Algebra: Elementary to Advanced Equations & Inequalities

Module 1: The Structure of Numbers

Georg Cantor was a famous mathematician who formalized the notion of set theory, which had a profound impact on research and teaching Sets and the relations between them for a basis for teaching the concept of the structure of Real numbers Starting with the concept of a natural number, {1,2,3, } the whole numbers, integers, rationals, and real numbers are developed, as well as operations defined on them Properties of the real numbers are formalized and applied as well

Module 2: Linear Equations

A linear relationship between two variables occurs when there is a constant increase or constant decrease in one variable with respect to the other. Linear equations have the property that any change in the independent variable results in a proportional change in the dependent variable Many physical situations can be modelled using a linear relationship When data is visualized on a scatterplot, we often are interested in the line of best fit or the regression line Linear equations occur frequently in all mathematics and their applications in physics and engineering, partly because non-linear systems are often well approximated by linear equations

Module 3: Solving Inequalities

The relative position of two points on a coordinate line is used to define an inequality relationship on the set of real numbers. We say that a is less than b, written a