Algebra Textbook 35.2

Algebra is a fundamental branch of mathematics characterized by the use of letters to represent numbers. An algebraic equation can be viewed as a balance, whereby actions taken on one side of the equation must also be reflected on the other side. The constants in these equations enable a broad range of mathematical representations, including real numbers, complex numbers, matrices, and vectors.

This field can be divided into two main areas: elementary algebra and abstract algebra. Elementary algebra encompasses basic concepts utilized widely in various disciplines such as mathematics, science, economics, medicine, and engineering. In contrast, abstract algebra delves into more theoretical aspects involving sophisticated numbers and equations, primarily employed in advanced mathematical contexts.

Below is an overview of the key topics typically covered within the study of algebra:

1. Numbers and Operations
2. Introduction to Equations, Inequalities, and Graphing
3. Systems of Equations
4. Functions
5. Linear Functions
6. Quadratic Functions and Factoring
7. Polynomials and Rational Functions
8. Exponents, Logarithms, and Inverse Functions
9. Matrices
10. Trigonometry
11. Conic Sections
12. Sequences and Series
13. Combinatorics and Probability
14. Complex Numbers and Polar Coordinates

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