Vectors, a Programmed Text for Introductory Physics
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Almost Regular Forms.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elementary College Algebra
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Classical Hopf Algebras and Their Applications
This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s.The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results.Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.
Galois Theory and Its Algebraic Background
Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.
Galois Theory and Its Algebraic Background
Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.
Introduction to Linear Algebra
This book is designed for students who have never been exposed to the topics in a linear algebra course. The text is filled with interesting and diverse application sections but is also a theoretical text which aims to train students to do succinct computation in a knowledgeable way.
Introduction to Linear Algebra
Introduction to Linear Algebra: Computation, Application, and Theory is designed for students who have never been exposed to the topics in a linear algebra course. The text is filled with interesting and diverse application sections but is also a theoretical text which aims to train students to do succinct computation in a knowledgeable way. After completing the course with this text, the student will not only know the best and shortest way to do linear algebraic computations but will also know why such computations are both effective and successful.Features: Includes cutting edge applications in machine learning and data analytics Suitable as a primary text for undergraduates studying linear algebra Requires very little in the way of pre-requisites
Introduction to Lattice Algebra
Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general. Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with a focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and - depending on the student's major - can be used for a senior undergraduate level or first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines. Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Contains numerous exercises.
Introduction to Matrix Theory
Matrix Operations.- Systems of Linear Equations.- Matrix as a Linear Map.- Orthogonality.- Eigenvalues and Eigenvectors.- Canonical Forms.- Norms of Matrices.- Short Bibliography.- Index.
Student Solutions Manual for Gallian’s Contemporary Abstract Algebra
Whereas many partial solutions and sketches for the odd-numbered exercises appear in the book, the Student Solutions Manual, written by the author, has comprehensive solutions for all odd-numbered exercises and large　number of even-numbered exercises.
Algebra
From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and na簿ve set theory.
Algebra and Galois Theories
Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.
Division of time, book I and book II
A book on nonlinear dynamics, Lorenz equations, Fourier and an advance of this, interdependent equations and Jacobians as well as Kammaa equations to solve and simulate . A collection of Tahir Iqbal's previous work on mathematics, encapsulating the books 'symmetry and balance, division of time books I and II. A host of applications of this thought are in this book, from weather equations and economics to MBA theories and advertising.
Extended Abstracts Geomvap 2019
This book comprises an overview of twelve months of intense activity of the research group Geometry, Topology, Algebra, and Applications (GEOMVAP) at the Universitat Polit癡cnica de Catalunya (UPC). Namely, it contains extended abstracts of the group meeting in Cardona and of the international Workshop of Women in Geometry and Topology aligned with a series of workshops in the topic. As such, it includes a panoramic view of the main research interests of the group which focus on varieties and manifolds from the algebraic, topological and differential perspective with a view towards applications. The GEOMVAP group has a long tradition working on various interfaces of algebra, geometry and topology. In the last decade, the group has become active contributor in interdisciplinary science and it is now focused on both a theoretical point of view and the transversal applications to several disciplines including Robotics, Machine Learning, Phylogenetics, Physics and Celestial Mechanics. The increasing interdisciplinarity of modern research and the fact that the boundaries between different areas of mathematics are vanishing, with a constant transfer of problems and techniques between them, makes it difficult to progress without a multidisciplinary approach. GEOMVAP gathers together experts in Algebraic, Symplectic and Arithmetic Geometry to stimulate the interaction between them and to allow the study of each object from different points of view. The book aims at established researchers, as well as at PhD and postdoctoral students who want to learn more about the latest advances in pure and applied Geometry and Topology.
(Mostly) Commutative Algebra
This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.
The Problem of Catalan
In 1842 the Belgian mathematician Eug癡ne Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 - 23 = 1 is the only solution of the equation xp - yq = 1 in integers x, y, p, q with xy 0 and p, q >= 2.In this book we give a complete and (almost) self-contained exposition of Mihăilescu's work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.
Symbol Correspondences for Spin Systems
In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. A detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is first followed by an introduction to the Poisson algebra of the classical spin system and then by a similarly detailed examination of its SO(3)-invariant decomposition. The book next proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. The book will be a valuable guide for researchers in this field and its self-contained approach also makes it a helpful resource for graduate students in mathematics and physics.
Abstract Algebra
This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic(linear) error-correcting codes, including cyclic codesruler and compass constructionscryptographysymmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.
Boolean Representations of Simplicial Complexes and Matroids
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.
Divisor Theory
0. A Theorem of Polynomial Algebra.- 1. The General Theory.- 2. Applications to Algebraic Number Theory.- 3. Applications to the Theory of Algebraic Curves.- References.
Classical and Discrete Functional Analysis with Measure Theory
Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.
What Are Tensors Exactly?
Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.
Abstract Algebra
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gr繹bner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Zero Product Determined Algebras
This book provides a concise survey of the theory of zero product-determined algebras, which has been developed over the last 15 years. It is divided into three parts. The first part presents the purely algebraic branch of the theory, the second part presents the functional analytic branch, and the third part discusses various applications. The book is intended for researchers and graduate students in ring theory, Banach algebra theory, and nonassociative algebra.
Problems in Linear Algebra and Matrix Theory
This is the revised and expanded edition of the problem book Linear Algebra: Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory. This new edition contains about fifty-five examples and many new problems, based on the author's lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida) and short lectures Matrix Gems at Shanghai University and Beijing Normal University.The book is intended for upper division undergraduate and beginning graduate students, and it can be used as text or supplement for a second course in linear algebra. Each chapter starts with Definitions, Facts, and Examples, followed by problems. Hints and solutions to all problems are also provided.
Chapter 1, Data Structures
This elementary math book covers arithmetic, modular arithmetic, Homomorphism, Permutations, Matrices, linear functions, Vector Algebra, algebraic extensions, polynomials, power series, and related topics.
Concise Pre Algebra
Postulates? Theorems? Just Practice! Learn these solutions in 2 days! x^2 + 2x^2 = ? x(2x^2+3x) = ?
Nonlinear Second Order Parabolic Equations
The parabolic partial differential equations model one of the most important processes in the real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion processes are ubiquitous and crucial in the physical and natural world as well as our everyday lives. This book is self-contained and covers key topics such as the Lp theory and Schauder theory, maximum principle, comparison principle, regularity and uniform estimates, initial-boundary value problems of semilinear parabolic scalar equations and weakly coupled parabolic systems, the upper and lower solutions method, monotone properties and long-time behaviours of solutions, convergence of solutions and stability of equilibrium solutions, global solutions and finite time blowup. It also touches on periodic boundary value problems, free boundary problems, and semigroup theory. The book covers major theories and methods of the field, including topics that are useful but hard to find elsewhere. This book is based on tried and tested teaching materials used at the Harbin Institute of Technology over the past ten years. Special care was taken to make the book suitable for classroom teaching as well as for self-study among graduate students. About the Author: Mingxin Wang is Professor of Mathematics at Harbin Institute of Technology, China. He has published ten monographs and textbooks and 260 papers. He is also a supervisor of 30 PhD students.
Computational Algebra
This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.
Lineare Algebra 2
In diesem Band des zweiteiligen Lehrbuchs zur Linearen Algebra werden zum einen verschiedene Anwendungen zu den Themen des ersten Bandes vertieft: Es wird die L繹sungstheorie linearer gew繹hnlicher Differentialgleichungen mit konstanten Koeffizienten vorgestellt. Zum anderen werden die formalen Konzepte der Linearen Algebra behandelt. Neben Quotientenkonstruktionen und der Theorie der symmetrischen und antisymmetrischen Bilinearformen wird vor allem die multilineare Algebra zusammen mit Tensorprodukten im Detail besprochen. Ein Anhang gibt einen Ausblick auf die Theorie der Kategorien und Funktoren.Wie schon im ersten Band ist der Zugang dieses Lehrbuchs eher klassisch: Die formalen Aspekte der wissenschaftlichen Mathematik werden stark betont. Noch st瓣rker als im ersten Band wird jedoch gerade aus den Anwendungen in der mathematischen Physik wichtige Motivation f羹r das Vorgehen gewonnen. Auf diese Weise ist das Lehrbuch sowohl f羹r Studierende der Mathematik als auch der Physik geeignet. Insgesamt 羹ber 120 umfangreiche ?bungen erleichtern das Selbststudium. Der Inhalt von Band 2: - Lineare Differentialgleichungen und die Exponentialabbildung- Quotienten- Multilineare Abbildungen und Tensorprodukte- Bilinearformen und Quadriken- Kategorien und Funktoren
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 Contents Introduction 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 Bibliography Jeff 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.
A Functorial Model Theory
This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Higher Mathematics for Engineering and Technology
Based on and enriched by the long-term teaching experience of the authors, this volume covers the major themes of mathematics in engineering and technical specialties. The book addresses the elements of linear algebra and analytic geometry, differential calculus of a function of one variable, and elements of higher algebra. On each theme the authors first present short theoretical overviews and then go on to give problems to be solved. The authors provide the solutions to some typical, relatively difficult problems and guidelines for solving them.The authors consider the development of the self-dependent thinking ability of students in the construction of problems and indicate which problems are relatively difficult. The book is geared so that some of the problems presented can be solved in class, and others are meant to be solved independently. An extensive, explanatory solution of at least one typical problem is included, with emphasis on applications, formulas, and rules.This volume is primarily addressed to advanced students of engineering and technical specialties as well as to engineers/technicians and instructors of mathematics.Key features: Presents the theoretical background necessary for solving problems, including definitions, rules, formulas, and theorems on the particular themeProvides an extended solution of at least one problem on every theme and guidelines for solving some difficult problemsSelects problems for independent study as well as those for classroom time, taking into account the similarity of both sets of problemsDifferentiates relatively difficult problems from others for those who want to study mathematics more deeplyProvides answers to the problems within the text rather than at the back of the book, enabling more direct verification of problem solutionsPresents a selection of problems and solutions that are very interesting not only for the students but also for professor-teacher staff
Computation of Generalized Matrix Inverses and Applications
This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra.The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i, j, ..., k} inverse and the Moore-Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore-Penrose's inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization.The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier-Faddeev method, method of Zhukovski, and variations of the partitioning method.
Invariance of Modules Under Automorphisms of Their Envelopes and Covers
The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.
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. Author Dr. 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.
![STAAR Grade 8 Math Book and Practice Problems [8th Edition Workbook]](https://cdn.kingstone.com.tw/english/images/product/1497/9781637751497m.webp "STAAR Grade 8 Math Book and Practice Problems [8th Edition Workbook]")
STAAR Grade 8 Math Book and Practice Problems [8th Edition Workbook]
Test Prep Books' STAAR Grade 8 Math Book and Practice Problems [8th Edition Workbook] Taking the STAAR Math Grade 8 test? Want to get a good score? Written by Test Prep Books, this comprehensive study guide includes: Quick OverviewTest-Taking StrategiesIntroductionNumerical Representations and RelationshipsComputations and Algebraic RelationshipsGeometry and MeasurementData Analysis and Personal Financial LiteracyPractice QuestionsDetailed Answer Explanations Studying is hard. We know. We want to help. You can ace your test. Each part of the test has a full review. This study guide covers everything likely to be on the STAAR Math Grade 8 test. Lots of practice test questions are included. Miss one and want to know why? There are detailed answer explanations to help you avoid missing the same question a second time. Are you a bad test taker? Use your time wisely with the latest test-taking strategies. Don't settle for just learning what is on the test. Learn how to be successful with that knowledge. Test Prep Books has drilled down the top test-taking tips. This will help you save time and avoid making common mistakes on test day.Get your STAAR Math Grade 8 study guide. It includes review material, practice test questions, and test-taking strategies.It has everything you need for success.
Algebra 4
This book, the fourth book in the four-volume series in algebra, discusses Lie algebra and representation theory in detail. It covers topics such as semisimple Lie algebras, root systems, representation theory of Lie algebra, Chevalley groups and representation theory of Chevalley groups. Numerous motivating illustrations have been presented along with exercises, enabling readers to acquire a good understanding of topics which they can then use to find the exact or most realistic solutions to their problems.
Advances in Lie Superalgebras
1 A. Alldridge, Z. Shaikh: Superbosonisation, Riesz superdistributions, and highest weight modules.- 2 K. Coulembier: Homological algebra for osp(12n).- 3 A. D'Andrea: Finiteness and orbifold vertex operator algebras.- 4 A. De Sole: On classical finite and affine W -algebras.- 5 M. Gorelik, D. Grantcharov: Q-type Lie superalgebras.- 6 C. Hoyt: Weight modules for the Lie superalgebra D(2,1, a).- 7 R. Fioresi, S. Kwok: On SUSY curves.- 8 V. G. Kac, P. Moseneder Frajria, P. Papi: Dirac operators and the Very Strange Formula for Lie superalgebras.- 9 V. Mazorchuk: Parabolic category O for classical Lie superalgebras.- 10 E. Poletaeva: On Kostant's Theorem for Lie superalgebras.- 11 V. Serganova: Classical Lie superalgebras at infinity.- 12 D. Valeri: Classical W-algebras within the theory of Poisson vertex algebras.- 13 J. van Ekeren: Vertex Operator Superalgebras and Odd Trace Functions.- 14 R. Zhang: Serre presentations of Lie superalgebras
Theory and Computation of Complex Tensors and Its Applications
Preface.- Introduction.- The pseudo-spectrum theory.- Perturbation theory.- Tensor complementarity problems.- Plane stochastic tensors.- Neural Networks.- US- and U-eigenpairs of complex tensors.- Randomized algorithms.- Bibliography.- Index.
Basics of Matrix Algebra for Statistics with R
A Thorough Guide to Elementary Matrix Algebra and Implementation in RBasics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject.The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling.In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers.Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.
Algebraic Computability and Enumeration Models
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets.This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.
Algebras, Rings and Modules, Volume 2
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.
Matrix Inequalities for Iterative Systems
The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
HP Prime Guide Algebra Fundamentals
Welcome to HP Prime Guide Algebra Fundamentals, HP Prime Innovation in Education Series. There is no one road to the learning of mathematics. Different approaches for different learners are needed to take learners to where they want to go. The goal of this guide is to give you the flexibility of various approaches aided by the use of the HP Prime to reach your goals. Manual explanations of math concepts in the guide are accompanied by HP Prime illustrations that can be used with the calculator, computer software, and iOS/ Android/ Windows app. Techniques, examples, and exercises can be done using any of the platforms. The HP Prime Guide Algebra Fundamentals emphasis is its attention on math standards that work. Significant time is spent on learning math by using methods that have shown to be successful in the classroom. There is additional emphasis given to building blocks topics. HP Prime Calculator, HP Prime/Pro, and HP Prime Free Revealed and Extended feature of the guide is used to show how the HP Prime Calculator, HP Prime/Pro, and HP Prime Free commands and functions can be used to work individual problems as well as how they can be extended to help us understand complex math concepts or create a set of tools that can help with problem solving. Upon mastery of the manual techniques apply the HP Prime Calculator, HP Prime/Pro, and HP Prime Free solutions to increase your efficiency and problem solving power. Concentrate on the solution without being bogged down with traditional labor-intense steps. Embrace failure; use your additional time, to attempt more word and real world problems. The HP Prime Guide Algebra Fundamentals is available in print and a digital learning eBook. In the digital eBook version, every example is followed by an interactive reinforcement exercise. Hyperlinks are used to references earlier discussions of a topic, future discussions of a topic, websites, Table of Contents entries, and Detailed Index entries. The hyperlinks are shown as underlined text in the print version. This enables us to see where the eBook's links are. The solutions to the reinforcement exercises are in the back of the printed and eBook versions with eBook's solution linked back to the topic's explanation. In addition to the print version, the guide is available on various eBook readers and eBook applications, be it a stand-alone reader, on a phone, tablet, pc, or through a web-browser. The content in the Guide uses mathematical notation, text, graphics, and HP Prime screenshots. The eBook version takes advantage of the resolution of the display. The real-time access, anytime, anyplace nature of the eBook version, allows a new way for you to gain the math knowledge and skills necessary to succeed in the classroom, at your job, and in your personal pursuit of learning. The print version gives you the option of using a traditional book. An innovative approach is to use HP Prime Calculator, HP Prime/Pro, and HP Prime Free Computer Algebra Solutions (CAS) as an aide in moving forward. In lessons requiring a concept that you have not yet mastered, use the HP Prime Calculator, HP Prime/Pro, and HP Prime Free CAS solutions to assist with class assignments, allowing you to keep current. You keep moving forward with the new material, giving you additional time to master the concept causing problems. Larry Schroeder
![Common Core Math Grade 7 Study Guide Workbook and Practice Test Questions with Detailed Answer Explanations [7th Edition]](https://cdn.kingstone.com.tw/english/images/product/5563/9781637755563m.webp "Common Core Math Grade 7 Study Guide Workbook and Practice Test Questions with Detailed Answer Explanations [7th Edition]")
Common Core Math Grade 7 Study Guide Workbook and Practice Test Questions with Detailed Answer Explanations [7th Edition]
Test Prep Books' Common Core Math Grade 7 Study Guide Workbook and Practice Test Questions with Detailed Answer Explanations [7th Edition]Made by Test Prep Books experts for test takers trying to achieve a great score on the Common Core 7th Grade Math exam.This comprehensive study guide includes: Quick Overview Find out what's inside this guide!Test-Taking Strategies Learn the best tips to help overcome your exam!Introduction Get a thorough breakdown of what the test is and what's on it!Ratios & Proportional Relationships Analyzing Proportional Relationships and Using Them to Solve Real-World ProblemsThe Number System Adding, Subtracting, Multiplying, and Dividing Rational NumbersExpressions & Equations Using Properties of Operations to Generate Equivalent Expressions; Solving Real-Life and Mathematical Problems Using Numerical and Algebraic Expressions and EquationsGeometry Drawing, Constructing, and Describing Geometrical Figures and Describing the Relationships Between Them; Drawing, Constructing, and Describing Geometrical Figures and Describing the Relationships Between ThemStatistics & Probability Using Random Sampling to Draw Inferences About a Population; Drawing Informal Comparative Inferences about Two Populations; Investigating Chance Processes and Developing, Using, and Evaluating Probability ModelPractice Questions Practice makes perfect!Detailed Answer Explanations Figure out where you went wrong and how to improve!Studying can be hard. We get it. That's why we created this guide with these great features and benefits: Comprehensive Review: Each section of the test has a comprehensive review created by Test Prep Books that goes into detail to cover all of the content likely to appear on the test.Practice Test Questions: We want to give you the best practice you can find. That's why the Test Prep Books practice questions are as close as you can get to the actual Common Core 7th Grade Math test.Answer Explanations: Every single problem is followed by an answer explanation. We know it's frustrating to miss a question and not understand why. The answer explanations will help you learn from your mistakes. That way, you can avoid missing it again in the future.Test-Taking Strategies: A test taker has to understand the material that is being covered and be familiar with the latest test taking strategies. These strategies are necessary to properly use the time provided. They also help test takers complete the test without making any errors. Test Prep Books has provided the top test-taking tips.Customer Service: We love taking care of our test takers. We make sure that you interact with a real human being when you email your comments or concerns.Anyone planning to take this exam should take advantage of this Test Prep Books study guide. Purchase it today to receive access to: 7th Grade Common Core Math review materials7th Grade Common Core Math practice test questionsTest-taking strategies
Linear Algebra
LINEAR ALGEBRA EXPLORE A COMPREHENSIVE INTRODUCTORY TEXT IN LINEAR ALGEBRA WITH COMPELLING SUPPLEMENTARY MATERIALS, INCLUDING A COMPANION WEBSITE AND SOLUTIONS MANUALS Linear Algebra delivers a fulsome exploration of the central concepts in linear algebra, including multidimensional spaces, linear transformations, matrices, matrix algebra, determinants, vector spaces, subspaces, linear independence, basis, inner products, and eigenvectors. While the text provides challenging problems that engage readers in the mathematical theory of linear algebra, it is written in an accessible and simple-to-grasp fashion appropriate for junior undergraduate students. An emphasis on logic, set theory, and functions exists throughout the book, and these topics are introduced early to provide students with a foundation from which to attack the rest of the material in the text. Linear Algebra includes accompanying material in the form of a companion website that features solutions manuals for students and instructors. Finally, the concluding chapter in the book includes discussions of advanced topics like generalized eigenvectors, Schur's Lemma, Jordan canonical form, and quadratic forms. Readers will also benefit from the inclusion of: A thorough introduction to logic and set theory, as well as descriptions of functions and linear transformations An exploration of Euclidean spaces and linear transformations between Euclidean spaces, including vectors, vector algebra, orthogonality, the standard matrix, Gauss-Jordan elimination, inverses, and determinants Discussions of abstract vector spaces, including subspaces, linear independence, dimension, and change of basis A treatment on defining geometries on vector spaces, including the Gram-Schmidt process Perfect for undergraduate students taking their first course in the subject matter, Linear Algebra will also earn a place in the libraries of researchers in computer science or statistics seeking an accessible and practical foundation in linear algebra.
