Sae's Notes

My cousin, when he was a toddler, would often combine the biggest number he would know and sandwich it together thinking it would be an even bigger number. I did this in my elementary years as well. "...gazillion billion billion million trillion..." Try to think of a really big number. The biggest number you can think of. Add however many zeroes you want but I bet you it will never be as big as something in mathematics called, "Graham's Number". Graham's number is a super big natural number designed by mathematician Ronald Graham. It is soooo big that if one was to write every single digit, it would not even fit within our universe. The scientific notation does not even come close to capturing the immensity of Graham's number. Instead, we use the "up-arrow" as the new system of notation. An arrow between two numbers means that the first number is multiplied by itself the second number of times.  So a 3 ↑ 3 is written as 3 * 3 * ...

As an undergraduate majoring in Economics and Political Science, I spend majority of my time studying and working on models that have been developed to explain our reality such as Game Theory. A quote by a famous statistician, George Box, has stuck with me since freshman year. "All models are wrong, but some are more useful than others." - George Box In many of my courses, we are introduced to a plethora of models that are used to explain our complex world and professors always attach critical assumptions. These models that we use are already too complicated and difficult to grasp but the truth is that models are just merely nothing but a simplified framework. So what is the purpose of models if they, at the end of the day, fail to explain the entirety of the world we live in with 100% accuracy? That may be true, but consider this. Let's say I am making a bet with my friend on whether the next coin flip will be a heads or tails. Basic probability will state th...

Among a plethora of concepts I have learned in my economics' classes, one of the more peculiar concept is the idea of utilities. I was introduced to this idea in my introduction class freshman year but was left scratching my head even more when delving into this concept in my intermediate microeconomics class last semester. The principle of utility is the capacity of a commodity (good and/or service) to give satisfaction or pleasure. It is simply a measure of how much satisfaction a consumer has from consuming a good or service. For example, imagine a very, very hungry individual craving a juicy hamburger. The very first hamburger consumed would heavily increase the utility of the individual. The second hamburger consumed would also increase its utility but not as the same effect as the first hamburger. Eventually, the individual would feel full and at a certain number of hamburger would have no effect in increasing its utility and/or may even decrease its utility. A utility ...

To take an AP or not to take an AP... Such a dilemma constantly left me preoccupied every time I had to begin looking at scheduling for my next year's classes. As I reflect upon the AP courses I have taken throughout my high school career, I began to observe a few key insights. To begin, I have taken a total of 13 AP courses. AP Human Geography AP Environmental Science AP Chemistry AP Biology AP Physics 1 AP US History AP World History AP US Government AP Psychology AP Calculus BC AP Statistics AP English Language and Composition AP English Literature Difficulty In terms of difficulty, I found that STEM courses usually were much harder. The easiest courses were your typical courses for incoming freshman such as Human Geography and Environmental Science. Now, do not be so discouraged over the difficulty of these courses. Your teachers are there to help so take advantage of them! Ask questions and do not hesitate in wanting to clarify a certain concept that ...