A Complete Course in Algebra
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Advanced Algebra
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Algebra
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Lectures on Fundamental Concepts of Algebra and Geometry
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Groups and Symmetry
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow's theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Elements of Quaternions; Volume 1
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High School Algebra
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Beginners’ Algebra
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Memoir On The Theory Of The Partitions Of Numbers; Volume 1
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Beginners' Algebra
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The Elements of the Theory of Algebraic Numbers
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Theorie und Anwendung der Determinanten
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Elements of Algebra
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Making Musical Time
This book is a comprehensive examination of the conception, perception, performance, and composition of time in music across time and culture. It surveys the literature of time in mathematics, philosophy, psychology, music theory, and somatic studies (medicine and disability studies) and looks ahead through original research in performance, composition, psychology, and education. It is the first monograph solely devoted to the theory of construction of musical time since Kramer in 1988, with new insights, mathematical precision, and an expansive global and historical context.The mathematical methods applied for the construction of musical time are totally new. They relate to category theory (projective limits) and the mathematical theory of gestures. These methods and results extend the music theory of time but also apply to the applied performative understanding of making music. In addition, it is the very first approach to a constructive theory of time, deduced from the recent theory of musical gestures and their categories.Making Musical Time is intended for a wide audience of scholars with interest in music. These include mathematicians, music theorists, (ethno)musicologists, music psychologists / educators / therapists, music performers, philosophers of music, audiologists, and acousticians.
Phlosophy & fun of Algebra
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An Elementary Treatise on the Theory of Equations
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The Elements of Algebra
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A Treatise On Algebra; Volume 1
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The Collected Mathematical Papers
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The Elements of Algebra
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A Drill-Book in Algebra
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New and Easy Method of Solution of the Cubic and Biquadratic Equations
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New and Easy Method of Solution of the Cubic and Biquadratic Equations
Tables of the Prime Numbers, and Prime Factors of the Composite Numbers, From 1 to 100,000; With the Methods of Their Construction, and Examples of Their Use
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A First Course in Group Theory
Preliminaries Notions.- Symmetries of Shapes.- Binary Operations.- Cyclic Groups.- Inverse Functions and Permutations.- Group of Arithmetical Functions.- Matrix Groups.- Translation and Scaling Matrices.- Cosets of Subgroups and Lagrange's Theorem.- Normal Subgroups and Factor Groups.- Some Special Subgroups.- Commutators and Derived Subgroups.- Maximal Subgroups.- Group Homomorphisms.- Homomorphisms and Their Properties.- Cayley's Theorem.- Another View of Linear Groups.
The Collected Mathematical Papers
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Pleasure With Profit
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An Elementary Treatise on the Theory of Equations
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The Theory of Equations
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Diophantos of Alexandria
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Higher Algebra
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Higher Algebra
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Linear Algebra
1 - Algebraic Preamble.- Groups, Rings and Fields.- Permutation Groups.- Problems 1.- 2 - Vector Spaces and Linear Maps.- Vector Spaces and Algebras.- Bases and Dimension.- Linear Maps.- Direct Sums.- Addendum - Modules.- Problems 2.- 3 - Matrices, Determinants and Linear Equations.- Matrices.- Determinants.- Systems of Linear Equations.- Problems 3.- 4 - Cayley-Hamilton Theorem and Jordan Form.- Polynomials.- Cayley-Hamilton and Spectral Theorems.- Jordan Form.- Problems 4.- 5 - Interlude on Finite Fields.- Finite Fields.- Applications - Linear Codes and Finite Matrix Groups.- Problems 5.- 6 - Hermitian and Inner Product Spaces.- Hermitian and Inner Products, and Norms.- Unitary and Self-adjoint Maps.- Orthogonal and Symmetric Maps.- Problems 6.- 7 - Selected Topics.- The Geometry of Real Quadratic Forms.- Normed Algebras, Quaternions and Cayley Numbers.- to the Representation of Finite Groups.- Problems 7.- Appendix A - Set Theory.- Sets and Maps.- Problems A.- Appendix B - Answers and Solutions to the Problems.- Notation Index.- Definition Index.- Theorem Index.
Foundation Algebra
This textbook teaches the fundamentals of algebra, keeping points clear, succinct and focused, with plenty of diagrams and practice but relatively few words. It assumes a basic knowledge but revises the key prerequisites before moving on. Definitions are highlighted for easy understanding and reference, and worked examples illustrate the explanations. Chapters are interwoven with exercises, whilst each chapter also ends with a comprehensive set of exercises, with answers in the back of the book. Introductory paragraphs describe the real-world application of each topic, and also include briefly where relevant any interesting historical facts about the development of the mathematical subject. This text is intended for undergraduate students in engineering taking a course in algebra. It works for the Foundation and 1st year levels.
Real Algebra
This book provides an introduction to fundamental methods and techniques of algebra over ordered fields. It is a revised and updated translation of the classic textbook Einf羹hrung in die reelle Algebra. Beginning with the basics of ordered fields and their real closures, the book proceeds to discuss methods for counting the number of real roots of polynomials. Followed by a thorough introduction to Krull valuations, this culminates in Artin's solution of Hilbert's 17th Problem. Next, the fundamental concept of the real spectrum of a commutative ring is introduced with applications. The final chapter gives a brief overview of important developments in real algebra and geometry--as far as they are directly related to the contents of the earlier chapters--since the publication of the original German edition. Real Algebra is aimed at advanced undergraduate and beginning graduate students who have a good grounding in linear algebra, field theory and ring theory. It also provides a carefully written reference for specialists in real algebra, real algebraic geometry and related fields.
New Perspectives in Algebra, Topology and Categories
This book provides an introduction to some key subjects in algebra and topology. It consists of comprehensive texts of some hours courses on the preliminaries for several advanced theories in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in the literature, where one begins articles by assuming a lot of knowledge in the field. This volume can both help young researchers to quickly get into the subject by offering a kind of roadmap and also help master students to be aware of the basics of other research directions in these fields before deciding to specialize in one of them. Furthermore, it can be used by established researchers who need a particular result for their own research and do not want to go through several research papers in order to understand a single proof. Although the chapters can be read as self-contained chapters, the authors have tried to coordinate the texts in order to make them complementary. The seven chapters of this volume correspond to the seven courses taught in two Summer Schools that took place in Louvain-la-Neuve in the frame of the project Fonds d'Appui ? l'Internationalisation of the Universit矇 catholique de Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers, within the Coimbra Group.
Calculus and Linear Algebra in Recipes
The understanding comes with this book all by itself by doingAll topics of mathematics that users really need in the first semester, explained in a comprehensible way using concrete proceduresDigestible Bites: Each chapter for a lecture double hourWith various hints for MATLABIn the 2nd edition extended by a chapter on the solution of partial differential equations by means of integral transformations, by a section on the numerical solution of the wave equation as well as by several additional tasks.
Linear Algebra with Machine Learning and Data
This book takes a deep dive into several key linear algebra subjects as they apply to data analytics and data mining. The book offers a case study approach where each case will be grounded in a real-world application. This text is meant to be used for a second course in applications of Linear Algebra to Data Analytics, with a supplemental chapter on Decision Trees and their applications in regression analysis. The text can be considered in two different but overlapping general data analytics categories: clustering and interpolation. Knowledge of mathematical techniques related to data analytics and exposure to interpretation of results within a data analytics context are particularly valuable for students studying undergraduate mathematics. Each chapter of this text takes the reader through several relevant case studies using real-world data. All data sets, as well as Python and R syntax, are provided to the reader through links to Github documentation. Following each chapter is a short exercise set in which students are encouraged to use technology to apply their expanding knowledge of linear algebra as it is applied to data analytics. A basic knowledge of the concepts in a first Linear Algebra course is assumed; however, an overview of key concepts is presented in the Introduction and as needed throughout the text.
