Purpose: To teach the student how to learn mathematics strictly on his own. Because of Artificial Intelligence and other resources, MATLAB for one example, it is possible to learn anything. But there are some exceptions, amongst which Mathematics is one of them. To learn Mathematics, one needs certain jumping off points.
That is exactly what this web site is intended to do, provide jumping off stagings.
The first topic to be explored is the very basis of all Mathematics, the idea of algebra. Without algebra there is no solving of problems. Then there is no calculus, therefore no engineering.
There is no one algebra, there are many of them. But if one learns just one algebra he can learn just about any algebra.
The combination of an algebra with an underlying set of elements is often referred to as a Topology.
What we refer to as arithmetic is an algebra that comes with a very complicated topology, the decimal system of numbers.
Why do we try to teach young children such a very complicated algebra?
Boolean Algebra is THE algebra that should be taught at the kindergarten and
1st Grade level. For one, the only values to be dealt with are zero and 1.
To implement Boolean Algebra, I have written a program using MATLAB as the primary computer language. This app is called… The Venn Dashboard.
To make it understandable to young children I have put forth considerable effort to write this app, which is for sale on this website. The Price is $100, My target buyer is a business or a person of authority like a school principal, any entity involved with K-12 education.
As I explained to my credit card commerce provider, a company named Stripe…
This app is sold without license provision. The buyer of The Venn Dashboard is free to resell this app to anyone he wishes to, to as many people as possible and at any cost he wants to resell it for. If I made just one sale and that sale resulted in widespread distribution that would be just fine with me. What I am after here is promulgation more than anything else.
Stripe approved my application. Today, in fact.
The Venn Dashboard presents 3 circles intersecting each other as much as possible. Then the player is asked to classify each of the resultant sections as to whether it is either inside or outside each of the 3 circles. There are, of course, rules to how these sections are classified.
Then, this game is turned into a Boolean Algebra where the circles represent sets, and all the structure and rules of an algebra come into play.
Say, the these very young students play this game for a year. I am certain they will know what an algebra is. And this is a very powerful start!
Now, which is the more powerful algebra?… Arithmetic or Boolean.
Well, Arithmetic has all that baggage with the decimal system and an unlimited number of elements to deal with, but it is only good for balancing one’s checkbook or doing accounting.
Boolean Algebra has legs! It can run computers. It is also the basis for Artificial Intelligence.
Then it will come time to solve linear equations starting at the very beginning with 1 equation in I unknown. This is as late as 8th grade in most schools.
So, how do you do that? Well, on each side of an equation are groups of elements multiplied together, separated by a plus or minus sign. Each of these groups is known separately as a term. Each element in the term is a cofactor.
- So, for each term on the right side of the equation add the additive inverse for each term that has the unknown cofactor to BOTH sides of the equation. What will happen is that all the terms that have the inverses of the unknown factor will be on the left side of the equation. And those same terms having the unknow cofactor will simply vanish on the right side of the equation because they will become equal to zero.
- Then do the same on the left side of the equation for all the terms that do NOT have the unknown cofactor. Now terms the inverses of terms NOT having an unknown cofactor will be on the right side of the equation and those terms WITHOUT the unknown factor will be on the right side of the equation.
- Now apply the Distributive Law to the left side of the equation.
- Next, on the left side of the equation the cofactor of the unknown will be a grouping of values (in parentheses) which can be reduced to a single value. The right side of the equation has all values which can be reduced to a single value. Use a calculator to reduce these values.
- Now divide both sides of the equation by the multiplicative inverse of the cofactor of the unknown.
Now the unknown is equal to a single value.
Using these steps is the map for solving any equation in one unknown.
Observe it is the inverses both Additive and Multiplicative that has done all the heavy lifting here, NOT the decimal system.
In Arithmetic algebra just reverse the sign of an element to get the Additive inverse and for the Multiplicative Inverse of an element just divide the element into 1, with a calculator, of course.
The reader should use his calculator or MATLAB to test out this process to teach himself.
And under the Lesson Plan it took 8 years to get this far??
Note that an inverse of an inverse of an element is that element itself.
Now I am going to change things up a bit and talk about another topic. For over at least 300 years no one has been able to solve the Riemann Hypothesis. And we are not going to solve it here!
But recently I came across an article on the internet which I found especially intriguing because it shed light on a most interesting aspect of the Riemann Hypothesis, that the solution has everything to do with prime numbers. A prime number is a whole number greater than 1 that has exactly two factors (or divisors): 1 and itself.
You see there are many known solutions to the RH, that is NOT the issue. These solutions account for the non-trivial solutions of the zeta function. The question is are these solutions always on the critical line? Or are they always on the critical line.
Well, the set of RH solutions can also split out prime numbers in graph form from non-prime numbers. This is truly amazing that these solutions can do this!
There is something in the very nature of these solutions to do what the author of the article is demonstrating. I think the author is onto something!
I shall see and follow his progress, and you can follow along with me in future articles on this website.
What is the zeta function? What are the non-trivial solutions? These are topics we are going to study. For now, is just the opening salvo.
But we must prepare for the day when the solution to the RH arrives. This is also a great opportunity to learn all about MATLAB.
Make no mistake, the solution to the RH is a key to the universe, something angels already know.
This is going to be a fun trip even if the secret to the RH is never resolved, a possibility!
So, there you have it… The Venn Dashboard is the alpha or beginning and the RH is the omega or end of our endeavor.
Between the alpha and omega will be several articles dealing with mathematics. Each month will have a new entry…
How Matrices came into being. Do you know that there is an algebra of matrices? How eigenvalues and eigenvectors work,
There will be a one-page app that allows the user to learn Trigonometry by moving a dial around a unit circle.
Pattern Recognition is an important aspect of AI. We will use Pattern Recognition to build an efficient Basic Assembly Language Multiplier.
An app to allow the user to place a derivative at any point on any graph. Very useful for understanding Differential Calculus.
App to find the area under the Gaussian curve. This is all about Integral Calculus,
An app to pay homage to the Fourier Series.
An Introduction to Quantum Mechanics.
How to find the value of financial Instruments based on market volatility. And the winning of the Nobel Prize in Mathematics in 1974.
Statistics.