Learner Calculus Scholarship

Calculus is known as the mathematical study of change, just as geometry is the study of shapes. No matter what STEM discipline it is, from medicine or computer science to mechanical engineering or data analysis (and everything in between), knowing how things change is integral to the goal of the respective fields (pun intended). What many students fail to realize is that calculus lives underneath everything; going back to medicine, for example, in order for doctors to prescribe the correct dosage of a drug and treatment plan (e.g., two pills twice a day for a week), the drug's concentration and effectiveness over time must be tracked. This is done through calculus! While doctors don’t need to know the nitty-gritty details that led to this conclusion, it wouldn’t have been possible without the application of calculus. Furthermore, calculus lives underneath even more scientific disciplines, ranging from discrete mathematics, statistics and probability, and linear algebra to biology (population growth) and weather and climate. On the other side, though, it’s well known that calculus is one of the pillars of most engineering disciplines and data science. It’s worth noting that most engineering disciplines, including but not limited to civil, mechanical, structural, and electrical engineering heavily use physics, which is rooted in calculus. And as for data science, while statistics and linear algebra complete the pillars of machine learning, we know they apply calculus concepts is ever-so-present in them as well. Unless you work in academia, however, it’s a difficult task to see the big picture of how calculus intertwines with various STEM fields. As a university student, life is so fast-paced and coursework is so demanding that the goal of the curriculum can be lost underneath the struggle for maintaining a high GPA, obtaining internships, and strengthening resumés for postgraduate life. Really though, calculus isn’t about the destination, it’s about the journey. Like most math courses, the goal is to gain a conceptual understanding of a topic and be able to apply it when necessary, not hand-solve complex problems. We live in a digitally heavy world; computers can do all the calculations for us, but they can’t tell us what they mean or how to make sense of them. STEM fields, to me, are all about problem-solving. Problem solving is the crux of engineering, but a case can be made that it should be applied to all of STEM. Current society is technology-driven; and in order for technology to work for the consumer, a multitude of problems must be solved before a piece of technology can even be put into production. Similarly, the goal of science is to understand the world around us. Calculus teaches students how to provide rigorous and thorough solutions to problems. While writing formal proofs aren’t necessarily an essential component of a single-variable or multivariable calculus course, the methodology behind the various theorems of calculus—from limits and continuity to the Extreme Value Theorem and everything in between—teaches learners how to think critically. Ultimately, calculus is important in the STEM field because calculus is fundamental to other STEM disciplines while simultaneously serving as a gateway to more rigorous math that serves an important role as well. The mathematical study of change couldn’t be more beneficial in our ever-changing world.

Calculus, and mathematics in general, is in essence, the foundation of STEM as a whole. Science, technology, and engineering are all fundamentally tied to mathematics in that mathematics makes each of these individual fields comprehensible. Without math, it would be impossible to understand and model the relationship between forces in our universe, to perform the computations that make harnessing electricity that makes all modern forms of technology possible, and of course to engineer otherwise more complex problems into smaller, more solvable ones. In particular, calculus is absolutely necessary for demonstrating the relationship between kinematic forces and properties. Derivatives and integrals allow for the analysis of the relationship between position, velocity, and acceleration, as well as lengths, areas, and volumes. Fundamentally, any form of engineering that relies on physics, or even more generally, any field of study that requires consideration of related variables or rates of change is built on calculus. Any form of optimization too is built on a core calculus concept of extreme values and the interpretation of graphs of derivatives. As one could potentially see by now, it may be harder to find any field, study, or discipline that doesn't use these concepts somewhere. Even the arts can use calculus! The crews for your favorite TV shows and movies ultimately track the movement of their cameras on paths that can be drawn mathematically, and even if they themselves aren't doing the calculations, the crews are provided the ability to create such productions with ease, and you the viewer are able to enjoy these productions as a result of someone else's understanding of calculus. How might you be able to know how quickly to turn a camera as a car accelerates past a certain curve or stretch of road? Believe it or not, it's calculus! The key to innovation, abstract thinking, and the ultimate progress of the sciences and even the arts is calculus. Math is capable of making otherwise impossible-to-comprehend relationships and patterns noticeable, and perhaps even trivial should you come to understand how to harness its power. If you wish to be someone who thinks outside of the box, or if you're simply someone who loves finding solutions to any sort of problem - you should absolutely learn to be a friend to calculus. The greatest lesson it can teach us is that any observed relationship can be the point of entry for understanding something - literally - exponentially more vast than what we can immediately observe. It's the language of optimization, and without it, how could a stock analyst predict the future of any particular company, or a doctor the long-term effects of their medications? How might we be able to create more efficient vehicles and manufacturing processes? How could we create more visually stunning, complex films and effects without understanding the core of what it is we wish to optimize? How could we be sure that our simulations of physics, space - the orbits and trajectories of our planets - are ultimately accurate without being sure of each measurable variable's role in our calculations? Without calculus, how can we be sure of anything; that some unknown force isn't acting upon what we believe to be understood? STEM is built on calculus, the arts are friends of calculus, and the luxuries and optimized experiences we often take for granted can all be argued to be a result of calculus as well. In the end, calculus is the key to the universe, to expanding the reach of our imagination and ingenuity, and to making the world a better place whether you recognize it or not.