Physical Sciences and Mathematics Commons^™

2016: "Maximizing Customer Convenience With Hill Climbing", Ankit Agarwal '17, William Tong '17, Robert Lou '17, George Moe '17

Distinguished Student Work

As technology advances and the pace of life quickens, companies are expected to continually provide better services, be more accessible, and respond to requests faster. While such expectations have led to the rapid growth of retail stores and service locations throughout the United States, delivery services have arguably been the most influenced by these rising demands.

Amazon.com is an online storefront that has seen tremendous growth throughout its lifetime, and it only continues to grow. Founded in 1994 as an online bookstore, the digital retailer eventually expanded its services to include technology, home goods, and even eBooks. Amazon’s response to …

2016: Himcm International Mathematics Modeling Contest: National Outstanding Paper, Suchet Kumar '19, Tommy Vadakumchery '19, Nathan Kim '19, Bert Cao '19

Distinguished Student Work

In the modern business world, maximizing profits is the highest priority. Businesses, especially small ones, should try to save money whenever possible. Along with cutting wages, removing competition, and increasing advertising and production, efficiency of company sites can save money. For example, a cheap 50 ft. by 100 ft. warehouse costs $35,000, but when coupled with the costs of maintenance and wages, increasing the number of warehouses significantly increases costs.

Clearly, warehouses are expensive, making it necessary to place them in optimal locations. In this problem, we attempt to reduce the number of warehouses while shipping to the entirety of …

05: Rats Grapher, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RatsGrapher.nb graphs rational functions and labels all holes and asymptotes.

Nucleon Decay, Atmospheric Neutrinos, And Cosmic Rays At Dune: September 2016 Progress Report, E. Church, D. Dwyer, H. Gallagher, M. Goodman, R. Hatcher, J. Hewes, A. Higuera, V. A. Kudryavtsev, L. Lin, N. Martinez, H. Méndez, J. L. Raaf, M. Robinson, G. Santucci, M. Sorel, A. Tonazzo, T. K. Warburton, K. Wood, T. Yang

Progress Reports

We report on the progress made within the Nucleon Decay, Atmospheric Neutrinos, and Cosmogenics Physics Working Groups since the DUNE CDR, and in particular in the period September 2015 { September 2016. This note is also intended to provide input for the September 2016 Preliminary Report of the Far Detector Task Force. We report jointly for the three WGs since they are tightly coupled. They make use of the same DUNE Far Detector for their physics studies, they share the same energy regime, and they are all characterized by random, non-beam triggers. Finally, cosmogenic events are a background for atmospheric …

Artificial Intelligence: Prospects, Pathways, Realities, Timur Javid '17, Tara Parkman '17, Nathaniel Smith '17

IMSAloquium Student Investigation Showcase

The specter of Artificial Intelligence (AI) looms before us, continuously growing in power, soon to match, and then exceed human capabilities. To explore this, we read and discussed books by experts, and learned about the exponential nature of technological progress and the difficulties of halting or even slowing it. Technological improvements trend towards an autonomous AI capable of replicating, if not exceeding human thought and interaction, a complex adaptive system with an input stream, isomorphic model of reality and output mechanism, fully capable of passing the Turing Test. How a system is organized is a key determinant of the processes …

Inferences Of Subglacial Processes Under The West Antarctic Ice Sheet From Grain Surface Textures, Aspen Wheeler '16

IMSAloquium Student Investigation Showcase

Subglacial sediment transport under Whillans Ice Stream in West Antarctica is inferred using samples collected from Subglacial Lake Whillans (SLW) and two sites at a location called “UpB”. The surface features on quartz grains between 125 and 1000 micrometers were described using a Scanning Electron Microscope. Mahaney’s Atlas of Sand Grain Surface Textures and Applications (2002) was used to uniformly and unbiasedly categorize surface features from SLW and UpB, for different grain sizes and depths in cores collected from subglacial till. Data showed three groups that can be used to delineate phases of the subglacial sediment. Phase one is shown …

Comparing Biodiversity Of Silurian Reefs In Illinois And Wisconsin Using Museum Collections And Unbiased Bulk Samples, Walker Weyland '17

IMSAloquium Student Investigation Showcase

Silurian (Wenlock) fossil reefs from the Racine Formation in Illinois measure over 100 meters tall and draping flanks beds extend over a mile. Biodiversity studies of reefs in Southeastern Wisconsin reveal complex, diverse communities with over 191 species. We hypothesized that the larger reefs reflect a more optimal environment and may have had higher diversity than reefs in Wisconsin. We compared diversity between the reefs using, identified fossils from the Field Museum, which were collected in Herscer, Romeo, Thornton, Bridgeport, and Hawthorn. Then we compared the results with those from Watkin’s (1997) counts, collected from Horlick, Ives, Franklin, and Francy …

Field-Programmable-Gate-Array Implemented On Time-To-Digital Converter: Improving Its Resolution, Soomin Park '17

IMSAloquium Student Investigation Showcase

The purpose of this investigation is to discover critical experimental factors that could lead to the variation of time measurement by a time-to-digital converter (TDC) implemented on field-programmablegate- array (FPGA). Two pulses were generated by a pulse generator, and the second pulse was given a 20 nanoseconds delay. In an ideal experiment, the mean of the entry data would have been 20 nanoseconds since the two channels (8,c) obtained pulses that were given the same delay. However, due to device errors and quantization errors, which is produced during analog-to-digital conversion, time difference between hits varied from 22.1 to 22.7 nanoseconds. …

Neural Networks And Machine Learning Applied To Classification Of Cancer, Sachin Govind '16

IMSAloquium Student Investigation Showcase

Using genome data to predict cancer type is an increasingly relevant practice as it provides a direct, noninvasive strategy to analyze genetic predisposition to malignant cancer types. More specifically, analysis of gene expression data across the genome can provide insight into the underlying gene interactions that propel the progression of tumors. A database containing expression levels for 16,063 genes was split into disjoint training and testing sets; these were subjected to a variety of machine learning methods and statistical analyses, including multinomial logistic regression across cancer phenotypes, k-means clustering analysis, optimization of a predictive support vector machine, and rooted random …

The Entangling Properties Of Knots And Links, Eshan Mehrotra '17

IMSAloquium Student Investigation Showcase

It has been conjectured that quantum entanglement operators can be lifted to braiding operators by the way of the topological quantum field theory axioms set forth by Witten and Atiyah. Moreover, it can be readily shown that quantum link invariants need entanglement to construct topological invariants. Given these results and the already dense mathematical framework underlying topology and quantum field theory, we propose that, through the usage of quantum algebra and bracket models, we can identify a significant area of overlap where entangling R-matrix solutions to the Yang-Baxter equation can be used to construct invariants of knots and links. Such …

Optimal Concentrations Of Ethanol And Isopropanol For The Dissolution Of Pmma, Maya Costales '16

IMSAloquium Student Investigation Showcase

Last year we studied the effectiveness of Alcohol/Water mixtures in dissolving PMMA. PMMA is a commonly used resist in electron beam lithography. Ethanol/Water mixtures in a 4:1 volume ratio developed PMMA such that they could replace mixtures of Methyl(isobutylketone) and Isopropanol. Raman spectroscopy revealed that Ethanol/Water mixtures in a 4:1 ratio and IPA/Water mixtures in a 3:1 ratio have different vibrations than those of pure Ethanol, IPA, and water. Our study this year will discuss the characteristics of Ethanol/Water and Isopropanol/Water solutions with dissolved Poly(methylmethracrylate). A fixed amount of 12,000 molecular weight PMMA was dissolved into a series of these …

Session E-1: Labs For Waves, Sound, And Optics, Brooke Schmidt

Professional Learning Day

I've been reworking our labs for waves, sound, and light this semester and I would like to share my work with you. These are a mix of both derivation and application experiments. I will also give suggestions for modifications for the middle school level.

Session E-2: Function Fundamentals, More Than X And Y, Carlo Ordonez, Steven M. Condie

Professional Learning Day

How many of your students say that √9 = ±3? This may have to do with a lack of understanding of functions. This session will highlight some of the nuances of functions with less formal, non-formula driven examples with which students can expand their understanding.

Session F-4: Developing Parametric Equations Using Mathematical Modeling, Mark Kammrath

Professional Learning Day

Designing project to develop student understanding of parametric equations and two modeling situations in which they are applied. No previous knowledge of parametrics is required by the students. The project requires two days of class time, with the remaining work done outside of class. This project is intended to be given three days into a unit on vectors.

Session F-3: “It Is Rocket Science”, Carmela Jones, Christine L. Moskalik

Professional Learning Day

All current NASA rocket launchers are no longer useable because all of the available rocket-fuel sources on Earth have been depleted. Participants will serve as NASA engineers tasked with developing non-fuel-based rocket launcher prototypes in an effort to maintain current and future NASA space programs and missions. Model how you will get your students to take off with Rocket Science.

Session F-1: Exploration Geometry: Hands-On Transformations, Lindsey Herlehy, David Hernandez, Karen Togliatti

Professional Learning Day

In this session, participants will engage in a series of hands-on, minds-on Geometry lessons designed to explore the four transformations. By completing several critical thinking challenges, teachers will use the Common Core Mathematical Practices and various manipulatives to investigate how figures rotate, dilate, translate, and reflect within a plane. Appropriate for multiple grade levels, teachers will leave the session with all instructional plans and various ways to adapt the lesson based on the needs of their students.

Session D-3: The Mathematical Wonders Of Pascal's Triangle, Donald Porzio

Professional Learning Day

Most mathematics teachers are aware of the some of the more straightforward connections Pascal's Triangle has to mathematics. Come explore some of the lesser known connections that can be used to peak your students' interest and entice them into exploring the mathematics behind these connections.

Session F-2: Simple Chemistry Labs And Activities To Teach Difficult And Important Concepts, Dave Devol, Deb Scarano, Anita White

Professional Learning Day

This will be a hands-on session where participants will perform four chemistry activities/experiments (two of the experiments will be a variation on one theme). The topics will include bonding, equilibrium, and stoichiometry. Teachers will be provided with copies of the activities to take back to their classes. In the spirit of learning together, we ask participants to bring their favorite activity/lab to share with the group (these labs will not be performed, just shared. Bringing an activity to share is optional, not required).

Session B-1: Model Building In Planetary Science And The Ngss, Eric Hawker

Professional Learning Day

In this session I will guide teachers through the steps my students take in Planetary Science to develop a conceptual model of how planetary interiors work. Teachers will then create concept maps from their conceptual models, and then use their models and maps to understand planetary systems other than Earth.

Session A-4: It’S A Wrap, Lindsey Herlehy, David Hernandez

Professional Learning Day

Investigate the concepts of surface area, measurement, ratio and proportion through a visual and kinesthetic mathematical investigation. Participants will be presented with the challenge of calculating how many sheets of toilet paper it would take to wrap one of their group members using a limited selection of tools. This session will provide teachers with a wonderful hands-on, minds-on activity that could easily be implemented into any classroom!

Session A-3: The Box Problem – An Introduction, Ruth Dover

Professional Learning Day

Create some simple boxes with paper and scissors. Then we'll measure the height, area of the base, and the volume. Find formulas, find regressions, and graph the functions. It's a simple activity to engage students and combine many different aspects of mathematics.

Session A-1: Teaching Fields In Introductory Physics, Peter Dong

Professional Learning Day

The concept of a field is integral to all areas of contemporary physics - perhaps as fundamental a concept as energy. Fields are mentioned in several NGSS standards and essential to understand physics at an advanced level. However, fields are not difficult and can be taught in an introductory course with minimal math. Students who understand the basic concept early should have less difficulty understanding electric and magnetic fields in later classes. I will discuss our implementation of a fields unit in our introductory physics course and give examples of simple labs and exercises to help students understand this basic …

Session C-2: “It Is Easy As Pi”, Christine L. Moskalik, Carmela Jones

Professional Learning Day

Participants will work together using pi to try to open an ancient chest filled with treasure!! The chest is protected by a passcode that can only be determined through the activities within the lesson. Enjoy a progressive exposure to pi through this two-part lesson (total 110 minutes) offering a FUN storyline within the context of geometry and circles. With "pi-day" right around the corner, this hands-on, fun, inquiry-based lesson is sure to be a hit with your budding mathematicians.

2016: "Analysis Of The Effectiveness Of Varying Car-Sharing Business Models", William Tong '17, Sachin Govind '16, Ankit Agarwal '17, David Xu '16, George Moe '17

Distinguished Student Work

A continually evolving field, the automotive industry consistently introduces a number of innovative technologies and services to ease the problem of transportation. One such service is termed Car-sharing. Car-sharing allows users to rent vehicles and use them for a short period of time without worrying about the additional costs associated with maintenance, fuel, and pollution, presenting a simple alternative to owning a car. Still an emerging concept, Car-sharing requires a great deal more analysis to fully understand the nuances and implications behind its implementation.

1. Coffee, Ruth Dover

Differential Equations

Newton’s Law of Cooling.

3: Drugs And De's, Ruth Dover

Differential Equations

Making a connection between discrete recursion and differential equations.

2. Population, Ruth Dover

Differential Equations

Introduction to logistic population growth.

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.

1. Measuring Speed, Ruth Dover

More on Derivatives

Tables of values to measure rates.

2. Intro To Concavity, Ruth Dover

More on Derivatives

Looking at changes in ƒ’ to understand concavity.