In our introductory lecture, Dr. Robert Snellman lays the foundation for understanding algebra by tracing its historical roots and highlighting its power as a language for representing quantities using variables and symbols. He illustrates the real-world relevance of algebraic expressions, equations, and inequalities through practical examples—such as calculating sales commissions and wages. The lecture concludes with a comprehensive discussion of inequality notation and solving techniques, emphasizing the importance of understanding when and why inequality signs flip during algebraic manipulations.

In lecture two, we study linear equations in two variables, focusing on their graphical representation in the Cartesian coordinate system and key characteristics such as slope, x-intercepts, and y-intercepts. We examine how to convert equations into slope-intercept form (y = mx + b) for easier graphing, and discuss practical applications through a physics example involving velocity and time. The lecture concludes by emphasizing how mathematical models, despite their simplifying assumptions, help us understand and approximate real-world phenomena.

In lecture three, we learn the fundamental rules of algebraic operations, focusing on exponents and their properties. We examine key concepts including zero exponents, negative exponents, and fractional exponents (roots), demonstrating how these rules apply to solving equations and real-world applications. Dr. Snellman includes practical examples of exponential relationships in compound interest calculations and drug half-life modeling, introducing the concept of functions.