Professional Algebra Homework Help
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Pre-algebra is a known term used for the course of middle school mathematics in United States. It is taught in seventh to ninth grades as an elementary subject. Pre-algebra is designed to cover basic mathematics such as Basic Operations, Ratios and Percentages, Basic Geometry, Basic Statistics and Probability, etc. Basic Algebra includes various topics of elementary mathematics like natural numbers arithmetic, integers, fractions, decimals, negative numbers, factorization of natural numbers, properties of operations, simple roots and powers, evaluation of expressions, basics of equations, rules for invariant manipulations of equations, basic geometry like area, volume, etc. Pre-algebra introduces with basics of mathematics and enables a student to join mathematics in higher classes. Although, it is an essential part of course curriculum, but it has been prepared to develop necessary skills and interest in mathematics so that the children can choose mathematics as an optional subject. Although it has a vast range of very basic mathematics but it gives enough knowledge of basic calculations, prime factorization, LCM GCF, integers their operations, manipulation of powers roots, fractions decimals including their manipulation, basic operations, , ratios percentages explanations, examples,practice problems, basic geometry, shapes angles, lines, transversals, circles, similar figures, perimeter circumference, area of polygon, triangle, circle, square and irregular shapes, area formulas, 3d objects (prisms, cylinders, cones, spheres), volume of prisms, cylinders pyramids, cones, spheres, surface area, Pythagorean theorem, basic statistics probability, mean, median, mode range, stem leaf plot, histograms, box whisker plots, scatter plots correlation, evaluating data making conjectures, probability, complementary mutually exclusive events, predicting vs. observing probability, compound events, basic counting principle, arithmetic, geometric exponential patterns, evaluating algebraic expressions, combining like terms, distributive property, solving one-step equations, two-step equations and more complex equation with variables, multiplying dividing of monomials, binomials, polynomials, graphing x-y points, graphing horizontal and vertical lines, slope intercept form, solving multiple equations by graphics. Pre-algebra has a connection with our daily life and enables a student to understand the basics of engineering and technological subject easily as well as it helps the students to develop his personal interest in science and mathematics to build a career in mathematics and concerned subjects.
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- Algebra is a major branch of pure mathematics and is concerned with the study of the rules of relations and operations and the constructions as well as concepts arising from them, including terms, polynomials, equations and algebraic structures. It has been divided in two subjection, Elementary algebra and complex algebra. Elementary algebra introduces the concept of variables representing numbers and is studied in secondary education. In algebra, statements based on variables are manipulated using the rules of applicable operations like addition, subtraction, etc. to solve the equation including other reasons. Algebra has its root in ancient Greek mathematics. They created geometric algebra to study the situations of objects. First authentic work on algebra is a book series named Arithmetica written by Diophantus (300 AD) who is identified as “the father of algebra”. In these books, Diophantus described various solutions to solve algebraic equation. Later it was developed by Arabic/Islamic mathematicians. In current history algebra was grown in Europe and become an essential branch of mathematics and engineering. Algebra can be sub-sectioned in following categories:
- Elementary algebra
- Abstract algebra or modern algebra
- Linear algebra
- Matrix algebra
- Universal algebra
Elementary algebra deals with the properties of operations on the real number system, their variables/constants the rules of mathematical expressions and equation. Abstract algebra is concerned with groups, rings and fields while the Linear algebra is a study of vector spaces and their properties. Besides this, the term algebra is also used to indicate various algebraic structures like algebra over a ring, algebra over a set, Boolean algebra, F-algebra and F-coalgebra, relational algebra, sigma algebra and T-algebras. Algebra has a vast range which encompasses various topics of mathematics such as Linear equations, Determinant, Binet formula, Cramer’s rule, Gaussian elimination, Strassen algorithm, Matrix theory, operators of matrix (addition, subtraction, multiplication, transformation ), Characteristic polynomial, Eigenvalue, eigenvector and eigenspace, Hamilton theorem, Matrix inversion, invertible matrix, Symmetric matrix, Congruence relation, Hermitian matrix, Antihermitian, Perronâ Frobenius theorem, List of matrices, Matrix decompositions (including Cholesky, LU, QR, Singular, Higher-order singular value, Schur), Spectral theorem, Computations, Vectors, Scalar multiplication, Linear combination, Linear span, Linear independence, Coordinates vector, Multilinear algebra, Tensor and treatment of tensors (classical, intermediate and component-free treatment), Tensor algebra, Exterior algebra, Symmetric algebra, Clifford algebra, Geometric algebra, transformation, Projective space and geometry.
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