Products related to Algebra:
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A History of Abstract Algebra : From Algebraic Equations to Modern Algebra
This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether.Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory.Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations.The book also describes the relationshipbetween Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s.Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic.With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
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Linear Algebra : A Modern Introduction
David Poole's innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics.Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning.Theoretical, computational, and applied topics are presented in a flexible yet integrated way.Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking.Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.
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Algebra
This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use.We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem.However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution.If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later.The book is divided into sections devoted to different topics.Some of them are very short, others are rather long.Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property.But let us first agree on notation.
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Schaum's Outline of Modern Abstract Algebra
Confusing Textbooks? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's Outlines.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams.Schaum's is the key to faster learning and higher grades in every subject.Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format.You also get hundreds of examples, solved problems, and practice exercises to test your skills.This Schaum's Outline gives youPractice problems with full explanations that reinforce knowledgeCoverage of the most up-to-date developments in your course fieldIn-depth review of practices and applicationsFully compatible with your classroom text, Schaum's highlights all the important facts you need to know.Use Schaum's to shorten your study time-and get your best test scores!Schaum's Outlines-Problem Solved.
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What is the difference between algebra and sigma-algebra?
Algebra is a collection of subsets of a set that is closed under complementation and countable unions and intersections. It is a structure used in set theory and abstract algebra. On the other hand, a sigma-algebra is a more specific type of algebra that is also closed under countable unions and intersections, but it is defined on a probability space and is used in measure theory and probability theory. In essence, a sigma-algebra is a more specialized and stricter form of algebra, with additional properties that make it suitable for use in probability and measure theory.
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What does this notation about vector spaces in linear algebra tell me?
This notation tells you that a vector space is a set of elements (vectors) that satisfy certain properties, such as closure under addition and scalar multiplication. The symbol "V" represents the vector space, and "F" represents the field over which the vectors are defined (e.g., real numbers or complex numbers). The notation also indicates that the vectors in the space can be added together and multiplied by elements of the field, and that these operations satisfy specific properties, such as associativity and distributivity. Overall, this notation provides a concise way to represent the fundamental properties of vector spaces in linear algebra.
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How do you determine the dimension of vector spaces in linear algebra?
In linear algebra, the dimension of a vector space is determined by finding the maximum number of linearly independent vectors in that space. This can be done by creating a basis for the vector space, which is a set of linearly independent vectors that span the entire space. The number of vectors in the basis is the dimension of the vector space. Another way to determine the dimension is by finding the number of elements in any basis for the vector space, as all bases for a given vector space have the same number of elements.
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Is relational algebra difficult?
Relational algebra can be difficult for some people, especially those who are new to the concept of relational databases and set theory. It involves understanding various operations such as selection, projection, join, and union, as well as the rules and properties associated with these operations. However, with practice and a solid understanding of the underlying principles, relational algebra can become more manageable. It is important to approach it with patience and persistence, and seek out resources and guidance to help grasp the concepts.
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Algebra Dominoes
Algebra dominoes include a 28 piece set on thick plastic dominoes. Dominoes come in a collectors tin for storage. Children will love the feel of real dominoes as they complete the algebra matching game. Ages 8
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Human Algebra
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Pre-Algebra
Boost grades and the understanding of early algebra concepts that can make or break the long-term study of algebra through middle and high school and on to college.Textbooks and classes cover so much over months at a time that the details at different stages of learning are passed up with expectations of students remembering all the details of every stage of learning.This 6 page laminated reference guide is expertly authored and designed to offer a quick detailed overview of all stages of early algebra learning.So all concepts can be seen at a glance before reading texts or listening to instructors, during study and homework, or further into the class for refreshing before quizzes and exams.It can help the math-rusty parent homework coach as well to get the algebra gears turning again so you can be the homework hero.Topics covered include: Number Systems; Operations; Algebra; Concepts; Translating Words into Algebraic Statements; Algebraic Equations; Algebraic Inequalities; Coordinate; Plane Geometry; Ratio; Portion; Percent.
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Linear Algebra
Linear Algebra is intended for a one-term course at the junior or senior level.It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form.The book also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem.The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants, and linear maps.However, the book is logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.
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What is boolean algebra?
Boolean algebra is a branch of algebra that deals with variables that can only take on the values of true or false, often represented as 1 or 0. It is used to analyze and simplify logical expressions and is fundamental to the design and analysis of digital circuits and computer systems. Boolean algebra operations include AND, OR, and NOT, which are used to manipulate and simplify logical expressions. It provides a formal mathematical framework for reasoning about logical statements and is widely used in computer science and engineering.
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How can one learn algebra?
One can learn algebra by starting with the basics such as understanding the fundamental concepts and rules. It is important to practice solving equations and working through problems to build a strong foundation. Utilizing resources such as textbooks, online tutorials, and practice problems can also help in mastering algebra. Seeking help from teachers, tutors, or study groups can provide additional support and guidance in learning algebra effectively.
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"Isn't Algebra 1 on there?"
Yes, Algebra 1 is on the list. It is an essential course for students to build a strong foundation in mathematical concepts and problem-solving skills. Algebra 1 covers topics such as linear equations, inequalities, functions, and graphing, which are fundamental for higher-level math courses and real-world applications.
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How can one simplify Boolean algebra?
One can simplify Boolean algebra expressions by using various laws and theorems such as the commutative, associative, distributive, identity, and complement laws. By applying these laws systematically, one can rearrange and simplify the expression to its simplest form. Additionally, using Karnaugh maps can help visualize and simplify Boolean expressions by grouping terms with common variables. Practice and familiarity with these laws and techniques are key to simplifying Boolean algebra effectively.
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