To me, math is more than a class to take or a homework assignment to complete. It is more than just symbols on a page or numbers to enter into a calculator. It is a language — a way of communicating things about how the world behaves and why. It is a way of thinking, revealing hidden connections and guiding one to answers. And it is a way of life — one that resonates with me and that brings me joy. Throughout my entire life, I have felt a very strong love for and connection to math. In my math classes, everything seemed to click, and I noticed that when presented with a new technique, I didn't just memorize how to do it and then apply it to problems when the "rules of math" said I had to. Instead, I found I could understand how the technique worked and how it could be used for a variety of applications. In fact much of math is connected, but the connections are not always apparent at first glance. When I take the time to explore what is going on behind the scenes, connections that were previously hidden become apparent, and it is so cool to see. In classes I have taken, we have discussed ways in which math applies to the real world. Especially in fields like calculus and number theory, there are so many fascinating applications, and math no longer has to just be theoretical, but exists tangibly and has real effects. The more math I learn, the more I realize how foundational math is to our world, and how without math, almost nothing could function as we know it. Beginning in my childhood, through my school years and now into college life, math has been a subject of fascination for me. It has kept me company, taught me new things, and created a framework through which I can view the world. A life full of math is the perfect life for me.

Without math, society as we know it could not exist. Math is foundational to our way of living, but its role in our lives is often overlooked. Every day, we rely on roads and bridges to get us places, phones to tell us the way to go, and messaging services to keep in touch with those we care about. And yet, without math, these things would be impossible to rely on. Without math, the creation of roads and bridges would be inefficient and dangerous. It would be impossible to know ahead of time how much material would be needed, which would lead to delays and losses. In addition, the capacity and strength of structures such as bridges are carefully calculated before anything is built to ensure safety. Without these calculations, unsafe structures could be built, leading to disaster. Our phones rely on math to function. Throughout their lives, these devices perform millions of computations and are guided by complex algorithms. Without a firm understanding of math, it would be impossible to create the algorithms necessary for phones to function. Messaging systems such as texting are often taken for granted. They are incredibly convenient, almost instantaneous, and offer immediate access to contacts around the world. Most people implicitly assume that these systems guarantee security, and most systems do in fact protect the messages sent. However, this encryption could not exist without discoveries made in the field of number theory. Almost wherever one turns, the world is running on math. I love to learn math because every new thing I learn shows me something new about how the world works, and because new connections within the realm of math appear seemingly out of the blue. At first, when I'm learning a new topic, things can seem a little random, with no apparent rhyme or reason. However, the more I learn, the more things make sense. Seeing the dots connect and all the different things fall into place is incredibly satisfying, and it makes me want to keep learning more so I can see even better how everything connects. Another reason I love to learn and do math is because of the thrill of accomplishment. Some problems are very difficult for me, and can even feel impossible. They take a lot of struggle to work through and often require several sessions of work. It can be very discouraging to come up against problems like this, but the joy of finally discovering a strategy and then the solution is worth all the work. Math also feels very intuitive to me, and it feels like a "language" that my mind speaks. When I am presented with a math problem, I am able to understand how to proceed to work through the problem and solve it, even if I haven't solved a problem like it before. When solving a problem, the math seems to fit into my head and flow smoothly, and it feels natural. When I'm doing math, I feel like I'm doing what I'm made to do.

Listening is a way to not only learn, but to grow closer to those around you. When you listen, you are allowing new information to enter your body. As you gain new information, you are able to grow as a person. For example, I am going to college next year, and there are a lot of decisions to make, like what school I go to, who I share a room with, and what extracurricular activities I do. I have asked my parents and friends for advice, and have listened to what they say. They have gone through these scenarios before, and have wisdom I don't yet have. Therefore, by listening to them, I am able to make wiser decisions. Besides gaining wisdom from the experience of others, listening also helps me to strengthen my relationships. Listening to someone shows that you care about that person and what they have to say. It shows that you think that they have worth and that you care about them enough to set aside other things and listen. I want to make my relationships with my friends and especially my family stronger, so I try to especially make time to listen to them. I am easily distracted, which means that if I have my laptop or phone out, it is easy for me to think about something else in the middle of the conversation, so I end up not really paying attention. So, I try to specifically have times where I am not using technology where I can genuinely listen to others. I have found that this helps me to be open to listen, and improves my relationships.

Giving is an expression of value. If you are willing to give up time, money, or other resources to something, then it means that you value whoever or whatever you are giving to. Giving to someone tells them "I think that you have worth." It is important to give to those near you, whether it is time, attention, or other things. My community has been an important part of my life, so I want to give back to my community. One of the biggest ways I have been able to do so is though my Eagle Scout Project. For my Eagle Scout Project, I started a math club at a local high school. I plan and lead two meetings every month. I also give back through my youth group. In my youth group, juniors and seniors are able to be leaders for the younger students. When I was younger, I had amazing leaders who really helped me grow in my faith. Because I can see what a huge impact having good leader had on me, and because I want other younger students to grow in their faith, I now serve as a student leader. I give time to the younger students so they can benefit. I also participate in service projects through my youth group. One of such service project is my church's Feeding Ministry. We provide meals to those in our community who need them. I help prepare the food, and then serve it to people who come to get food. For much of my life, I had not had a job, so it had been hard for me to give financially. However, I have made giving a part of me by giving back to others through service.

One personal finance lesson that affects the way I spend my money is the idea of thriftiness. Essentially, I try not to buy unnecessary things that do not have significant benefits to me. For example, some people buy coffee from Starbucks every day. Although this coffee tastes good, it is expensive, and 4 dollars a day adds up to over $1400 a year! I make coffee at home, and save lots of money. Occasionally, I go get coffee with some of my friends. However, the purpose of this is not only to get coffee, but to connect with my friends. Because I gain stronger relationships, I consider this expense an investment. So, I have learned that it is good to spend money if there is a good purpose behind it. However, if there is not a good reason to spend money, I try to save it. In addition, when I spend money, I try to get a good deal for the money I spend. For example, I am saving up to buy a car. I have the option of buying a new car or a used car. To get the best deal, I plan to buy a used car because the quality is still very good, but it is a fraction of the price. Overall, I try to make sure that I make meaningful purchases. If a purchase will not actually be beneficial to me, then I try to find a better use for my money.

One of my favorite hobbies is music. I love to listen to music, but I especially love to play music. I have played to piano for 11 years, but also play the trombone, the viola, bass guitar, and several other instruments. I also am in choir. I love to learn and play music because learning a new song gives me a feeling of accomplishment. I also love to express myself through songs, and playing music makes me feel happy. I have many friends who also play music, so I am able to hang out with my friends and relax by enjoying music. Besides music, I also like to collect baseball cards. I played baseball for many years, and I really enjoy it. I especially like to collect cards from the Reds because they are my favorite team. I like to play simulated games of baseball by using the statistics of each card as well as dice to add some randomness. Another one of my hobbies is actually doing math. Although it may seem that math is normally something that people do for school, I like to explore math on my own time. I can use math to express my creativity. I like to write problems that use creative applications of skills that I have learned. This helps me challenge myself, and it is also fun.

To me, confidence involves the ability to go into a difficult or uncomfortable situation and trust that you will be able to perform well. For example, I participate in theater as an actor, so I have to memorize lines. It can be easy for me to get nervous about forgetting lines or messing up my movements. However, I know that I have practiced what I need to do, and I also know that if I mess up, it is not the end of the world. So, because I feel that I am well-prepared for the show, I do not have to worry. In other words, I have confidence. Throughout life, there are many difficult circumstances that I will have to face. For example, I will have to participate in job interviews. In these interviews, there will be questions that I had not anticipated. However, I still need to have confidence in these circumstances. In order to build confidence for these scenarios, I review what I have done and can do so I have a good grasp of who I am as an applicant. I also practice possible interview questions. That way, I am prepared for most questions that will be asked, and if there is a question I did not specifically prepare for, I have the base knowledge to address it. One of the ways I work to become more confident in myself is through leadership. I have been very involved in Boy Scouts as a leader. When I first joined Scouts, I was afraid of speaking in front of others. However, I served in various leadership positions, and gradually was in charge of more people. Eventually, I got used to leading others. To build confidence, I gradually put myself into more uncomfortable scenarios, growing my comfort zone.

Although many students dread taking calculus because it is difficult and may require a different approach than other branches of math, it is actually very important in the STEM field. I have found that my experience with calculus has helped me in higher-level classes that study the foundations of math. I have taken Complex Analysis, and it has helped me understand why earlier fields of math such as trigonometry behave the way they do. However, in order to understand how complex analysis works, I had to first understand how calculus works. This implies that to fully understand how math behaves, we need to use calculus. In addition, calculus can be directly applicable to some parts of the STEM field. For example, architects need to know how large each part of a building is, how much weight it can support, and how much it weighs. For simple shapes such as bricks or spheres, this volume and mass is not hard to find. However, modern buildings tend to use abstract shapes, sometimes smooth, sometimes pointy, with many irregular angles. It would be very difficult to find a way to measure the volume of such shapes without calculus. It is very impractical to just manufacture the part and then realize that it does not meet specs. However, using calculus, estimating the volume and mass is relatively easy. If the border of a shape can be approximated by a function, then the cross-sectional area and then volume can also be approximated, which gives the engineer an excellent way to find the weight of an abstractly shaped part. Some branches of science are heavily reliant on calculus. For example, physics uses calculus a lot. As an example, many applications of physics involve velocity or acceleration. However, acceleration can be expressed using a derivative, which is a part of calculus. In fact, the applications of calculus to physics go beyond just derivatives. Calculus is used to find moment of inertia, mass, and is even used in certain applications of Newton's Laws. In fact, spacecraft use certain applications of calculus to navigate through space. Calculus does not just relate to "pure math" fields, but can actually be used in medicine. Calculus can be used to determine how well a fluid can flow through a space. When a surgeon is performing an operation, they need to know at what angle they should put the blood vessels. With calculus, they can find the ideal angle so that the patient can remain healthy. Another STEM application of calculus is in economics. When running a business, you want to maximize your profits. These profits are based on how many customers use the business and on the profit margin. However, if profit margin is higher, then fewer customers tend to use the business. So, the right profit margin must be chosen to maximize revenue. Calculus is perfect for optimization. So, if a general formula can be estimated for revenue based on the profit margin, then calculus can be used to select the best margin. Even though calculus may seem like an unnecessary class to high-school students, it is actually vitally important in the STEM field. Many different STEM fields use calculus, from mathematics and economics to robotics and medicine. Without calculus, our world would look very different.

One of my favorite ways to serve others is to serve as a student leader for my youth group. Each week, we meet to study the Bible, play a game, sing songs, and do a skit. I want to help younger students enjoy youth group and grow in their faith. I play bass guitar in the worship band, and also help lead skits. Each week, we have a Bible study, and I help moderate it. I am not required to do this, and it takes work each week, but I want to help the younger students grow in their faith. Another way I help others is by leading a math club at a local high school. The high school did not have a club for people who liked math, but it had other clubs, and other nearby high schools had math clubs. This put the high school and its students at a disadvantage. So, because I like math and wanted to help other students with it, I volunteered to start a math club where students would be able to learn more about math and hang out with other people who like math. I organized the club, planned out meetings, and led the meetings. I also sent out reminders so people would not forget to attend. Because I gave time to this club, students were able to meet together and enjoy math. I have participated in many service projects through Boy Scouts and my youth group. Recently, I helped move furniture to prepare a house for a family of Afghan refugees that will be arriving in my town. I have also helped serve food to hungry individuals through my church's Feeding Ministry. I try to make service a part of my everyday life.

I am an Eagle Scout, which is one of my proudest accomplishments. However, getting to this point was hard, and I have had to persevere through many obstacles. To earn the rank of Eagle, I had to earn 7 different ranks, as well as 21 merit badges. Each of these ranks and merit badges has different requirements to fulfill. Some of these requirements were difficult for me. For example, I had to create a 13-week fitness plan. This was hard for me because some of the activities I had to do were very difficult, and I had to make time to do them. However, I persevered, and I finished that merit badge. One of the hardest things for me to stick with was my Eagle Project. For my project, I founded and ran a math club at a local high school. I had to get my project approved by the school and Scouting, and then complete it. Some of the Scout leaders were resistant to the idea of my project being a club, because they were used to construction. However, I explained how the club satisfied the requirements, and they approved my project. However, even though the project was approved, it will still difficult to make the club successful. Math can have a bad reputation with students, so I had to fight against students' presuppositions. In addition, there are several other clubs at the high school, some of which meet on the same day as math club. So, the club had to compete for students with these clubs. So, I created fliers for the club, and invited many of my friends. Eventually, the club gained a steady membership, and my perseverance paid off.

Math is very important to our world, even though many people might not realize it. I think that mathematics is actually the foundation for almost everything. Our world is becoming increasingly reliant on technology. Many people require technology to do their jobs. Mathematics is a vital part of our technological culture. In order to have cybersecurity, we must encrypt sensitive data. One of the best ways to encrypt data is to use products of large primes. In order to maintain proper security measures, we need to have a good understanding of what primes are and how they work. In addition, in order to build safe buildings, architects need to understand how weight will be distributed, and what shapes can best support weight. Mathematics is the answer to this problem. Computer programs can now be created that can calculate exactly how much weight an object can help so architects can create safe and efficient buildings. Besides necessary applications, math is also an integral part of other parts of life, like music. Beautiful harmonies in music are a result of ratios of frequencies. By understanding how frequencies work and how the ratios relate, we are able to have a better understanding of why music sounds the way it does. I love learning math because, to me, it seems very logical, and I like learning why things work the way they do. I have always loved math. It is super exciting to be working on a problem and suddenly have a breakthrough, finding what I was looking for. Sometimes I struggle to understand a concept, and then become frustrated. However, if I go through and check the underlying information and learn a bit more about the subject, I am often able to understand it. Finally understanding a difficult problem or topic is an amazing feeling. It is like attaining a goal, such as climbing a mountain or running a mile. It is something that required a lot of work, but when I finally complete it, it feels very satisfying. In addition, I know that I am stronger and more experienced so I will be better prepared for the next problem. In addition, mathematics seems to be very connected, so different fields of math actually support each other even though they may seem unrelated. In one of my recent classes, I learned that trigonometric functions are actually related to the numerical constant e, and it seemed really weird. However, when I learned more about how they were related, it actually made a lot of sense. I love discovering how different areas of math are connected. The more I learn about math, the more I see how parts of it are connected, and the more beautiful it seems.

I am a homeschooled high school senior. I am very involved in my community. One of my biggest community involvements has been Boy Scouts. I recently earned the rank of Eagle Scout. As my Eagle Scout Project, I created and ran a math club at a local high school. I have always loved math and science, and love to learn more about new fields of math or areas of science I have not learned about before. If there is something I don't know, I like to learn about it so that I have a better understanding of how the world works. I am a Christian, and this motivates me to become a better person. Because of my faith, there is a certain way I want to live. I also want to be successful in life, which gives me a desire to do what will help me later in life. In addition, I am a leader for my youth group, which means that I act as an example for younger students. I want them to have a good example to look up to, so I therefore pay attention to how I act, being careful about what I say or do. One character trait that I really admire in people is the ability to make people feel welcome. When I was younger, I really appreciated when someone made me feel welcome at an event where I was new. Because of my memories of that welcoming atmosphere, I try to emulate that character trait so I can make others feel more comfortable. I would like to be able to use mathematics to help other people. There are many different ways that mathematics can be useful. One of the ways I have learned about is mathematical modeling. In this method, mathematicians can create a simulation that can replicate how a certain event might occur. For example, one application of this is fluid dynamics. Mathematicians can create simulations of how water flows through a pipe in order to design the most efficient way to create a plumbing system. One application of mathematical modeling that I think would be very useful today is the modeling of the spread of disease. COVID-19 has been a huge problem over the past 2 years, and I would like to help the world get back to normal. I would like to create a model for the spread of COVID-19, based on what we know about it and data about its spread. Then, we would be able to predict how it would spread so we would be able to take the necessary precautions. Therefore, we would be able to figure out how best to prevent it spreading, so we could get rid of unnecessary limitations.

One song that inspires me is "God Bless the USA." This song reminds me that I am blessed to live in a free country, and that I should do my best to protect the freedoms it provides. This song helps me remember to help other people out as well. I am reminded to treasure what I have. I made this playlist because the songs share similar themes to "God Bless the USA." They talk about freedom, and helping others.

I’ve been playing chess for about as long as I can remember. The day I was introduced to this mind-opening game stands out clearly in my mind. I must have been about seven. That day, my family went to a fair at our local YMCA. There were all sorts of booths promoting various activities and programs, but one table off to the side drew me over. The table had a board on it for some game, with a bunch of pieces. Seated at the table was a man. I don’t remember much about this man. All I remember is that he was referred to as a “chess master.” I stopped by, and he offered to teach me the game. I accepted, and he went over the basics with me: How the pieces move, check, checkmate, and so on. I specifically remember going over how bishops move: They stay on one color, move in diagonals, and can’t jump. Once I had an understanding of the basics, he challenged me to a friendly game of chess to test what I had learned. Naturally, he beat me handily, but in the process, a seed was planted deep within me. This seed would sprout and grow, creating in me a deep love for chess. Over the years, this sprout has grown, extending its tendrils into many areas of my life. One area that my love of chess has affected is my love of math and problem solving. I have a deep love for math, and I believe that playing chess has helped me as a mathematician, and vice versa. By playing chess, I have been able to develop analytical thinking skills that have aided me in my mathematical endeavors. By playing chess, I’ve learned to look ahead and see what could possibly happen in a problem. This skill also applies in my everyday life. It helps me choose a course of action based on what I already know, so that I can solve whatever challenges arise in my daily activities. Another skill that playing chess has helped me gain is the ability to adapt when things don’t go the way I expected. In chess, I often make a plan on how to get to my opponent’s king, but often enough, they launch a counterattack or block my advance. Then, I have to block their moves, and reconsider my strategy. This strategy also applies to other areas of my life. One area this applies to in my life is navigation. One day, I was driving home from school, but I couldn’t go on my regular route, because a street was blocked. However, because of my ability to adapt, I found a new route, and made it home safely. In the future, I plan to study mathematics, with the hope of entering the mathematics research field. I believe that my studies of chess will help me in this field. Chess has helped me improve my critical thinking, as well as my problem-solving abilities, both of which are crucial in research. Critical thinking will help with many aspects of research, including finding new areas to investigate, as well as planning the correct course of action for a study. I plan to stay active as a chess player, and continue to build my knowledge and ability. Chess has been an important part of my life, and it will continue to be as I enter the next stages of my life. Chess has been a way to amuse myself, a way to challenge myself and others, and a way for me to grow intellectually and as a person. I’m extremely glad I discovered the joy of chess, and I want to share that joy with others.