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.

Offered By

## About this Course

## Offered by

### Johns Hopkins University

The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.

## Syllabus - What you will learn from this course

**3 hours to complete**

## 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.

**3 hours to complete**

**3 hours to complete**

## 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.

**3 hours to complete**

**2 hours to complete**

## 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<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.

**2 hours to complete**

**2 hours to complete**

## Module 4: Systems of Equations

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.

**2 hours to complete**

## About the Algebra: Elementary to Advanced Specialization

This specialization is intended for students looking to solidify their algebra and geometry necessary to be successful in future courses that will require precalculus and calculus. Quantitiative skill and reasoning are presented throughout the course to train students to think logically, reason with data, and make informed decisions.

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