In the summer of 2021, I got an email that would change my life. I’d been attending the UCLA math circle for almost a decade at that point, and I had a good relationship with the head of the program, Prof. Oleg Gleizer. But I was surprised when he sent me an email saying, “We may have a research opportunity at USC this Summer.” Prof. Salman Avestimehr of USC (University of Southern California) was doing research into distributed machine learning techniques, and he had reached out to Prof.

During the first visit to my friend’s house since the pandemic had started, the first thing I did was wash my hands. The first thing I noticed was the eye-catching shape of the water projecting from the faucet. While the sinks I had used for the past year emitted frothy, turbulent jets, the water in this sink fell over a flat edge and created a laminar cascade of water that appeared to take the shape of mutually orthogonal chain links.

Human brains are way too complicated with billions of neurons and hundreds and even thousands of trillion connections that are still not completely understood. Because of this, studying a smaller “brain” permits one to better understand how the brain and the neural network influences the behavior of a creature. The C. elegans’ connectome is the ideal network to research because of its simplicity (only consisting of 302 neurons and the fact that it has been completely mapped out.

One evening in the summer of 2020, well after the severity and endurance of the COVID-19 pandemic had become evident, I was having a chat with my father at the dinner table. Both STEM people, our talks often leaned towards the topic of science, especially in the realm of current events. This time, it was the matter of COVID testing that made its appearance. Testing, so essential to managing an outbreak, yet so scarce when it was needed.

The main problem of our project was investigating whether or not there was an efficient 2D analog to the segment tree. Here, instead of updating and querying arbitrary ranges of a list of numbers, we want to update and query arbitrary submatrices of a matrix of numbers. When updating a submatrix, we add all numbers in the submatrix with an arbitrarily chosen constant value; when querying a submatrix, we find the minimum of all numbers in the submatrix.

My research was motivated by my profound interest in how adolescents use social media, and TikTok in particular, which stemmed from my own personal experience with the platform and my previous scientific research in this area. I had already begun to conduct research on TikTok during my junior year, so I knew that there was very little scientific literature about this youth-dominated platform. My junior year research project was focused on the socioemotional well-being of adolescent TikTok users, and was conducted to satisfy my personal concern about how my usage might be impacting my own moods.

My first real encounters with physics were in Year 9 (the United Kingdom equivalent of 8th grade). It was here that my passion for the subject was sparked, thanks to my teacher at the time: Mr. Andrew Brittain. His immense enthusiasm rubbed off on me. Two of his lessons, in particular, are imprinted in my memory. One was devoted entirely to particle physics and in the second, he discussed quantum tunnelling.

Climate change impacts all people living on the Earth. The El Ni�o Southern Oscillation (ENSO) is a system which influences the climate around the globe. For this reason, it would be helpful to create a procedure for predicting ENSO each year, allowing the population to understand and prepare for a potential climate in their area, months in advance. This study developed a procedure to create predictions of ENSO every year. This procedure is simple, using basic statistics and computer science to create forecasts more accurate than those currently existing.

As I entered high school I became interested in learning about different areas of mathematics but I was also interested in the research process. It was one thing to read about mathematics, but what was inventing it like? Eventually, this path led me to the MIT PRIMES program where I was paired up with a graduate student to work on a project in combinatorics. The problem I worked on was a conjecture by Prof.

Last year, the researcher outlined the mathematical basis of a new quantum secure direct communication (QSDC) protocol. QSDC protocols are methods of information transfer which gain security from the use of quantum mechanical effects. Due to the measurement principle, quantum communication reveals eavesdroppers with a probability arbitrarily near unity. In a world where traditional encryption is increasingly threatened by quantum computers and Shor’s Algorithm, QSDC protocols provide impregnable security to banking transfers, diplomatic wires, and general communications.

During an evening quantum computing seminar at Portland State University, Professor Marek Perkowski discussed the relatively new area of quantum machine learning. As the lecture continued, I gradually realized that I had come across a field with an ideal intersection between my passions for mathematics and machine learning. Following this seminar, I started reading published works in the field which introduced quantum analogs of algorithms ranging from support vector machines to k-nearest neighbors … My proposed quantum machine learning algorithm is a novel approach which converts the learning samples into an incompletely specified Boolean function for classification problems.

My advice to high school students looking to work on a research project that combines science and mathematics is to be invested in learning a lot of new things and keep an open mind as high schoolers, there’s a lot of mathematics we are unfamiliar with, and sometimes it’s easy to get overwhelmed. However, I would say that the beauty of combined science and math research is that you learn so much about mathematical theory that can be applied to the science a double-pronged approach, if you will!

When I was in sixth grade, I first became aware of my family history of heart disease. My dad battling chronic hypertension, close relatives passing away from heart failure, and me knowing that I could be next in line … During my freshman year of high school, my curiosity to investigate better heart disease therapies drove me to take honors biology. I was especially intrigued by our discussion of the incredible healing potential of pluripotent stem cells.

It is actually impossible to explain my experience in math research without beginning with my experience in math contests. As a relatively accomplished contestant over my high school years, including participating the United States of America Junior Mathematical Olympiad (USAJMO) and twice in United States of America Mathematical Olympiad (USAMO), I fell in love with the mathematics and the often slick and beautiful solutions in these contests. However math contest can be incredibly deceiving as in most serious mathematics the necessary background knowledge can be quite cumbersome for high school students.

I researched the efficiency of modern algorithms that test whether large integers are prime or not. As it turns out, this question is fundamental to modern cryptography: many modern encryption algorithms used for internet security purposes require a steady supply of large prime numbers. Although many different primality tests are used in cryptography, I focused on the strong Lucas pseudoprime test, which relies on concepts from algebraic number theory. To begin working on my project, I did over a month of background reading on algebraic number theory.

Since my freshman year of high school, when I became increasingly bored with school math, I would look up things on my own which interested me. More than that, I would play around with them. Continued fractions? Sounds interesting - now let’s try and see if I can derive a closed form if I vary the parameters this way. Sums involving the harmonic number? Let’s see if I can generalize them with another parameter.

With the advent of the smartphone, cameras have suddenly become very convenient. Like many others, I enjoy taking pictures on my rather old, outdated phone. I became interested in how to take better-quality photos despite my device’s limitations, and a Google search pointed me toward high dynamic range (HDR) imaging. The process involves taking multiple photos instead of just one to produce a final image that shows a real-world scene more completely.

Number theory is a field that has, for me, always held a special kind of magic. There is something about reading an elegant proof that sticks with me, gives me a certain feeling of gratification like the sensation experienced at the conclusion of a mystery novel. I have always believed that the objective of any mystery is to figure it all out before the grand reveal, to make the leaps of intuition before Sherlock Holmes.

About a year ago, I fascinated over a computer simulation called Conway’s Game of Life. This simulation consisted of a two-dimensional grid. Its cells could be filled or empty, which corresponded to alive and dead, respectively. This grid followed four simple rules: any live cells with fewer than two live neighbors dies, any live cell with two or three live neighbors lives to the next generation, any live cell with more than three neighbors dies, and any dead cell with exactly three neighbors becomes a live cell.

Bioinformatics is a field that draws from mathematics, computer science, and engineering to develop biological understanding [26]. Bioinformatics uses many techniques and analyses to identify the biological mechanisms that underlie biological data. Bioinformatic analysis begins with data such as sequences of DNA, structural information about a protein, or measures of gene expression. Much of this data is available online in publicly accessible repositories. Using these repositories, researchers can apply various machine learning techniques to high-quality data without incurring the cost of generating the data themselves.

Constructing and n-dividing different polar curves through the use of straight- edge and compass constructions are proven using Field Theory. Some of the solved systems include arc length divisions for circles, hypocycloids, and lemniscates. However, little has been done in terms of n-dividing area of pre-drawn polar curves. Using theory allows for a closed determination of the possible n-divisions, since it gives a closed form for possible lengths and angles. Constructibility can be applied to the long-standing ancient Greek “unsolvable” problems, roots of unity in complex analysis, and computer science through binary digits.

That summer, I applied to and was accepted to the Wolfram Science Summer School (WSSS) WSSS2012 was hosted at Curry College in Milton, Massachusetts. At WSSS2012, I met Stephen Wolfram, members of the Wolfram Science team, and numerous computer science enthusiasts from around the world, all with unique and interesting backgrounds. It was after talking to Dr. Wolfram for the first time that I decided to study long-distance cellular automata, or LDCA, a field of cellular automata that had not been extensively documented before.

A year ago I investigated a mathematical problem relating to Latin squares. Most people, whether knowing it or not, have actually seen a Latin square at some point in their lives and many newspapers actually include partial Latin squares on a daily basis in the form of a sudoku puzzle. A Latin square is a grid of cells with numbers in each cell such that no number is repeated in any row or column, so any completed sudoku puzzle is really a 9x9 Latin square.

Combinatorics is a field of mathematics that has always fascinated me. Specifically, graph theory, a branch of combinatorics, has always piqued my interest. In general, graph theory deals with the study of mathematical structures, modeled by vertices with edges connecting them. While these graphs can be very simple, they can also get exceedingly complicated in structure; indeed, there are very interesting properties we can say about these graphs. The field is both enormously complex as well as incredibly enlightening … In the summer of ninth grade, I had my first experience with graph theory at a summer math camp called PROMYS.

I’ve always been interested in mathematics. It is the pinnacle of human logic and is unquestionably correct, leading to wonderful models of predicting weather and making transistors. I found math to be a beautiful art form with a personality; some equations are humble, some are lawless, and some are mysterious, teasing for further inquiry … I have conducted research in representation theory, the backbone of many mathematical ideas in algebra, topology, and particle physics.

It all started with social media. Like many Facebook fans of my age, a significant part of my life was spent on social media. As we take knowledge from the infinite pool of cyberspace, cyberspace, in return, instilled appalling social habits, and my social interactions simply became competitions of who can glue eyes to their screen the most. Consequently, for me (and my 819 friends), my speech patterns rescinded to a level akin to OMG LOL I have to get to class.

The title of my paper was “The Sky’s the Limit- An Investigation of Cloud Cover on Major League Baseball Performance.” My research project was inspired by a genuine passion for the game of baseball and my desire to learn more about its subtle nuances. I often wondered how much weather variables such as sun, clouds and shadows affected the outcome of a game or individual player performance. My curiosity prompted me to do some preliminary research to identify whether these questions were previously investigated.

To predict the response of estuarine ecosystems to anthropogenic and natural changes, process-based physical computer models serve as an important tool for simulation of estuarine salinity. Among the school of data-driven parametric models as alternative tools for process-based physical models to simulate environmental variables, artificial neural networks (ANNs) have become an increasingly popular modeling technique over the past two decades (Maren et al., 1990; Schalkoff, 1997; Dawson and Wilby, 2001; Maier and Dandy, 2001; Dawson et al.

Oftentimes, there are “bad guys” such as diseases, wildfires, or thieves that the “good guys” such as the CDC, firemen, or police wish to control or capture. However, the good guys only have a limited quantity of assets such as money, people, and time, so it is important for them to use the least amount of resources. One well-known way of analyzing such problems is known as “Cops and Robbers on a Graph”.

I am fascinated by problems that require a blend of computational topology, geometry, and number theory. I have also been studying fractals which interesting geometrical objects that have been used in diverse applications such as cryptography, seismology, network optimization, and even weather forecasting. However, despite the wide range of applications and interest in fractals, the general theory of these objects is still in its infancy. My work on this research project has developed some theorems and conjectures in the field of combinatorics and has begun to shed some light on some areas of fractals, one-cell automata and dynamical systems … This need for optimization has become increasingly more important in today’s society from the perspective of both resource management as well as leveraging new opportunities.

I began to appreciate such simplicity, and to redefine my understanding of mathematics. I came to see it as being much more than just its constituent symbols and equations, but a beautiful language capable of describing the logical foundations of all the natural sciences. Over time, that same beauty began to appear everywhere I looked … Aortic stenosis (AS) is a lethal disease that can lead to severe cardiac complications if left untreated.

I am especially interested in Colony Collapse Disorder (CCD) as an environmental issue as well as an economic and policy issue. Within the United States honeybees contribute to the success of one-third of U.S. agriculture; furthermore these insects are responsible for countless jobs and many billions of dollars in revenue. They are the unsung heroes of harvests of numerous fruits, berries, and nuts, and therefore crucial to the long-term viability of our global economy.

In order to build my own guitar I clearly needed to research how I would go about the task. Thus began, unbeknownst to me, my first true application of the scientific method that would eventually inspire me to become an Intel participant. I researched multiple designs in order to create something that felt both original and practical and then I made detailed lists of the necessary supplies. I collected materials from around my house, online, and occasionally even the garbage can.

In 1997, The New York Times quoted a Bronx High School of Science administrator regarding the then- surprising increase in behavioral science honorees in the prestigious Westinghouse (now Intel) Science Talent Search competition: ‘It [behavioral science] does provide another outlet for some students whose strength may not be in empirical science and math,’ said the chairwoman of the school’s biology department (A Fine Hour For Squishy Sciences, NYT 2/16/97). Oh really?

Autism is a mental disorder that impairs the mental and social development of children on their way to adulthood. Not everyone with autism has the same severity of symptoms and therefore researchers refer to the variance of the disorder as autism spectrum disorders (ASDs). In recent years, there has been an increase in children diagnosed with autism (Groom, 2009). Reasons for such a peak in diagnoses range from a vaccine link to simply just more accurate methods of testing (Downs, 2009).

How many times does a child hear his or her parent say, turn your phone off before going to bed or don’t sleep with your phone on next to you or stop texting at night because you won’t get enough sleep? I know I’ve heard those words countless times. But, I’ve always wondered if using my phone, or any other technological device, could actually hinder me from getting the best quality sleep I can get.

It is difficult to say when my passion for mathematics was first kindled. I have liked doing number problems and logic puzzles for as long as I can recall: one of my earliest memories is of using toothpicks to guide a brave mouse across shark-infested waters to steal the king’s cheese (a challenge found in The Puzzle Book, which I owned when I was younger). My interest was further strengthened by participation in math competitions and a math club organized by Professor Ron Ji at IUPUI.

I have long been fascinated by math, and more recently by biology. When my high school presented the opportunity to participate in research at a local university two years ago, I looked for a project that could help me see how the mathematics I learned in the classroom could be applied to help us better understand questions in biology . . . My advisor found Dr. David Eisenberg’s lab at the Molecular Biology Institute at UCLA, a lab studying, among other things, amyloid fibers and Alzheimer’s disease.

Despite the changes in custom and language that occurred simultaneously in my life as I moved from South Korea to America, math was the one thing that made me feel secure and confident. Math provided me with a sense of direction through the confusion and cultural difference I had to overcome. Therefore, I began to devote my time to mathematics, taking advantage of all the research opportunities that were available in the field .

I wanted to work on something related to game theory. During my sophomore and junior years, I had bounced back and forth between various math concepts, but I always came back to game theory because it can describe interpersonal interactions in mathematical terms, an idea that was very intriguing to me. However, I looked for something beyond game theory’s most common applications, namely in economics, social psychology, and evolutionary biology. While searching for this new application of game theory, I noticed that cells, especially cancer cells, can behave strategically.

I love working on conjectures. Just as in the various Mathematical Olympi- ads in which I have participated, the conditions are already set; the challenge consists in cleverly using the hypotheses of the problem to produce the conjectured conclusion. Number theory, the study of properties of the ordinary counting numbers 1; 2; 3; : : :, is particularly rich in this type of problems, which range from puzzles for the general audience to the challenges on the Interna- tional Mathematical Olympiad to famous conjectures, such as Fermat’s Last Theorem and the Twin Prime Conjecture, which commonly remain unsolved for hundreds of years.

The summer after my junior year, I went to the Research Science Institute (RSI) program at MIT. I had a blast there, and I strongly encourage any eligible students reading this to apply. I had two mentors: a graduate student named Dustin Clausen and a professor named Pavel Etingof. My mentors contacted me before the program to tell me about a potential project on representation theory in complex rank, following a paper of Deligne that laid the groundwork and beginning work on a program that Etingof himself had proposed in a talk at the Newton Institute.

Mathematics has always been important to me. When I was little, I liked to do mathematical puzzles out of a book I had bought from a catalog. I would think and ponder about these puzzles and discuss them with my family and friends. The answers were not straightforward, and I found the solutions interesting to read. Doing the puzzles, I discovered that mathematics is more than just a set of drills to memorize.

I hit numerous impasses and sometimes spent hours at my local university’s library thinking and looking for theorems and tools. For example, when I started to parameterize my space curve, I ran into the problem that one of Wang et al.’s theorem that was crucial in parameterization failed for my intersection space curve projection. I was stuck, but I knew I could adapt it some way. I read ahead. I tried multiple ways of attacking this problem.

My advice to other high school students who wish to pursue math and science is to never feel intimidated. Problem solving techniques in engineering and science involve application of mathematics spanning various facets, such as statistics to calculus to abstract algebra and topology. When it becomes necessary to learn and apply them, do not feel intimidated by their complexity; it may be hard to understand some of these concepts at first, but it is important to be persistent.

Math can be an intimidating field. To work on some problems, one must know decades or centuries of background before one can even understand the question. However, what tends to get lost in all of that is that math can be fun, even for the relatively uninitiated. There are problems in mathematics that are discrete (essentially, self-contained) and with some combination of background research, mathematical thought, and appropriate mentoring, they are easily within reach of the high school student.

For nearly an entire week, I spent many hours a day in MIT’s Hayden Library, immersing myself in introductory books on number theory and abstract algebra. It was a near-overwhelming amount of new notations, concepts, and ideas to absorb in such a short period of time, but I enjoyed the challenge and enthusiastically threw myself into mastering the mathematics necessary to solve my problem. In that short period of time, I learned the basics of group theory, radix representations, and residue classes, just to name a few….

I was no longer at a junction where I could ask my parents for the answers, nor indeed any being living or dead… Read More

I have been interested in mathematics since kindergarten. I always loved searching for and finding patterns in sequences of numbers. I used to read whatever information I could in order to learn more about the wonders of math. In fifth grade I was part of my school’s program for gifted math students. There the teacher introduced me to a wonderful sequence of numbers called the Fibonacci sequence, named after the 13th century mathematician Leonardo da Pisa Fibonacci.

In the summer of 2002, my family and I traveled to St. Petersburg, Russia to visit my grandparents. While there, my father told me about an intriguing theorem in geometry that he himself learned in 1972 from Dr. Zalman A. Skopets (1917-1984) who was married to my grandmother’s best friend. Dr. Skopets was a prominent geometer and headed the Department of Geometry at the Yaroslavl’ State Pedagogical University for many years.

Prior to my Intel research project, I had tried to get a research project with several local universities. However, all of my attempts collapsed for a variety of reasons. To be honest, I had given up on trying to find research opportunities when I received a letter of acceptance from the Research Science Institute (RSI). Sponsored by the Center for Excellence for Education (CEE), RSI accepts about 50 high school students every year, typically students who have finished their junior year.

Intel Science Talent Search project was a four year labor of love that tested my patience more than any undertaking that I had ever attempted in my life. Once, after a particularly frustrating day in the lab, I told my mentor how upset I was about spending the previous three hours wiring a cryogenic thermometer only to have it break as it was inserted into the liquid helium Dewar. ìSounds like youíre doing research,î he replied.