A Work in Progress.
Why calculus? Why not? I find this course of study to be the most balanced and interesting of those in general maths studies. If you know it, then you are good to go in most every standard competence of mathematics.
Calculus is the study of change and it exists to make definitions of the infinitesimal. One of the common fun lessons in math is that of Zeno’s Paradox. These people do an excellent job of teaching and explain at all levels. You don’t have to understand it all but keep considering the paradox itself.
Where to start? Counting is the standard place to begin math. It is an old habit and we have evidence of animals keeping count.
Numbers, discrete to themselves, are constant. This means that is a number has a name, like 2, sqrt(5), e , then it is a constant. Note: Infinity has its own rules and zero is here to break things.
There is only so much you can do with numbers. Mostly, put together or take apart. You can rearrange them as well. It’s really all the same thing.
It can be a challenge.
Check out the arcade for number games to help make it fun.
Seriously, if you can’t add fractions, play Whole until you can do pretty well. The game is fun.
Sets become super important down the road. At this juncture, they are good for building definitional clarity within mathematics. The problems are most straightforward but you need to be precise in how you express your maths for it to make sense. They slick became everything even though they were a late bloomer.
Math is Fun has good notes. https://www.mathsisfun.com/sets/sets-introduction.html Continue onto the next section on Venn Diagrams for more that goes with this video, starring Ratatouille.
Numbers represent a quantity. Distance is a quantifiable element. Once numbers were tied to distance, shape became formalized in the language of mathematics.
Geometry is the study for which our academic education is the epicenter. To this day, it inspires many and vexes others. It is tired formulae and proofs of why a line is straight until one sees the world in a Platonic sense.
Measurement and numbers became locations. Really, it was locations that led to this point for it was the stars and where they where that got the counting to this point but now they are going back to being locations but in the most abstract sense as defined by coordinates. The first thing this did was to make some old impossible geometry problems solvable and then it brought on graphing. Functions, in whatever variation they had been known before, quickly evolved into a tentpole of study.
The importance of physics in the course of our mathematics creation called Calculus is always known in name through Newton but the key steps in reasoning always seemed to be made by those solving the way the universe worked. They were the ones to count time and quantify movement.