In this case study, a newly appointed medical examiner uncovers an unusual trend in drowning cases, which she suspects may be the work of a serial murderer. To prove that she is right, she must rely on instrumentation designed and tested by a team of students from the local university. Students read the case, then design and build a device for the detection of blood stains. The case was developed for use in an undergraduate laboratory course sequence in photonics for junior and senior level students. It would be suitable for any undergraduate course in physics, chemistry, or electrical engi eering that covers topics in optics, photonics, or spectroscopy.

Students learn about gear ratios and power by operating toy mechanical cranes of differing gear ratios. They attempt to pick up objects with various masses to witness how much power must be applied to the system to oppose the force of gravity. They learn about the concept of gear ratio and practice calculating gear ratios on worksheets, discovering that smaller gear ratios are best for picking objects up quickly, and larger gear ratios make it easier to lift heavy objects.

Students are challenged to design a method for separating steel from aluminum based on magnetic properties as is frequently done in recycling operations. To complicate the challenge, the magnet used to separate the steel must be able to be switched off to allow for the recollection of the steel. Students must ultimately design, test, and present an effective electromagnet.

In this lesson, students continue their education on cells in the human body. They discuss stem cells and how engineers are involved in the research of stem cell behavior. They learn about possible applications of stem cell research and associated technologies, such as fluorescent dyes for tracking the replication of specific cells.

Students explore the definition of a function by playing an interactive game called "Club Function." The goal of the game is to be in the club! With students each assigned to be either a zebra or a rhinoceros, they group themselves according to the "rules" of the club function. After two minutes, students freeze in their groups, and if they are not correctly following the rules of the club function, then they are not allowed into the "club." Through this activity students come to understand that one x-coordinate can only have one corresponding y-coordinate while y-coordinates can have many x-coordinates that correspond to it.

In this optics activity, learners discover that not all shadows are black. Learners explore human color perception by using colored lights to make additive color mixtures. With three colored lights, learners can make shadows of seven different colors. They can also explore how to make shadows of individual colors, including black. Use this activity demonstrate how receptors in the retina of the eye work to see color.

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

Students continue an examination of logarithms in the Research and Revise stage by studying two types of logarithms—common logarithms and natural logarithm. In this study, they take notes about the two special types of logarithms, why they are useful, and how to convert to these forms by using the change of base formula. Then students see how these types of logarithms can be applied to solve exponential equations. They compute a set of practice problems and apply the skills learned in class.

Students examine different types of fabric and their characteristics. Using magnifying glasses and sandpaper, they test and observe the weave and wear quality of fabric samples. By comparing the qualities of different fabrics they come to understand why so many different types of fabric exist and are able to recognize or suggest different uses for them.

In small groups, students experiment and observe the similarities and differences between human-made objects and objects from nature. They compare the function and structure of hollow bones with drinking straws, bird beaks, tool pliers, bat wings and airplane wings. Observations are recorded in a compare & contrast chart, and then shared in a classroom discussion, along with follow up assessment activities such as journal writing and Venn diagrams.

In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately).

Students learn about complex networks and how to represent them using graphs. They also learn that graph theory is a useful mathematical tool for studying complex networks in diverse applications of science and engineering, such as neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Topics covered include set theory, defining a graph, as well as defining the degree of a node and the degree distribution of a graph.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

CAD, or computer-aided design, is a powerful modeling tool that technical professionals use. This course will introduce the student to the process of modeling 2- and 3-D objects with computer-aided design; the student will learn the basics of drafting by hand as well. Upon successful completion of this course, students will be able to: Describe the design process and basic CAD practices for engineering design and drawing; Identify CAD representations like orthographic projections, 3D modeling, and section views; Identify and use CAD annotation and presentation skills like dimensioning, tolerance, and assembly drawings; Create 2D sketches and parts using CAD software; Edit and modify 2D sketches and parts using CAD software; Print and present 2D sketches and parts using CAD software; Model basic and advanced 3D parts using CAD software; Edit and modify basic and advanced 3D parts using CAD software; Create 3D assemblies using CAD software; Create 2D projections from 3D models and assemblies and learn how to annotate projections; Apply the skills attained from 2D and 3D modeling to design working drawings by using CAD software. (Mechanical Engineering 104)

Computer science is the study of computational systems and their use in representing important problems in science and society. Major topics include computational science, software systems, network systems, theory of computation, machine learning, and human-computer interaction.

Students analyze video clips of kids rolling down a hill on skates, scooters, and bikes to determine whether mechanical energy is conserved.

Control Systems is an inter-disciplinary engineering text that analyzes the effects and interactions of mathematical systems. This book is for third and fourth year undergraduates in an engineering program.

This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms. The aim is to develop the core analytical and algorithmic issues of continuous optimization, duality, and saddle point theory using a handful of unifying principles that can be easily visualized and readily understood.

A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.