This course is intended for students looking to create a solid algebraic foundation of fundamental mathematical concepts from which to take more advanced courses that use concepts from precalculus, calculus, probability, and statistics. This course will help solidify your computational methods, review algebraic formulas and properties, and apply these concepts model real world situations. This course is for any student who will use algebraic skills in future mathematics courses. Topics include: the real numbers, equalities, inequalities, polynomials, rational expressions and equations, graphs, relations and functions, radicals and exponents, and quadratic equations.

# Algebra: Elementary to Advanced - Equations & Inequalities

This course is part of Algebra: Elementary to Advanced Specialization

Taught in English

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Instructor: Joseph W. Cutrone, PhD

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9 quizzes

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## There are 5 modules in this course

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.

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2 videos5 readings2 quizzes

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.

#### What's included

3 videos5 readings2 quizzes

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<b, when the real number a lies to the left of the real number b on the coordinate line. From this definition, other inequalities naturally follow.

#### What's included

2 videos4 readings2 quizzes

Recall that a single linear equation in two variables is an equation of the form Ax + By = C, where A and B are both nonzero real constants. There are infinitely may ordered pairs that satisfy a single linear equation. In applications however, we are often interested in finding a single ordered pair that satisfies a pair of linear equations. In this section, we discuss several methods for solving this problem.

#### What's included

2 videos4 readings2 quizzes

Congratulations on reaching the final exam! This final assessment will be cumulative in nature, covering all aspects of the course. Use this final as a teaching tool: justify what you know and identify areas for improvement. Use scrap paper as you take this final. Try to use any formula sheets or outside resources as a tool and not a crutch. Check your answers before you submit. After the test, review any incorrect answers to find your mistakes. Try to separate "silly" mistakes from the more substantial mistakes in understanding. Good luck!

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1 quiz

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Johns Hopkins University

Johns Hopkins University

Johns Hopkins University

University of North Texas

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