How do artists create a story that provides a message or provokes emotions in that single frame? This lesson will help students analyze ways in which the composition of a painting contributes to telling the story or conveying the message through the placement of objects and images within the painting.

In a multi-week experiment, students monitor the core temperatures of two compost piles, one control and one tended, to see how air and water affect microbial activity. They daily aerate and wet the "treated" pile and collect 4-6 weeks' worth of daily temperature readings. Once the experiment is concluded, students plot and analyze their data to compare the behavior of the two piles. They find that the treated pile becomes hotter, an indication that more microbes are active and releasing heat. Through this activity, students see that microbes play a role in composting and how composting can be used as a carbon management process.

Students explore the concept of biodegradability by building and observing model landfills to test the decomposition of samples of everyday garbage items. They collect and record experiment observations over five days, seeing for themselves what happens to trash when it is thrown "away" in a landfill environment. This shows them the difference between biodegradable and non-biodegradable and serves to introduce them to the idea of composting. Students also learn about the role of engineering in solid waste management.

This short video and interactive assessment activity is designed to teach fourth graders about compound unit multiplication - word problems.

This task is preliminary to F-LE Compounding Interest with a 5% Interest Rate which further develops the relationship between e and compound interest.

This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically addresses the standard (F-BF), building functions from a context, a auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (F-LE) domain of tasks.

A rubric designed by educators from Lawrence Public Schools to be used in its annual review process of openly licensed educational resources.

This online textbook addresses the population of individuals with disabilities that experience complex lifelong needs across multiple areas in their lives. Drs. Sennott and Loman drafted this book (along with the help from some friends) with the hope of providing pertinent, practical, and current resources to future special educators who plan to serve individuals with complex disabilities.

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.

Fundamental concepts and results for the compressible flow of gases. Topics include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Meyer function; and self-similar compressible flows. Emphasis on physical understanding of the phenomena and basic analytical techniques. 2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Meyer function; and self-similar compressible flows. The emphasis will be on physical understanding of the phenomena and basic analytical techniques.

6.004 offers an introduction to the engineering of digital systems. Starting with MOS transistors, the course develops a series of building blocks ‰ŰÓ logic gates, combinational and sequential circuits, finite-state machines, computers and finally complete systems. Both hardware and software mechanisms are explored through a series of design examples. 6.004 is required material for any EECS undergraduate who wants to understand (and ultimately design) digital systems. A good grasp of the material is essential for later courses in digital design, computer architecture and systems. The problem sets and lab exercises are intended to give students hands-on" experience in designing digital systems; each student completes a gate-level design for a reduced instruction set computer (RISC) processor during the semester."

This course covers the algorithmic and machine learning foundations of computational biology combining theory with practice. We cover both foundational topics in computational biology, and current research frontiers. We study fundamental techniques, recent advances in the field, and work directly with current large-scale biological datasets.

A computational camera attempts to digitally capture the essence of visual information by exploiting the synergistic combination of task-specific optics, illumination, sensors and processing. In this course we will study this emerging multi-disciplinary field at the intersection of signal processing, applied optics, computer graphics and vision, electronics, art, and online sharing through social networks. If novel cameras can be designed to sample light in radically new ways, then rich and useful forms of visual information may be recorded -- beyond those present in traditional photographs. Furthermore, if computational process can be made aware of these novel imaging models, them the scene can be analyzed in higher dimensions and novel aesthetic renderings of the visual information can be synthesized.We will discuss and play with thermal cameras, multi-spectral cameras, high-speed, and 3D range-sensing cameras and camera arrays. We will learn about opportunities in scientific and medical imaging, mobile-phone based photography, camera for HCI and sensors mimicking animal eyes. We will learn about the complete camera pipeline. In several hands-on projects we will build physical imaging prototypes and understand how each stage of the imaging process can be manipulated.

This course is an introduction to computational theories of human cognition. Drawing on formal models from classic and contemporary artificial intelligence, students will explore fundamental issues in human knowledge representation, inductive learning and reasoning. What are the forms that our knowledge of the world takes? What are the inductive principles that allow us to acquire new knowledge from the interaction of prior knowledge with observed data? What kinds of data must be available to human learners, and what kinds of innate knowledge (if any) must they have?

Introduces design as a computational enterprise in which rules are developed to compose and describe architectural and other designs. The class covers topics such as shapes, shape arithmetic, symmetry, spatial relations, shape computations, and shape grammars. It focuses on the application of shape grammars in creative design, and teaches shape grammar fundamentals through in-class, hands-on exercises with abstract shape grammars. The class discusses issues related to practical applications of shape grammars.

Study and discussion of computational approaches and algorithms for contemporary problems in functional genomics. Topics include DNA chip design, experimental data normalization, expression data representation standards, proteomics, gene clustering, self-organizing maps, Boolean networks, statistical graph models, Bayesian network models, continuous dynamic models, statistical metrics for model validation, model elaboration, experiment planning, and the computational complexity of functional genomics problems.

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.

This course introduces programming languages and techniques used by physical scientists: FORTRAN, C, C++, MATLAB, and Mathematica. Emphasis is placed on program design, algorithm development and verification, and comparative advantages and disadvantages of different languages.

Wave equations for fluid and visco-elastic media. Wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides. Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media. Seismo-Acoustic modeling of seabeds and ice covers. Seismic interface and surface waves in a stratified seabed. Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides. Numerical modeling of target scattering and reverberation clutter in ocean waveguides. Ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research.

The theoretical frameworks of Hartree-Fock theory and density functional theory are presented as approximate methods to solve the many-electron problem. A variety of ways to incorporate electron correlation are discussed. The application of these techniques to calculate the reactivity and spectroscopic properties of chemical systems, in addition to the thermodynamics and kinetics of chemical processes, is emphasized. This course also focuses on cutting edge methods to sample complex hypersurfaces, for reactions in liquids, catalysts and biological systems.