Physical Sciences and Mathematics Commons^™

2017: Himcm International Mathematics Modeling Contest: Finalist Rating, Aryan Walia, Katie Lu, Mia Ye, Kevin Mikos

Distinguished Student Work

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken into account including the …

2017: "Lighting Up The Night", Shyam Sai, Istvan Kovach, Abhay Gupta, James Wei

Distinguished Student Work

Drone technology is beginning to permeate many aspects of life in the modern world, and for good reason. Delivery drones can efficiently deliver packages better than any existing methods. Medical drones can reach emergency patients faster than any ambulance. Security drones can surveil areas more quickly and more thoroughly than a team of human guards. The advent of commercial and industrial uses for drones, however, begets the vital question of how can drones be used outside the workplace. Intel's answer? Entertainment.

Thus, the Intel Shooting Star^TM drone was born, a quadcopter explicitly built for producing breathtaking aerial light shows …

2017: Himcm International Mathematics Modeling Contest: Meritorious Rating, Spoorthi Jakka, Claire Wang, Amy Wang, Claudia Zhu '18

Distinguished Student Work

Restatement of the Problem:

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken …

2017: "The Wasatch Range Ski-Matic", Andy Liu, Bert Cao, Joshua Eberhardt, Allen Chen

Distinguished Student Work

Ski resorts are very popular among both avid skiers and families who are looking to have fun. In fact, winter resorts account for over 3 billion dollars in revenue, with an annual growth of 2.6% [IBI]. In addition to their use as recreational areas, ski resorts are also used for various winter competitions, most famously the Olympics. Our job was to design and create a suitable ski resort for both the Olympics and for recreational use in the Wasatch Peaks Range property. In addition, we were advised to create over 160km of trails and maintain a 20%- 40%-40% balance between …

Session A-3: Three-Act Math Tasks, Lindsey Herlehy

Professional Learning Day

Participants will engage in a Three-Act Math task highlighting the application of properties of geometrical figures. Developed by Dan Meyer, an innovative and highly regarded mathematics instructor, Three-Act Math tasks utilize pedagogical skills that elicit student curiosity, collaboration and questioning. By posing a mathematical problem through active storytelling, this instructional approach redefines real-world mathematics and clarifies the role that a student plays in the learning process. Participants will be given multiple resources where they can access Three-Act Math tasks appropriate for upper elementary grades through Algebra and Geometry courses.

2017: "From Sea To Shining Sea: Looking Ahead With The National Park Service", Abhay Gupta '18, James Wei '18, Istvan Kovach '18, Shyam Sai '18, Darius Hong '18

Distinguished Student Work

There is a natural inclination for humanity to view the Earth as our steadfast, never-changing home. After all, it seems as permanent as the ground beneath our feet. However, nothing could be further from the truth, especially in today’s rapidly changing climes. Global temperatures are on the rise, and with them comes an increase in sea levels, wildfires, and hurricanes, three serious, expensive issues. Unfortunately for the National Park Service (NPS), who guard ninety-seven coastal units, coastlines are especially vulnerable to such problems. Thus, the NPS must take extra precautions and expenditures to maintain and protect them. With limited budget, …

2017: "Park2vec: A Vector Representation Of Our National Parks’ Climate Change Susceptibility", William Tong '17, Ankit Agarwal '17, George Moe '17, Aakash Lakshmanan '17

Distinguished Student Work

With over 400 units, between them covering almost 850 million acres of carefully preserved land, the National Park Service (NPS) acts as steward to the nation’s natural treasures. In the move to the Twenty-First century, the NPS faces numerous looming challenges, particularly those related to a rapidly changing climate. It was our task to strategize with the Service in addressing three such issues, leveraging our experience in mathematical modelling and data analysis to aid them in the quest to protect and to preserve.

The first problem under consideration was determining the risk associated with sea-level change for five different coastal …

06: Reciprocal Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ReciprocalFunctions.nb asks the user to input a function. The notebook will graph the original function and its reciprocal.

10: Roots Of Unity, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RootsOfUnity.nb offers some solutions to x⁶ -1=0 and then graphs and labels the complex roots of unity up through x⁸ -1=0 .

07: Tan Animation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

TanAnimation.nb is a nice little animation to illustrate similar triangles to show why the graph of y = tan(x) looks the way it does.

08: Sine Transformations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SineTransformations.nb allows you to use sliders to see the effects of parameters on the amplitude, period, phase shift, and vertical shift.

13: Polar Reciprocal, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarReciprocal.nb first shows a transformation of the circle r = 3 into the circle r = 3sin (theta). Second, it shows the original and reciprocal graphs through the animation. Interesting stuff!

03: Poly Basics 2, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics2.nb looks for patterns in polynomial graphs with three different factors when each factor is raised to various powers.

15: Koch Snowflakes, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

KochSnowflakes.nb contains several animations that show several steps of graphical iteration for Koch Snowflakes and several other patterns.

16: Sequences And Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.

04: Domain And Range, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DomainAndRange.nb allows you to graph various types of functions and shows the domain and/or range along the appropriate axis.

12: Polar Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarPath.nb allows the user to input any polar function and use a slider to see how the path is created. That is, it will allow the user to see the order in which the petals or loops are created.

11: Parametric Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.

09: Solving Trig Equations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SolvingTrigEquations.nb develops the idea of solving trigonometric equations with special angles by looking at a sequence of problems. The student is asked to think about solutions and to do more problems along the way.

14: Polar Vs Rectangular Animation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarVsRectangularAnimation.nb allows the user to input a polar function and then relates the graphs of r = ƒ(theta) and y = ƒ(x).

02: Poly Basics 1, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics1.nb deals with the graphs of polynomial functions of higher degrees. In this notebook, each factor is linear.

01: Quadratic Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

QuadraticFunctions.nb examines the path of the vertex of quadratic polynomial graphs as each parameter a, b, and c changes.

02: Derivative Approximation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DerivativeApproximation.nb contains two sections. Both allow the user to input a function and an x-window and to vary the center point. Then the value of h may be changed. The first section will show a symmetric approximation while the second shows a one-sided approximation.

11: Eulers Method, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

EulersMethod.nb asks for a differential equation, an x-interval, a specific point, and the step size. It shows the graphical approximation given by Euler's Method. This notebook has setups that allow it to be used with one DE or with a system of two DE's.

05: Limit Definition, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

LimitDefinition.nb asks the user to input a function. Then use the vertical slider to change the size of E. An appropriate value of 8 will be given.

09: Slope Field, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SlopeField.nb does just what it says! Enter a differential equation in the form y = … and choose the window. It is also possible to choose the number of marks in each direction.

08: Accumulator, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

Accumulator.nb takes a function ƒ and other information to sketch both the graph of ƒ and the graph of F(x) = Integral of ƒ(t) from a to x. Use the slider for the x-value to see how the accumulated area under ƒ helps to create the graph of F.

12: Parametric Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.

10: Slope Fields + Solns, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SlopeFields+Solns.nb follows similarly from the previous notebook. Here, however, there is a 2D slider that shows a specific solution function as you move the initial point.

07: Riemann Sums, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RiemannSums.nb allows the user to input a function, and x-interval, and a maximum value of n, the number of rectangles. This animates Riemann and trapezoidal sums.