Here are innovations to accelerate, clarify and simplify logic lesson in or outside of mathematics. Three common notions of rules being obeyed, disobeyed or not disobeyed are employed to make key ideas simpler to understand and explain. The word logic stems from the Greek logos for thought. The explanation or derivation of results in algebra and geometry, and higher mathematics, depends on the use of implication rules, one at a time, and one after another, to directly or indirectly arrive at conclusions, one at a time and one after another. All routes followed here require a mastery of the algebra - shorthand notation for recording and developing thoughts on paper in a way mostly better seen and read silently than spoken or read aloud in full.
Some routes are easier than others to follow or explain.
Calculus or Why Slopes Calculus in the first instance is the subject of slope related computations and interpretations for linear and nonlinear functions. The reversal of slope computation justifies formulas in subjects wherever computation is required. Why slope examples in Volume 3 will show students and instructors that learning and teaching in calculus and beyond has been harder than need-be. Algebraic reasoning appears at many levels in calculus. Traditional calculus courses do not put the easiest level first.