TEACHING TRUE MATHEMATICS, AP seeks the super easiest calculus possible on Earth-- polynomials as the only valid functions-- thus, and therefore, making derivative and integral as easy as Power Rule- 14 year olds master calculus. Because the Power Rule is merely add or subtract 1 from exponent so we can teach calculus in High School.

Only Math textbooks with the true numbers of mathematics-- Decimal Grid Numbers, not the insane silly Reals & Complex with their crank crackpot imaginary b.s.

I doubt the two math cranks Andrew Wiles and Terence Tao will ever understand mathematics for they continue to refuse to admit to even the most simple truths of mathematics-- slant cut of cone is Oval, not ellipse. A cylinder slant cut is ellipse, never cone.

Old Math is in a world of hurt for it does not even have the correct numbers of mathematics. Old Math was arrogant and ignorant starting year 1900 when Quantum Mechanics in physics took off and it means the world is discrete and not continuous. Yet the foolish bozos of Old Math stuck with their continuous Reals and even had the idiotic notion of going further out on the limb of madness with Cohen's continuum hypothesis, while Quantum Mechanics gave us a new age in physics with their discrete world. One would think the idiots of Old Math would finally look at physics and pay attention and learn something. No. They never did. And so today in October of 2023 we still have idiots of math teaching calculus with never a valid proof of Fundamental Theorem of Calculus, because Reals are not the true numbers of mathematics, the Decimal Grid Number System is the true numbers of math for they are discrete, and they make calculus, a billion, perhaps a trillion times easier to study , to learn to understand. In fact, we TEACHING TRUE MATHEMATICS, teaches calculus to 13 and 14 year olds. Because calculus is as easy as add or subtract 1 from the exponent.

TEACHING TRUE MATHEMATICS the fake calculus of Thomas Hales, Andrew Wiles, Ken Ribet, Ruth Charney, Terence Tao, John Stillwell with their fake "limit analysis" for a true proof of Fundamental Theorem of Calculus (FTC) has to be a geometry proof for the integral is area under a graphed function. This is why only a polynomial can be a valid function of math, for the polynomial is a function of the straightline Y --> mx + b. All the other so called functions have no straightline-- they are curves of continuum and cannot give a proof of the fundamental theorem of calculus.

The proof of FTC needs a empty space Discrete Geometry from one point to the next point so as to allow for the construction of a midpoint between point A to point B and thus to hinge up from A at the midpoint and to determine the next point B in the derivative. This is why Calculus is so enormously a tool for physics, as point A predicts point B.

Discrete Geometry is required for the proof of FTC and that requires the true numbers of mathematics be Decimal Grid Numbers, for they cannot be the continuum idiocy of Reals and Complex.

To make a half circle function in True Math, we have to go out to something like 10^6 Grid to make the points close enough together for the function visual to start looking like a half circle. But still there are holes in between one point and the next point to allow the existence of calculus.

On a downward slope function, we have a different graphics than the usual upward slope function. For the upward slope requires the midpoint in the empty space to predict the next point of the thin rectangle that occupies that empty space (see the graphics below and in my books TEACHING TRUE MATHEMATICS). In a downward slope function graph we still have those thin rectangles occupy the empty space for integral but we do not need to construct the midpoint, we simply shave away a right triangle that reveals-- predicts point B starting from point A on the other side.

TEACHING TRUE MATHEMATICS, AP seeks the super easiest calculus possible on Earth-- polynomials as the only valid functions-- thus, and therefore, making derivative and integral as easy as Power Rule- 14 year olds master calculus. Because the Power Rule is merely add or subtract 1 from exponent so we can teach calculus in High School.

Old Math makes and keeps Calculus as classroom torture chambers with their 1,000s of different functions yet the polynomial is the only valid function of math, and makes it super super easy to learn calculus

TEACHING TRUE MATHEMATICS, AP seeks the super easiest calculus possible on Earth-- polynomials as the only valid functions-- thus, and therefore, making derivative and integral as easy as Power Rule- 14 year olds master calculus.

If you come to me with a pathetic non polynomial especially that ugly trig functions, I have you go home and convert your nonsense to a polynomial. The Lagrange interpolation converts stupid nonfunctions like trig, into valid functions of polynomials.

TEACHING TRUE MATHEMATICS textbooks, makes calculus as easy as adding or subtracting 1 from exponent--only valid functions are polynomials contrast with mainstream--vomiting during exams, torture chamber and nervous breakdown by sado-masochist teachers. Old Math is thousands of different kook functions with thousands of different rules. AP Calculus is one function-- the polynomial for we care about truth in math, not on whether kooks of math become rich and famous off the suffering-backs of students put through a torture chamber that is present day calculus. If you come to math with a function that is not a polynomial, you have to convert it to a polynomial. Once converted, calculus is super super easy. But math professors seem to enjoy torturing students, not teaching them. Psychology teaches us that when a kook goes through a torture chamber and comes out of it as a math professor-- they want to be vindictive and sado masochists and love to torture others and put them through the same torture chamber that they went through. AP says-- stop this cycle of torture and teach TRUE CORRECT MATH.

TEACHING TRUE MATHEMATICS textbooks, makes calculus as easy as adding or subtracting 1 from exponent--only valid functions are polynomials contrast with mainstream--vomiting during exams, torture chamber and nervous breakdown by sado-masochist teachers. Old Math is thousands of different kook functions with thousands of different rules. AP Calculus is one function-- the polynomial for we care about truth in math, not on whether kooks of math become rich and famous off the suffering of students put through a torture chamber that is present day calculus. If you come to math with a function that is not a polynomial, you have to convert it to a polynomial. Once converted, calculus is super super easy. But math professors seem to enjoy torturing students, not teaching them.

Old Math calculus textbooks like Stewart are more than 1,000 pages long and they need that because they have a mindless thousand different functions and no valid proof of Fundamental Theorem of Calculus. AP's calculus is less than 300 pages, because we have a valid geometry proof of Fundamental Theorem of Calculus which demands the only valid function of math be a polynomial function. We can teach calculus in Junior High School for the calculus is reduced to adding or subtracting 1 from the exponent. The only hard part of calculus in New Math is to convert the boneheaded function into a polynomial that was brought to the table by the boneheaded math professor who thinks that a function does not need to be a polynomial.

AP calculus transforms the calculus classroom. It is no longer vomiting during exams. No longer a torture chamber for our students of youth, and no longer a nightmare nor nervous breakdown for our youthful students, who, all they ever wanted was the truth of mathematics.

Teaches that derivative predicts next point of function graph--silly Old Math has derivative as tangent to function graph unable to predict. The great power of Calculus is integral is area under function graph thus physics energy, and its prediction power of the derivative to predict the next future point of function graph thus making the derivative a "law of physics as predictor". Stupid Old Math makes the derivative a tangent line, while New Math makes the derivative the predictor of next point of function graph. No wonder no-one in Old Math could do a geometry, let alone a valid proof of Fundamental Theorem of Calculus, for no-one in Old Math even had the mind to realize Calculus predicts the future point in the derivative.

TEACHING TRUE MATHEMATICS-- only math textbooks with a valid proof of Fundamental Theorem of Calculus--teaches that derivative predicts next point of function graph--silly Old Math has derivative as tangent to function graph unable to predict. This is why calculus is so important for physics, like a law of physics-- predicts the future given nearby point, predicts the next point. And of course the integral tells us the energy. Silly stupid Old Math understood the integral as area under the function graph curve, but were stupid silly as to the understanding of derivative-- predict the next point as seen in this illustration:

From this rectangle of the integral with points A, midpoint then B

______
| |
| |
| |
---------

To this trapezoid with points A, m, B

B
/|
/ |
m /----|
/ |
| |
|____|

The trapezoid roof has to be a straight-line segment (the derivative)
so that it can be hinged at m, and swiveled down to form rectangle for
integral.

Or going in reverse. From rectangle, the right triangle predicts the next successor point of function graph curve of B, from that of midpoint m and initial point of function graph A.

My 134th published book

Introduction to TEACHING TRUE MATHEMATICS: Volume 1 for ages 5 through 26, math textbook series, book 1 Kindle Edition
by Archimedes Plutonium (Author)

The only math textbooks with the actual true numbers of mathematics-- Decimal Grid Numbers arising from Mathematical Induction, not the arrogant and ignorant Reals with their continuity program while physics via Quantum Mechanics teaches us space is discrete, not continuous.

AP

The only math textbooks with the actual true numbers of mathematics-- Decimal Grid Numbers arising from Mathematical Induction, not the arrogant and ignorant Reals with their continuity program while physics via Quantum Mechanics teaches us space is discrete, not continuous.

AP

The only math textbooks with the actual true numbers of mathematics-- Decimal Grid Numbers arising from Mathematical Induction, not the arrogant and ignorant Reals with their continuity program while physics via Quantum Mechanics teaches us space is discrete, not continuous.

And we make Calculus super super simple and easy by recognizing Polynomials are the only **valid functions** in mathematics. This allows us to obtain all derivatives by subtracting 1 from exponent and all integrals by adding 1 to exponent.

Question: what if the function is not a polynomial like the ugly and hairy and ghoulish trig functions? Easy, we can convert any fake function like trig functions into being polynomials over a given interval, and modern day computers can easily do the Lagrange Interpolation. In Old Math, the bizarre horror story math, their calculus textbooks like Stewart are over 1,100 pages long. In new simple calculus, we need only 300 pages to cover all of Freshman Calculus, in fact we teach calculus in High School, so simple and easy it has become.

AP