Compact Matrix Quantum Groups and Their Combinatorics
An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.
Commutative Algebra
The primary audience for this book is students and the young researchers interested in the core of the discipline. Commutative algebra is by and large a self-contained discipline, which makes it quite dry for the beginner with a basic training in elementary algebra and calculus. A stable mathematical discipline such as this enshrines a vital number of topics to be learned at an early stage, more or less universally accepted and practiced. Naturally, authors tend to turn these topics into an increasingly short and elegant list of basic facts of the theory. So, the shorter the better. However, there is a subtle watershed between elegance and usefulness, especially if the target is the beginner. From my experience throughout years of teaching, elegance and terseness do not do it, except much later in the carrier. To become useful, the material ought to carry quite a bit of motivation through justification and usefulness pointers. On the other hand, it is difficult to contemplate these teaching devices in the writing of a short book. I have divided the material in three parts. starting with more elementary sections, then carrying an intermezzo on more difficult themes to make up for a smooth crescendo with additional tools and, finally, the more advanced part, versing on a reasonable chunk of present-day steering of commutative algebra. Historic notes at the end of each chapter provide insight into the original sources and background information on a particular subject or theorem. Exercises are provided and propose problems that apply the theory to solve concrete questions (yes, with concrete polynomials, and so forth).
6th Grade Mathematics
In this book, you will find 112 Questions, mostly multiple-choice, with several constructed response questions. The questions span seven units: Whole Numbers, Fractions, Decimals and percents, ratios and proportions, Measurement, Geometry, Algebra, and Statistics. The Book employs a wide variety of stories from all the cultures of South Sudan. South Sudan Primary School Curriculum.
Exercises in Algebra and Trigonometry
This book contains exercises that a student can complete to learn algebra and trigonometry. Though it is designed to serve as a companion to another book by the same author, namely Algebra and Trigonometry, the exercises herein are typical for the subjects and do not pertain exclusively to that particular text.
100 Comprehensive Solutions in Algebra
This compilation presents comprehensive and step by step progressive solutions involving Algebra Problems. Covers major topics in algebra which include solving word problems involving age, mixture, investment, work, motion, arithmetic and geometric sequences, exponential and logarithmic functions, quadratic functions, variations, circle, parabola, ellipse, imaginary numbers, rational and quadratic equations.
Mathematics for the Practical Man
First published in 1910, this book aims to present and explain, in simple terms, all the elements of algebra, geometry, trigonometry, logarithms, coordinate geometry, and calculus. Mathematics For The Practical Man constitutes the ideal introduction to some of mathematics more tricky elements, and it is not to be missed by collectors of vintage literature of this ilk. The contents include: - Fundamentals of Algebra. Addition and Subtraction - Fundamentals of Algebra. Multiplication and Division, I - Fundamentals of Algebra. Multiplication and Subtraction, II - Fundamentals of Algebra. Factoring - Fundamentals of Algebra. Involution and Evolution - Fundamentals of Algebra. Simple Equations Many vintage books such as this are becoming increasingly scarce and expensive. We are republishing this volume now in an affordable, high-quality, modern edition complete with the original text and images.
Inverse Problems - Recent Advances and Applications
Inverse Problems - Recent Advances and Applications examines some recent advances in inverse problems, new aspects of their mathematical modeling of inverse problems regarding in relation to their applications in physical systems and used the computational methods used. It consists of five chapters divided into two sections. Section 1, "Modeling and Formulations of Inverse Problems", discusses new approaches to modeling and formulations of inverse problems in some physical systems. Section 2, "Some Computational Aspects", contains research related to mathematical methods of solving some inverse problems.
The Square Root of Two to One Million Digits
A conundrum faced ancient mathematicians. Which number to use for the square root of 2? Ancient Babylonians used the fraction 305470/216000. This was accurate to about six decimal places. Ancient Indians used the fraction 577/408. This fraction is accurate to five decimal places. Today, mathematicians understand that the square root of 2 is irrational, its digits go on forever without repeating. It is calculated using an infinite series. This book lists the first million digits of the square root of 2.
Geometry of Continued Fractions
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects.Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics.The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Algebra 1 Through Stories
Unravel the Mysteries of AlgebraStep into a thrilling mathematical escapade with "Algebra 1: The Mystery of the Algebraic Artifact"! This dynamic guide offers a unique spin on mastering Algebra 1 concepts, making it an excellent supplementary resource for students aged 11-13 (8th-9th grade) and a compelling teaching tool for educators.A Novel Approach to LearningNo more wading through old-fashioned, dry textbooks! This book cleverly intertwines vital algebraic ideas into an exciting story that captures students' attention, making learning a captivating and effortless process.Essential Topics UncoveredOur journey uncovers all the key Algebra 1 concepts. The 19 exciting chapters delve into: Equations and ExpressionsInequalitiesLinear FunctionsExponents and PolynomialsQuadratic EquationsSystems of EquationsCompound InequalitiesReinforce and Validate UnderstandingEach chapter includes a comprehensive review and a carefully selected range of practice problems that reinforce understanding and allow the application of newly gained knowledge in various situations. These end-of-chapter exercises empower students to flex their algebraic muscles and gain confidence in their understanding.Ideal For"Algebra 1: The Mystery of the Algebraic Artifact" is a valuable resource for: 8th-9th graders studying Algebra 1, aiming to supplement their learning with an engaging twist.Parents looking for innovative methods to encourage and support their child's math education.Teachers in search of an engaging, narrative-driven technique to illuminate algebra concepts.With "Algebra 1: The Mystery of the Algebraic Artifact", algebra becomes an epic quest filled with adventure and intrigue. Join us as we unlock the wonders of Algebra 1 and make math an exciting mystery to solve!
Application-Inspired Linear Algebra
This textbook invites students to discover abstract ideas in linear algebra within the context of applications. Diffusion welding and radiography, the two central applications, are introduced early on and used throughout to frame the practical uses of important linear algebra concepts. Students will learn these methods through explorations, which involve making conjectures and answering open-ended questions. By approaching the subject in this way, new avenues for learning the material emerge: For example, vector spaces are introduced early as the appropriate setting for the applied problems covered; and an alternative, determinant-free method for computing eigenvalues is also illustrated. In addition to the two main applications, the authors also describe possible pathways to other applications, which fall into three main areas: Data and image analysis (including machine learning); dynamical modeling; and optimization and optimal design. Several appendices are included as well, oneof which offers an insightful walkthrough of proof techniques. Instructors will also find an outline for how to use the book in a course. Additional resources can be accessed on the authors' website, including code, data sets, and other helpful material. Application-Inspired Linear Algebra will motivate and immerse undergraduate students taking a first course in linear algebra, and will provide instructors with an indispensable, application-first approach.
Matrix Mathematics
Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.
Algebraic Curves and Surfaces
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Abstract Algebra
This book is translated from the Chinese version published by Science Press, Beijing, China, in 2017. It was written for the Chern class in mathematics of Nankai University and has been used as the textbook for the course Abstract Algebra for this class for more than five years. It has also been adapted in abstract algebra courses in several other distinguished universities across China.The aim of this book is to introduce the fundamental theories of groups, rings, modules, and fields, and help readers set up a solid foundation for algebra theory. The topics of this book are carefully selected and clearly presented. This is an excellent mathematical exposition, well-suited as an advanced undergraduate textbook or for independent study. The book includes many new and concise proofs of classical theorems, along with plenty of basic as well as challenging exercises.
Abstract Algebra
This book is translated from the Chinese version published by Science Press, Beijing, China, in 2017. It was written for the Chern class in mathematics of Nankai University and has been used as the textbook for the course Abstract Algebra for this class for more than five years. It has also been adapted in abstract algebra courses in several other distinguished universities across China.The aim of this book is to introduce the fundamental theories of groups, rings, modules, and fields, and help readers set up a solid foundation for algebra theory. The topics of this book are carefully selected and clearly presented. This is an excellent mathematical exposition, well-suited as an advanced undergraduate textbook or for independent study. The book includes many new and concise proofs of classical theorems, along with plenty of basic as well as challenging exercises.
Character Map in Non-Abelian Cohomology, The: Twisted, Differential, and Generalized
Linear Algebra
There are numerous linear algebra textbooks available on the market. Yet, there are few that approach the notion of eigenvectors and eigenvalues across an operator's minimum polynomial. In this book, we take that approach. This book provides a thorough introduction to the fundamental concepts of linear algebra. The material is divided into two sections: Part I covers fundamental concepts in linear algebra, whereas Part II covers the theory of determinants, the theory of eigenvalues and eigenvectors, and fundamental results on Euclidean vector spaces. We highlight that: Consider hypothetical manufacturing models as a starting point for studying linear equations. There are two novel ideas in the book: the use of a production model to motivate the concept of matrix product and the use of an operator's minimal polynomial to describe the theory of eigenvalues and eigenvectors. Several examples incorporate the use of SageMath., allowing the reader to focus on conceptual comprehension rather than formulas.
Vedic Mathematics
Vedic Mathematics is a collection of Techniques/Sutras to solve mathematical arithmetic in easy and faster way. It consists of 16 Sutras (Formulae) and 13 sub-sutras (Sub Formulae) which can be used for problems involved in arithmetic, algebra, geometry, calculus, conics. Vedic mathematics, simplifies arithmetic and algebraic operations, and has increasingly found acceptance the world over. Vedic Mathematics helps find solutions in a single or a few steps where as conventional methods require multiple steps. These include: Identifying Basic Geometrical Shapes and FiguresDrawing AnglesBisecting Line Segments and AnglesConstructing AnglesCalculating the Size of Missing AnglesConstructing TrianglesAnalyzing CirclesSo I thought to write about the book on Famous Mathematician and their Contribution. In this eBook, we talked about World Famous Mathematician, his contribution, theorem, quotes, and a story about him. This mathematical eBook is a must-have for every Student and Math Lover.The Primary Purpose of this book is to make you aware of World Great Mathematicians and their Contribution. After reading this book, we expect you to expand your knowledge about mathematicians.
Fundamentals of Algebra
This book provides students with a tool to improve their knowledge of Algebra in preparation to learning Calculus. This book is intended to be a quick review of the fundamental concepts of Algebra studied in high-school.It starts with the Concepts in Algebra. From associative property introduction to powers, and logarithms to radicals and ordered pairs. Then it follows with Straight lines chapter. Linear relations, distance between points, to slope of a line. It follows with Linear Equations. One step, two steps linear equations to straight line graphs, horizontal and vertical lines to parallel and perpendicular lines. Next chapter deals with linear inequalities. Next are the polynomials and factoring polynomial expressions. Next chapter is about Functions. Linear and quadratic, inverse functions, piecewise and trigonometric functions, to logarithmic functions. The next deals with transformation of functions. The last chapter is about linear systems of equations.
A Course on Hopf Algebras
This textbook provides a concise, visual introduction to Hopf algebras and their application to knot theory, most notably the construction of solutions of the Yang-Baxter equations. Starting with a reformulation of the definition of a group in terms of structural maps as motivation for the definition of a Hopf algebra, the book introduces the related algebraic notions: algebras, coalgebras, bialgebras, convolution algebras, modules, comodules. Next, Drinfel'd's quantum double construction is achieved through the important notion of the restricted (or finite) dual of a Hopf algebra, which allows one to work purely algebraically, without completions. As a result, in applications to knot theory, to any Hopf algebra with invertible antipode one can associate a universal invariant of long knots. These constructions are elucidated in detailed analyses of a few examples of Hopf algebras. The presentation of the material is mostly based on multilinear algebra, with all definitions carefully formulated and proofs self-contained. The general theory is illustrated with concrete examples, and many technicalities are handled with the help of visual aids, namely string diagrams. As a result, most of this text is accessible with minimal prerequisites and can serve as the basis of introductory courses to beginning graduate students.
Matrix Theory - Classics and Advances
Matrix Theory - Classics and Advances examines matrix theory and its application in solving a series of problems related to natural phenomena and applied science. It consists of eleven chapters divided into two sections. Section 1, "Theory and Progress", discusses the classical problems of matrix theory and its contribution to different fields of pure mathematics. Section 2, "Applications", contains the research related to the application of matrix theory in applied science.
High Accuracy Detection of Mobile Malware Using Machine Learning
As increasingly sophisticated and evasive malware attacks continue to emerge, more effective detection solutions to tackle the problem are being sought through the application of advanced machine learning techniques. This reprint presents several advances in the field including: a new method of generating adversarial samples through byte sequence feature extraction using deep learning; a state-of-the-art comparative evaluation of deep learning approaches for mobile botnet detection; a novel visualization-based approach that utilizes images for Android botnet detection; a study on the detection of drive-by exploits in images using deep learning; etc. Furthermore, this reprint presents state-of-the-art reviews about machine learning-based detection techniques that will increase researchers' knowledge in the field and enable them to identify future research and development directions.
Many-Electron and Multiphoton Atomic Processes
This Special Issue contains contributions from colleagues, former students and collaborators of the late Prof. Miron Amusia, who was a world-leading figure in theoretical atomic physics over the past half a century. The focus of this Special Issue is on many-electron and multiphoton atomic processes that are at the forefront of contemporary atomic and molecular physics. Special attention is given to the many-electron correlation problem and its interplay with strong field laser-atom interactions. These scientific advances represent the lasting legacy of Prof. Amusia and his school.
GATE 2022 Mathematics - 22 Years Chapter-wise Solved Papers 2000-2021
Lakhs of students write the GATE exam annually. The level of competition is fierce, owing to the increasing competition every year for a limited number of seats. If you are a serious aspirant, it is advisable to prepare for GATE with the right books. A major game-changer is the habit to practice and revise the concepts and this is why our GATE 2022 Chapter-wise Solved Papers are your best bet to be GATE ready! This book consists of GATE previous years' solved papers of the last 22 years (2000-2021) in chapter-wise order. Solved papers enable an aspirant to get acquainted with the exam pattern and the weightage of each topic and Section. With the right effort and proper guidance, we're sure that you will be able to face GATE 2022 confidently. Features: 22 years' solved papers Chapter-wise arrangement Comprehensive analysis of previous years' papers Thoroughly revised and updated.
The Congruences of a Finite Lattice
The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years. It features the author's signature "Proof-by-Picture" method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include: an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensionscomplete proofs, an extensive bibliography and index, and over 180 illustrationsadditional chapters covering new results of the lastseven years, increasing the size of this edition to 430 pages, 360 statements, and 262 referencesThis text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions: "[This] monograph...is an exceptional work in lattice theory, like all the contributions by this author. The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. -- Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." -- Mathematical Reviews
A Study on Generalized Topological Simple Groups and Related Concepts
"A Study on Generalized Topological Simple Groups and Related Concepts" is a comprehensive book written by Selvi C, an expert in the field of mathematics. This scholarly work is an exploration of the study of generalized topological simple groups and related concepts, and is an essential resource for researchers and scholars in the fields of algebra, topology, and group theory.The book covers a wide range of topics, including the classification of generalized topological simple groups, the relationship between topological groups and algebraic groups, and the theory of locally compact groups. It also includes in-depth discussions of related concepts such as abstract algebra and functional analysis, making it a valuable resource for students and researchers alike.The author's clear and concise writing style makes the material accessible to readers with a range of mathematical backgrounds, and the book includes numerous examples and exercises to help readers reinforce their understanding of the concepts covered. Whether you are a researcher in the field of mathematics or a student looking to expand your knowledge, "A Study on Generalized Topological Simple Groups and Related Concepts" is an indispensable resource that should not be missed.
Integral Inequalities and Generalized Convexity
The book covers several new research findings in the area of generalized convexity and integral inequalities. Integral inequalities using various type of generalized convex functions are applicable in many branches of mathematics such as mathematical analysis, fractional calculus, and discrete fractional calculus.The book contains integral inequalities of Hermite-Hadamard type, Hermite- Hadamard-Fejer type and majorization type for the generalized strongly convex functions. It presents Hermite-Hadamard type inequalities for functions defined on Time scales. Further, it provides the generalization and extensions of the concept of preinvexity for interval-valued functions and stochastic processes, and give Hermite-Hadamard type and Ostrowski type inequalities for these functions. These integral inequalities are utilized in numerous areas for the boundedness of generalized convex functions.Features: Covers Interval-valued calculus, Time scale calculus, Stochastic processes - all in one single book Numerous examples to validate results Provides an overview of the current state of integral inequalities and convexity for a much wider audience, including practitioners Applications of some special means of real numbers are also discussed The book is ideal for anyone teaching or attending courses in integral inequalities along with researchers in this area.
Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification
This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference "Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification", held on the occasion of Chari's 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari's significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorificationQuantum affine algebras and cluster algebrasSteinberg groups for Jordan pairsDynamical quantum determinants and PfaffiansInteractions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
Algebra II for Beginners
Algebra II for Beginners provides students with the essential tools and skills necessary for success in Algebra II courses. This comprehensive guide includes hundreds of examples, over 1,500 skill-building exercises, and two practice tests to ensure thorough preparation for the Algebra II final exam. It will help improve math abilities, increase confidence, and sharpen problem-solving skills. Algebra II for Beginners offers complete coverage of all Algebra II concepts and aligns with national and state standards. The dynamic design and interactive activities make learning engaging and concrete, while targeted practices build essential skills. All exercise solutions are included, allowing students to check their understanding and progress.This comprehensive textbook for Algebra II is the perfect resource for students looking to review core content, refine their math skills, and achieve their best results on the Algebra II course. Key Features of Algebra II for Beginners: In-Depth Understanding: The book provides the essential tools and skills necessary for success in Algebra II courses, presenting hundreds of examples and over 1,500 skill-building exercises to ensure comprehensive preparation for the Algebra II final exam.Boost Confidence and Skills: This guide is designed to enhance math abilities, increase confidence, and sharpen problem-solving skills, ultimately leading to improved academic performance.Comprehensive Coverage: All Algebra II concepts are thoroughly covered in alignment with national and state standards.Engaging and Interactive: The book's dynamic design and interactive activities make learning engaging and concrete. It turns abstract concepts into tangible knowledge, making learning more enjoyable and effective.Targeted Practices: The book includes targeted practices that help build essential skills. Students can immediately apply what they have learned, thereby reinforcing understanding.Solutions Provided: All exercise solutions are included, allowing students to check their understanding and monitor their progress.Perfect for Review and Refinement: This comprehensive textbook for Algebra II is ideal for students looking to review core content, refine their math skills, and achieve their best results on the Algebra II course.Suitable for Self-Study and Classroom Use: Algebra II for Beginners offers a comprehensive approach to excelling in Algebra II, whether studying individually or being used as a classroom resource.Digital Support: The book includes a unique online resource feature. For each topic covered, a QR code and link are provided, directing to a web page that offers further information, supplementary exercises, and explanatory videos. This digital integration enhances understanding and caters to various learning styles.Full-Length Practice Tests: Two full-length Algebra II practice tests are provided at the end of the book. These tests simulate the format and difficulty of the actual exam, helping students gauge their readiness, identify areas of improvement, and build confidence for their Algebra II final exam.This comprehensive textbook for Algebra II is the perfect resource for students looking to review core content, refine their math skills, and achieve their best results on the Algebra II course. Ideal for both self-study and classroom use, Algebra II for Beginners offers a comprehensive approach to excelling in Algebra II.
Essential Mathematics for Undergraduates
This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. It guides STEM students towards developing knowledge and skills to enrich their scientific education. In doing so it avoids the common mechanical approach to problem-solving based on the repetitive application of dry formulas. The presentation preserves the mathematical rigour throughout and still stays accessible to undergraduates. The didactical focus is threaded through the assortment of subjects and reflects in the book's structure.Part 1 introduces the mathematical language and its rules together with the basic building blocks. Part 2 discusses the number systems of common practice, while the backgrounds needed to solve equations and inequalities are developed in Part 3. Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry. Two appendices form Part 5: the Greek etymology of frequent terms and a list of mathematicians mentioned in the book. Abundant examples and exercises are disseminated along the text to boost the learning process and allow for independent work.Students will find invaluable material to shepherd them through the first years of an undergraduate course, or to complement previously learnt subject matters. Teachers may pick'n'mix the contents for planning lecture courses or supplementing their classes.
Linear and Complex Analysis for Applications
Linear and Complex Analysis for Applications aims to unify various parts of mathematical analysis in an engaging manner and to provide a diverse and unusual collection of applications, both to other fields of mathematics and to physics and engineering. The book evolved from several of the author's teaching experiences, his research in complex analysis in several variables, and many conversations with friends and colleagues. It has three primary goals: 　to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work, to unify many distinct and seemingly isolated topics, to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems.　The book realizes these goals by beginning with reviews of Linear Algebra, Complex Numbers, and topics from Calculus III. As the topics are being reviewed, new material is inserted to help the student develop skill in both computation and theory. The material on linear algebra includes infinite-dimensional examples arising from elementary calculus and differential equations. Line and surface integrals are computed both in the language of classical vector analysis and by using differential forms. Connections among the topics and applications appear throughout the book.The text weaves abstract mathematics, routine computational problems, and applications into a coherent whole, whose unifying theme is linear systems. It includes many unusual examples and contains more than 450 exercises.
Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck
This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource formany researchers in geometry, analysis, and mathematical physics.
Linear Algebra and Group Theory for Physicists and Engineers
This textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience. Being approached together at the same time, these two topics complete one another, allowing students to attain a deeper understanding of both subjects. The opening chapters introduce linear algebra with applications to mechanics and statistics, followed by group theory with applications to projective geometry. Then, high-order finite elements are presented to design a regular mesh and assemble the stiffness and mass matrices in advanced applications in quantum chemistry and general relativity.This text is ideal for undergraduates majoring in engineering, physics, chemistry, computer science, or applied mathematics. It is mostly self-contained--readers should only be familiar with elementary calculus. There are numerous exercises, with hints or full solutions provided. A series of roadmaps are also provided to help instructors choose the optimal teaching approach for their discipline.The second edition has been revised and updated throughout and includes new material on the Jordan form, the Hermitian matrix and its eigenbasis, and applications in numerical relativity and electromagnetics.
Linear Algebra
This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.
Algebra.zip
This book is the elementary guide to the world of algebra leaded by the students' idea and their thinking process.
Algebra for the Use of Colleges and Schools
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Quaternions; Volume 1
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Algebra for Beginners
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Matrix Inversion and the Solution of Linear Equations
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Algebra for Colleges and Schools
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Study of certain vibrational problems in magneto elasticity
This thesis is the outcome of the research carried out by the author under the supervision of Dr. Surya Narain, Senior Reader & Head, Department of Mathematics & Statistics, Harish Chandra Post Graduate College, Varanasi (an affiliated college of VEER BAHADUR SINGH PURVANCHAL UNIVERSITY, JAUNPUR). This research work is original and nothing has been harrowed from any books or journals, The thesis has been divided into four chapters and each chapter is subdivided into a number of articles. Chapter I is the General introduction. It gives a brief idea of Stress, Strain Stress equation of Equilibrium, Stress-Strain relation, Propagation of elastic waves, Rayleigh waves, Visco-elasticity, Magneto-elasticity, and Bessel's function. The relevant equations of books and journals used have been mentioned in the references at the end of each chapter. The equations in each chapter have been numbered as (m, n, p) where m denotes the chapter, n is the article and p is the number of equations.
A Primer of Quaternions
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
High School Algebra
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Theory of Equations
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Linear Algebra I - Summaries of Theory and Exercises Solved
Linear Algebra I is a book for university students of any university branch of science. You will find summaries of theory and exercises solved, of the following topics: Matrices, Resolution of Linear Systems Equations, Vector Spaces, Linear Transformations, Diagonalization of endomorphism, and Bilinear and Quadratic Forms. I have 20 years of experience teaching mathematics at the university level. And, as a teacher of Algebra, Calculus, Statistics, etc., of university students, and, as a result of the needs that I have seen in my students, I have written this book. This book is characterized by being practical and didactic. It is also useful as a guide for the student. I hope it will be useful to you, above all.
Tracts On the Resolution of Affected Algebr瓣ick Equations by Dr. Halley’s, Mr. Raphson’s, and Sir Isaac Newton’s, Methods of Approximation
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
