Mathematics Without Accidents

This book introduces calculus in Galois fields. Everywhere is digital, quantum. We see that the concept of "continuity" is excluded from Nature. The Curry-Howard correspondence, in mathematics, indicates that there is also no continuity in analysis, in mathematics. Calculus can become beautiful and useful! Forget the old contradictions, they are just contra. This is explained here, in terms of Why and How, to motivate discussions. The final book will teach the basis of the techniques of differential and integral calculus in mathematics, with a minimum of wasted effort -- entirely made as a DIY guide, with programmed instruction giving alternative readings, so that it goes deeper, directly, into subjects that are simple but critical to know, like type theory, and study by yourself, at your own pace, without distractions. The idea for it grew out of teaching its basic principles to kindergarten students, reaching Calculus at the end of elementary school. Later, in college level instruction, in many universities and organizations, this allowed an accelerated progression also in higher mathematics, theoretical computer science, chemistry, biology, physics, software, and even English (e.g., a verb is a function).