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.

This course is an introduction to problem solving; logic, sets, and operations on sets; and properties and operations on whole numbers, integers, rational numbers, irrational numbers, and real numbers. Modelling techniques necessary for future elementary educators will also be covered in this course.

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

This course is the first of a two term sequence in modeling, analysis and control of dynamic systems. The various topics covered are as follows: mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices, analytical and computational solution of linear differential equations, state-determined systems, Laplace transforms, transfer functions, frequency response, Bode plots, vibrations, modal analysis, open- and closed-loop control, instability, time-domain controller design, and introduction to frequency-domain control design techniques. Case studies of engineering applications are also covered.

Modeling, Functions, and Graphs covers the content of a typical college algebra course with an emphasis on functions and modeling; when combined with a trigonometry text or supplement, this text can be used in a precalculus course.

The text employs a variety of applications to motivate mathematical thinking. Each chapter opens with a problem of historical or contemporary significance highlighting the material in the chapter, and includes by an Investigation that previews the skills to be introduced. These Investigations can be used in class as guided explorations or as projects for small groups. We have also provided a set of more challenging Projects at the end of each chapter.

A collaboration between the National Aeronautics and Space Administration (NASA) and the CK-12 Foundation, this book provides high school mathematics and physics teachers with an introduction to the main principles of modeling and simulation used in science and engineering. An appendix of lesson plans is included.

In this activity, students interact with 12 models to observe emergent phenomena as molecules assemble themselves. Investigate the factors that are important to self-assembly, including shape and polarity. Try to assemble a monolayer by "pushing" the molecules to the substrate (it's not easy!). Rotate complex molecules to view their structure. Finally, create your own nanostructures by selecting molecules, adding charges to them, and observing the results of self-assembly.

Multi-scale systems (MuSS) consist of components from two or more length scales (nano, micro, meso, or macro-scales). In MuSS, the engineering modeling, design principles, and fabrication processes of the components are fundamentally different. The challenge is to make these components so they are conceptually and model-wise compatible with other-scale components with which they interface. This course covers the fundamental properties of scales, design theories, modeling methods and manufacturing issues which must be addressed in these systems. Examples of MuSS include precision instruments, nanomanipulators, fiber optics, micro/nano-photonics, nanorobotics, MEMS (piezoelectric driven manipulators and optics), X-Ray telescopes and carbon nano-tube assemblies. Students master the materials through problem sets and a project literature critique.

While current economic theory focuses on prices and games, this book models economic settings where harmony is established through one of the following societal conventions:

• A power relation according to which stronger agents are able to force weaker ones to do things against their will.
• A norm that categorizes actions as permissible or forbidden.
• A status relation over alternatives which limits each agent's choices.
• Systematic biases in agents' preferences.

These four conventions are analysed using simple and mathematically straightforward models, without any pretensions regarding direct applied usefulness. While we do not advocate for the adoption of any of these conventions specifically – we do advocate that when modelling an economic situation, alternative equilibrium notions should be considered, rather than automatically reaching for the familiar approaches of prices or games.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"People with diabetes who require basal insulin to achieve blood glucose control can be at risk of hypoglycaemia, where blood glucose levels drop too low. In randomised clinical trials (or RCTs), use of second-generation basal insulin analogues, such as insulin glargine 300 units/mL (known as glargine 300) and insulin degludec, results in similar glycated haemoglobin reductions compared with first-generation basal insulin analogues, such as glargine 100 and insulin detemir, but with less hypoglycaemia. However, it is not known whether these results translate directly to routine clinical practice, as RCTs often apply strict inclusion and exclusion criteria, meaning that they may not be generalisable to real-life situations. Electronic medical records are a source of rich real-world data, but using them to make comparisons between different treatments can be difficult because results might be biased by confounding data, something that the randomisation in RCTs is designed to minimise..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

Solar energy in the form of light is available to organisms on Earth in abundance. Natural systems and other organisms have structures that function in ways to manage the interaction with and use of this energy. Using these natural examples, humans have (in the past) and continue to design and construct homes which manage solar energy in passive and active ways to reduce the need for energy from other sources. In this storyline, students will explore passive and active solar energy management through examples in the natural world. Students will use knowledge gained to design a building that maximizes the free and abundant energy gifts of the sun.

Technological advancements over the last decade mean that many fish are now swimming around with their own personal computers. These new tools allow researchers to track movements and behaviors in more complex ways without ever getting wet. Join NOAA marine biologist Heidi Dewar to learn about the intriguing discoveries researchers have made and how these high-tech efforts have advanced ocean management and conservation. (54 minutes)

The size and complexity of the oceans present a considerable challenge to those who want to mimic the movement of ocean water and understand ocean dynamics. Join Scripps Oceanography physical oceanographer Paola Cessi as she describes how a new age of supercomputers is allowing ocean modelers to begin investigating how the deep ocean responds to changes in the surface temperature and fresh water inputs from the highest latitudes of our Planet. (56 minutes)

What do plants eat? This unit explores plants and how they make food.

6.334 examines the application of electronics to energy conversion and control. Topics covered include: modeling, analysis, and control techniques; design of power circuits including inverters, rectifiers, and DC-DC converters; analysis and design of magnetic components and filters; and characteristics of power semiconductor devices. Numerous application examples will be presented such as motion control systems, power supplies, and radio-frequency power amplifiers. The course is worth 6 engineering design points.

Assessment is the gathering of information to improve decision-making. There are many approaches to psychological assessment that can be used to assess people’s thoughts, emotions, and behaviors, including self-report questionnaires, questionnaires reported by others, interviews, observations, biopsychological assessments, performance-based assessments, archival approaches, and combinations of these. However, the field has paid insufficient attention to measurement. There has been a proliferation of pseudoscience in assessment, including inaccurate assessments that can potentially cause harm. It is crucial to use assessments that are supported by science—with strong psychometric properties, including reliability and validity, and to develop better assessments.

This book discusses the principles of psychological assessment to help researchers and clinicians better develop, evaluate, administer, score, integrate, and interpret psychological assessments. It is intended for use by graduate students, faculty, researchers, and practicing psychologists. The book discusses psychometrics (reliability and validity), the assessment of various psychological domains (behavior, personality, intellectual functioning), various measurement methods (e.g., questionnaires, observations, interviews, biopsychological assessments, performance-based assessments), and emerging analytical frameworks to evaluate and improve assessment, including generalizability theory, structural equation modeling, item response theory, and signal detection theory. The book also discusses considerations of ethics, test bias, and cultural and individual diversity.

The book provides analysis examples using the free software, R, to help readers apply the principles to research and practice. The text, analysis code/syntax, R output, figures, and interpretation are all integrated to help guide readers. The book uses the freely available petersenlab package for R, which includes many functions relevant for assessment. The dissemination of these principles and tools will promote the development of more efficient and accurate assessment strategies that will lead to important scientific advancements and improved intervention.

Building on their understanding of graphs, students are introduced to random processes on networks. They walk through an illustrative example to see 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. This demonstrates how scientists and engineers use mathematics to model and simulate random processes on complex networks. Topics covered include random processes and modeling disease spread, specifically the SIR (susceptible, infectious, resistant) model.

Delve into a microscopic world working with models that show how electron waves can tunnel through certain types of barriers. Learn about the novel devices and apparatuses that have been invented using this concept. Discover how tunneling makes it possible for computers to run faster and for scientists to look more deeply into the microscopic world.

This class deals with the modeling and analysis of queueing systems, with applications in communications, manufacturing, computers, call centers, service industries and transportation. Topics include birth-death processes and simple Markovian queues, networks of queues and product form networks, single and multi-server queues, multi-class queueing networks, fluid models, adversarial queueing networks, heavy-traffic theory and diffusion approximations. The course will cover state of the art results which lead to research opportunities.