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A Computational Introduction to Number Theory & Algebra
This textbook that introduces number theory and algebra with a focus on computational methods and real-world applications, particularly in cryptography and coding theory. Designed for students in computer science or mathematics, the book requires min . . . READ MORE
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Topological Groups: Yesterday, Today, Tomorrow - Morris
This text offering a comprehensive overview of topological group theory. It traces the field's development from foundational questions posed by David Hilbert in 1900 to contemporary research.
It required half a century of effort by several generati . . . READ MORE
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Algebraic Topology by Allen Hatcher
Allen Hatcher's Algebraic Topology is a widely used textbook that introduces the field of algebraic topology. In most major universities it's often used in graduate-level courses and is appreciated for its clear, geometric approach.
This introductor . . . READ MORE
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Model Theory, Algebra, and Geometry by Deirdre Haskell
Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. This text explores how model theory applies to various areas of algebra and geometry. The book demonstrates how abstract concepts in . . . READ MORE
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Modeling, Functions, and Graphs: Algebra for College
This book is a comprehensive algebra textbook designed for college students. It focus on three core themes throughout their textbook: Modeling, Functions, Graphs and motivate students to acquire the skills and techniques of algebra by placing them in . . . READ MORE
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Metric Algebraic Geometry by Paul Breiding - PDF
This text combines algebraic geometry and differential geometry to solve real-world problems. It focuses on understanding shapes and spaces defined by polynomial equations, which is useful in areas like data science, machine learning, and computer vi . . . READ MORE
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Set Theoretic Approach to Algebraic Structures in Math
This text explains how using subsets and small pieces inside big algebra systems like semigroups, rings, and vector spaces can create new, useful structures. Instead of working with an entire ring or vector space, the authors focus on key subsets and . . . READ MORE
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Group Theory for the Standard Model of Particle Physics
This text is a graduate and advanced undergraduate level textbook that introduces the mathematics of Lie groups and Lie algebras through their vital role in modern particle physics. It will help students understand current knowledge about the standar . . . READ MORE
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Explorations in Algebraic Graph Theory by Chris Godsil
Algebraic graph theory is a fascinating subject concerned with the interplay between algebra and graph theory. Algebraic tools can be used to give surprising and elegant proofs of graph theoretic facts, and there are many interesting algebraic object . . . READ MORE
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Classical Algebraic Geometry A Modern View by Igor V. D
The main purpose of this text present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times.
This is . . . READ MORE
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Higher Algebra by Jacob Lurie - PDF
Higher Algebra is a complex mathematics book that builds upon his earlier work, Higher Topos Theory. It introduces advanced concepts like infinity-categories (8-categories) into algebra, developing ideas such as E-algebras, 8-operads, and stable 8-ca . . . READ MORE
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Algorithms in Real Algebraic Geometry by Saugata Basu
This is a well known foundational graduate-level textbook that provides a comprehensive and self-contained introduction to the algorithmic aspects of real algebraic geometry. It covers core topics such as semi-algebraic sets, cylindrical algebraic de . . . READ MORE
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Algorithms for Modular Elliptic Curves by J. E. Cremona
This text is a comprehensive resource in computational number theory, with numerous applications in such areas as cryptography, primality testing and factorisation. It focusing on algorithms for studying elliptic curves over the rationals. The book i . . . READ MORE
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Orbital Integrals Reductive Lie Groups Their Algebras
This text offers a comprehensive exploration of global analysis, focusing on the integration over topological groups and their algebras. The text delves into the applications of orbital integrals in harmonic analysis and representation theory. It ser . . . READ MORE
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Quaternion Algebras by John Voight - PDF
This graduate-level textbook gives a clear, step-by-step introduction to quaternion algebras (a class of non-commutative algebraic structures). It developed algebra, arithmetic, analysis, geometry, and arithmetic geometry of quaternion algebras. It's . . . READ MORE
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Computer Algebra in Scientific Computing by Andreas Web
This text is a book made up of research papers that show how math done by computers (called symbolic algebra) can help in science and engineering. Instead of just giving numbers, this kind of math keeps formulas in symbolic form, which helps scientis . . . READ MORE
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Hopf Algebras, Quantum Groups and Yang-Baxter Equations
Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are presented in this text. This equation helps scientists understand things like quantum physics, knots, and how particles behave. The algebraic approach to . . . READ MORE
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On Lie Algebras Of Prime Characteristic George Seligman
This influential monograph is best studying restricted Lie algebras over fields of prime characteristic. This text present memoir is to demonstrate the applicability, under certain restrictions on the algebra and the base field, of the techniques use . . . READ MORE
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The Construction and Study of Certain Important Algebra
This short monograph is based on lectures Professor Chevalley gave at the University of Tokyo in 1954 and published in 1955. The book is an important historical work. It explores key algebraic structures like graded, tensor, exterior, and Clifford al . . . READ MORE
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The Algebra of Invariants by J. H. Grace, A. Young
Daniel Rogalski's An Introduction to Noncommutative Projective Geometry is a foundational text that provides a comprehensive introduction to the field of noncommutative projective geometry. It introduces key topics such as Artin–Schelter regular alge . . . READ MORE
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An introduction to Noncommutative Projective Geometry
Daniel Rogalski's An Introduction to Noncommutative Projective Geometry is a foundational text that provides a comprehensive introduction to the field of noncommutative projective geometry.
It introduces key topics such as Artin–Schelter regular al . . . READ MORE
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An Introduction to the Algebra of Quantics by E Elliott
The book is an introduction to the algebraic theory of quantics, which is the study of polynomial equations with multiple variables. The book covers topics such as the fundamental theorem of algebra, symmetric functions, and the theory of invariants. . . . READ MORE
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Algebraic Invariants by Leonard E. Dickson - PDF
This monograph offering one of the early systematic treatments of invariant theory. This introduction to the classical theory of invariants of algebraic forms is divided into three parts. The first uses geometric examples (like conics and cubics) to . . . READ MORE
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An introduction to Algebra and Topology by Pierre Schap
These short lecture notes cover the abstract algebra (modules, tensor products, complexes, derived functors) with foundational topology and sheaf theory. The notes include exercises and focus on using category theory and homology (like sheaf cohomolo . . . READ MORE
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Lectures On Unique Factorization Domains Pierre Samuel
These lectures are a short, clear introduction to rings where every element can be broken down into “prime-like” building blocks in only one way (apart from ordering or harmless differences). It starts with basic ideas like the integer factorization . . . READ MORE
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Noncommutative Rings by Michael Artin (PDF)
Michael Artin’s Noncommutative Rings is a set of graduate-level lecture notes that explore the structure and theory of rings where multiplication is not necessarily commutative. The text warmly clarity and depth, often used in advanced algebra course . . . READ MORE
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Algebraic Logic by Hajnal Andreka, I. Nemeti, I. Sain
Algebraic Logic by Hajnal Andréka, István Németi, and Ildikó Sain explores the deep connections between logic and algebra, focusing especially on translating logical systems (like first-order logic) into algebraic structures such as relation and cyli . . . READ MORE
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Infinite Dimensional Lie Algebras by Iain Gordon
Kac–Moody is a special kind of algebra called algebras, which are important in both mathematics and physics. The book covers how these algebras work, how they can be used, and how they connect to things like number theory and symmetry. Iain Gordon . . . READ MORE
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A Treatise on the Theory of Invariants by Oliver Glenn
This text is a foundational work in classical invariant theory. It presents a clear and systematic introduction to the subject, covering symbolic and non-symbolic methods, fundamental theorems like Gordan’s, and applications to binary and ternary for . . . READ MORE
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Smarandache Near-rings by W. B. Vasantha Kandasamy
Near-rings are one of the generalized structures of rings. This is a book on Smarandache near-rings where the Smarandache analogues of the near-ring concepts are developed. The reader is expected to have a good background both in algebra and in near- . . . READ MORE
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Smarandache Rings by W. B. Vasantha Kandasamy
The author embarked on writing this book on Smarandache rings (S-rings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several important and innovative properties about S-rings. On writing this book on Smar . . . READ MORE
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Smarandache Loops by W. B. Vasantha Kandasamy
This book explores a special type of mathematical structure called a loop. A loop is like a group (a group is a well-known concept in algebra), but it doesn’t require everything to follow the rule of associativity (where the grouping of terms doesn’t . . . READ MORE
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Smarandache Semirings, Semifields Semivector Spaces PDF
Kandasamy explores some special types of mathematical structures. These are based on the idea that a large system may contain a smaller part that is more structured or follows stronger rules. For example, a Smarandache semiring is a type of number sy . . . READ MORE
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Clifford Algebra, Geometric Algebra, and Applications
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction (the . . . READ MORE
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Universal Algebra for Computer Science by Eric G. Wagne
Universal Algebra for Computer Scientists by Wolfgang Wechler is a rigorous and well-structured textbook that introduces universal algebra through a model-theoretic lens, specifically tailored for computer science applications. The book offers a self . . . READ MORE
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Commutator Theory for Congruence Modular Varieties
This text is about understanding how certain types of mathematical structures work. It looks at something called commutators and how they behave in certain kinds of algebraic structures, called varieties. It cover the basic theory of commutators in . . . READ MORE
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The Octonions by John Baez (PDF) FreeMathematicsBooks
This text offers a deep and accessible overview of the octonions, the most exotic and least familiar of the normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of m . . . READ MORE
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Invitation to General Algebra Universal George Bergman
This book provide the basic notations and results of general algebra; also, it is a detailed and self-contained introduction to general algebra from the point of view of categories and functors. Starting with a survey, in non-category-theoretic terms . . . READ MORE
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A Course in Universal Algebra by Stanley Burris
This text is not intended to be encyclopedic, rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. This classic text develops the subject's most general and fundament . . . READ MORE
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Lie Algebras by Shlomo Sternberg - FreeMathematicsBooks
Shlomo Sternberg’s Lie Algebras is a book that dives deep into the world of Lie algebras, important in both mathematics and physics. It’s not just a list of formulas. It’s a comprehensive guide to how Lie algebras are structured and how they show up . . . READ MORE
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Introduction to Nonassociative Algebras Richard Schafer
This little book is an expanded version of the lectures on nonassociative algebras which author has gave at an Advanced Subject Matter Institute in Algebra, which was held at Oklahoma State University in the summer of 1961 under the sponsorship of th . . . READ MORE
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