Course Materials
Select course materials are below. These courses were all either developed by either myself or co-developed with Blain Patterson.
Thanos Population Dynamics
In the end of the “Avengers Infinity War,” the villain Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long term behavior of various species?
Investigate the validity of his claim by modeling various population dynamics such as unconstrained growth, constrained growth, competing species and predator-prey. Full instructor versions and supplemental materials are available for free through SIMIODE.
Sarah Elizabeth Ritchey Patterson; Blain Patterson (2019), "1-087-S-ThanosPopulationDynamics," https://www.simiode.org/resources/6441.
Investigate the validity of his claim by modeling various population dynamics such as unconstrained growth, constrained growth, competing species and predator-prey. Full instructor versions and supplemental materials are available for free through SIMIODE.
Sarah Elizabeth Ritchey Patterson; Blain Patterson (2019), "1-087-S-ThanosPopulationDynamics," https://www.simiode.org/resources/6441.
ThanosPopulationDynamics |
Blain Patterson; Sarah Elizabeth Ritchey Patterson (2019), "3-087-S-ThanosPopulationDynamicsInteractingSpecies," https://www.simiode.org/resources/6733.
ThanosPopulationDynamicsInteractingSpecies.pdf |
Go with the Flow: Fluid Dynamics for Everyone
Are you ready to make some waves? Navier-Stokes equation is used to model waves, aquatic animal locomotion, aerodynamics, blood flow, thin film lubrication, and much more! These models help researchers predict the weather, develop new medications, and create realistic animation in films. In this course, we will look at how to mathematically model fluid motion and many other natural phenomena. You will learn the meaning behind several differential equations including Navier-Stokes equation. You will also numerically solve various differential equations using basic programming techniques. No calculus or programming experience required.
GoWithTheFLowSyllabus |
GoWithTheFlowSlidesPart1 |
GoWithTheFlowSlidesPart2 |
An Information Age: Math and Technology of Data
We live in an era of information. If you are interested in a topic, you can type it into a search box and page after page of information will appear. How does Amazon know which products to recommend that you buy? How does Netflix know which titles you may like? We will investigate the answers to these questions and more by diving into the field of mathematics and computer science known as machine learning. This intensive weekend course for high school students explores the basics of machine learning and several machine learning algorithms including k-nearest neighbors, classification trees, k-means, and regression.
InformationAgeSyllabus |
InformationAgeSlides |
InformationAgeProjectTopics |
From Startups to World Hunger: A Mathematical Perspective
How should we approach the big problems of the world such as energy conservation and world hunger? One way is to attempt to solve these social and economic problems through mathematical modeling. Mathematical models include graphical, numerical, symbolic, and verbal representations of some real world phenomenon. In this course, students will work in groups to solve an open ended problem of their choice. Their solution to this problem will be written up and presented to the class at the end of the two weeks. Mathematical and statistical software such as Matlab and Excel will be used to work with large sets of data. Professionals in the fields of medicine, technology, and energy conservation will come and discuss how they use mathematical models in their work. Students will visit the Duke Smart House, the EPA Center, and Bronto to observe how mathematical modeling is used in practice. The remainder of class time will be spent learning about various mathematical tools that can be used to model and solve problems, including statistical methods and numerical approximations. This is an intensive 2 week long course for high school students.
ModelingSyllabus |
ModelingProblems |
ModelingProjectTopics |
Puzzles and Problem Solving
Do you like playing games and solving puzzles? Come learn about the mathematics and logic behind SET, Nims, Magic Squares, and Tower of Hanoi. While they are often used for fun and games, there are a lot of connections between these games and puzzles and the mathematics used to solve complex real world problems. In this course, put your puzzle solving skills to the test in an interactive and hands-on day of fun! This weekend course is geared toward students in 5th and 6th grade.
PuzzlesSyllabus |
PuzzlesSlides |
Codebreaking: Mathematics of Espionage
Do you have what it takes to be a spy? In this course, you will be introduced to cryptography, or the study of sending and receiving secret messages. From the beginning of time, people have always wanted to keep information safe. Now more than ever, we are looking for new ways to keep information private and secure. Come learn about various ciphers used throughout history and how we can used mathematics, logic, and a little bit of luck to break them. This weekend course is geared toward students in 5th and 6th grade.
CodebreakingSyllabus |
CodebreakingSlides |