Category Archives: Math and Technology

How I Redefine Addition – Baiting

Addition: https://www.tes.com/lessons/ZeGyGhKptzKMpA/addition

In my last blog, I talked about my plan for the semester, why I want to study abstract algebra, and some basic concepts involving mapping. In this blog, I will first provide some update on Modeling the Future, a team math competition we have been working on, and how I redefine addition in group theory. I will also talk about my plan for the science fair.

Modeling the Future is a competition that requires us to pick a potential cure for a pervasive disease. Then, we need to analyze the impact of the cure on the health insurance industry. After some discussion, we picked gene therapy for Alzheimer’s Disease (AD).

As the model builder of the team, I decided to find some of the variables, they are:

C: Cost of the Therapy, C>0;

P: Price of the insurance, P>0;

K: Percentage of the cost of the therapy covered by the insurance, 0<k<1. Since gene therapies are expensive, insurance companies are not likely to covered all the costs.

Q: Quantity of insurance sold. Or, the number of people purchase the insurance. We also assume Quantity equals demand as insurance companies sell as many insurance as demanded. There is no shortage. Q>0;

R: Risk of having Alzheimer’s Disease. 0<R<1;

A: Affordability. Given that the person purchases the insurance, has the disease, and the insurance covers only part of the expensive therapy, A indicates the percentage of customers who are willing to cover the uncovered expenses. 0<A<1;

https://www.coinwire.com/new-crypto-exchange-security-scoring-model-provides-insurance-rates-for-coin-owners

I will not talk about our model in the blog for this time as we are still in the process of finalizing it. The idea is, we need to build a supply curve of the insurance based on all these variables and some data we find, then we need to find a proper demand curve from the internet. Finally, we will use the demand-supply model from economics to decide the quantity and price of the insurance so that the company will make the most profit.

After something about MTF, let’s see what I have done to redefine addition.

Addition is one of the basic operations we use every day. In algebraic numbers, addition makes perfect sense, as we all know 1+1=2. However, the definition in Abstract Algebra or group theory is often unclear. In this more inclusive redefinition of addition, the idea applies to any set, group, or algebraic number.

If you are curious about why we need to prove all these properties, please visit here. The reason in short is we need to make sure our new definition doesn’t contradict with the conventional one. This source is particular helpful for me since it provides both the English and Chinese.

image
http://sparkandshine.net/en/algebraic-structure-primer-group-ring-field-vector-space/

So here are all I did in the past two weeks. Since Word Press does not support some of the math notations, so I decided to write them down in a Word Document and paste them here. In the following blog, I will provide another update for Modeling the Future and talk about how I plan to prove Lagrange’s Theorem and Fermat’s Little Theorem. As you may notice in my redefinition, some concepts in math really get abstract. However, this is the beauty of mathematics, as it is only through these abstract ideas that our knowledge system becomes more and more perfect.

References

Calder, K. (n.d.). Addition [Image]. Retrieved from https://www.tes.com/lessons/ZeGyGhKptzKMpA/addition

Group-like structures [Illustration]. (n.d.). Retrieved from http://sparkandshine.net/en/algebraic-structure-primer-group-ring-field-vector-space/

Herstein, I. (1990). Abstract algebra (2nd ed.). New York: Macmillan.

moneysense.ca. (2018, November 14). New Crypto Exchange Security Scoring Model Provides Insurance Rates for Coin Owners [Image]. Retrieved from https://www.coinwire.com/new-crypto-exchange-security-scoring-model-provides-insurance-rates-for-coin-owners

“代数结构入门:群、环、域、向量空间” [“An Introduction to the Algebra Structure: Group, Loop, Field, and Vector Space”]. Spark & Shine, 24 Feb. 2015, sparkandshine.net/algebraic-structure-primer-group-ring-field-vector-space/. Accessed 27 Jan. 2019.

Abstract Algebra: A NEW Start – Baiting

Retrieved from https://www.booktopia.com.au/abstract-algebra-gerhard-rosenberger/prod9783110250084.html

In this blog, I would like to briefly review my Fall semester and share my plan for the Spring.

In the past four months, I worked on Differential Equations and its related topics. Through following the MIT Open Course Ware, I learned different methods to solve DEs and their implications in real life.

Continue reading

The Fourier Series: An Introduction – Baiting

In the past few weeks and Thanksgiving break, I finished Unit II and moved on to Unit III. In this unit, I will primarily focus on the Fourier Series, Laplace Transformation, their connections with Differential Equations, and their applications in reality. In this blog, I will introduce the Fourier Series of periodic functions, including the trigonometry functions, the sin and cos. Continue reading

What Makes a Game Great – Dylan

This week we took a break from the technical practice and stepped in to a new realm. What truly makes a game fun to play? In class this week we talked about game design, less about creating a game, and more about designing one. In class we sat and discussed, what made our favorite games special, and what did we dislike about them?

Most people chose series of many games, or a single game that has been updated over several years, which allowed us to discuss our likes and dislikes over time.  People mostly chose well enjoyed series like Animal Crossing or Fallout. I personally chose the Pokemon DS games as well as World of Warcraft (WoW), two very different games. Continue reading

The Spring Model Continued – Baiting

ΦΘΙΝΟΥΣΕΣ ΤΑΛΑΝΤΩΣΕΙΣ(6)

In the past two weeks, I worked on Second Order Differential Equations with constant coefficients and learned more about the Spring-Damper Model. In this blog, I will provide a brief recap of the basic knowledge, and then provide further analysis of the same model. If you are interested in my last blog, please visit here. Continue reading

A Failed Attempt – Alina

This past week marks the end of the data collection period of my project. After I figured out how to scrape data generally on websites with simple structures in the last blog post, I had been experimenting with pulling data down from the Expedia website which was way more complex. However, as I tried to do this, I encountered some difficulties. At first, I decided to start experimenting with data that should be easily pulled to see if the code would indeed even work for this site. Therefore, I picked the date of the flight shown on the website. It had the tag class=”title-date-rtv“. I put this value into the code. Continue reading

The Trigonometry of Blasters! – Dylan

Blasters are such a staple to video games. Think back to space invaders, that game is almost completely just a simple blaster that moves side to side. That works great if you only want to shoot in a single direction, but what happens when you would like to aim in a full 360 degrees? Continue reading

Data Collection Continued – Alina

Updated Table

If you remembered from my last blog, my focus in this project has recently been on figuring out a way to scrape data off of the travel websites using code instead of doing it manually since it is indeed a tedious job. Of course, while working on the code, I have also kept with the primitive collecting method since data collection is the objective of this month’s work in my project. So here’s an updated version of my data table: Continue reading

Power-ups! – Dylan

What is the best part of a game to you? The sweet end music? The awesome rewards? Well, for me, it was always power-ups, there is nothing more staple in video games than a power up. I mean, who doesn’t know what a Mario mushroom looks like by 2018? That’s what I have been working on lately, making simple power-ups that make a game feel more alive. Continue reading