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Articles 1 - 30 of 50
Full-Text Articles in Mathematics
2016: "Maximizing Customer Convenience With Hill Climbing", Ankit Agarwal '17, William Tong '17, Robert Lou '17, George Moe '17
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
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 …
The Entangling Properties Of Knots And Links, Eshan Mehrotra '17
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 …
Session E-2: Function Fundamentals, More Than X And Y, Carlo Ordonez, Steven M. Condie
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
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-1: Exploration Geometry: Hands-On Transformations, Lindsey Herlehy, David Hernandez, Karen Togliatti
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
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 A-4: It’S A Wrap, Lindsey Herlehy, David Hernandez
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
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 C-2: “It Is Easy As Pi”, Christine L. Moskalik, Carmela Jones
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
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
3: Drugs And De's, Ruth Dover
3: Drugs And De's, Ruth Dover
Differential Equations
Making a connection between discrete recursion and differential equations.
2. Population, Ruth Dover
2. Population, Ruth Dover
Differential Equations
Introduction to logistic population growth.
4. Dragging Along, Ruth Dover
1. Measuring Speed, Ruth Dover
2. Intro To Concavity, Ruth Dover
2. Intro To Concavity, Ruth Dover
More on Derivatives
Looking at changes in ƒ’ to understand concavity.
3. Derivatives Of Exponential Functions, Ruth Dover
3. Derivatives Of Exponential Functions, Ruth Dover
More on Derivatives
Exploring the derivative of exponential functions.
Limits3, Ruth Dover
More Limits, Ruth Dover
Limits2, Ruth Dover
Limits2, Ruth Dover
Limits
More on limits, both algebraic and graphical, including one-sided limits.
Limits5, Ruth Dover
Limits1, Ruth Dover
Limits4, Ruth Dover
Rate Of Change 1, Ruth Dover
Rate Of Change 4, Ruth Dover
Rate Of Change 3, Ruth Dover
Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover
Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover
A Simple Introduction to Rates
Before beginning this section of handouts, students will be introduced to a variety of vocabulary words often associated with calculus. These words will be used in an intuitive sense only and will not have been formally defined. Vocabulary should include graphical terms such as continuous, increasing, decreasing, maximum and minimum points, concave up, concave down, and point of inflection. In addition, discussion of the concept of "rate of change" should begin. It should be mentioned that many quantities change – population, cost, and temperature, to name just a few. All that is specifically required at this point can be related …
Rate Of Change 2, Ruth Dover
Approximations 1, Ruth Dover