math research project high school

12 Math Project Ideas for Middle and High School Students

By János Perczel

Co-founder of Polygence, PhD from MIT

6 minute read

Mathematics serves as the foundation for most fields of science, such as physics, engineering, computer science, and economics. It equips you with critical problem-solving skills and the ability to break down complex problems into smaller, more manageable parts. It helps you avoid ambiguity and communicate in what is often called “the universal language,” so-called because its principles and concepts are the same worldwide. Beyond the fact that studying math can open up many career opportunities, some mathematicians also simply find beauty in the equations and proofs themselves.

In this post, we’ll give you ideas for different math research and passion projects and talk about how you can showcase your project.

How do I find my math passion project focus?

Because math is so foundational in the sciences, there are many different directions you can take with your math passion project. Decide which topics within mathematics most speak to you. Maybe you’re more interested in how math is used in sports statistics, how you can harness math to solve global problems, or perhaps you’re curious about how math manifests itself in the physical realm. Once you find a topic that interests you, then you can begin to dive deeper. 

Keep in mind that some passion projects may require more technical skills, such as computer programming, whereas others may just explore theoretical concepts. The route you take is totally up to you and what you feel comfortable with, but don’t be afraid to pursue a project if you don’t currently have the technical skills for it. You can view it as an opportunity to learn new skills while also exploring a topic you’re excited about.

Do your own research through Polygence!

Polygence pairs you with an expert mentor in your area of passion. Together, you work to create a high quality research project that is uniquely your own.

What are the best math project ideas?

1. the mathematical properties of elections.

In recent years, there has been a lot of discussion about which election mechanism is most effective at achieving various goals. Proposed mechanisms in United States elections include majority elections, the electoral college, approval voting, and ranked-choice voting. All of these mechanisms have benefits and drawbacks, and it turns out that no perfect election mechanism exists. Look at the work being done by mathematicians to understand when elections fail, and what can be done to improve them. Choose the strongest mechanism and use evidence to support your claim.

Idea by math research mentor Grayson

2. Knot theory

A knot is simply a closed loop of string. Explore how mathematicians represent knots on a page. Learn how knots can be combined, and how to find knots that can't be created by combining other knots. You can learn techniques for determining whether or not two knots are distinct, in the sense that neither can be deformed to match the other. You can also study related objects, such as links and braids, and research the application of knots in the physical sciences.

Idea by math research mentor Alex

3. Bayesian basketball win prediction system

The Bayes’ Rule is crucial to modern statistics (as well as data science and machine learning). Using a Bayesian model to predict the probability distribution of basketball performance statistics, you can attempt to predict a team’s win and loss rate versus another team by drawing samples from these distributions and computing correlation to win or loss. Your project could be as simple or as complicated as you want. Based on your interest and comfort level, you could use simple normal models, mixture models, Gibbs sampling , and hidden Markov models. You can also learn how to code a fairly simple simulation in R or Python. Then, you’ll need to learn how to interpret the significance of statistical results and adjust results over time based on the success/failure of your model over time.

Idea by math research mentor Ari

4. Finding value in Major League Baseball free agency

Here’s another sports-related project idea. Every offseason, there are hundreds of professional baseball players who become free agents and can be signed by any team. This project involves determining which players might be a good "value" by deciding which statistics are most important to helping a team win relative to how players are generally paid. After deciding which stats are the most important, a ranked list of "value" can be produced based on expected salaries.

Idea by math research mentor Dante

5. Impact of climate change on drought risk

Are you interested in environmental economics, risk analysis, or water resource economics?

You can use historical data on precipitation, temperature, soil moisture, drought indicators, and meteorological models that simulate atmospheric conditions to train a machine-learning model that can assess the likelihood and intensity of droughts in different regions under different climate scenarios. You can also explore your assessments' potential adaptation strategies and policy implications. This project would require some skills in data processing, machine learning, and meteorological modeling.

Idea by math research mentor Jameson

Go beyond crunching numbers

Interested in Math? We'll match you with an expert mentor who will help you explore your next project.

6. Making machines make art 

You can program a computer to create an infinite number of images, music, video game levels, 3D objects, or text using techniques like neural style transfer, genetic algorithms, rejection sampling, Perlin noise , or Voronoi tessellation . Your challenge then is to create a functioning content generator that you could then showcase on a website, research conference, or even in a gallery exhibition.

Idea by math research mentor Sam

7. Measuring income inequality and social mobility

If you’re interested in the intersection of mathematics and public policy, here’s an idea. Use data from the World Bank, the Organization for Economic Co-operation and Development (OECD), and other sources to calculate the Gini coefficient and the intergenerational elasticity of income for different countries and regions over time. Explore the factors that influence these measures and their implications for economic development and social justice. You will need to have some skills in data collection, analysis, and visualization.

8. Rocket (fuel) science

Rockets are mainly made out of fuel. When the fuel burns, it gets heated and expelled out, producing thrust. Fuel is heavy and, for long-range space missions, we need to carry around the fuel for the rest of the mission the whole way. It is important that the fuel gives us the most bang for our buck (i.e., the most acceleration per unit of fuel). Compare the amount of fuel (weight) required to get to various celestial objects and back using current electric and chemical propulsion technologies . Then do a cost analysis and compare how long it would take.

Idea by math research mentor Derek

9. COVID-19 and the global financial crisis

It is shocking how the economic effects of COVID-19 have far outweighed the ones from the Global Financial Crisis in 2007-08 . How much is the difference in terms of employment? Production? Let's go to the data!

Idea by math research mentor Alberto

10. Modeling polarization in social networks

We've all seen or heard about nasty political arguments and echo chambers on social media, but how and why do these happen? To try and find out, construct a mathematical and/or computational model of how people with different opinions interact in a social network. When do people come to a consensus, and when do they become more strongly divided? How can we design social networks with these ideas in mind?

Idea by math research mentor Emily

11. The world of mathematics

The history of mathematics dates all the way back to the very first civilizations and followed throughout history all over the globe. This development leads us to our way of living and thinking today. Rarely taught in math courses, the origins of math can provide clear insight into the necessities of learning math and the broad applications that math has in the world. Conduct research on a chosen time period, location, or figure in mathematics and describe the impacts this innovation or innovator had on the development of math as we know it today.

Idea by math research mentor Shae

12. Simulating the stock market

Here’s an idea for a beginner-to-intermediate statistics and programming project centered around Monte Carlo simulations. Monte Carlo simulations are random methods for modeling the outcome of a complicated process. These methods are used in finance all the time. How could you code a program that uses the Monte Carlo technique to "simulate" the stock market? You will need some familiarity with statistics, basic finance, and basic programming in any language to complete this project.

Idea by math research mentor Sahil

How can I showcase my math project?

After you’ve done the hard work of completing your mathematics passion project, it’s also equally important to showcase your accomplishments . You can see that in many of the project ideas above, there is a clear topic, but how you want to present the project is open-ended. You could try to publish a research paper , create a podcast or infographic, or even create a visual representation of your concept. You’ll find that although many project ideas can simply be summarized in a paper, projects can also be showcased in other creative ways.

Polygence Scholars Are Also Passionate About

What are some examples of math passion projects completed by polygence students.

There are several examples of math projects Polygence students have completed through enrolling in our programs; we’ll highlight two here.

Ahmet's mathematical passion project offers detailed breakdowns of the first introduced quantum algorithm Deutsch-Jozsa, and the first quantum algorithm proven to be faster than classical algorithms, Grover’s Algorithm. It also includes a side-by-side comparison of the quantum algorithms and their classical counterparts. He uploaded his paper on Github and plans to submit it to an official publication soon.

Anna’s finance project provides an overview of topics related to personal finance, covering tax and benefits, tax-deferred savings, interest rates, cost of living, investing, insurance, and housing to help young adults manage their savings. To further her understanding of how different areas of finance influence one's life consumption, she created a life consumption plan for a hypothetical person and produced a paper. 

How can I get guidance and support on my math project?

In this post, we covered how to find the right mathematics project for you, shared a dozen ideas for physics passion projects, and discussed how to showcase your project.

If you have a passion for math–or are generally curious about exploring mathematical concepts–and are interested in pursuing a passion project, Polygence’s programs are a great place to start. You’ll be paired with a mathematics research mentor with whom you’ll be able to meet one-on-one. Through these virtual mentorship sessions, your mentor can help you learn new concepts, troubleshoot issues you encounter along the way to bringing your math project to completion, and brainstorm with you on how to showcase your passion project .

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How I Advocated for Students as an Admission Officer When They Wrote About Passion Projects

Summer 2024 Admissions Open Now. Sign up for upcoming live information sessions here (featuring former and current Admission Officers at Havard and UPenn).

5 Free Virtual Research Opportunities For High School Students

Virtual research opportunities for high school students are programs that provide hands-on experience and research projects in various STEM fields, such as mathematics, computer science, computational biology, physics, neuroscience, and engineering. These programs are designed to deepen students’ understanding of STEM and help them develop the skills needed to succeed in their academic and professional careers. 

Participating in these programs can also help high school students expand their knowledge and skills in their areas of interest and work on exciting, unsolved problems with established researchers from top-tier universities. 

Virtual research opportunities are especially useful for high school students who are unable to attend in-person programs due to distance, cost, or other factors. They offer a flexible and accessible way to gain valuable experience and knowledge from the comfort of their own homes. In this article, we will discuss five free virtual research opportunities available for high school students.

1. MIT Primes  

MIT PRIMES is a free, year-long after-school program that provides research projects and guided reading to high school students in the areas of mathematics, computer science, and computational biology. The program is designed for students living within driving distance from Boston, and it offers four sections: PRIMES, PRIMES-USA, Menezes Challenge PRIMES Circle, and Yulia’s Dream.

PRIMES is a research-focused program in which participants work with MIT researchers to solve exciting, unsolved problems. PRIMES-USA is a distance mentoring math research section for high school juniors and sophomores from across the United States. Menezes Challenge PRIMES Circle is a math enrichment section for underrepresented groups living within commuting distance from Boston. Yulia’s Dream is a math enrichment and research program for exceptional high school students from Ukraine.

In addition to these sections, PRIMES runs two collaborative initiatives: MathROOTS, a two-week summer program for high-potential high school students from underrepresented backgrounds or underserved communities, and CrowdMath, a year-long online collaborative research project open to all high school and college students worldwide.

Finally, PRIMES STEP is a year-long math enrichment program for middle school students from Greater Boston.

Overall, MIT PRIMES aims to provide challenging and engaging opportunities for students with a passion for mathematics and science. Through research projects, guided reading, and collaborative initiatives, PRIMES seeks to foster the intellectual growth and development of high school and middle school students, and to inspire them to pursue their interests in these fields.

MIT PRIMES is a prestigious year-long after-school program that offers research projects and guided reading to high school students interested in mathematics, computer science, and computational biology. 

The admissions for the 2023 cycle are closed, and the admission decisions are made by February 1. However, for the 2024 cycle, new problem sets will be posted on October 1, 2023, and applicants will have until November 30, 2023, to solve the relevant problem set(s). 

To apply for MIT PRIMES, you must be a high school student (or a home-schooled student of high school age) living in the Greater Boston area, able to come to MIT weekly from February to May.

To apply, you need to fill out a questionnaire, ask for two or three letters of recommendation, and submit your solutions of the PRIMES problem set. Applicants to the Math section must solve the Math problem set (at least 70%), and applicants to the Computer Science and Computational Biology sections must solve the Computer Science problem set (100%) and the General part of the Math problem set (at least 70%). Admission decisions are based on all components of your application, and there is no application fee.

MIT PRIMES suggests a list of recommended readings as a preparation for entering the program and as a background for further research. By participating in MIT PRIMES, students can gain hands-on experience working on exciting, unsolved problems with MIT researchers and expand their knowledge and skills in these areas.

The Summer Academy for Math and Science (SAMS) is a program that provides opportunities for underrepresented high school students to explore STEM fields. The program is designed to deepen students’ understanding of STEM through traditional classroom instruction, hands-on projects, and sustained engagement with faculty and staff mentors. 

SAMS Scholars are taught by renowned faculty and staff who are deeply committed to their success. They also have the opportunity to collaborate and develop meaningful relationships with peers from across the country. Through SAMS and other outreach initiatives, the program aims to develop a diverse and supportive community of STEM Scholars interested in attending top-tier universities.

The program consists of two parts: Part one is a virtual jumpstart that will occur prior to the start of the residential program. This will focus on skill-building that will be needed for the in-person program. Part two is a 5-week in-person Pre-College program where students will move into the residence halls and attend full days of courses and meetings. The academic portion of the program will conclude with a symposium, and students will move out of the residence halls at the end of the program. 

SAMS is a fully funded, merit-based program, and there is no cost for scholars to participate. To be eligible for the program, students must be at least 16 years old, a U.S. citizen or permanent resident, and a junior in high school at the time of application submission. Scholars are expected to participate fully for the duration of the program and cannot participate in any other programs if selected for SAMS.

3. University of Illinois – High School Summer Research Program

The High School Summer STEM research program invites current 9th-11th graders from Illinois, Indiana, Kentucky, Missouri, Iowa, or Wisconsin to apply for an authentic six-week STEMM research experience at a world-class research university. Participants will be matched with another student, and in some cases, a teacher from their school. 

The program aims to provide hands-on experience in various STEMM fields, including cancer immunology, neuroscience, artificial intelligence, physics, quantum mechanics, bioengineering, and electrical engineering.

Participants will work with established researchers in engineering, computer science, and medicine and attend weekly seminars on topics such as college admission processes and support available, communicating scientifically, and preparing research posters etc. Students will also interact with faculty, post-doctoral researchers, graduate students, undergraduate students, and local high school teachers.

Participants will showcase their research with a research poster and symposium at the end of the program. They should plan for 30-35 hours per week of research and professional development time, with a majority of activities taking place on the University of Illinois campus. 

The program covers some transportation/parking expenses, meals, and a monetary award.

High school teachers play an essential role in the program, with some research projects requiring a teacher to be a co-researcher, and others having a teacher mentor who checks in weekly with the students to discuss their research progress and address any issues or challenges. 

Teachers and students do not need to come from the same school, and interested individuals should apply regardless of whether they can recruit others from their school to apply.

The program also invites research faculty, staff, and graduate student researchers affiliated with The Grainger College of Engineering and the Carle Illinois College of Medicine to propose a high school research project for consideration. The proposals will be mentored by POETS YS, GEnYuS, or SpHERES research teams, which will guide two high school juniors/seniors from limited understanding to completion of a related project of their own and poster presentation explaining their research.

In summary, the High School Summer STEM research program provides high school students with an opportunity to engage in authentic STEMM research and develop professional and college-ready skills. Participants work with established researchers, attend weekly seminars, and showcase their research at the end of the program. 

The program aims to provide hands-on experience and build confidence in students as scientists and engineers.

4. Simons Summer Research Program

The Simons Summer Research Program is a highly selective program that offers high school students the opportunity to conduct hands-on research with Stony Brook faculty mentors. Founded in 1984, the program attracts applicants from all over the country, with Simons Fellows being paired with a faculty mentor, joining a research group or team, and taking responsibility for a project. Students are encouraged to demonstrate independence, creativity, and an aptitude for hands-on work, with a strong interest in science. The program takes place during the summer before the student’s senior year of high school, with students participating in the program from June 26, 2023 to August 11, 2023.

In addition to working on their research project, Simons Fellows attend weekly faculty research talks, special workshops, tours, and events. At the closing poster symposium, students present their research project through a written research abstract and a research poster. Participants receive a stipend award.

The Simons Summer Research Program is supported by the Simons Foundation and is open to US citizens and/or permanent residents who are at least 16 years of age by the start of the program. The program is an opportunity for high school students interested in science to learn valuable techniques, experience life at a major research university, and develop independence, creativity, and an aptitude for hands-on work. The program aims to give students a glimpse into the world of scientific research and inspire them to pursue careers in science.

5. EnergyMag Internship

EnergyMag is offering virtual internships for high school and college students interested in increasing the share of renewable energy in the world and gaining work experience in the energy storage industry. 

The internships aim to provide students with research and analysis skills that will be valuable for their future professional lives. The virtual internship allows students to complete their internship hours virtually, providing flexibility to fit the experience into their busy personal and professional lives. Additionally, virtual interns enjoy the unique rewards of learning from experts regardless of their geographic location and strengthening their information and computer skills. 

The internships are strong resume boosters for employers, graduate college programs, and undergraduate programs. 

EnergyMag offers half-time and quarter-time virtual internships. Half-time internships are available in the summer for two to eight weeks, with interns expected to work approximately 20 hours per week. Quarter-time internships are available all year round for one to nine months, with interns expected to work approximately eight hours per week. The internships are unpaid, and interns work from home while maintaining daily electronic contact with EnergyMag and their mentor. 

Depending on the student’s graduation date, academic record, and experience, interns will be asked to research and analyze a specific company, technology, or market. The intern will be mentored, briefed, supervised, and assisted in producing a draft analysis report. If the report is publishable, EnergyMag will give the intern an internship Letter of Accomplishment. 

The application process for college and high school internships requires an application explaining why EnergyMag should grant an internship, a Skype or voice interview, and a writing sample upon request. College interns are also required to provide their academic record, and high school interns should have at least one honors science or English class with a GPA above 3.25. 

EnergyMag believes that internships provide the opportunity for students to learn on-the-job skills that are not easy to acquire at school but will make a big difference in their future professional success, such as learning how to research a scientific or business issue, approach strangers with positions of authority in a friendly and professional manner, analyze and synthesize information from multiple sources, and communicate professionally in writing.

The blog highlights five virtual research opportunities for high school students, providing hands-on experience and research projects in various STEM fields such as mathematics, computer science, physics, neuroscience, and engineering. These virtual research opportunities aim to provide students with a deeper understanding of STEM and develop the necessary skills to succeed in academic and professional careers. Furthermore, these programs help expand knowledge and work on unsolved problems with established researchers from top-tier universities.

Virtual research opportunities for high school students provide a flexible and accessible way to gain valuable experience and knowledge from the comfort of their own homes. These programs aim to foster the intellectual growth and development of high school and middle school students, and inspire them to pursue their interests in these fields.

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Virtual Math Circle: Research Opportunities for High School Students

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Math Circle virtual summer camps bring together rising 9th–12th grade math enthusiasts to:

• learn material not typically taught in a high school curriculum;
• traverse the complex world of college mathematics;
• conduct mathematical research with guidance from university faculty and graduate students;
• present a 45-minute, colloquial-style poster session;
• hone research and communication skills through a capstone project.

Each student project may potentially:

• qualify as a fall science fair project;
• evolve into deeper research experiences with faculty;
• merit financial support towards future travel to conferences, or for publication costs;
• enhance college applications.

Math Circle virtual summer camps are an outreach collaboration between the LSU Department of Mathematics and the LSU Gordon A. Cain Center for STEM Literacy .

Work with a mentor and peers

At the start of the summer camp, research mentors give virtual talks on their area of research and potential research topics. Students in groups of 4 will meet virtually with their mentor, Monday–Friday for 2–3 hours each day, for a duration of 3 weeks. Students will be exposed to a wide variety of topics in each field and will gain a solid foundation in university-level mathematics.

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Wolfram High School Summer Research Program

Formerly known as the Wolfram High School Summer Camp

Bentley University , Boston, MA June 25–July 13, 2024

A project-based research opportunity for motivated high-school students to move beyond the cutting edge of computational thinking and artificial intelligence.

The Wolfram High School Summer Research Program is an intensive two-week program designed to advance high-school students' programming and problem-solving skills. Through a curriculum of active-learning activities, hands-on workshops and lectures, students explore the power of modern computation and deep dive into STEM fields while gaining mastery of Wolfram Language, computational thinking and research skills.

Under the guidance of expert mentors, students research and implement solutions to cutting-edge problems selected in collaboration with Stephen Wolfram. Projects are novel contributions to the field and are personalized to the students' interests and skill sets. Each student writes a computational essay and an interactive research paper and publishes their work at the end of the program. Successful projects can be submitted to STEM competitions, turned into academic papers or presented at the Wolfram Technology Conference.

This program was brilliant for research, and I got to meet so many great, qualified people here at Wolfram. From selecting my project topic with Stephen Wolfram to talking with my mentor about technical concepts and my college trajectory, I gained so much knowledge from this program.

Hyunjae Chung

This was not only an academically enriching experience but also an introduction to an incredibly bright community of dedicated, driven and kind people. Perhaps even more important than the practical skills gained and excellent work that each student came away with from their projects, this program was an opportunity to connect like-minded and truly passionate students and experts from around the world and develop lasting connections.

Victor Zhou

I'm so glad I was given this experience. I now know that it's very possible to explore on your own and make your own projects. We were given the opportunity to talk with so many knowledgeable people who answered so many of our questions, no matter how technical or philosophical.

Arianna Cao

After the summer, successful students enter our ecosystem of education opportunities. This may include doing an advanced project at the Wolfram Emerging Leaders Program , joining our teaching team, connecting with professional mentors or engaging with fundamental physics and metamathematics research at the Wolfram Institute . Particularly successful students are invited to complete internships at Wolfram Research.

We are seeking motivated high-school students interested in solutions-driven research and creating innovative technology. As we are committed to enabling ambitious students, regardless of background or resources, we provide needs-based scholarships and offer a pre-programming workshop for students with limited coding experience.

Featured Projects

Generating animated guitar tutorials

My project uses chords or MIDI files as input and creates an animated tutorial video. My implementation finds the pitches that match a chord on the fretboard in a localized area. To account for some commonly used patterns, I use the CAGED system on guitar. This project also includes an implementation of major scale patterns and tab sheet implementation.

Nikhil Mani

Class of 2023

Multiway sequential cellular automata

The study of cellular automata is useful for modeling many evolving systems. In my project, I examine a novel variant of cellular automata that uses sequential updating with multiple sets of rules, resulting in multiway sequential cellular automata. This structure has the potential for modeling many aspects of quantum mechanics, including possibly quantum spin chains. A deeper exploration highlights the impact of specific subsets of multiway circular sequential cellular automata rules on the directionality, behavior, symmetry and causal invariance of the resulting states graphs.

Margaux Wong

Class of 2022

Generate Super Mario Bros. levels

Super Mario Bros. is one of the top-selling video games of all time and is known for its excellently designed platforming levels, which pioneered the platforming video game genre. My project uses a convolutional neural network to help determine whether an array is a Mario level and to generate them using levels from Super Mario Bros. and its sequel Super Mario Bros.: The Lost Levels.

Samion Suwito

Implementing counter machines

The objective of this project was to implement counter machines in Wolfram Language and establish which counter machine was the most unpredictable. I designed a general counter machine function and used this function to demonstrate five types of counter machines. I determined which counter machines were unpredictable and explored complexity by adding more registers.

Samikshaa Natarajan

Class of 2021

Building a graph-based reaction network

When performing syntheses in a lab, it can be challenging to find the shortest path and to avoid exceptions and pitfalls. A computational system for predicting synthesis pathways can help take the burden off of a chemist and can allow for more consistent results. By transcribing common reactions computationally and applying them recursively, a network can be generated to inform decisions in the lab. My project focused on building the groundwork for this in Wolfram Language, providing informative and computationally significant results and paving the way for comprehensive computational synthesis design.

Joseph Stocke

Automatic Metrical Scansion of Latin Poetry in Dactylic Hexameter

Many significant works of Latin poetry follow the format of dactylic hexameter, meaning that each line is composed of some combination of six metrical feet, each of which is either two long syllables or a long syllable followed by two short syllables. Scansion is the process of identifying the pattern of syllable lengths. Through this project, I use machine learning to scan lines of Latin poetry in dactylic hexameter.

Class of 2019

Colorful Fraud: Exposing Vulnerabilities in Neural Networks

In a day and age where many consider deep learning an off-the-shelf solution to any and all classification/prediction problems, it's important that people examine whether their neural network models are vulnerable to targeted attacks. This project implements a framework for generating adversarial examples: input data crafted to cause the neural network to produce unexpected or targeted incorrect behavior.

Projects From the Wolfram Summer Research Program

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Math Project Ideas for High School

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Are you tired of hearing, “When will we ever use this type of math?” Explore the world of applied math with these math projects for high school students.

High School Math Project Ideas by Subject

Math projects are an ideal way to increase your students’ enthusiasm for math.

Math is not a dull subject! With these math projects, students will use the skills of research, problem-solving, critical thinking, and creativity.

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Algebra Math Project Ideas

These algebra math project ideas for high school bring algebra into the real world.

Modeling Real-World Situations

Are your students interested in the population of endangered species? Or the growing population of the planet?

Are they curious about investing and seeing their money grow?

Teach them to create mathematical models of real-life situations and use these tools to analyze the data.

Data Analysis and Statistics

Students can collect data on a topic of interest, such as sports, weather patterns, or social media usage, and perform statistical analysis using algebraic techniques.

They can create scatter plots, calculate regression lines, analyze correlation coefficients, and draw conclusions based on their findings.

Fantasy Football Mathematical Modeling

Do you have students who love fantasy football?

Give them an edge by incorporating algebra!

Students can use algebraic concepts to analyze various aspects of the game.

They can explore topics such as scoring trends, player performance evaluation, or game strategies using mathematical models and statistical analysis.

Algebraic Art

On graph paper, students can plot various algebraic functions (linear, quadratic, or exponential).

(You could also use a digital graphing program.)

Where the functions overlap, color the shapes.

Explore symmetry, transformations, and creativity through this combination of math and art!

Financial Literacy Project

Students pick a future career and a hypothetical budget based on that income.

Use algebraic equations to calculate savings, loan payments, and interest.

Explore the concepts of compound interest and debt repayment.

Geometry Math Project Ideas

These geometry math project ideas for high school highlight all that is weird and wonderful about shapes!

Exploring Fractals

Fractals are fascinating! They involve a shape that branches into smaller versions of itself.

They are found in nature (think ferns and snowflakes), have applications to tech, and make for incredible artwork!

Check out some digital art involving fractals.

Students can research and create visual representations of different fractals, such as the Sierpinski Triangle, Koch Snowflake, or Mandelbrot Set.

Investigating Polyhedra

Students can study different types of polyhedra, such as platonic solids or Archimedean solids.

They can construct physical models (straws and pipe cleaners, anyone?).

They can also use software to explore their properties, such as the number of vertices, edges, and faces.

Students can learn about their various patterns of symmetry.

Designing a Geometric City

Students can design a fictional city using geometric principles.

They can create a layout for the city, incorporating different shapes, angles, and proportions.

Make the project cross-curricular by creating a story of life in the fictional city.

Urban Planning

Students can explore how geometric concepts are applied in urban planning and architecture.

Which cities of the world are the most geometric in their design?

Which architectural styles are the most “Euclidean”?

Analyzing Tessellations

Students can investigate tessellations and their properties. This is an excellent jumping-off point to the various types of symmetry.

They can create their own tessellation patterns using regular polygons or explore famous examples of tessellations found in art and nature.

Geometry in Art

Students can explore the relationship between geometry and art.

They can research different artists who incorporate geometric principles in their work, such as Piet Mondrian or M.C. Escher.

(You can even find fractals in Jackson Pollock paintings!)

They can analyze the use of symmetry, proportion, and geometric shapes in these artworks.

Go one step further and have students create their own geometric art pieces.

Calculus Math Project Ideas

Calculus helps us understand our world. Make it come alive with these calculus math project ideas for high school students.

Optimization Problems

How does calculus intersect with the real world? Knowing calculus can save money!

It has implications in product design and even backyard projects!

Students can explore optimization problems by finding functions’ maximum or minimum values in various contexts.

They can explore real-world scenarios, such as maximizing the volume of a box given a fixed amount of material or minimizing the cost of constructing a fence.

The Trouble with Tribbles

(Okay, okay, this is a Star Trek reference no student will likely get.)

You can riff on this episode with fun exponential growth or decay scenarios.

(In fact, Fibonacci himself conceptualized his sequence by imagining a colony of rapidly mating rabbits.)

Students can use calculus to analyze the growth or decay of their imaginary species.

The Shape of Water

Calculus is geometry’s much cooler big brother.

Bring in three-dimensional shapes (like water bottles, bowling pins, etc.) and show students how to find the surface area of these shapes using integral calculus.

They can then try it on their own!

Calculus in Physics

Students can explore the application of calculus in physics problems.

They can choose topics such as motion, forces, or energy and use calculus concepts to analyze these phenomena.

Have them give a demonstration of these applications to the class.

Calculus in Engineering

Students can explore how calculus is used in engineering applications.

They can choose topics such as fluid flow, structural analysis, or electrical circuits and use calculus to model and solve engineering problems.

Calculus in Tech

Explore how technology uses calculus (for example, GPS and image processing).

Analyze algorithms and mathematical models. What are the limitations? How can this technology improve?

High School Math Project Ideas

These math projects for high school will help your students see the purpose (and fun) in math).

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Innovative Statistics Project Ideas for Insightful Analysis

Table of contents

• 1.1 AP Statistics Topics for Project
• 1.2 Statistics Project Topics for High School Students
• 1.3 Statistical Survey Topics
• 1.4 Statistical Experiment Ideas
• 1.5 Easy Stats Project Ideas
• 1.6 Business Ideas for Statistics Project
• 1.7 Socio-Economic Easy Statistics Project Ideas
• 1.8 Experiment Ideas for Statistics and Analysis
• 2 Conclusion: Navigating the World of Data Through Statistics

Diving into the world of data, statistics presents a unique blend of challenges and opportunities to uncover patterns, test hypotheses, and make informed decisions. It is a fascinating field that offers many opportunities for exploration and discovery. This article is designed to inspire students, educators, and statistics enthusiasts with various project ideas. We will cover:

• Challenging concepts suitable for advanced placement courses.
• Accessible ideas that are engaging and educational for younger students.
• Ideas for conducting surveys and analyzing the results.
• Topics that explore the application of statistics in business and socio-economic areas.

Each category of topics for the statistics project provides unique insights into the world of statistics, offering opportunities for learning and application. Let’s dive into these ideas and explore the exciting world of statistical analysis.

Top Statistics Project Ideas for High School

Statistics is not only about numbers and data; it’s a unique lens for interpreting the world. Ideal for students, educators, or anyone with a curiosity about statistical analysis, these project ideas offer an interactive, hands-on approach to learning. These projects range from fundamental concepts suitable for beginners to more intricate studies for advanced learners. They are designed to ignite interest in statistics by demonstrating its real-world applications, making it accessible and enjoyable for people of all skill levels.

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AP Statistics Topics for Project

• Analyzing Variance in Climate Data Over Decades.
• The Correlation Between Economic Indicators and Standard of Living.
• Statistical Analysis of Voter Behavior Patterns.
• Probability Models in Sports: Predicting Outcomes.
• The Effectiveness of Different Teaching Methods: A Statistical Study.
• Analysis of Demographic Data in Public Health.
• Time Series Analysis of Stock Market Trends.
• Investigating the Impact of Social Media on Academic Performance.
• Survival Analysis in Clinical Trial Data.
• Regression Analysis on Housing Prices and Market Factors.

Statistics Project Topics for High School Students

• The Mathematics of Personal Finance: Budgeting and Spending Habits.
• Analysis of Class Performance: Test Scores and Study Habits.
• A Statistical Comparison of Local Public Transportation Options.
• Survey on Dietary Habits and Physical Health Among Teenagers.
• Analyzing the Popularity of Various Music Genres in School.
• The Impact of Sleep on Academic Performance: A Statistical Approach.
• Statistical Study on the Use of Technology in Education.
• Comparing Athletic Performance Across Different Sports.
• Trends in Social Media Usage Among High School Students.
• The Effect of Part-Time Jobs on Student Academic Achievement.

Statistical Survey Topics

• Public Opinion on Environmental Conservation Efforts.
• Consumer Preferences in the Fast Food Industry.
• Attitudes Towards Online Learning vs. Traditional Classroom Learning.
• Survey on Workplace Satisfaction and Productivity.
• Public Health: Attitudes Towards Vaccination.
• Trends in Mobile Phone Usage and Preferences.
• Community Response to Local Government Policies.
• Consumer Behavior in Online vs. Offline Shopping.
• Perceptions of Public Safety and Law Enforcement.
• Social Media Influence on Political Opinions.

Statistical Experiment Ideas

• The Effect of Light on Plant Growth.
• Memory Retention: Visual vs. Auditory Information.
• Caffeine Consumption and Cognitive Performance.
• The Impact of Exercise on Stress Levels.
• Testing the Efficacy of Natural vs. Chemical Fertilizers.
• The Influence of Color on Mood and Perception.
• Sleep Patterns: Analyzing Factors Affecting Sleep Quality.
• The Effectiveness of Different Types of Water Filters.
• Analyzing the Impact of Room Temperature on Concentration.
• Testing the Strength of Different Brands of Batteries.

Easy Stats Project Ideas

• Average Daily Screen Time Among Students.
• Analyzing the Most Common Birth Months.
• Favorite School Subjects Among Peers.
• Average Time Spent on Homework Weekly.
• Frequency of Public Transport Usage.
• Comparison of Pet Ownership in the Community.
• Favorite Types of Movies or TV Shows.
• Daily Water Consumption Habits.
• Common Breakfast Choices and Their Nutritional Value.
• Steps Count: A Week-Long Study.

Business Ideas for Statistics Project

• Analyzing Customer Satisfaction in Retail Stores.
• Market Analysis of a New Product Launch.
• Employee Performance Metrics and Organizational Success.
• Sales Data Analysis for E-commerce Websites.
• Impact of Advertising on Consumer Buying Behavior.
• Analysis of Supply Chain Efficiency.
• Customer Loyalty and Retention Strategies.
• Trend Analysis in Social Media Marketing.
• Financial Risk Assessment in Investment Decisions.
• Market Segmentation and Targeting Strategies.

Socio-Economic Easy Statistics Project Ideas

• Income Inequality and Its Impact on Education.
• The Correlation Between Unemployment Rates and Crime Levels.
• Analyzing the Effects of Minimum Wage Changes.
• The Relationship Between Public Health Expenditure and Population Health.
• Demographic Analysis of Housing Affordability.
• The Impact of Immigration on Local Economies.
• Analysis of Gender Pay Gap in Different Industries.
• Statistical Study of Homelessness Causes and Solutions.
• Education Levels and Their Impact on Job Opportunities.
• Analyzing Trends in Government Social Spending.

Experiment Ideas for Statistics and Analysis

• Multivariate Analysis of Global Climate Change Data.
• Time-Series Analysis in Predicting Economic Recessions.
• Logistic Regression in Medical Outcome Prediction.
• Machine Learning Applications in Statistical Modeling.
• Network Analysis in Social Media Data.
• Bayesian Analysis of Scientific Research Data.
• The Use of Factor Analysis in Psychology Studies.
• Spatial Data Analysis in Geographic Information Systems (GIS).
• Predictive Analysis in Customer Relationship Management (CRM).
• Cluster Analysis in Market Research.

Conclusion: Navigating the World of Data Through Statistics

In this exploration of good statistics project ideas, we’ve ventured through various topics, from the straightforward to the complex, from personal finance to global climate change. These ideas are gateways to understanding the world of data and statistics, and platforms for cultivating critical thinking and analytical skills. Whether you’re a high school student, a college student, or a professional, engaging in these projects can deepen your appreciation of how statistics shapes our understanding of the world around us. These projects encourage exploration, inquiry, and a deeper engagement with the world of numbers, trends, and patterns – the essence of statistics.

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Call for High School Projects

Machine learning for social impact .

The Thirty-Eighth Annual Conference on Neural Information Processing Systems (NeurIPS 2024) is an interdisciplinary conference that brings together researchers in machine learning, neuroscience, statistics, optimization, computer vision, natural language processing, life sciences, natural sciences, social sciences, and other adjacent fields. 

This year, we invite high school students to submit research papers on the topic of machine learning for social impact.  A subset of finalists will be selected to present their projects virtually and will have their work spotlighted on the NeurIPS homepage.  In addition, the leading authors of up to five winning projects will be invited to attend an award ceremony at NeurIPS 2024 in Vancouver.  

Each submission must describe independent work wholly performed by the high school student authors.  We expect each submission to highlight either demonstrated positive social impact or the potential for positive social impact using machine learning. Application areas may include but are not limited to the following:

• Agriculture
• Climate change
• Homelessness
• Food security
• Mental health
• Water quality

Authors will be asked to confirm that their submissions accord with the NeurIPS code of conduct and the NeurIPS code of ethics .

Submission deadline: All submissions must be made by June 27th, 4pm EDT. The system will close after this time, and no further submissions will be possible.

We are using OpenReview to manage submissions. Papers should be submitted here . Submission will open June 1st.  Submissions under review will be visible only to their assigned program committee. We will not be soliciting comments from the general public during the reviewing process. Anyone who plans to submit a paper as an author or a co-author will need to create (or update) their OpenReview profile by the full paper submission deadline. 

Formatting instructions:   All submissions must be in PDF format. Submissions are limited to four content pages , including all figures and tables; additional pages containing only references are allowed. You must format your submission using the NeurIPS 2024 LaTeX style file using the “preprint” option for non-anonymous submission. The maximum file size for submissions is 50MB. Submissions that violate the NeurIPS style (e.g., by decreasing margins or font sizes) or page limits may be rejected without further review.  Papers may be rejected without consideration of their merits if they fail to meet the submission requirements, as described in this document. 

Mentorship and collaboration:  The submitted research can be a component of a larger research endeavor involving external collaborators, but the submission should describe only the authors’ contributions.  The authors can also have external mentors but must disclose the nature of the mentorship.  At the time of submission, the authors will be asked to describe the involvement of any mentors or external collaborators and to distinguish mentor and collaborator contributions from those of the authors.  In addition, the authors may (optionally) to include an acknowledgements section acknowledging the contributions of others following the content sections of the submission. The acknowledgements section will not count toward the submission page limit.

Proof of high school attendance: Submitting authors will also be asked to upload a signed letter, on school letterhead, from each author’s high school confirming that the author was enrolled in high school during the 2023-2024 academic year.

Supplementary artifacts:  In their submission, authors may link to supplementary artifacts including videos, working demonstrations, digital posters, websites, or source code.  Please do not link to additional text.  All such supplementary material should be wholly created by the authors and should directly support the submission content. 

Review process:   Each submission will be reviewed by anonymous referees.  The authors, however, should not be anonymous.  No written feedback will be provided to the authors.  

Use of Large Language Models (LLMs): We welcome authors to use any tool that is suitable for preparing high-quality papers and research. However, we ask authors to keep in mind two important criteria. First, we expect papers to fully describe their methodology.  Any tool that is important to that methodology, including the use of LLMs, should be described also. For example, authors should mention tools (including LLMs) that were used for data processing or filtering, visualization, facilitating or running experiments, or proving theorems. It may also be advisable to describe the use of LLMs in implementing the method (if this corresponds to an important, original, or non-standard component of the approach). Second, authors are responsible for the entire content of the paper, including all text and figures, so while authors are welcome to use any tool they wish for writing the paper, they must ensure that all text is correct and original.

Dual submissions:  Submissions that are substantially similar to papers that the authors have previously published or submitted in parallel to other peer-reviewed venues with proceedings or journals may not be submitted to NeurIPS. Papers previously presented at workshops or science fairs are permitted, so long as they did not appear in a conference proceedings (e.g., CVPRW proceedings), a journal, or a book.  However, submissions will not be published in formal proceedings, so work submitted to this call may be published elsewhere in the future. Plagiarism is prohibited by the NeurIPS Code of Conduct .

Paper checklist: In order to improve the rigor and transparency of research submitted to and published at NeurIPS, authors are required to complete a paper checklist . The paper checklist is intended to help authors reflect on a wide variety of issues relating to responsible machine learning research, including reproducibility, transparency, research ethics, and societal impact. The checklist does not count towards the page limit and will be entered in OpenReview.

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New $90 Million Project to Create Digital Research Hub Focused on K-12 Education

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The National Science Foundation has awarded Rice University $90 million to build what is being described as a first-of-its-kind education research hub that will leverage data from an array  of major digital learning platforms currently serving tens of millions of students. 

The university recently announced the investment as its largest ever federal research grant. OpenStax at Rice, a major publisher of open education resources, will build the research and development hub known as SafeInsights .

The project will focus on producing “research-informed insights about teaching and learning for educators, institutions and learning platforms to use to create tailored programs, pedagogies and policies that will equip learners to thrive.”

“Just like there are bigger telescopes that let astronomers see deeper into the night, SafeInsights’ goal is to have this large student population that will enable researchers to see deeper into the student learning experience,” Slavinsky said in an interview. 

The SafeInsights hub will take five years to build, he said, with early research projects b eginning in 16 to 18 months, and full-scale research operations starting in 2029. 

School districts’ commitment to seeking and using research-based educational strategies is uneven at best. Many district officials complain that academic and other scientifically based research is too abstract, disconnected from their work, and outdated to be of practical use in their decision-making.

When surveyed recently by EdWeek Market Brief on what sorts of research they value most when choosing products and services, district and school leaders were much more likely to point to data on student outcomes, or product usage data than they were rigorous, experimental research.

Data Security in Focus 

At $90 million, the award is NSF’s largest investment in research and development infrastructure for education at a national scale, the university said.

In the past, education research has been hampered by small study groups and short time frames, but the recent boom in digital learning can provide researchers with a plethora of data needed to better understand academic outcomes, Slavinsky said. 

SafeInsights’ goal is to have this large student population that will enable researchers to see deeper into the student learning experience. J.P. Slavinsky, Executive Director, SafeInsights

And research will not be limited to only STEM (science, technology, engineering, and math) areas. Schools, education companies, and researchers participating in SafeInsights will bring their own research agenda, Slavinsky said.

Protecting student data is a major concern within school districts, particularly as  schools’ and students’ reliance on technology  has steadily grown.

The data collected as part of the new project will remain secure, Slavinsky said. No student information will be revealed to researchers. 

Instead, researchers will submit their inquiries to SafeInsights, and the research hub will have the data in question analyzed where it is originally stored — by schools or on a digital platform — and provide researchers with aggregate results. 

The research and development project will be a central hub for 80 partners and collaborating institutions. That number is expected to grow, Slavinsky said. 

“One of the great things about SafeInsights is that it is very scalable,” he said. “And we want to build this community, so we can get a better and better picture of the students and the teachers we’re trying to help.” 

Follow  EdWeek Market Brief  on Twitter  @EdMarketBrief  or connect with us on  LinkedIn .

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ACS Project SEED Program – Bringing Research and High School Students Together

This summer, 17 high school students in the American Chemical Society Snake River Section will have the opportunity to conduct research through the ACS Project SEED program.

Project SEED, originally “Summer Experiences for the Economically Disadvantaged,” was born in 1968. Now 56 years old, the program has provided hands-on summer research experiences and webinars to over 13,000 students across the U.S. and its territories. The Project SEED Mission is “to provide sustained STEM research, learning, and growth opportunities for high school students with diverse identities and socioeconomic backgrounds so they can be empowered to advance and enrich the chemical science enterprise.”

Each year, high school students spend 10 weeks in an industry lab or at host institutions like Boise State University working alongside PIs and qualified mentors on cutting-edge research projects. In addition to the technical skills learned in the lab, students will participate in professional development activities to enhance skills in time management, teamwork, and research presentation. The Project SEED webinars cover topics such as personal and chemical safety, career exploration, college readiness, resume building, and mental health and wellness. The summer experience is culminated in a poster presentation where the student present their research, with this year’s presentations being held at the Idaho Conference on Undergraduate Research.

The ACS Snake River Section Project SEED coordinator is Boise State’s Dr. Don Warner, a professor in the Department of Chemistry and Biochemistry. This year he placed 17 students, 8 of whom are returning participants. He received 70 applications and conducted 24 initial interviews to fill the 9 open spots. Two students are going to Northwest Nazarene University to work with Jerry Harris on synthesizing and characterizing zinc oxide nanoparticles with enhanced antimicrobial properties. Two more will go to Danny Xu’s lab at Idaho State University – Meridian to research the effects of Lunar and Martian regolith on zebrafish.

The remaining 13 students will be working in several laboratories across campus at Boise State University this summer. The PIs hosting students, and their projects, are:

• Oliviero Andreussi: Computational Study of Materials for Electro-Catalysis
• Leonora Bittleston: 4: Exploring the effects of leaf chemistry on microbial colonization
• Eric Brown: Development of molecules that inhibit a bacteria’s ability to cause disease
• Ken Cornell: Analysis of Antimicrobial Activity of Nanoparticles and Organometallic Complexes
• Jenée Cyran & Brian McClain: Developing innovative Physical Chemistry Lab Modules
• Owen McDougal: Chemistry of Food Systems
• Konrad Meister: Cool Molecules: Understanding the Mode of Action of Ice-Binding Macromolecules
• Don Warner: Synthesis of small molecules for inhibition of tumor metastasis
• Claire Xiong: Sodium Ion Batteries

Participants in the Project SEED program are awarded a stipend for their efforts, providing low-income students the opportunity to participate while earning money to help support their families. This crucial funding in 2024 is largely from the American Chemical Society, but also contributed to by Northwest Nazarene University, the ACS Snake River Local Section, and from Boise State University’s College of Arts & Sciences, Research and Economic Development, Materials Science and Engineering, Chemistry & Biochemistry, several individual PIs, and the university itself. Some of the program’s graduates will also receive scholarships from Project SEED to help fund their undergraduate education.

For more information on this amazing program, visit ACS News to read Project SEED’s Impact Continues to Grow .

Interested in getting involved? Visit Project SEED on the American Chemical Society’s webpage.

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UCSB Research Mentorship Program (RMP) 2024

The UCSB Research Mentorship Program (RMP) is seeking graduate students, postdocs, and researchers to mentor high school students through a research project in STEM, humanities, social sciences, or education. Up to $1300 per project, per student. Application deadline is June 1. Learn More!

The UCSB Research Mentorship Program (RMP) is seeking graduate students, postdocs, and researchers for a paid mentorship opportunity this summer. RMP is a highly selective and competitive six-week summer program that engages qualified, talented high school students from all over the world in interdisciplinary, hands-on, university-level research. RMP is seeking mentors who can guide students through a research project in STEM, humanities, social sciences, or education.

Program Details :

RMP students are highly qualified and expect to work independently; in addition, students are well-prepared and have extensive programming, lab, and primary source analysis experience.

Mentors must meet mentees regularly to guide students through projects. 

Prospective Mentors may submit up to 2 projects (up to 2 students per project for a compensation of up to $5,200).

The proposed project must have a hands-on component (lab, field, computational, theory, archival, primary source analysis, etc.).

Mentor Eligibility:

Graduate Student, Postdoctoral Researcher, Research Scientist, or Faculty

Must be available (on campus) during the program dates—short travel trips are acceptable during this period as long as it does not impact student support

All disciplines considered in STEM, Humanities, Social Sciences, and Education (interdisciplinary preferred)

Dates : RMP is offered during Summer Session A (June 17-August 2).

Mentor Stipend : $1,300 per project, per student

Application Deadline: June 1, 2024  *Space is limited! Mentor applications are accepted and approved on a rolling basis.

For more program information or to apply , please visit:  summer.ucsb.edu/rmp/ mentors General questions, please email:  [email protected]

High School Student Researches Real-Life Marketing

Authentic exploratory research hones students’ business and analysis skills..

Posted May 1, 2024 | Reviewed by Monica Vilhauer

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This is the second post in a series.

What if high school students could conduct methodical research on important questions like graduate students and researchers do? Well, as the students at Laguna Beach High School (LBHS) are demonstrating, they can.

In Part I of this series I interviewed Jun Shen, the passionate teacher and edtech coordinator who runs LBHS’s Authentic Exploratory Research (AER) Program . AER is an independent research course inspired by Palo Alto Unified School District’s Advanced Authentic Research program . The program pairs students with adult mentors (such as LBUSD staff, industry experts, and academics) who assist the teens in researching their own big questions in fields of their choice. Shen’s explanation of how the AER program works, combined with students’ input through the rest of this interview series, lets us glimpse some of the different ways students can use the program to pursue individual passions , as well as how other educators can implement such a program.

LBHS student Aryana Mohajerian was the first to give us an account of her experience in AER and the findings that her AER research produced. Mohajerian’s answers follow each question below.

Jenny Grant Rankin: In short, what was your research study about?

Aryana Mohajerian: In short, my research was about marketing a membership program to different target demographics in a small, high-end, health-conscious, confectionary business in Hawaii.

I analyzed how new marketing efforts will help increase overall revenue and cash flow in the business. The new strategies I implemented were creating a set target market using survey data. I also created a brand kit with all the customer values, color palettes for the website, and copy.

JGR: What were your most important findings?

AM: My most important findings were that it is critical to know the psychology of business and be able to put yourself in the customer’s shoes. I had to figure out what a target market’s values, goals , and mindset are like to better appeal to their logic and emotions when trying to make a sale.

I distributed a survey to better understand the company’s current customers, what their values are, and what draws them towards purchasing.

When proposing ideas for what draws customers to the company, my hypothesis proved correct. 100% of people selected that they value environmental sustainability and the farm-to-table process. 70% of people selected that they are health-conscious consumers and 85% love the Hawaii-island, beachy lifestyle. With these proven conclusions, I created three new membership plans for Lonohana, each targeting a specific audience, according to the survey results.

The first membership was family-oriented, catering to children and their parents. The customer values were inclusivity, appeals to a health-conscious family, and living an active lifestyle in the great outdoors. The second membership caters to young adults. For example, college students or recent graduates living a youthful, and spontaneous lifestyle. This membership was an affordable line of products, since young adults like to have fun on a budget. These young individuals love the island lifestyle of Hawaii and love trying Lonohana’s unique flavors. The third membership was targeted toward more professional and formal individuals. These high-end customers value luxury products and the education behind making them. This membership included informational cards on each bar, describing how it was made and where the ingredients come from.

JGR: What was the biggest thing you learned about conducting research?

AM: The biggest thing I learned about conducting research is that it requires thorough planning and first making a hypothesis of what the results will be. Understanding the psychology behind why people spend money on luxury items was essential because it guided me on how I worded my survey to get the most honest responses from customers. For example, a customer value I noted was a sense of family and community involvement. Therefore, I concluded that customers are likely to purchase membership boxes to have enough gifts on hand for family or community gatherings, which was proven true based on the survey.

JGR: What was the biggest thing you learned about communicating research?

AM: The biggest thing I learned about communicating research is that I need to create an eye-catching, yet simple poster to present at the AER Symposium. When I did my presentation, I mainly focused on the visuals of my project and some easy-to-read graphs. I brought the marketing materials I had made, such as brochures, business cards, and the printed-out brand kit to show my audience. I found that having a hands-on experience with cohesively colored materials helped me get my message across in a fun way that did not bore anyone. Having all these materials helped invoke questions from my audience as well.

JGR: What was your favorite part about AER?

AM: My favorite part about AER was the fact that I was able to work with a real-world company while in high school alongside a mentor who was working my dream job. AER was such a unique opportunity for me to learn about my interest in marketing and the psychology behind why we buy luxury items. Although this was a class, it did not feel like traditional learning because I went out into the real world to enhance a business’s marketing tactics. Learning by doing is the best way to gain experience. I learned a lot more about marketing through my AER project than I did taking “Intro to Marketing” in a dual-enrollment community college class.

It’s exciting to find that the program advanced not only Mohajerian’s research skills but her career skills, as well. That is a common theme in students’ accounts of their AER experiences.

Jenny Grant Rankin, Ph.D., is a Fulbright Specialist for the U.S. Department of State.

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• Neuroscience

Other programs for high school students, which stimulate the development of math research skills

• APEX-Maths (Academic Program of EXcellence in Mathematics) is an intensive and immersive 3-weeks-long summer residential program in Romania offering a unique opportunity to get a taste of mathematical research and scientific discovery. The participants - a maximum number of 40 - will be able to experience the world of research from within, as they will explore new mathematical concepts under the guidance of top internationally recognized university professors and PhD students.
• Canada/USA Mathcamp is an intensive 5-week-long summer program for mathematically talented high school students. More than just a summer camp, Mathcamp is a vibrant community, made up of a wide variety of people who share a common love of learning and passion for mathematics. At Mathcamp, students can explore undergraduate and even graduate-level topics while building problem-solving skills that will help them in any field they choose to study.
• Girls’ Angle is a math club for girls (grade 5-12), based in Cambridge, Mass., whose mission is to foster and nurture girls’ interest in mathematics and empower them to tackle any field no matter the level of mathematical sophistication. At the Club, girls work directly with their mentors and members of the Support Network. The Support Network consists of professional women who use math in their work and are eager to show the members how and for what they use math.
• HCSSiM (Hampshire College Summer Studies in Mathematics) is an intensive six-week encounter with college-level mathematics for talented and highly motivated high school students. Participants spend a major portion of each day actively engaged in doing mathematics (not simply learning the results of mathematics).
• MasterScholar (North Carolina Math Camp) is a two-week summer program staffed with faculty and students from Duke University. It emphasizes the development of students' ability to think deeply about simple concepts, guides students to approach challenging, unseen mathematical problems from outside the box, and includes research presentations as well as paper write-ups.
• MathILy (serious Mathematics Infused with Levity) is an intensive residential summer program for mathematically excellent secondary students. Instructors provide the framework, and students get to make (and prove!) the conjectures. They encounter new ideas, improve their problem-solving skills, learn lots and lots of advanced mathematics, and hone their overall thinking skills.
• PROMYS (Program in Mathematics for Young Scientists) is a six-week summer program at Boston University designed to encourage strongly motivated high school students to explore in depth the creative world of mathematics in a supportive community of peers, counselors, research mathematicians, and visiting scientists.
• Prove it! is a two-week summer camp at Colorado State University, which provides a challenging and rigorous introduction to mathematical proof with applications to advanced topics chosen from the instructors' areas of expertise and interest. The program simulates the major aspects of the research process in mathematics.
• Ross Mathematics Program is an intensive summer experience designed to encourage motivated pre-college students to explore mathematics. During those weeks, students are immersed in a world of mathematical discovery. First year participants take an inquiry-based course in number theory; returning students participate in other courses.
• RSI (Research Science Institute) is a five week research internship at MIT where students conduct individual projects under the tutelage of mentors who are experienced scientists and researchers. During the final week of RSI, students prepare written and oral presentations on their research projects.
• SUMaC (Stanford University Mathematics Camp) offers two courses with unique topics for each course. Both programs feature the research project where participants pursue course topics in greater depth. For this activity, participants initially work in groups under the leadership of the Teaching Assistants, and using journal articles, advanced textbooks, and other materials. At the end of the course, participants give presentations on their topics to their peers.
• Yau Mathcamp is a summer camp in China for mathematically talented and strongly motivated secondary school students from China and all over the world. A highly selected group of students are invited to join a rigorous month-long program to explore the art of creative problem solving with masters. Yau Mathcamp also offers a great opportunity for students to work on research projects through collaborative discoveries guided by their coaches and teachers.

See also programs run by PRIMES students and alumni:

• GirlsxMRO (Math Research Outreach for Girls), a five-week summer program dedicated to introducing rising 8th to 10th grade girls to the world of math beyond competitions, including advanced topics and research.
• MATH ROCs (Math Research Outreach Conference), an open two-day event, where you can learn about higher math and how to get involved with high school research.

Other opportunities:

• Mathematical Opportunities from the American Mathematical Society
• Young Scholars Programs , recipients of AMS Epsilon Award
• Mathematics summer programs for elementary/middle/high school on the Art of Problem Solving website

With questions, contact PRIMES Program Director Slava Gerovitch at

Facility for Rare Isotope Beams

At michigan state university, international research team uses wavefunction matching to solve quantum many-body problems, new approach makes calculations with realistic interactions possible.

FRIB researchers are part of an international research team solving challenging computational problems in quantum physics using a new method called wavefunction matching. The new approach has applications to fields such as nuclear physics, where it is enabling theoretical calculations of atomic nuclei that were previously not possible. The details are published in Nature (“Wavefunction matching for solving quantum many-body problems”) .

Ab initio methods and their computational challenges

An ab initio method describes a complex system by starting from a description of its elementary components and their interactions. For the case of nuclear physics, the elementary components are protons and neutrons. Some key questions that ab initio calculations can help address are the binding energies and properties of atomic nuclei not yet observed and linking nuclear structure to the underlying interactions among protons and neutrons.

Yet, some ab initio methods struggle to produce reliable calculations for systems with complex interactions. One such method is quantum Monte Carlo simulations. In quantum Monte Carlo simulations, quantities are computed using random or stochastic processes. While quantum Monte Carlo simulations can be efficient and powerful, they have a significant weakness: the sign problem. The sign problem develops when positive and negative weight contributions cancel each other out. This cancellation results in inaccurate final predictions. It is often the case that quantum Monte Carlo simulations can be performed for an approximate or simplified interaction, but the corresponding simulations for realistic interactions produce severe sign problems and are therefore not possible.

Using ‘plastic surgery’ to make calculations possible

The new wavefunction-matching approach is designed to solve such computational problems. The research team—from Gaziantep Islam Science and Technology University in Turkey; University of Bonn, Ruhr University Bochum, and Forschungszentrum Jülich in Germany; Institute for Basic Science in South Korea; South China Normal University, Sun Yat-Sen University, and Graduate School of China Academy of Engineering Physics in China; Tbilisi State University in Georgia; CEA Paris-Saclay and Université Paris-Saclay in France; and Mississippi State University and the Facility for Rare Isotope Beams (FRIB) at Michigan State University (MSU)—includes  Dean Lee , professor of physics at FRIB and in MSU’s Department of Physics and Astronomy and head of the Theoretical Nuclear Science department at FRIB, and  Yuan-Zhuo Ma , postdoctoral research associate at FRIB.

“We are often faced with the situation that we can perform calculations using a simple approximate interaction, but realistic high-fidelity interactions cause severe computational problems,” said Lee. “Wavefunction matching solves this problem by doing plastic surgery. It removes the short-distance part of the high-fidelity interaction, and replaces it with the short-distance part of an easily computable interaction.”

This transformation is done in a way that preserves all of the important properties of the original realistic interaction. Since the new wavefunctions look similar to that of the easily computable interaction, researchers can now perform calculations using the easily computable interaction and apply a standard procedure for handling small corrections called perturbation theory.  A team effort

The research team applied this new method to lattice quantum Monte Carlo simulations for light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. Using precise ab initio calculations, the results closely matched real-world data on nuclear properties such as size, structure, and binding energies. Calculations that were once impossible due to the sign problem can now be performed using wavefunction matching.

“It is a fantastic project and an excellent opportunity to work with the brightest nuclear scientist s in FRIB and around the globe,” said Ma. “As a theorist , I'm also very excited about programming and conducting research on the world's most powerful exascale supercomputers, such as Frontier , which allows us to implement wavefunction matching to explore the mysteries of nuclear physics.”

While the research team focused solely on quantum Monte Carlo simulations, wavefunction matching should be useful for many different ab initio approaches, including both classical and  quantum computing calculations. The researchers at FRIB worked with collaborators at institutions in China, France, Germany, South Korea, Turkey, and United States.

“The work is the culmination of effort over many years to handle the computational problems associated with realistic high-fidelity nuclear interactions,” said Lee. “It is very satisfying to see that the computational problems are cleanly resolved with this new approach. We are grateful to all of the collaboration members who contributed to this project, in particular, the lead author, Serdar Elhatisari.”

This material is based upon work supported by the U.S. Department of Energy, the U.S. National Science Foundation, the German Research Foundation, the National Natural Science Foundation of China, the Chinese Academy of Sciences President’s International Fellowship Initiative, Volkswagen Stiftung, the European Research Council, the Scientific and Technological Research Council of Turkey, the National Natural Science Foundation of China, the National Security Academic Fund, the Rare Isotope Science Project of the Institute for Basic Science, the National Research Foundation of Korea, the Institute for Basic Science, and the Espace de Structure et de réactions Nucléaires Théorique.

Michigan State University operates the Facility for Rare Isotope Beams (FRIB) as a user facility for the U.S. Department of Energy Office of Science (DOE-SC), supporting the mission of the DOE-SC Office of Nuclear Physics. Hosting what is designed to be the most powerful heavy-ion accelerator, FRIB enables scientists to make discoveries about the properties of rare isotopes in order to better understand the physics of nuclei, nuclear astrophysics, fundamental interactions, and applications for society, including in medicine, homeland security, and industry.

The U.S. Department of Energy Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of today’s most pressing challenges. For more information, visit energy.gov/science.