Mathematics & Quantitative Modeling: Real World Skills Gained by Polygence Math Projects
11 minute read
SCHOLARS IN THIS ARTICLE:
Anoushka Choudhary - Published in Research Archive of Rising Scholars
Aditi Gargeshwari - Accepted to "dream school" Harvey Mudd College
Imagine predicting the spread of a virus, optimizing a city's traffic flow, or designing a cutting-edge video game. These are just a few of the exciting possibilities that mathematics and mathematical modeling opens up. Mathematical modeling isn't just about numbers; it's about solving real-world problems and making impactful decisions in fields like urban planning and public health, to financial investments and software development. Mathematical modeling is an important process to familiarize yourself with. Moreover, students well-versed in quantitative and mathematical modeling problems gain a competitive edge in regard to higher education and future career opportunities. If you're passionate about math and eager to tackle complex challenges, consider embarking on a Polygence passion project, as well as explore various math summer programs.
Introduction to Mathematical Modeling
Mathematical modeling is a useful tool that often plays a huge role in the decision-making process across various industries. After all, mathematical models account for many factors, and are often the most accurate way to predict future outcomes, especially as they relate to factors such as cost, health, risk, and safety. In this article we will look at plenty of mathematical modeling examples and discuss the various ways mathematical and quantitative modeling can be used to improve society, the economy, technology, and more. So if you’re wondering “what is a mathematical model, anyway?” don’t worry, you’ve come to the right place.
What is Mathematical Modeling?
To start off, what is mathematical modeling? Let’s look at a quick mathematical modeling definition before we dive into specifics: Mathematical modeling is the process of describing real-world phenomena through mathematical equations so that you can make predictions about future outcomes.
Mathematical models analyze how variables (both independent and dependent) interact and influence one another. The best models give us valuable insights into a system so we can discover patterns, make predictions, consider various ways to approach a problem, and come up with meaningful solutions.
Creating a mathematical model can be a challenging endeavor, but rest assured, mathematical modeling for beginners does exist. What’s more, there are concrete steps for you to follow as you familiarize yourself with mathematical modeling techniques:
Define the problem by coming up with a concise question to guide your research.
Simplify your problem by only considering the most important variables.
Define your variables. (Independent variables will remain constant in your equation, while dependent variables will be determined by data collection).
Make your model, i.e. come up with your equation.
Come up with data.
Analyze and assess your model. (Are the answers reasonable? Does the model work as expected?) Test your model by using past data.
Share your findings in simple straightforward language so that a general audience will understand your findings.
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.
Importance of Mathematical Modeling in Real-World Applications
The best mathematical models answer real-world, open-ended questions, such as:
How can we best reduce local traffic jams?
What populations are most at-risk for contracting a specific disease?
How will climate change affect local weather patterns?
Which financial investments pose the least risk for our client?
Which recycling program is best for our city?
How can local land trusts best support native plants?
As you can see, mathematical models have a wide range of applications and are often used to address problems in various fields, such as Epidemiology, Environmental Science, Finance, Urban Planning, Performance Analysis in Sports, Pharmaceutical Development, Astrophysics, and Social Sciences.
Mathematical models also play a key role in the development of various technologies, including pharmaceuticals, computer software, artificial intelligence, and more. The careers that are most often invested in mathematical modeling include finance, healthcare, and engineering. Needless to say, there are lots of examples of math in the real world. And Polygence math projects help students find meaningful ways to apply mathematical modeling to real-world scenarios.
Skills Gained Through Polygence Math Projects
Polygence Math Projects are a great introduction to data collection and other research practices, both of which are valuable skill sets. Creating your own mathematical model is also a great way to hone your creative thinking abilities and analytical reasoning skills.
Broadly speaking, there are countless benefits to creating a mathematical model. Let’s look at some of these benefits more closely:
Analytical Thinking and Problem-Solving
First, completing a Polygence math project of your own design will help you cultivate analytical thinking and problem-solving skills. By using mathematical and computational thinking, students learn to approach complex problems methodically. This enhances logical reasoning abilities and helps bolster critical thinking skills.
Polygence alum, Aditi Gargeshwari, shares the following insights about her experience:
“I enjoyed and succeeded in my math classes, but I really wanted more depth and unconventional exploration in what I learned. As such, I wanted to translate that hunger inside of me into something beautiful and technical that others could appreciate. Piggybacking off of a simple calculus formula I had taken an interest in, I worked with a Polygence mentor to implement this depth into my work by creating a proof of the formula using real analysis – a different, seemingly-unrelated area of mathematics. My finished project truly opened my eyes to the full-circle nature of math, showing me how the most abstract areas of real-number analysis could help prove the most tangible, visualizable formula.”
Data Analysis and Interpretation
Passion projects for math that focus on quantitative modeling teach students how to collect and analyze data sets, as well as draw meaningful conclusions from data. As students work towards designing their mathematical model, they will also need to continuously evaluate their underlying assumptions and how these assumptions are guiding their work. Overall, math projects focused on quantitative models challenge students to think critically, look for potential flaws, and honestly reflect on their findings to gauge whether the model is working effectively.
Collaboration and Communication
Two of the many skills that Polygence projects cultivate are collaboration and communication. In fact, students interested in participating in one of our Pod programs will have the opportunity to work effectively in team settings and engage in peer reviews. Additionally, students will learn how to present their findings clearly and persuasively. Needless to say, these are valuable skills that will serve students well in the classroom and beyond. In fact, Polygence students are well-prepared for a variety of ventures, including participating in mathematical modeling competitions.
Polygence alum, Anoushka Chaudhury, reflects on how working with her mentor taught her valuable communication and collaboration skills:
“My mentor was knowledgeable at every step and often simplified core concepts to help me understand them better. He helped me set core deadlines for the project which helped the development cycle go very smoothly. We also spent numerous hours debugging pieces of code which was incredibly helpful to my learning process. He provided me with tougher reading material to strengthen my concepts and brought his expertise of quantum computing into supporting me.”
Polygence alum, Ahmet Tunga, reflects on his Quantum Algorithms project :
The guidance [my mentor] provided was priceless, and after a few weeks I couldn't believe I was working on quantum algorithms that seemed impossible to understand at the beginning. I am very thankful for his mentorship and I could not expect a better experience!”
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Real-World Applications of Mathematical Modeling
The many real-world applications of mathematical modeling can feel incredibly rewarding. Especially as students realize that they can make a tangible impact through math. From The Effects of Black Holes on the Space-Time Continuum and a Quantum Circuit Simulator using Python, to Digital Marketing in the Makeup Industry and Predicting Netflix Stock Prices, Polygence students have done it all!
So whether you’re interested in exploring public health, climate change, social issues, sports performance, economics, or finance, learning about common mathematical modeling techniques and tools used — such as mathematical modeling software like SimSolid, SIMUL8, MATLAB, and AnyLogic — will empower you to envision your future in math.
How Polygence Projects Prepare Students for College Admissions
Beyond the benefits previously discussed, Polygence projects demonstrate genuine intellectual curiosity and initiative, qualities that college admissions officers find far more compelling than a long list of generic extracurricular activities. Students who can articulate the personal growth and key insights gained through their Polygence projects stand out as the kind of engaged, independent learners that colleges want on their campuses. Furthermore, throughout the Polygence process, students learn how to speak about their interests, passions, and intellectual inquiries that will enhance not only their college interviews but also their college essays.
Building a Standout Portfolio
A Polygence math project is a great way to build a standout portfolio, one that you’ll be able to use for college applications and beyond. Polygence math projects are unique, which makes them memorable. Cultivating an impressive and diverse portfolio is important because it demonstrates your ability to think outside the box and find creative solutions to complex problems.
Check out some of the math projects past Polygence students have completed:
Demonstrating Applied Knowledge in College Applications
Submitting a strong portfolio and knowing how to speak about your past successes with confidence and enthusiasm is a great way to demonstrate how you can apply your skills to future endeavors. Polygence alumni consistently connect their projects to their future goals.
For example, Polygence alum, Anoushka Choudhary, shares:
“I am applying for majors in computer science and data science and hope to study statistics as well in college, so I am most definitely going to be using the skills I gained from my experience at Polygence. While my project has not influenced the universities I'm applying to, it definitely adds a lot to my portfolio in terms of skills, practicality, and diversity of interests. I do plan to continue researching and do more projects similar to the one at Polygence in the future.”
Success Stories from Polygence Alumni
Polygence alumni continue to strive for excellence, often crediting their success to the inspiration and guidance they received during their projects. Many students go on to attend top math colleges, such as Aditi Gargeshawari, who shares that:
“In the fall, I'm heading to Harvey Mudd for engineering (one of my long-time dream schools), and my first project truly serves as my original inspiration to study the mathematics of engineering. More than anything, this 5-month-long project taught me how to systematically approach and solve large problems presented to me. In my higher education and beyond, I will undoubtedly apply the rigor and essence of the methods I used for my first research paper.”
Overall, Polygence students are 4x more likely to get accepted to a Top 25 University, which in turn, will help them find meaningful Career Opportunities with a Math Degree.
Getting Started with Polygence Math Projects
Now that we’ve explained all of the benefits of completing a Polygence project, and provided you with lots of examples of student projects, it’s time to cover some logistics:
Overview of Available Projects and Mentorship
There are many types of math projects offered by Polygence. Really, the only limiting factor is your imagination! Whether you’re interested in completing our individualized, 10-session Core Program or participating in one of our 6-week online courses (Pods) with like-minded peers, there are plenty of options to choose from. Regardless of the path you choose, keep in mind that not only are Polygence mentors experts in their fields, but they are also skilled teachers.
Polygence alum, Aliza Fatima, reflects that:
“My mentor was extremely helpful in guiding me through the process of this project. She provided me with detailed feedback and answered all my questions with a high degree of effectiveness. She helped me become more excited for my future in astrophysics and made my experience with Polygence interesting and fun. She gave me information on how a future in physics might look and made me very excited to pursue a future of research.”
How to Choose the Right Project for You
After assessing your interests and strengths, you’ll want to match your project to your career goals. Although this isn’t strictly necessary, it will give you a headstart in your prospective field. Especially when you consider the value of having an established portfolio that showcases your potential and past achievements.
Steps to Begin Your Polygence Journey
Ready to begin your Polygence journey? There are lots of resources and support available for new students. In addition to reviewing our Frequently Asked Research Program Questions, you’ll want to familiarize yourself with past student projects, and maybe even read a Polygence research paper or two! These examples can provide you with project ideas and inspiration for your own work.
Next Steps
Now that we’ve answered the question “what is a mathematical model?” and you’ve familiarized yourself with the many benefits of mathematical models, it’s time to start thinking about math project ideas. And if you’re not sure where to start, don’t worry! Our trusted mentors are more than capable of helping you brainstorm and discover your underlying passions through our “Launchpad Program.” Alternatively, you may be interested in joining one of our “Pods,” online short courses where you work with world-class mentors alongside peers who share your passion. Understanding the fundamental mathematical principles and the appropriate mathematical language will be essential as you embark on this journey.
Polygence Scholars Are Also Passionate About
Recap of Benefits of Mathematical Modeling
As previously discussed, math projects focused on mathematical models are an excellent way to cultivate academic growth, along with professional potential. Math projects teach critical and creative thinking skills. They also teach students how to collect, work with, and interpret large sets of data, as well as communicate their findings in a meaningful way, allowing them to directly apply the mathematical principles and advanced math skills they have acquired through project-based learning, making their education both practical and impactful. The benefits really are endless.
Encouragement to Explore Polygence Math Projects
Pairing ambitious students with Polygence mentors empowers students to delve fully into their passions and interests while feeling certain that their work has real-world applications. Furthermore, students will gain the ability to speak about their work with confidence and enthusiasm — a skill set that will serve them well during both college and job interviews. All in all, Polygence has a unique array of opportunities that is sure to benefit any motivated student. For more details, see Getting Started with Polygence Math Projects and How Polygence Projects Prepare Students for College Admissions.
Don’t wait to unlock your full potential! Sign up for a Polygence passion project today and start transforming your math skills into real-world solutions. Explore our programs, connect with expert mentors, and embark on a journey that will set you apart in college applications and beyond. Your future in mathematics and quantitative modeling starts now!