containing parameters.The book takes care to introduce topics with a description of the basic properties of the functions under study, as well as simple, typical tasks necessary for the initial study of the subject. Each topic concludes with problems for readers to solve, some of which may require serious effort and solutions are provided in all cases. Many of these problems were specifically created for this book and are set at university entrance exam or mathematical Olympiad level.The authors both have extensive experience in conducting and compiling tasks for exams and Olympiads. They seek to continue and share the traditions of Russian mathematical schools with schoolchildren, math teachers, and everyone who loves to solve problems.
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).
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.
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.
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.
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.
Analytic Perturbation Theory for Matrices and Operators
No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".
