Foundations of Algebra: Sets, Variables, and Equations

Many students struggle with algebra because the foundational concepts of numbers and operations are confusing. This course builds a rigorous base, starting with the very definitions of mathematical structure. By the end of this course, you will have a solid understanding of how algebraic expressions are constructed, how variables function, and how to confidently apply the rules of arithmetic and algebra to simplify expressions and solve introductory equations. What you'll learn: * Understand the classification and properties of number systems, including integers, rationals, and real numbers. * Define and apply set theory concepts, including set notation, operations, and relationships between sets. * Master the order of operations and the properties of equality and inequality used in algebraic manipulation. * Practice translating word problems into algebraic expressions and modeling simple real-world scenarios with variables. * Apply the distributive property and combining like terms to simplify complex algebraic expressions. * Solve linear equations and inequalities using systematic, step-by-step written methods. The course begins by defining fundamental mathematical structures like sets and number systems. It then progresses through the rules of arithmetic and algebra, culminating in the application of these rules to solve basic linear equations and inequalities using clear, written explanations and practice problems. This course is designed for absolute beginners, high school students, or anyone seeking a thorough review of pre-algebra and foundational algebra concepts. No prior algebraic knowledge is required. Start building your essential mathematical toolkit today.