In this design challenge lesson, students examine their school food system and develop an investigation about food waste in order to know what should change.

In this lesson, students explore how human activities will continue to impact Antarctic ice, discuss human contributions to climate change, and investigate what we can do to stop/reverse these negative effects.

Students use scaling from real-world data to obtain an idea of the immense size of Mars in relation to the Earth and the Moon, as well as the distances between them. Students calculate dimensions of the scaled versions of the planets, and then use balloons to represent their relative sizes and locations.

Intermediate Algebra is a textbook for students who have some acquaintance with the basic notions of variables and equations, negative numbers, and graphs, although we provide a "Toolkit" to help the reader refresh any skills that may have gotten a little rusty. In this book we journey farther into the subject, to explore a greater variety of topics including graphs and modeling, curve-fitting, variation, exponentials and logarithms, and the conic sections. We use technology to handle data and give some instructions for using a graphing calculator, but these can easily be adapted to any other graphing utility.

This course provides a foundation to the design of the environment from the scale of the object, to the building to the larger territory. The design disciplines of architecture as well as urbanism and landscape are examined in context of the larger influence of the arts and sciences. Students are expected to develop skills in thinking and analysis, spatial representation, and design methodologies. Through lectures and design exercises, students are provided an opportunity to establish a reference for understanding the discipline of architecture and environmental design, and are given an introduction to design fundamentals and the design process.

Students are introduced to the concepts of evolution by natural selection and digital evolution software. They learn about the field of evolutionary computation, which applies the principles of natural selection to solve engineering design problems. They learn the similarities and differences between natural selection and the engineering design process.

During this course, we will be exploring basic questions of architecture through several short design exercises. Working with many different media, students will discover the interrelationship of architecture and its related disciplines, such as structures, sustainability, architectural history and the visual arts. Each problem will focus on one of these disciplines and one exploration and presentation technique.

This course introduces principles, algorithms, and applications of machine learning from the point of view of modeling and prediction. It includes formulation of learning problems and concepts of representation, over-fitting, and generalization. These concepts are exercised in supervised learning and reinforcement learning, with applications to images and to temporal sequences.
This course is part of the Open Learning Library, which is free to use. You have the option to sign up and enroll in the course if you want to track your progress, or you can view and use all the materials without enrolling.

This introduction to mathematical modeling was developed for an audience of college seniors pursuing an undergraduate degree in mathematics with emphasis in applied mathematics, the life sciences, or engineering. The course builds on knowledge of calculus, linear algebra, and differential equations to address the basic techniques and thought processes that are fundamental to mathematical modeling. The style is deliberately casual and the main goal is to explain how mathematics learned in core undergraduate classes may be used to understand simple phenomena that arise in physics and biology, and how the corresponding models are put together, tested, and analyzed.

The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.

Students learn about complex networks and how to use graphs to represent them. They also learn that graph theory is a useful part of mathematics for studying complex networks in diverse applications of science and engineering, including neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Students are also introduced to random processes on networks. An illustrative example shows how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students, and demonstrates how scientists and engineers use mathematics and computers to model and simulate random processes on complex networks for the purposes of learning more about our world and creating solutions to improve our health, happiness and safety.

The learning of linear functions is pervasive in most algebra classrooms. Linear functions are vital in laying the foundation for understanding the concept of modeling. This unit gives students the opportunity to make use of linear models in order to make predictions based on real-world data, and see how engineers address incredible and important design challenges through the use of linear modeling. Student groups act as engineering teams by conducting experiments to collect data and model the relationship between the wall thickness of the latex tubes and their corresponding strength under pressure (to the point of explosion). Students learn to graph variables with linear relationships and use collected data from their designed experiment to make important decisions regarding the feasibility of hydraulic systems in hybrid vehicles and the necessary tube size to make it viable.

Isaac Newton's famous thought experiment about what would happen if you launched a cannon from a mountaintop at a high velocity comes to life with an interactive computer model. You are charged with the task of launching a satellite into space. Control the angle and speed at which the satellite is launched, and see the results to gain a basic understanding of escape velocity.

Students groups act as aerospace engineering teams competing to create linear equations to guide space shuttles safely through obstacles generated by a modeling game in level-based rounds. Each round provides a different configuration of the obstacle, which consists of two "gates." The obstacles are presented as asteroids or comets, and the linear equations as inputs into autopilot on board the shuttle. The winning group is the one that first generates the successful equations for all levels. The game is created via the programming software MATLAB, available as a free 30-day trial. The activity helps students make the connection between graphs and the real world. In this activity, they can see the path of a space shuttle modeled by a linear equation, as if they were looking from above.

We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, usually a linear first order, difference or differential equation, collect data, estimate parameters, and compare their model prediction with their actual data.

This course introduces students to machine learning in healthcare, including the nature of clinical data and the use of machine learning for risk stratification, disease progression modeling, precision medicine, diagnosis, subtype discovery, and improving clinical workflows.

Students measure the relative intensity of a magnetic field as a function of distance. They place a permanent magnet selected distances from a compass, measure the deflection, and use the gathered data to compute the relative magnetic field strength. Based on their findings, students create mathematical models and use the models to calculate the field strength at the edge of the magnet. They use the periodic table to predict magnetism. Finally, students create posters to communicate the details their findings. This activity guides students to think more deeply about magnetism and the modeling of fields while practicing data collection and analysis. An equations handout and two grading rubrics are provided.

The Nature of Geographic Information is an orientation to the properties of geographic data and the practice of distance learning. The purpose of this course is to promote understanding of the Geographic Information Science and Technology (GIS&T) enterprise. GIS&T is the intersection of professions, institutions, and technologies that produce geographic data and render information from it. It is a rapidly growing and evolving field. Learning is a way of life for all GIS&T professionals. With this in mind, I hope that this text may contribute to your lifelong exploration of how geospatial technologies can be used to improve the quality of life-yours and your neighbors', locally and globally, now and in the future.

As a weighted plastic egg is dropped into a tub of flour, students see the effect that different heights and masses of the same object have on the overall energy of that object while observing a classic example of potential (stored) energy transferred to kinetic energy (motion). The plastic egg's mass is altered by adding pennies inside it. Because the egg's shape remains constant, and only the mass and height are varied, students can directly visualize how these factors influence the amounts of energy that the eggs carry for each experiment, verified by measurement of the resulting impact craters. Students learn the equations for kinetic and potential energy and then make predictions about the depths of the resulting craters for drops of different masses and heights. They collect and graph their data, comparing it to their predictions, and verifying the relationships described by the equations. This classroom demonstration is also suitable as a small group activity.

Repeated motion is present everywhere in nature. Learn how to 'make waves' with your own movements using a motion detector to plot your position as a function of time, and try to duplicate wave patterns presented in the activity. Investigate the concept of distance versus time graphs and see how your own movement can be represented on a graph.