This is a spin on the traditional game of using numbers and operations to form an expression equal to a certain number. The game uses dominoes and multiple target numbers.

Multi-scale systems differ from traditional macro-scale systems in that the multi-scale systems use components from two or more scales (i.e. nano, micro, meso, and macro-scales). Subject provides the skills required to design and manufacture multi-scale systems. Emphasis is placed on understanding the fundamental differences between traditional macro-scale system design and the design of multi-scale systems. Topics include design methodologies, modeling approaches, analytic tools, and manufacturing processes. Examples drawn from a diverse range of applications, including automobiles, fiber optic equipment, electronic test equipment, and micro/meso-scale machinery. Students master the materials through problem sets and a substantial term project.

Languages and compilers to exploit multithreaded parallelism. Implicit parallel programming using functional languages and their extensions. Higher-order functions, non-strictness, and polymorphism. Explicit parallel programming and nondeterminism. The lambda calculus and its variants. Term rewriting and operational semantics. Compiling multithreaded code for symmetric multiprocessors and clusters. Static analysis and compiler optimizations.

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

Computer-aided design methodologies for synthesis of multivariable feedback control systems. Performance and robustness trade-offs. Model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; nonlinear effects. Computer-aided (MATLAB) design homework using models of physical processes. This course uses computer-aided design methodologies for synthesis of multivariable feedback control systems. Topics covered include: performance and robustness trade-offs; model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; and nonlinear effects. The assignments for the course comprise of computer-aided (MATLABĺ¨) design problems.

Growth and development of normal bone and joints, the process of mineralization, the biophysics of bone and response to stress and fracture, calcium and phosphate homeostasis and regulation by parathyroid hormone and vitamin D, and the pathogenesis of metabolic bone diseases and disease of connective tissue, joints, and muscles, with consideration of possible mechanisms and underlying metabolic derangements.

Directed composition of larger forms of original writing involving voices and/or instruments. Includes a weekly seminar in composition for the presentation and discussion of student work in progress. Students are expected to produce at least one substantive work, performed in public, by the end of the term. Contemporary compositions and major works from twentieth-century music literature are studied. Meets with graduate subject 21M.505, but assignments vary.

"This course is a survey of perceptual and cognitive aspects of the psychology of music, with special emphasis on underlying neuronal and neurocomputational representations and mechanisms. Basic perceptual dimensions of hearing (pitch, timbre, consonance/roughness, loudness, auditory grouping) form salient qualities, contrasts, patterns and streams that are used in music to convey melody, harmony, rhythm and separate voices. Perceptual, cognitive, and neurophysiological aspects of the temporal dimension of music (rhythm, timing, duration, temporal expectation) are explored. Special topics include comparative, evolutionary, and developmental psychology of music perception, biological vs. cultural influences, Gestaltist vs. associationist vs. schema-based theories, comparison of music and speech perception, parallels between music cognition and language, music and cortical action, and the neural basis of music performance."

Begins with the premise that the 1960s mark a great dividing point in the history of twentieth-century Western musical culture, and explores the ways in which various social and artistic concerns of composers, performers, and listeners have evolved since that decade. Focuses on works by classical composers from around the world. Topics to be explored include: the impact of rock, as it developed during the 1960s-70s; the concurrent emergence of post-serial, neo-tonal, Minimalist, and New Age styles; the globalization of Western musical traditions; the impact of new technologies; and the significance of music video, video games, and other versions of (digital) multimedia. Interweaves discussion of these topics with close study of seminal musical works, evenly distributed across the four decades since 1960. Works by MIT composers included.

An introduction to the analysis of tonal music. Students develop analytical techniques based upon concepts learned in Harmony and Counterpoint I and II. Students study harmony, counterpoint, melodic line and motivic relationships at local and large scale levels of musical structure. Three 7-page papers, one revised paper, and one oral presentation required.

This course examines the history, techniques, and aesthetics of mechanical and computer-aided approaches to algorithmic music composition and generative music systems. Through creative hands-on projects, readings, listening assignments, and lectures, students will explore a variety of historical and contemporary approaches. Diverse tools and systems will be employed, including applications in Python, MIDI, Csound, SuperCollider, and Pure Data.

"This course is an investigation into the history and aesthetics of music and technology as deployed in experimental and popular musics from the 19th century to the present. Through original research, creative hands-on projects, readings, and lectures, the following topics will be explored. The history of radio, audio recording, and the recording studio, as well as the development of musique concr?te and early electronic instruments. The creation and extension of musical interfaces by composers such as Harry Partch, John Cage, Conlon Nancarrow, and others. The exploration of electromagnetic technologies in pickups, and the development of dub, hip-hop, and turntablism. The history and application of the analog synthesizer, from the Moog modular to the Roland TR-808. The history of computer music, including music synthesis and representation languages. Contemporary practices in circuit bending, live electronics, and electro-acoustic music, as well as issues in copyright and intellectual property, will also be examined. No prerequisites."

This course is a creative, hands-on exploration of contemporary and historical approaches to live electronics performance and improvisation, including basic analog instrument design, computer synthesis programming, and hardware and software interface design.

Focuses on musical traditions of West Africa. A variety of musical practices and their cultural contexts are explored through listening, reading and written assignments with an emphasis on class discussion. Subject includes in-class instruction in Senegalese drumming, song and dance, as well as live lecture-demonstrations by guest performers from throughout West Africa. This course is an introduction to selected musical traditions of West Africa. A variety of musical practices and their cultural contexts will be explored through listening, reading, and written assignments, with an emphasis on class discussion. The course includes in-class instruction in West African drumming, song and dance, as well as lecture-demonstrations by guest artists. After an introductory unit, the course will be organized around four main geographical areas: Senegal, Mali, Ghana, and Nigeria. An in-depth study of music from these countries will be interspersed with brief overviews of Southern, Central, and East Africa.

Focuses on Hindustani classical music of North India, and also involves learning about the ancient foundations of the rich classical traditions of music and dance of all Indian art and culture. Practice of the ragas and talas through the learning of songs, dance, and drumming compositions. Develops insights through listening, readings, and concert attendance.

This lesson will explore the connections between magnetism in natural materials and electromagnetism. The ultimate goal will be for students to form an understanding that the source of magnetism in natural materials is moving charges. It is helpful, but not required, for the students to have some work with electricity, and other distance forces (such as gravity or the electric force). The lesson will probably take two 50-minute periods to complete. Although the video footage is brief, the activities are in depth, inquiry-based, and can take time for the students to explore. The materials are not specifically prescribed, but can include things such as bar magnets, compasses, iron filings, wire, batteries, steel bolts, coils, straws, and hot glue. The activities include drawing the magnetic fields of bar magnets and electromagnets. The activities also include making a magnet from a drinking straw and iron filings.

In this video lesson, the concept of momentum applied to hard-body collisions is explained using a number of simple demonstrations, all of which can be repeated in the classroom. Understanding Newton's Laws is fundamental to all of physics, and this lesson introduces the vital concepts of momentum and energy, and their conservation. Only some preliminary ideas of algebra are used here, and all the concepts presented can be found in any high-school level physics book. In terms of materials required, getting hold of large steel balls may not be easy, but large ball bearings can be procured easily. On the basis of what students have learned in the video, teachers can easily generate a large number of questions that relate to one's daily experiences, or which pose new challenges: for example, in a collision between a heavy and light vehicle, why do those inside the lighter one suffer less injury?

How people make sense of their worlds symbolically through myth, ritual, metaphor, and cosmology. The structure of symbols, the natural and social elements they draw on, their social use, and the messages they convey. Students learn to record and analyze myth and ritual.