Syllabus of Math Essentials

This syllabus is for those starting college who are either anxious to survive or eager to excel in higher math classes; high school students learning calculus for the first time and want to succeed; anyone who has had a bad experience with higher math before and wishes things had gone differently; those with a decent grasp of algebra, trigonometry, and logarithms, who might not yet recognize their readiness for higher math; those simply curious about advanced mathematics.
Linear algebra and calculus team up to address both static and dynamic systems. Together they lay the foundations for all branches of mathematics. We have made careful, sometimes difficult decisions not to include many very nice but non-essential or more complicated ideas, such as Determinants, Eigenvalue Decomposition (EVD), Singular Value Decomposition (SVD), Multivariable Calculus, Partial Differential Equations (PDEs), etc.
Instead, we focus solely on concepts sufficient and necessary for solving linear ordinary differential equations, calculating the length of a complex vector, and functions' inner products. In essence, this syllabus serves as a math survival kit for anyone entering college. While this syllabus won't replace math classes or comprehensive learning, it will serve as a catalyst to make math feel a lot more natural and enjoyable for learners of all levels.
Think of it as your map and compass, guiding through the intricacies of your mathematical journey. Within these pages, by simplifying complex math concepts into manageable pieces of 15 key ideas and three major patterns, we get to see not only the stars but also the constellation. It's like learning a game of chess. Through clear visuals and a focus on essentials, we blend geometric intuition with algebraic reasoning in a simple, clear, and straightforward way. Our goal is to make math feel more intuitive rather than intimidating.
Whether you're new to linear algebra, calculus, or seeking fresh insights in math, this syllabus will offer you a bird's eye view of the key concepts in higher mathematics.