What is Advanced College Math with Calculus?
Mathematics is a way of thinking. One side of human brains does all of it.
Mathematics is a closed functional system, defined by is axioms (core rules).
Like any closed functional system, the power of the proof, and with it, the power of prediction is possible.
Mathematics inherently contains the power of prediction as long as you stay with a given set of axioms. Like a game, it is only that game if you follow all the rules set for it (the axioms).
Change a single rule, and you are playing a different game.
There are several Domains in mathematics, achieved by making a minor change in an axiom.
The Real Mathematics Domain is the one taught to you in school. You know, with infinitely small points, infinitely long lines, etc.
The calculus first appeared as differential calculus. Later, integration became possible, through the efforts of Newton and Leibnitz.
Mathematics is not a college, class, university, book, government funding, research program, website, magazine, pamphlet, search engine, magazine, or journal.
The same can be set about science.
Neither uses consensus.
Certain branches of mathematics lose their ability to predict, due to the use of random numbers. These include probability math, random number mathematics, and statistical mathematics as examples.
Einstein was good at math, but lacked the ability to describe a tensor properly. He need this for his theories of relativity. He wrote to a friend who was good at math, and Einstein learned how to construct the tensor properly so he could complete his theories.
Tensors are used in engineering to describe stress of materials, calculate aerodynamic or hydrodynamic drag, in game engines, graphics libraries, so-called 'AI' software that generates or analyzes images, etc.
Calculus has many uses. The speedometer on your car is a differential machine. A single revolution on the output shaft of your transmission means the car moves a certain fixed distance. The speedometer, by measuring RPM on this output shaft, and countering with a spring providing an opposing force, can give speed, rather than the distance travelled. (Speed is the differential of distance over time).
An accelerometer is likewise is a differential machine, this time measuring acceleration (acceleration is the differential of the change of speed, or speed changing by time). Acceleration is a differential of a differential.
Integral calculus allows you to 'reverse engineer' these values, by taking acceleration, and integrating a speed value out of it, and again by integrating speed into distance traveled in that time. When you convert 60mph to a "mile a minute", you are actually conducting an integration in a simple way, using the hour as the average (60 minutes in an hour).
Often described as 'higher mathematics', it really is just mathematics. Anyone can learn it if they want to.
Grade school is supposed to give you an understanding of arithmetic, geometry, trigonometry, calculus, algebra, etc.
I find most high school graduates are very poor at arithmetic (they can't even make change properly), are poor at algebra, and have almost no understanding of geometry, trigonometry, or calculus.
I find COLLEGE kids in about the same level of understanding of mathematics.
There are exceptions, of course.
