Although, I have loved Math since I was in 7th grade, it wasn't until I got to later High School Math, Trig, Calculus, and Statistics that I started to see just how fascinating Math really is!
I will get to in a little bit what really fascinates me about Math. People say that Math was so easy until they started to add the "x" and it gets more and more complicated. While I agree every new topic adds a level of complexity, I will argue that the more advanced Math gets, the EASIER life gets in some aspects. For example, the multiplication sign is saving us time from having to add the same thing multiple times. The geometric series is there to help us save time adding up things that increase or decrease by an amount. Counting techniques help us to find unique ways to listing an individual item or groups without having to list them all. The theta symbol makes it a lot easier to see an angle like the red octagon sign on the road is a stop sign.
Let's say you bought a musical instrument and you only learned how to play one note or even a few notes. You wouldn't say, this is so boring and useless, all this instrument does is play a note and I don't care how that note sounds. And that's how I look at it whenever people say, "This is so boring/useless/I don't care about what x" and other variations of the same complaint.
The very first time I ever watched Jurassic Park I thought, "What a boring movie. It's just this guy outside explaining to everyone dinosaur eggs". My little brother said, "That's not even the beginning of the movie!" And that's how I see whenever people bringing out something similar about "finding x". One thing I find so beautiful in Math is moving different pieces around, finding how something is expressed in a different way, substitutions, variable transformations, and how you start to see movement. In our high school math, we are only used to either seeing a line or a specific shape curve. Well, in Calculus we are introduced to polar coordinates (which allow us to draw flowers and other cool stuff as well), and parametric equations which allow us to draw more unique curves. We then get into 3D and we use the same parametric equations to see how an object moves over time and we get to see how things interact in space. Also, in Statistics, we are introduced to the concept of random variables and we get to see how different variables interact with one another, then we analyze two variables working together, and we make transformations out of them to get easier to work with as well as to increase accuracy.
But in order to get there, we have to learn the basic stuff that get us there. And there is a lot to learn for us to be able to appreciate it and get to that level. But once you start putting in the pieces, you start to be the beauty of it all and it becomes a beautiful musical piece. And it's the same with learning a language as well.
One of the things that made me fall in love with Mathematical Statistics (MathStat) is the concept of variable substitutions and transformations.
An example of this is when we learned about the U-substitution in Calc 2.
The idea is we take what would be a difficult to solve integral, convert it to a simpler integral, and we can either transform back to the original variables or we can change the integration limits to the variable u and solve for that.
When you get into 3-D, it's it's even more fascinating. We use the Jacobian method of transformation to transform the surface into a whole new coordinate system. (U,V)
In Mathstat, we use this not only to make numbers easier to work with but we want to get a clear view of what's going on with that image and the image we get doesn't give us a clear view of what is happening there. And I find the process of converting from the (X,Y) coordinate system to the (U,V) something so cool!!!! And in Mathstat,the probability distribution of the (X,Y) world is the same as a different probability distribution of the (U,V) world.
If you look at the top row, before the bivariate transformation, those circles (we call them level curves in Calc 3) are very crooked.
And for me, anything of this world is in the (X,Y) coordinate system that we see and take for granted and everything spiritual we can't see is in the (U,V) coordinate system. And when we beat ourselves up too much, we are not looking at ourselves in the (U,V) coordinate system which is how God sees us. And what's cool is that there are infinite dimensions!!!!
And I close with one of my favorite quotes from Marianne Williamson often attributed to Nelson Mendela:
Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light, not our darkness that most frightens us. We ask ourselves, 'Who am I to be brilliant, gorgeous, talented, fabulous?' Actually, who are you not to be? You are a child of God. Your playing small does not serve the world. There is nothing enlightened about shrinking so that other people won't feel insecure around you. We are all meant to shine, as children do. We were born to make manifest the glory of God that is within us. It's not just in some of us; it's in everyone. And as we let our own light shine, we unconsciously give other people permission to do the same. As we are liberated from our own fear, our presence automatically liberates others.
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