Foundations of Advanced Mathematics: Algebra and Calculus

Many foundational technical fields rely heavily on a strong understanding of advanced mathematics. Are you ready to master the core concepts of algebra and calculus that underpin modern science and engineering? By the end of this course, you will be able to confidently manipulate matrices, understand the behavior of complex functions, and apply differential calculus techniques to solve real-world optimization problems, preparing you thoroughly for advanced academic work. ### What you'll learn * Understand the properties of relations and functions, including injectivity, surjectivity, and finding inverse functions. * Master matrix algebra, including operations, determinants, and finding the inverse using adjoints. * Analyze systems of linear equations using matrix inversion techniques, a core concept in modern computing. * Apply the concept of limits and continuity to determine function behavior over various intervals. * Calculate derivatives using first principles and standard rules, including the product, quotient, and chain rules. * Practice using derivatives to find tangents, normals, and determine maxima and minima for optimization problems. This course begins with foundational concepts in set theory and functions before moving into the practical techniques of matrix algebra. The final sections focus on the core principles of differential calculus, emphasizing continuity and applications of the derivative. All concepts are reinforced with written explanations and practical exercises. This course is ideal for high school students, self-learners, and anyone preparing for standardized academic exams who needs a thorough, text-based introduction to advanced mathematics. No prior advanced math knowledge is required. Begin building your indispensable mathematical foundation today.