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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.

Course 1 of 3 in the Algebra: Elementary to Advanced Specialization

### Syllabus

**WEEK 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.

**WEEK 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.

**WEEK 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

**WEEK 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.

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