The Complete Algebra
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Lectures on Fundamental Concepts of Algebra and Geometry
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Advanced Algebra
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A Complete Course in Algebra
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Lectures on Fundamental Concepts of Algebra and Geometry
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Elements of Quaternions; Volume 1
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Algebra
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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.
Beginners' Algebra
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Memoir On The Theory Of The Partitions Of Numbers; Volume 1
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High School Algebra
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The Elements of the Theory of Algebraic Numbers
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Beginners' 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.
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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A Treatise On Algebra; Volume 1
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The Elements of Algebra
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The Collected Mathematical Papers
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The Elements of Algebra
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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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New and Easy Method of Solution of the Cubic and Biquadratic Equations
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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Pleasure With Profit
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The Collected Mathematical Papers
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An Elementary Treatise on 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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The Theory of Equations
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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.
Topics in Groups and Geometry
This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov's pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov's theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today.The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
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.
