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Thought-Process to Discover Knowledge
Algebra is introduced in the exactly relevant form -- anchors the algebra in the numerical arithmetics.
• numbers are symbols representing value of quantities. The same can be represented with letters or symbols called variables
• numerical expressions are expressions with numbers and arithmetic operations between them. Algebraic expressions are similar.
• numerical equations are statement of equality between two numerical expressions. Algebraic equations are similar. The above is used to explain polynomials and algebraic identities.
A revolutionary and ingenious formal foundation (at 9th grade level) is given in the topic "Foundation of Algebra in Numerical Arithmetics". This course is a simplified version of that designed for 6th to 8th grades.
(click for the list of lessons in this topic)
Algebra: Variables and Expressions
Algebra is introduced in the exactly relevant form -- anchors the algebra in the numerical arithmetics. It covers the following
• numbers and variables
• numerical expressions and algebraic expressions
• numerical equations and algebraic equations.
This course is designed for 6th to 8th grades. Other advanced readers are directed to the revolutionary and ingenious formal foundation in the topic "Foundation of Algebra in Numerical Arithmetics".
Polynomials - Basics
Welcome to the simplified and refreshingly new explanation to what are polynomials. Algebraic expressions are expressions with constants, variables and arithmetic operations between them. Polynomials are simplified form of algebraic expressions. To understand how this simplified form is useful, please read the lesson.
The classification of polynomials based on the following are also discussed.
• number of variables (polynomial of n variables)
• number of terms (monomials, binomials, polynomials of n terms)
• power of variables (linear, quadratic, cubic, polynomials of nth power)
Like numbers or numerical expressions, polynomials can be added, subtracted, multiplied or divided. This page provides a simple-though-process to understand these.
Basic Algebraic Identities
Identities are statements equating two expressions. In this, standard algebraic identities are introduced and explained in a simple-thought-process.