**Best Reference Books on Algebra**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Algebra Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Algebra below.

- Basic Algebra
- Algebra
- Abstract Algebra
- Commutative Algebra
- Introduction to Algebraic Geometry
- Algebraic Topology
- Linear Algebra
- Applied Linear Algebra
- Linear, Matrix, Banach, Commutative, Lie Groups and Lie Algebra

## 1. Basic Algebra

1."Complex Variables and Applications" by R V Churchill and J W Brown
“Complex Variables and Applications” Book Review: The book offers a comprehensive perspective on complex variables, blending theory with practical insights. It provides a lucid introduction to the subject, covering a wide range of topics. The early chapters delve into complex numbers, analytical functions, elementary functions, integrals, series, residues, and poles, exploring their applications and mapping by elementary functions. The later chapters delve into the intricacies of conformal mapping, along with its applications, the Schwarz-Christoffel transformation, and detailed explanations of integral formulas of the Poisson types. The book also showcases the diverse applications of complex variables in various fields and subjects.
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2."Applied and Computational Complex Analysis Vol.I" by P Henrici
“Applied and Computational Complex Analysis Vol.I” Book Review: The book offers a balanced approach, presenting fundamental theories and practical applications of analytic functions with one or multiple complex variables. It covers a comprehensive range of topics including formal power series, function analytic at a point, analytic continuation, complex navigation, conformal mapping, polynomials, and partial fractions. Detailed discussions on solving algebraic and transcendental equations are provided. Each chapter concludes with notes and assignments for readers to engage in self-study and self-assessment.
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3."Applied and Computational Complex Analysis Vol.II" by P Henrici
“Applied and Computational Complex Analysis Vol.II” Book Review: This book masterfully combines core theoretical concepts and practical applications of complex analysis. Its chapters cover a wide range of topics, including infinite products, ordinary differential equations, special functions, integral transforms, asymptotic methods, and continued fractions. Abundant notes and assignments are interspersed throughout the book, facilitating deeper comprehension and allowing readers to practice their skills. Numerous problems are featured within the text to enhance understanding and provide ample opportunity for application. The book culminates with a bibliography and an appendix, which includes additional problems for further exploration.
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4."Basic Algebra I" by Nathan Jacobson
“Basic Algebra I” Book Review: This book provides a comprehensive exploration of both conceptual and theoretical aspects of elementary algebra. Its chapters delve into various topics, including set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra, offering detailed explanations. Moreover, advanced subjects such as Lie and Jordan algebras, lattices, and Boolean algebras are thoroughly covered. The book presents intuitive and precise proofs to enhance understanding. A multitude of exercises are included throughout the textbook, making it an ideal resource for undergraduate mathematics students.
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5."Algebra - The Very Basics" by Metin Bektas
“Algebra – The Very Basics” Book Review: This book is designed for beginners in the field of algebra, providing a solid foundation in the subject. Its chapters encompass all the essential topics and concepts, including exponents, brackets, linear equations, and quadratic equations. The book is meticulously organized and offers a comprehensive approach to learning. Each chapter is concise and written in a manner that is accessible and easy to comprehend. The topics are effectively elucidated through well-chosen examples. To ensure a strong understanding, numerous exercises with solutions are incorporated throughout the text. Individuals with an interest in calculus and mathematical physics will particularly find this book valuable in their studies.
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6."Practical Algebra: A Self-Teaching Guide" by Peter H Selby and Steve Slavin
“Practical Algebra: A Self-Teaching Guide” Book Review: This book serves as an introduction to the fundamental principles and practical applications of algebra in problem-solving. It commences with an in-depth exploration of the number system. The chapters encompass a wide range of topics, including monomials and polynomials, factoring algebraic expressions, handling algebraic fractions, exponents, roots, radicals, linear equations, and fractional equations. Furthermore, the book thoroughly explains functions, graphs, quadratic equations, inequalities, ratio, proportion, and variation. These techniques and methodologies are valuable tools for addressing problems in various fields such as engineering, biology, chemistry, physical sciences, psychology, sociology, and business administration. Real-life examples and applications of algebra are thoughtfully included to enhance practical knowledge and foster reader engagement. This book will greatly benefit students and professionals in engineering and the sciences.
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7."Algebra I Workbook For Dummies" by Mary Jane Sterling
“Algebra I Workbook For Dummies” Book Review: The book serves as a guide for students studying algebra. Its chapters thoroughly cover topics such as fractions, exponents, factoring, linear and quadratic equations, inequalities, and graphs. The concepts and formulas presented in this textbook are explained efficiently. The topics and methodologies are concise, precise, and elaborated step-by-step. The book includes numerous practice problems, enabling readers to develop important algebraic skills.
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8."Basic Algebra II" by Nathan Jacobson
“Basic Algebra II” Book Review: This book combines theoretical and conceptual aspects of algebra, providing a comprehensive understanding of the subject. It delves into various topics, including categories, universal algebra, modules, basic structure theory of rings, classical representation theory of finite groups, elements of homological algebra, commutative ideal theory, and formally real fields, offering detailed discussions. Each chapter reflects a wealth of information on the featured topics, accompanied by their proofs. The book also highlights the practical applications of categories and functors. Numerous exercises are included throughout the book, allowing readers to engage in self-study and self-assessment. It serves as a valuable resource for first-year graduate courses in algebra.
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9."Basic Algebra" by Richard G Brown and Geraldine D Smith
“Basic Algebra” Book Review: The book’s objective is to present the fundamental principles and essential concepts of algebra. Its chapters are designed to be straightforward, comprehensive, and accessible to readers. Emphasizing problem-solving techniques, the book meticulously describes and clearly explains the featured topics and concepts, employing suitable examples to enhance comprehension. Numerous problems are included throughout the book to facilitate understanding and provide practice opportunities for readers. It serves as an ideal reference for beginners venturing into the realm of algebra.
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10."Basic Math and Pre-Algebra Workbook For Dummies" by Mark Zegarelli
“Basic Math and Pre-Algebra Workbook For Dummies” Book Review: This book empowers readers to review and enhance their general mathematical skills. It starts by addressing fundamental topics such as pattern interpretation, number line navigation, rounding numbers, and estimating solutions. It then emphasizes the basics of addition, subtraction, multiplication, and division, while also discussing the practical applications of commutative, associative, and distributive properties. The chapters delve into negative numbers, units, inequalities, exponents, square roots, and absolute value, providing insights into their appropriate usage. A dedicated section is devoted to statistics and sets. Overall, the book assists readers in developing and improving their problem-solving abilities.
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## 2. Algebra

1."Topics in Algebra" by I N Herstein | |

2."Algebra" by Vivek Sahai and Vikas Bist
“Algebra” Book Review: The book offers a concise and comprehensive introduction to the fundamentals of linear algebra. It covers various topics, including vector space, subspace, basis, and dimension. Additionally, the book incorporates a series of activities spanning different levels of difficulty. This resource proves valuable not only to graduates and mathematicians but also to professionals seeking to deepen their understanding of linear algebra.
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3."Fundamentals of Abstract Algebra" by D S Malik | |

4."HIGHER ALGEBRA" by Hall and Knight
“HIGHER ALGEBRA” Book Review: This book delves into topics such as proportion, variation, arithmetic progression, geometric progression, harmonic progression, as well as the associated theorems. It also covers notation scales, surds, imaginary quantities, quadratic equations, and miscellaneous equations, providing a thorough explanation of these concepts.
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5."Algebra" by Artin
“Algebra” Book Review: This book provides a concise and comprehensive introduction to the fundamental principles of linear algebra. It covers various topics, including vector spaces, subspaces, basis, and dimension. The book also includes a series of activities at varying difficulty levels to reinforce understanding and practice skills. It serves as a valuable resource for graduates, mathematicians, and professionals seeking to enhance their knowledge of linear algebra.
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6."Algebra For Beginners" by Hall and Knight
“Algebra For Beginners” Book Review: This book offers a comprehensive course in abstract algebra, covering all the essential concepts and major theorems. The exercises in the book incorporate important facts and provide ample practice opportunities. Additionally, the book presents well-constructed examples to aid understanding and includes a range of practice and challenging problems. It serves as a valuable resource for graduates, mathematicians, and professionals seeking to deepen their understanding of abstract algebra.
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7."Contemporary Abstract Algebra" by Joseph A Gallian | |

8."Algebra (Step-By-Step Maths)" by V Petris Joannou
“Algebra (Step-By-Step Maths)” Book Review: The book provides a concise and comprehensive introduction to the fundamentals of linear algebra. It covers various topics, including vector spaces, subspaces, basis, and dimension. The inclusion of activities at different difficulty levels allows for practical application and reinforcement of concepts. This book is valuable for graduates, mathematicians, and professionals seeking to solidify their understanding of linear algebra.
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9."Algebra: A Complete Introduction: Teach Yourself" by Hugh Neill | |

## 3. Abstract Algebra

1."Contemporary Abstract Algebra" by Joseph A Gallian
“Contemporary Abstract Algebra” Book Review: This book is a useful resource for students studying algebra. The book covers a wide range of topics, including groups, rings, fields, and Galois theory. Each chapter provides clear explanations and examples to help readers grasp the concepts effectively. Additionally, the book offers numerous exercises to reinforce understanding and problem-solving skills. The author’s writing style is engaging and accessible, making complex algebraic concepts more approachable. Whether you are a beginner or an advanced learner, this comprehensive textbook is a valuable tool for studying abstract algebra.
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2."Abstract Algebra" by David S Dummit
“Abstract Algebra” Book Review: The 4th Edition of Abstract Algebra aims to provide readers with an appreciation for the power and elegance that arises from the interplay between various mathematical fields. The book meticulously develops the theory of diverse algebraic structures, commencing with fundamental definitions and culminating in advanced results, with the help of numerous examples and exercises to enhance comprehension. As a result, readers will recognize how mathematical structures and their interactions lead to compelling conclusions and perspectives in various contexts.
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3."Basic Abstract Algebra" by Bhattacharya
“Basic Abstract Algebra” Book Review: This book serves as a comprehensive course in abstract algebra, offering instructors flexibility in selecting topics. Each topic is discussed in a direct and detailed manner, providing complete proofs for all theorems without omitting important details. It includes fully worked-out examples and a range of practice problems, with solutions for odd-numbered problems at the end. The new edition introduces lattices, a chapter on tensor products, and discusses the 1993 approach to the Lasker Noether theorem. With over 100 new problems and examples, the book connects abstract concepts to concrete situations. It is valuable for graduates, mathematicians, and professionals seeking to reinforce their understanding.
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4."Topics in Abstract Algebra" by Parthasarathi M
“Topics in Abstract Algebra” Book Review: This book is designed to align with the new UGC syllabus for undergraduate, advanced honours, and post-graduate students in Indian universities. It also caters to students preparing for exams like NET, GATE, SLET, and MCA. The book covers the curriculum requirements of Abstract Algebra in engineering courses as well. The latest edition includes a dedicated chapter on Boolean Algebra, as well as discussions on the Chinese remainder theorem and Euler’s Phi function in the appendix. Notable features of the book include numerous examples, visual illustrations, explanatory footnotes, relevant problems with recent developments, references to web resources, historical insights, a substantial number of solved exercises, and well-structured graded exercises with objective and multiple-choice questions. The book also provides answers (with hints) for a significant portion of the exercises.
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5."A Course In Abstract Algebra" by V K Khanna
“A Course In Abstract Algebra” Book Review: This is a comprehensive textbook that offers a thorough introduction to abstract algebra. The book covers essential topics such as groups, rings, fields, and vector spaces, providing clear explanations and detailed examples. Each chapter includes exercises that range from basic to advanced, allowing readers to practice and reinforce their understanding. The author’s writing style is accessible and concise, making complex concepts more manageable. With its comprehensive coverage and practical approach, this book is an excellent resource for students studying abstract algebra at the undergraduate level.
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6."Algebra: Abstract and Modern" by Swamy and Murthy
“Algebra: Abstract and Modern” Book Review: With its 16 chapters, this book provides a comprehensive introduction to the fundamentals of algebra, delving into topics such as group theory and field theory with thoroughness. Each chapter is enriched with a combination of challenging exercises and illustrative examples, augmenting the learning experience. Covering all essential subjects in the field, this textbook serves as an excellent resource for undergraduate mathematics courses, offering a solid foundation in algebra.
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7."Schaum's Outline of Modern Abstract Algebra" by Frank Ayres
“Schaum’s Outline of Modern Abstract Algebra” Book Review: This comprehensive study guide on abstract algebra serves as a valuable resource for mastering the subject. It offers a step-by-step approach, providing sample problems with detailed solutions, including proofs of key theorems. Additional practice problems are included to help you reinforce your understanding and work at your own pace. The guide covers essential topics such as sets, integers, groups, polynomials, and vector spaces. With practice problems accompanied by thorough explanations, it consolidates knowledge and incorporates the latest developments in the field. Compatible with your classroom text, Schaum’s Outline concisely presents the important facts, allowing you to optimize your study time and achieve your best test scores.
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8."Topics in Algebra" by I N Herstein
“Topics in Algebra” Book Review: This is a classic textbook that delves into various topics in algebra. The book covers algebraic structures such as groups, rings, and fields, with a focus on abstract and theoretical aspects. The chapters explore concepts like homomorphisms, quotient groups, factor rings, and Galois theory. Each chapter is accompanied by numerous examples and exercises to enhance the reader’s understanding. Herstein’s clear and concise writing style makes complex ideas accessible. With its comprehensive coverage and rigorous approach, this book is highly recommended for advanced undergraduate and graduate students studying algebra.
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9."A First Course in Abstract Algebra" by Fraleigh | |

10."Abstract Algebra" by Dipak Chatterjee
“Abstract Algebra” Book Review: This third edition of the book, designed for undergraduate courses, introduces new chapters on Galois Theory and Module Theory, along with additional solved problems and exercises in group theory, boolean algebra, and matrix theory. The text offers a systematic and elegant treatment of abstract algebra, covering topics such as set theory, algebraic structures, extension theory, vector space theory, and matrix theory. The development of the book also includes boolean algebra due to its relation to abstract algebra. Rigorous proofs and numerous worked examples help students understand essential results, while chapter-end exercises promote exploration and connection of key concepts. This text is suitable for both undergraduate and postgraduate students of mathematics.
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11."Computer Algebra Recipes: An Advanced Guide to Scientific Modeling" by Richard H Enns
“Computer Algebra Recipes: An Advanced Guide to Scientific Modeling” Book Review: This book offers advanced guidance on scientific modeling using computer techniques, targeting students, teachers, and professionals in the field. It explores the application of mathematical equations and computer-aided techniques to tackle complex problems, aiming to simplify the process. Prior knowledge of algebra and scientific modeling is assumed. The book features comprehensive mathematical and theoretical explanations, supplemented by numerous diagrams and graphs to facilitate understanding. Additionally, it provides a wealth of solved and unsolved examples with detailed explanations, enhancing practical application and learning.
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## 4. Commutative Algebra

1."Commutative Algebra" by D Eisenbud
“Commutative Algebra” Book Review: This comprehensive book explores the intersection of geometric concepts and algebraic geometry, covering topics from basic to advanced. It delves into localization, primary decomposition, dimension theory, differentials, homological methods, free resolution, duality, and their connections with algebraic mathematics. With a multitude of exercises, including extended chapter-end exercises, it offers an in-depth understanding of the theory. Notably, it features a dedicated chapter on Grobner’s teaching and constructivist approaches, along with their applications in commutative algebra and algebraic geometry. Suitable for students at all levels, this book provides practical applications, project suggestions, and insights into computer algebra to enhance conceptual knowledge.
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2."Commutative Ring Theory" by H Matsumura
“Commutative Ring Theory” Book Review: This book serves as a fundamental resource in both algebraic geometry and complex geometry. It offers an intriguing and profound exploration of each topic it covers. From dimension theory to advanced concepts like Ratliff’s theorems in primary chains, the book provides a comprehensive understanding. It discusses various types of rings, including Cohen-Macaulay rings, Gorenstein rings, Krull rings, and valuation rings. While the book is self-contained, a basic knowledge of modern algebra is recommended for beginners. Additionally, chapter-end exercises are included for each section, with selected hints provided at the end of the book to assist readers.
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3."Cohen-Macaulay Rings" by W Bruns and J Herzog
“Cohen-Macaulay Rings” Book Review: This comprehensive book delves into the significant topics of commutative algebra. It is a self-contained resource that covers introductory aspects of homological and combinatorial theory in Cohen-Macaulay rings and Gorenstein rings. It devotes a separate chapter to Hilbert functions, featuring Macaulay’s theorem and the associated numerical invariants. The general theory is applied to various contexts, including Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. The concluding chapters explore Hochster’s perspective on Cohen-Macaulay modules and their applications, such as the Pasnean-Szpiro theorem. With numerous solved examples and exercises, this book is highly valuable for graduate-level algebra courses and essential reading for researchers in commutative algebra, as it provides the only modern and comprehensive account of the subject.
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4."Introduction To Commutative Algebra" by Michael Atiyah
“Introduction To Commutative Algebra” Book Review: This book is primarily aimed at third-year undergraduates at Oxford University and provides a comprehensive introduction to Commutative Algebra. While it assumes a foundational understanding of general algebra, it is not meant to replace extensive texts like Zariski-Samuel or Bourbaki. Instead, the book focuses on specific central topics and delves deeper into areas like field theory. Compared to Northcott, this book covers more fundamental concepts and offers a distinct and clearer content. It aligns with modern trends in the field, placing emphasis on modules and localization.
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5."Introduction To Commutative Algebra" by Michael Atiyah | |

6."Commutative Algebra: An Introduction" by William Hoffman and Xiaohong Jia
“Commutative Algebra: An Introduction” Book Review: The primary objective of this book is to introduce fundamental concepts in commutative algebra and algebraic geometry. It explores intriguing research topics centered around Grobner bases, resultants, and syzygies. With the goal of preparing readers for future research in algebraic geometry, the book offers a comprehensive blend of definitions, proofs, and illustrative examples. Additionally, it demonstrates the practical use of software such as Mathematica and Singular. Striking a harmonious balance between theory and applications, each part of the book provides a clear understanding of the concepts. Certain chapters cater to readers familiar with small fluctuations algebra and algebraic geometry, offering guidance on captivating research areas. What sets this book apart is its unique amalgamation of essential methods and current research findings, equipping students with fundamental tools for both algebraic and geometric exploration, and fostering the initiation of specific research projects in related domains.
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7."The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra" by David Eisenbud
“The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra” Book Review: This book offers a comprehensive collection of fundamental examples and techniques in the field of algebraic geometry and commutative algebra. It showcases the application of syzygies across various geometric concepts, spanning from compilation to the examination of canonical curves. Drawing upon the author’s experience in graduate studies at Berkeley, Brandeis, and Paris, the text strikes a balance between algebra and geometry, making it accessible to students with basic knowledge in both disciplines. To further assist readers, the appendix provides a concise summary of flexible algebra, incorporating key examples and major results from diverse topics.
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8."A Course in Commutative Algebra" by Gregor Kemper
“A Course in Commutative Algebra” Book Review: This book provides a contemporary introduction to commutative algebra, making it an ideal textbook for a one or two-semester course or self-study. Written in a clear and accessible manner, it emphasizes the central concepts and results of the field. With a continuous focus on the geometric aspects, the book enables readers to develop a deeper understanding of the subject. While the theory is thoroughly explored, three chapters are dedicated to computational aspects, enhancing practical understanding. Abundant with examples and exercises, this book offers ample opportunities for readers to enrich their comprehension of the material.
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9."Commutative Algebra" by N S Gopalakrishnan | |

10."An Introductory Course in Commutative Algebra" by A W Chatters and C R Hajarnavis
“An Introductory Course in Commutative Algebra” Book Review: This concise book provides an introduction to various topics in commutative algebra, highlighting the practical examples and applications. It successfully blends solid algebraic theory with connections to number theory. Additionally, it explores problems from classical Greek geometry and delves into the theory of finite fields, which find significant applications in other scientific disciplines. The book covers essential subjects, including rings and Euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups, and finite fields. Its content serves as a foundation for future studies in abstract algebra and can even form the basis of a complete course.
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## 5. Introduction to Algebraic Geometry

1."Algebraic Geometry for Scientists and Engineers" by S S Abhyankar
“Algebraic Geometry for Scientists and Engineers” Book Review: This book is a valuable resource for graduate students and advanced undergraduates in mathematics, as well as for engineers and scientists specializing in computer science. Its chapters delve into the concepts of modern algebraic geometry, as well as algebraic curves and surfaces. The book provides in-depth explanations of topics such as rational and polynomial parameterization, functions and differentials on curves, branches and valuations, and resolution of singularities. Moreover, it emphasizes the practical applications and the relevance of algebraic geometry in various scientific fields and industries.
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2."Algebraic Curves" by W Fulton | |

3."Undergraduate Algebraic Geometry" by M Reid
“Undergraduate Algebraic Geometry” Book Review: This book provides a reader-friendly introduction to algebraic geometry, covering fundamental concepts such as plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. It emphasizes the connections between algebraic geometry and other areas of mathematics, including commutative algebra, topology, differential geometry, and number theory. The content is reinforced with numerous examples and exercises throughout the book. With its accessible approach, this book is suitable for undergraduate mathematicians seeking to delve into the field of algebraic geometry.
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4."Basic Algebraic Geometry" by I R Shafarevich | |

5."Introduction to Algebraic Geometry" by Justin R Smith
“Introduction to Algebraic Geometry” Book Review: This well-structured and self-contained book serves as a comprehensive introduction to linear algebra. It covers all the major topics, including classical results, affine varieties, varieties and schemes, projective varieties, and curves. Point-set topology is also thoroughly explained. The book concludes with appendices on algebra, commutative algebra, sheaf theory, and cohomology. To provide practical knowledge and real-world relevance, the book also explores the applications of algebraic geometry in fields such as robotics. With its broad coverage and accessible approach, this book is valuable for graduate and advanced undergraduate students of mathematics.
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6."Introduction to Algebraic Geometry" by Serge Lang
“Introduction to Algebraic Geometry” Book Review: This book offers a comprehensive exploration of Weil-Zariski algebraic geometry, encompassing its fundamental concepts, principles, and key aspects. The early chapters delve into the theory of places, algebraic varieties, absolute theory of varieties, product, projections, correspondence, and normal varieties. Subsequent chapters tackle topics such as divisors and linear systems, differential forms, theory of simple points, algebraic groups, and the Riemann-Roch theorem. Additionally, the book introduces Weil’s Foundations and incorporates the latest topics and recent advancements in the field of algebraic geometry. It serves as an invaluable resource for gaining a deep understanding of Weil-Zariski algebraic geometry.
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7."Introduction to Algebraic Geometry" by Brendan Hassett
“Introduction to Algebraic Geometry” Book Review: This book provides a comprehensive introduction to the fundamental concepts of algebraic geometry. It goes beyond theory and highlights the practical applications of algebraic geometry in diverse fields, including engineering, computer science, statistics, and computational biology. The text incorporates essential computational techniques and concepts that are crucial for modern processes. Numerous examples and algorithms are included to illustrate the content effectively. Suitable for advanced undergraduate and graduate students in mathematics, as well as researchers in various application areas, this book serves as a valuable resource for exploring the intersection of algebraic geometry and real-world applications.
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8."Introduction to Algebraic Geometry" by W Gordon Welchman
“Introduction to Algebraic Geometry” Book Review: This book provides a well-structured and comprehensive exploration of projective geometry, including its extension to higher-dimensional spaces. Beginning with an analysis of basic principles and foundations, it establishes a solid understanding for tackling advanced topics. The book delves into the theory of conics, metrical geometry, the applications of matrix algebra, and the study of invariants and covariants. It also emphasizes the practical applications of these techniques across various fields and subjects. With its rich content, this book serves as an ideal resource for mathematics students, professionals, and anyone interested in the history of education.
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9."An Introduction to Manifolds" by Loring W Tu
“An Introduction to Manifolds” Book Review: The book provides a comprehensive introduction to the fundamental theory of manifolds, covering key concepts, principles, and major topics. The chapters delve into various aspects of algebra, topology, analysis, and manifolds. The practical applications of these concepts in classical mechanics, general relativity, and quantum field theory are clearly demonstrated. The book equips readers with computational skills in simple spaces and includes a variety of problems and exercises with helpful hints for solutions. It is a suitable resource for undergraduate mathematics students, offering a solid foundation in manifold theory.
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10."Introduction to algebraic geometry" by J G Semple “Introduction to algebraic geometry” Book Review: The book provides an insightful overview of the geometric aspects of algebraic equations. It covers the latest advancements, modern techniques, and recent developments in the field of algebraic geometry. The book emphasizes the practical impact and applications of algebraic geometry in diverse areas such as plane curves, quadratic transformations, line systems’ geometry, and the projective characteristics of curves and surfaces. This text is a valuable resource for individuals seeking in-depth knowledge and understanding of algebraic geometry. | |

## 6. Algebraic Topology

1."Introduction to Functional Analysis" by A Taylor and D Lay
“Introduction to Functional Analysis” Book Review: This well-structured and self-contained book focuses on the theory of normed linear spaces and linear mappings. It serves as a fundamental resource for further studies in various areas of analysis. The chapters cover important topics such as Banach algebras, weak topologies and duality, equicontinuity, the Krein-Milman theorem, and the theory of Fredholm operators. Additionally, the book sheds light on the challenges encountered in linear algebra, classical analysis, and differential and integral equations. It is a valuable reference for students and researchers in the field of mathematics.
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2."Collectively Compact Operator Approximation Theory" by P M Anselone | |

3."Introduction to Functional Analysis" by A H Siddiqi
“Introduction to Functional Analysis” Book Review: This book provides a comprehensive overview of functional analysis, covering major aspects and important topics. The chapters explore fundamental theorems related to properties of functionals and operators, including the Hahn-Banach theorem, Banach-Steinhaus theorem, Open mapping theorem, and Closed graph theorem. The book also emphasizes the practical applications of functional analysis in areas such as operator equations, boundary value problems, optimization, variational inequalities, finite element methods, optimal control, and wavelets. It serves as a valuable resource for students and professionals looking to delve deeper into the field of functional analysis.
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4."Algebraic Topology" by Allen Hatcher
“Algebraic Topology” Book Review: This book provides a comprehensive introduction to algebraic topology, catering to students, researchers, professionals, and engineers interested in its development. It covers all the fundamental concepts, making it well-suited for self-study. The chapters delve into key topics such as fundamental groups and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory. Numerous examples and exercises are included throughout the book to enhance understanding. With its accessible approach, this book serves as a valuable resource for students and teachers alike in the field of algebraic topology.
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5."Algebraic Topology: A First Course" by William Fulton
“Algebraic Topology: A First Course” Book Review: This book offers a comprehensive exploration of algebraic topology, covering essential concepts and their applications across different areas of mathematics. The chapters delve into topics such as the relationship between homology and integration, plane domains, Riemann surfaces, winding numbers, degrees of mappings, and fixed-point theorems. The text also includes various applications of algebraic topology, such as the Jordan curve theorem and invariance of domain. With its broad coverage and practical examples, this book serves as a valuable resource for students of mathematics and science seeking a deeper understanding of algebraic topology.
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6."Algebraic Topology" by C R F Maunder
“Algebraic Topology” Book Review: This book provides a comprehensive introduction to basic algebraic topology with a focus on homotopy theory. Each chapter explores essential topics, including the construction of homology and homotopy groups of topological spaces, homotopy theory, CW-complexes, and cohomology groups associated with a general Ω-spectrum. The book emphasizes the applications of algebraic topology in solving various topological problems, such as surface classification and duality theorems for manifolds. Numerous examples and exercises are included throughout the text to enhance reader understanding. Suitable for undergraduate and first-year graduate students interested in homotopy or homology theory, this book offers valuable insights into the subject matter.
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7."Algebraic Topology" by Robert M Switzer
“Algebraic Topology” Book Review: This contemporary book explores the latest topics and unexplored aspects of homotopy and homology theory. Its comprehensive and precise chapters delve into homotopy groups of spheres and the computation of various cobordism groups. The book also covers stable homotopy theory, providing a solid understanding of its fundamental concepts, key methods, and applications across different fields. With its wealth of insights, this book serves as an excellent resource for professionals and experts in the field of algebraic topology.
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8."A Concise Course in Algebraic Topology" by J P May
“A Concise Course in Algebraic Topology” Book Review: This book is specifically designed for advanced graduate students and teachers in the field of mathematics. Its well-structured chapters provide comprehensive and self-contained coverage of various topics in algebraic topology. The later section of the book offers insightful glimpses into significant areas of algebraic topology. Notably, the book emphasizes the applications of algebraic topology in advanced fields such as geometry, topology, differential geometry, algebraic geometry, and Lie groups. Additionally, the book includes numerous problems that enable self-study and self-assessment for the readers.
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9."Basic Algebraic Topology" by Anant R Shastri
“Basic Algebraic Topology” Book Review: This book provides in-depth knowledge of real analysis, point-set topology, and fundamental algebra. It is divided into three sections that cover the introduction to algebraic topology, cell complexes and simplicial complexes, and covering spaces and fundamental groups, respectively. The book extensively explores topics such as Poincaré duality, De Rham theorem, cohomology of sheaves, and Čech cohomology. It also delves into higher homotopy groups, Hurewicz’s isomorphism theorem, obstruction theory, Eilenberg-MacLane spaces, and Moore-Postnikov decomposition. The content of the book is further enriched with numerous exercises and applications of algebraic topology. This book is highly suitable for graduate students, researchers, and working mathematicians in the field of algebraic topology.
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10."Elements of Algebraic Topology" by James R Munkres
“Elements of Algebraic Topology” Book Review: This book is designed to establish a solid understanding of algebraic topology for readers. The chapters are approachable, self-contained, and provide a detailed exploration of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, and duality in manifolds. The book also highlights the applications of algebraic topology in classical theorems of point-set topology. It serves as an excellent resource for beginners in algebraic topology, as it adeptly explains complex and advanced topics in a clear and efficient manner.
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## 7. Linear Algebra

1."Elementary Linear Algebra with Applications" by H Anton
“Elementary Linear Algebra with Applications” Book Review: This book offers a comprehensive introduction to linear algebra, designed specifically for freshman and sophomore students. The book focuses on presenting the core principles of linear algebra in a clear and easily understandable manner. It assumes a basic knowledge of calculus and provides numerous labeled exercises and examples, making it suitable for students concurrently studying calculus. These exercises not only reinforce understanding but also aid in skill development. While the use of calculators with linear algebra capabilities is optional, the book includes additional exercises at the end of each chapter to encourage further exploration of the topics covered.
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2."Linear Algebra and its Applications" by G Strang
“Linear Algebra and its Applications” Book Review: This book provides a student-friendly approach to teaching mathematics, with a focus on real-world applications. Students will encounter a significant shift in their understanding, particularly starting with the introduction of vector spaces. The book presents the theory in a clear and comprehensive manner, enabling students to explore both pure and applied mathematics. The exercises are carefully designed, incorporating numerous new problems and incorporating topics such as singular value decomposition. Additionally, the book introduces the connection between linear algebra and algorithms, including an introduction to complex numbers. Computer science students will find this book particularly beneficial, as it offers valuable insights and applications relevant to their field of study.
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3."Linear Algebra - A Geometric Approach" by S Kumaresan
“Linear Algebra – A Geometric Approach” Book Review: This book focuses on linear algebra and is intended for undergraduate mathematics courses. It is highly readable, clear, and concise. The main objective is to provide a clear view of the topic by emphasizing analytical geometry explanations. The book starts with simultaneous linear equations and their geometric interpretation, which serves as the central theme. It incorporates abstract algebraic concepts along with geometric notions, setting it apart from others. The content is designed to support students in their studies of multivariable calculus and differential geometry. The explanations and concepts are well-presented throughout the book, ensuring a solid understanding of the subject.
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4."Advanced Engineering Mathematics" by E Kreyszig
“Advanced Engineering Mathematics” Book Review: This well-designed book offers a comprehensive understanding of engineering mathematics, making it highly regarded among engineering students. It serves as a textbook in various engineering colleges due to its well-crafted problem sets, which facilitate the revision of fundamental mathematical concepts. The book has been thoroughly updated to reflect the advancements in the field, providing coverage of advanced topics such as linear algebra, vector calculus, partial differential equations, optimization, graphs, complex analysis, statics, and probability. By relating these topics to practical problems, students can develop a strong grasp of their applications.
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5."Introduction to Linear Algebra" by Gilbert Strang
“Introduction to Linear Algebra” Book Review: This well-described book offers a straightforward approach to linear algebra and introduces several breakthroughs within the subject. With its easy-to-read style, it covers all the essential topics necessary for a comprehensive understanding of the subject. The book focuses on teaching the theoretical foundations behind each concept, enhancing engagement with the material. It includes a wide range of challenging problems to strengthen comprehension. Organized into seven distinct sections, including differential calculus, graph theory, statics, Fourier transformation methods, linear programming problems (LPP), and computer graphics, this book provides a thorough overview of the subject.
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6."Linear Algebra: Step by Step" by Kuldeep Singh
“Linear Algebra: Step by Step” Book Review: This book provides a wealth of examples with step-by-step explanations for each topic. It simplifies the subject matter in a manner suitable for distance learning, offering concise solutions to the problem sets, which are readily available. At the end of each chapter, the book includes a range of miscellaneous exercises sourced from past papers and various university exams, allowing readers to enhance their confidence and skills. Additionally, it features short historical biographies of influential figures in the field of Linear Algebra. With its dynamic and engaging style, the book emphasizes understanding methods rather than rote learning, incorporating question-answer tests to solidify comprehension. Furthermore, it offers exclusive interviews with professionals who apply the topic in real-life scenarios.
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7."Linear Algebra and Its Applications" by David C Lay and Steven R Lay
“Linear Algebra and Its Applications” Book Review: This book presents Linear Algebra in a familiar and concrete manner, making it relatively easy for students to understand traditional Linear Algebra texts. It addresses the challenges students often encounter with abstract topics such as linear independence, spanning, subspace, vector space, and transformations. The book acknowledges that these topics require time to assimilate, and it provides clear and explanatory demonstrations to enhance accessibility and comprehension for students.
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8."Linear Algebra" by Georgi E Shilov
“Linear Algebra” Book Review: This book enhances the accessibility and usefulness of the course material. It starts from the elementary level and progresses seamlessly to cover advanced topics, making it suitable for both undergraduate and beginning graduate courses. The material is presented in a straightforward and simplified style. The book includes a wide range of problems and provides answers at the back, allowing students to practice and apply the techniques learned. It offers a valuable experience of the topic’s applicability and serves as a useful resource for both self-study and classroom learning.
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9."Linear Algebra For Dummies" by Mary Jane Sterling
“Linear Algebra For Dummies” Book Review: This book serves as a user-friendly guide to the topic, providing a clear understanding of the real-world applications of Linear Algebra in various fields such as programming and engineering. It covers the content typically found in a college-level linear algebra course, starting with basic operations and gradually delving into abstract concepts like vector spaces, linear transformations, determinants, and eigenvalues & eigenvectors. The book equips students with both theoretical knowledge and practical problem-solving techniques. It presents the information in a manner that not only teaches how to solve problems but also explains the underlying reasons and motivations behind each solution.
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10."Linear Algebra Done Right" by Sheldon Axler
“Linear Algebra Done Right” Book Review: This book on linear algebra is suitable for both graduate and undergraduate students. It takes a narrative approach, focusing on the main objective of understanding linear operations on finite-dimensional vector spaces. The book covers important topics such as linear maps, eigenvalues, and eigenvectors. It also explores inner-product spaces, leading to the finite-dimensional spectral theorem and its implications. The concepts in the book are presented concisely, with simple proofs, and each chapter includes a variety of interesting exercises to enhance students’ understanding and ability to manipulate linear algebra objects. The book includes updated examples that illustrate the key ideas of linear algebra, including product spaces, quotient spaces, and dual spaces. There are no specific prerequisites for this book, other than having mathematical maturity.
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11."A Concise Introduction to Linear Algebra" by Geza Schay G Za Schay Schay
“A Concise Introduction to Linear Algebra” Book Review: This book offers a comprehensive introduction to linear algebra, covering the essential mathematical concepts and exploring various intriguing applications, such as computer graphics. It includes a dedicated chapter on numerical methods and incorporates numerous exercises and examples utilizing MATLAB. Real-world problems are presented, along with detailed solutions accompanied by theoretical and mathematical explanations. With a focus on students and teachers in engineering and science disciplines, this book is thoughtfully designed to provide a thorough understanding of linear algebra and its practical implications.
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12."Introduction to Linear Algebra" by Lang
“Introduction to Linear Algebra” Book Review: This book provides a detailed introduction to linear algebra, discussing the relationship between geometry and algebra in the subject. It includes concrete examples of linear algebra notions such as linear equations, matrices, and Gaussian elimination. The book also covers topics like vector spaces, linear maps, scalar products, determinants, and eigenvalues. It contains exercises to enhance understanding. The target audience for this book includes students and teachers in engineering and science fields.
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13."Introduction to Linear Algebra" by Inder K Rana
“Introduction to Linear Algebra” Book Review: This book offers a comprehensive introduction to linear algebra, covering essential topics such as Euclidean space, systems of linear equations, determinants, vector spaces, and more. It explores advanced concepts including linear transformations, inner product spaces, orthogonal projections, orthogonal basis, isometries, and orthogonal matrices. The inclusion of numerous solved and unsolved examples helps readers deepen their understanding of the subject. Designed with students and teachers in engineering and science fields in mind, this book provides a solid foundation in linear algebra.
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## 8. Applied Linear Algebra

1."Linear Algebra" by K Hoffman and R Kunze
Book Review: This book provides a comprehensive introduction to linear algebra, covering both basic and advanced concepts. It offers intuitive explanations and includes examples that illustrate key ideas and demonstrate the application of various theorem results. The book covers a wide range of topics, including linear equations, vector spaces, linear transformations, polynomials, determinants, elementary canonical forms, rational forms, Jordan forms, inner product spaces, operators, and bilinear forms. Whether you are a beginner or have some background in linear algebra, this book is an ideal resource for anyone interested in the subject.
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2."Matrix Computations" by G H Golub and C F Van Loan
Book Review: This book is a useful resource for computer science students, providing valuable information on the mathematical foundations and algorithmic skills necessary for the development of numerical software. It covers a wide range of topics including matrix multiplication problems, parallel matrix computations, CS decomposition treatment, floating-point arithmetic operations, the Gram-Schmidt process, and concepts such as GMRES and QMR that address sparse unsymmetric linear system problems. The revised chapters in this book offer updated and comprehensive coverage of these topics, making it a highly useful textbook for anyone studying computer science and numerical computing.
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3."Functional Analysis" by G Bachman and L Narici
Book Review: The book covers a wide range of topics in linear algebra, advanced calculus, engineering, and physics, providing comprehensive information on both basic and advanced concepts. It includes chapters on inner product spaces, normed spaces, metric spaces, topological spaces, orthonormal sets, the Hahn-Banach theorem, and various other important topics. Each chapter is accompanied by exercises that allow readers to test their understanding and reinforce their knowledge. Additionally, the book includes a glossary of definitions and detailed proofs of theorems, making it a valuable resource for readers seeking a deeper understanding of the subject matter.
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4."Introductory Functional Analysis with Applications" by Erwin Kreyszig
Book Review: The book offers an introduction to functional analysis, covering its various applications and providing practical insights for the study of mathematics and natural sciences. It includes worked examples focusing on Hilbert space theory and Banach spaces, emphasizing important concepts, principles, methods, and major applications in functional analysis. The book delves into the study of spaces of functions and also explores topics such as differential and integral equations, calculus of variations, and quantum mechanics. It serves as a valuable resource for readers seeking a deeper understanding of functional analysis and its diverse applications.
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5."Applied Linear Algebra and Optimization Using MATLAB" by Rizwan Butt
“Applied Linear Algebra and Optimization using MATLAB” Book Review: This book offers a wealth of resources including m-files, practical examples, and applications to tackle problems related to linear algebra and optimization. It provides concise MATLAB programs for solving various problems such as systems of linear equations, matrices, vectors, and computer graphics. Additionally, the book comes with a CD-ROM containing figures, m-files for all the programs, and MATLAB simulations from industry. It strikes a balance between theoretical principles and practical applications, recognizing the importance of computational speed and accuracy. Designed for computer scientists, engineers, physicists, and students in computational courses, this book equips readers with the tools and knowledge to effectively apply linear algebra and optimization techniques.
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6."APPLIED LINEAR ALGEBRA AND MATRIX ANALYSIS" by Thomas S Shores
“Applied Linear Algebra and Matrix Analysis” Book Review: This book presents a cohesive approach that combines theory, computation, and practical applications of matrix and linear algebra, highlighting their interconnectedness. The experimental nature of linear algebra is emphasized through the inclusion of examples, computer exercises, and projects. The book does not rely on any specific hardware or software platforms, ensuring accessibility to a wide range of readers. Each chapter is supplemented with a set of exercises to reinforce learning. Designed for engineering and science students, this book is ideal for a one-semester course, providing a comprehensive understanding of matrix and linear algebra.
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7."HANDBOOK OF APPLIED LINEAR ALGEBRA" by SYLVESTER MURRAY | |

8."Linear Algebra: Pure & Applied" by Edgar G Goodaire
“Linear Algebra: Pure & Applied” Book Review: This book offers a thorough exploration of the essential definitions and theorems in linear algebra, with a focus on pseudoinverse and singular value decomposition using a matrix-oriented approach. The geometric aspects of linear combination, linear independence, and span are introduced within the context of Euclidean 3-space. The concept of vector spaces is extended to Euclidean n-space, and linear transformations are connected to matrices. The book also delves into various practical applications of linear algebra, such as Markov chains, electric circuits, facial recognition, computer graphics, quadratic forms, and conic sections. Additionally, it covers coding theory and least squares, with a specific emphasis on the system Ax=b. Whether you are a student, researcher, or professional, this book serves as an ideal resource for expanding your understanding of linear algebra.
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9."Linear Algebra over Commutative Rings" by Mcdonald
“Linear Algebra over Commutative Rings” Book Review: The lecture notes contained in this book cover the subject of linear algebra over commutative rings, as taught at the University of Oklahoma. The book begins with an introduction to matrix theory over commutative rings and then delves into the analysis of the structure theory of a projective module. This book is intended for use by students, researchers, and professors.
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10."THEOREMS AND APPLIED PRINCIPLES IN LINEAR ALGEBRA" by Prof. Febe Czetyrbok
“Theorems and Applied Principles in Linear Algebra” Book Review: This comprehensive book thoroughly explores theorems, principles, and practical applications of linear algebra in various real-world scenarios. It covers a wide range of topics, including population growth, stability analysis, signal processing, normal modes of oscillations, waves, Markov chains, and electrostatics. Whether you are a student or a professional seeking to understand and apply linear algebra concepts, this book serves as an invaluable reference.
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## 9. Linear, Matrix, Banach, Commutative, Lie Groups and Lie Algebra

1."Algebra II Workbook For Dummies" by Mary Jane Sterling
“Algebra II Workbook For Dummies” Book Review: This book is specifically designed to help readers solve various types of Algebra II problems through a systematic step-by-step approach. Each problem is accompanied by detailed explanations to enhance skills and boost performance. The topics covered include linear and quadratic equations, polynomials, inequalities, graphs, sequences, and sets. Additionally, the book provides comprehensive coverage of complex numbers, matrices, and algebraic operations with step-by-step solutions.
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2."Schaum's Outline of Linear Algebra, 5th Edition: 612 Solved Problems + 25 Videos" by Seymour Lipschutz
“Schaum’s Outline of Linear Algebra, 5th Edition: 612 Solved Problems + 25 Videos” Book Review: This book comprises a collection of 612 fully solved problems, along with examples and practice exercises, aimed at enhancing problem-solving skills. To provide additional support, the book includes 25 detailed videos featuring math instructors who expertly explain how to solve commonly tested problems. Organized in a topic-wise format, the book offers a comprehensive coverage of various concepts, accompanied by illustrative examples, solved problems, and ample practice exercises.
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3."3,000 Solved Problems in Linear Algebra (Schaum's Solved Problems Series)" by Seymour Lipschutz
“3,000 Solved Problems in Linear Algebra (Schaum’s Solved Problems Series)” Book Review: This book is a valuable resource for students seeking to enhance their understanding and problem-solving skills in linear algebra. The book presents a vast collection of 3,000 solved problems, covering a wide range of topics in linear algebra. The chapters cover fundamental concepts such as systems of linear equations, matrices, determinants, vector spaces, eigenvalues, and eigenvectors. Each problem is solved step-by-step, providing clear explanations and demonstrating various approaches. This book is a useful companion for students looking to practice and master the principles of linear algebra.
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4."Matrix Algebra: Exercises and Solutions" by David A Harville
“Matrix Algebra: Exercises and Solutions” Book Review: This book consists of 300 exercises and their corresponding solutions covering various topics in matrix algebra. It provides comprehensive summaries of important terminology and notation used in the subject. The book specifically addresses topics that are of special interest and relevance in statistics and related disciplines. It serves as a valuable guide for students, researchers, mathematicians, and statisticians seeking to deepen their understanding of matrix algebra. Additionally, the book promotes an interactive and engaging learning environment.
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5."Lie Groups and Lie Algebras for Physicists" by Susumu Okubo and Ashok Das
“Lie Groups and Lie Algebras for Physicists” Book Review: This book is specifically designed to benefit graduate students studying theoretical physics and quantum mechanics, as well as researchers exploring the applications of Lie group theory and Lie algebras in physics. It provides a comprehensive exploration of the inter-relationships between representation theories of Lie groups and their corresponding Lie algebras. The book offers valuable insights and knowledge in this specialized field of study.
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6."Lie Groups Lie Algebras And Some Of Their Applications" by Robert Gilmore
“Lie Groups Lie Algebras And Some Of Their Applications” Book Review: This book is specifically designed to provide upper-level undergraduate students with a clear understanding of Lie group theory and its applications in physics. It is tailored for modern physical theories where the calculations remain consistent across different fields, with variations only in terms of symbols and language used. The book introduces classical groups, continuous groups, Lie groups, and Lie algebras, covering topics such as root spaces, Dynkin diagrams, real forms, and contractions and expansions. To enhance comprehension, the book includes numerous exercises, solved problems, figures, and illustrations.
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7."Complex Semisimple Lie Algebras" by Jean-Pierre Serre and Glen Jones
“Complex Semisimple Lie Algebras” Book Review: This book offers a comprehensive introduction to the fundamental theory of semi-simple Lie algebras over the complex numbers. It covers various topics, including the general properties of nilpotent and solvable Lie algebras, Cartan subalgebras, root systems, and linear representations. The book also explores the connections between Lie algebras, complex groups, and compact groups. It serves as a valuable resource for understanding the key concepts and structures associated with semi-simple Lie algebras.
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8."Non-commutative Gelfand Theories: A Tool-kit for Operator Theorists and Numerical Analysts (Universitext)" by Steffen Roch and Pedro A Santos
“Non-commutative Gelfand Theories: A Tool-kit for Operator Theorists and Numerical Analysts (Universitext)” Book Review: This book serves as an introduction to the fundamental concepts of Banach algebras. It covers topics such as algebra with a polynomial identity (Pl-algebra) and provides selected examples that demonstrate the successful application of this theory in operator theory and numerical analysis. The book also explores non-commutative Gelfand theories, PI-algebras, Mellin techniques, and limit operator techniques. It is designed to help readers develop a solid understanding of analysis, functional analysis, and algebra. Suitable for 4th-year mathematics or physics students, as well as researchers in operator theory, numerical analysis, and the general theory of Banach algebras.
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9."Banach Embedding Properties of Non-Commutative $Lp$-Spaces" by Haagerup and Rosenthal
“Banach Embedding Properties of Non-Commutative $Lp$-Spaces” Book Review: This is a comprehensive and insightful book written by Haagerup and Rosenthal. It delves into the study of Banach spaces and their embedding properties in the realm of non-commutative $Lp$-spaces. The book explores various topics, including operator space theory, interpolation theory, and the geometry of Banach spaces. It provides a rigorous treatment of the subject matter, presenting theorems, proofs, and examples to support the discussions. This book is a valuable resource for researchers, graduate students, and mathematicians interested in the fascinating field of functional analysis and Banach space theory.
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10."Linear Algebraic Groups" by T A Springer
“Linear Algebraic Groups” Book Review: This book focuses on the theory of linear algebraic groups over algebraically closed fields. It provides a comprehensive coverage of the theory, including discussions on arbitrary fields, prerequisites from algebraic geometry and commutative algebra, and fundamental results on reductive groups. Designed for introductory graduate courses, this book serves as a valuable guide for studying linear algebraic groups.
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