Re-Introduction to Algebra with Intuition: Algebraic Foundation for Calculus, Computer Science, Physics, and Engineering

As a high school or college student, you were probably taught a boatload of math, mostly algebra. However, you may feel like what you have learned is just a bunch of jumbled up ideas and a myriad of mind-numbing ways to manipulate numbers and symbols. Making matters worse, you may feel that you can hardly explain why you ever learned those things, or how any of the concepts you learned are related to each other. If you feel that way and are yearning to understand the intuition behind what you have learned, and how all of those seemingly unrelated concepts are related, this book is for you. While studying math, you may have bumped into many unexplained conundrums. Why do we get a positive number when we multiply two negative numbers together? What’s the practical use of functions, operators, equations, composition, inverse, roots, and parameters, and how they fit into a bigger picture? Why do we need so many different types of functions, like linear, quadratic, power, polynomial, exponential, logarithmic, trigonometric, etc., and what makes each different from the others? Why do we need complex numbers and vectors when we already have real numbers? What does a matrix really represent and why is matrix multiplication so weird? What’s the real-world significance of dot products and cross products, and why isn’t simple multiplication sufficient? Where can you actually see an infinite series in real life? Is there any method to this madness? If questions like these have been bothering you, you will find immense satisfaction in the narrative provided in this book showing intuition behind algebraic concepts, and how one concept naturally leads to another. That’s not all. If you are even remotely interested in computer programming, this book builds a step-by-step connection between algebra and programming, providing a fresh look at both fields. You will be pleasantly surprised by the similarities between the two fields and how they enrich each other. Similarly, this book will serve as an excellent companion to algebra textbooks, especially those on Pre-Calculus, and will help you decipher algebraic models used in Physics and Engineering. This book offers numerous real-world examples, illuminating pictures, and intuitive explanations to show you the real meaning and hidden relationships in algebra.