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FUNDAMENTAL CONCEPTS OF ALGEBRA
Jan 12, 2009 · A textbook on number systems, number theory, polynomials, and trigonometry. Covers the basic arithmetic and algebraic properties of natural numbers, integers, rational …
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Basic Algebra with Applications - 6th Edition - Open …
Dec 6, 2022 · Download a free PDF of this open textbook by Ivan G. Zaigralin, covering all concepts expected in a basic algebra textbook. See reviews, table of contents, and ancillary materials for instructors and developers.
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Math Handbook of Formulas, Processes and Tricks
Chapter 1 Basics Algebra Graphing with Coordinates Graphs in two dimensions are very common in algebra and are one of the most common algebra applications in real life. Coordinates The …
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Algebra
Branch of mathematics
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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. It is a generalization of arithm…
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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication. Elementary algebra is the main form of algebra taught in school and examines mathematical statements using variables for unspecified values. It seeks to determine for which values the statements are true. To do so, it uses different methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It provides methods to find the values that solve all equations in the system at the same time, and to study the set of these solutions. Abstract algebra studies algebraic structures, which consist of a set of mathematical objects together with one or several operations defined on that set. It is a generalization of elementary and linear algebra, since it allows mathematical objects other than numbers and non-arithmetic operations. It distinguishes between different types of algebraic structures, such as groups, rings, and fields, based on the number of operations they use and the laws they follow. Universal algebra and category theory provide general frameworks to investigate abstract patterns that characterize different classes of algebraic structures. Algebraic methods were first studied in the ancient period to solve specific problems in fields like geometry. Subsequent mathematicians examined general techniques to solve equations independent of their specific applications. They described equations and their solutions using words and abbreviations until the 16th and 17th centuries, when a rigorous symbolic formalism was developed. In the mid-19th century, the scope of algebra broadened beyond a …
Wikipedia
Famous algebraists
He is regarded as the founder of modern algebraic notation, and his work In artem analyticem isagoge introduced the use of letters to represent both known and unknown quantities, as well as the rules for manipulating them.
François Viète
He is credited with the invention of analytic geometry, which combines algebra and geometry, and his work La Géométrie introduced the Cartesian coordinate system and the notion of functions.
René Descartes
He is one of the pioneers of calculus, which is a branch of algebra that deals with limits, derivatives, and integrals, and his work Principia Mathematica contains many applications of algebra to physics and astronomy.
Isaac Newton
He is one of the founders of abstract algebra, and his work Réflexions sur la résolution algébrique deséquations introduced the concepts of groups, fields, and permutations, as well as the Lagrange's theorem and the Lagrange resolvent.
Joseph-Louis Lagrange
He is considered the prince of mathematics, and his work Disquisitiones Arithmeticae is a landmark in algebraic number theory, while his contributions to modular arithmetic, polynomial equations, and quadratic forms are also significant.
Carl Friedrich Gauss
Who was the driving force in developing Algebra towards the end of the 16th century?
A
Francois Viete
B
Jennifer Anniston
C
Angelina Jolie
Timeline
2000 BC
Babylonians solve linear and quadratic equations
1637 AD
Descartes introduces coordinate geometry and algebraic notation
1770 AD
Euler develops the theory of algebraic functions
1832 AD
Galois establishes the connection between algebra and group theory
1854 AD
Cayley invents matrix algebra and linear transformations
1872 AD
Dedekind defines algebraic numbers and ideals
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The History of Algebra almost started from the 9th century and the contributions of mathematics of different countries are infinite.
Algebra emerged in Europe in the late 1500s. François Vieta, a French mathematician, is credited as the father of algebra. He was the first to use letters to represent unknown numbers in equations.
Algebra was first used by the ancient Babylonians and Egyptians. They used it to solve problems in trade, taxes, and measurements.
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Gauss was a prodigy and a polymath who made many discoveries and advances in number theory, algebra, geometry, analysis, and physics.
Carl Friedrich Gauss
Galois was a genius who died young, but left behind a legacy of groundbreaking results in group theory, field theory, and the theory of equations.
Évariste Galois
Noether was a pioneer and a leader in abstract algebra, especially in ring theory, invariant theory, and the connections between algebra and physics.
Emmy Noether
Hilbert was a giant of mathematics who formulated many influential problems and conjectures in various fields, including algebra, geometry, analysis, logic, and foundations.
David Hilbert
Lagrange was a prolific and versatile mathematician who made important contributions to number theory, algebra, analysis, mechanics, and astronomy.
Joseph-Louis Lagrange
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