Algebra describes relationships between quantities and lets us rewrite those relationships without changing their meaning. Functions describe how an output depends on an input, while sequences describe values arranged or generated in an order.
This chapter begins with fractions, ratios, and rates because they are common ways to compare quantities. It then develops equations, powers, logarithms, inequalities, graphs, composition, inverse functions, and repeated updates. These ideas appear throughout mathematics, science, computing, and everyday reasoning. Later chapters apply them to vectors, probability, calculus, and machine learning.
The emphasis is on valid steps and clear interpretation. Small examples make each operation visible, and substitution or numerical checks help confirm that a rewritten expression still says what the original expression said.
The previous chapter introduced the notation used here. Ordinary arithmetic is the only other prerequisite.