Learn Algebra by Derek Banas

About this course

Algebra stops feeling like a set of random rules when you understand what each symbol is doing and why every step is allowed. This free online course is designed to help you move from uncertainty to clarity by building strong fundamentals and then connecting them to the kinds of problems you meet in school, entrance exams, and everyday reasoning. You will learn to translate ideas into expressions, interpret variables correctly, and work through solutions in a way that is organized, checkable, and repeatable.

You will strengthen core skills like using the distributive property, solving equations and inequalities, and handling the special rule changes that happen when you multiply or divide by a negative number. From there, the course expands into two-variable relationships and lines, helping you see how algebra links to geometry through slope, rate of change, and equations determined by points. As you progress, you will gain the ability to solve systems using different methods and choose the approach that best fits the problem, whether you are working with standard forms or visual solution regions.

The course also introduces powerful tools from matrix algebra, determinants, inverses, reduced row echelon form, and Cramer’s Rule, giving you a practical foundation for more advanced math and applications. You will become more comfortable with polynomials, factoring strategies, radicals, and quadratic equations, while learning how discriminants and key theorems reveal what kinds of solutions to expect. Functions and graphing are treated as a way of thinking, not memorizing: you will practice domains, symmetry, fundamental graph shapes, and transformations so you can predict how changes in an equation change the picture.

To round out your skills, you will work with logarithms, exponential equations, and important properties that simplify complex-looking expressions. You will also explore conic sections, building fluency with circles, parabolas, ellipses, and hyperbolas, including how to identify key features from equations. Throughout the course, targeted exercises and word problems reinforce each idea so you can apply algebra confidently to ratios, real scenarios, and multi-step reasoning—without getting lost halfway through.