This brief guide to a range of fundamental, basic algebra could be a helpful catalyst to understanding for high school and first-year college students. Parents can find their own path to insight here, while teachers may find some classroom capsules to enliven lectures.
The author tries very hard, almost with exasperation, to avoid any definition without motivation, any explanation with linkage to intuition. Azad excitedly brings light to imaginary numbers as the arithmetic of rotation, natural logarithms in terms of time to grow, and exponentials as growth over time. The Pythagorean Theorem and Euler’s Formula round out the work with a brief, visual tease pointing towards calculus with a rainbow of infinitesimals hinting at exhaustive methods for area and volume.
For many that are feeling lost in their initial foray into algebra, this earnest and enlightening work will demystify through explanations not often seen in textbooks and frequent diagrams.
Tom Schulte is an Instructor at Oakland Community College.