This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

Phenomenology of mechanical behavior of materials at the macroscopic level. Relationship of mechanical behavior to material structure and mechanisms of deformation and failure. Topics include: elasticity, viscoelasticity, plasticity, creep, fracture, and fatigue. Case studies and examples drawn from a variety of classes of materials including: metals, ceramics, polymers, thin films, composites, and cellular materials.

Introduction to statics and the mechanics of deformable solids. Emphasis on the three basic principles of equilibrium, geometric compatibility, and material behavior. Stress and its relation to force and moment; strain and its relation to displacement; linear elasticity with thermal expansion. Failure modes. Application to simple engineering structures such as rods, shafts, beams, and trusses. Application to design. Introduction to material selection. This course provides an introduction to the mechanics of solids with applications to science and engineering. We emphasize the three essential features of all mechanics analyses, namely: (a) the geometry of the motion and/or deformation of the structure, and conditions of geometric fit, (b) the forces on and within structures and assemblages; and (c) the physical aspects of the structural system (including material properties) which quantify relations between the forces and motions/deformation.

Students investigate the ways in which ancient technologies six types of simple machines and combinations are used to construct modern buildings. As they work together to solve a design problem (designing and building a modern structure), they brainstorm ideas, decide on a design, and submit it to a design review before acquiring materials to create it (in this case, a mural depicting it). Emphasis is placed on cooperative, creative teamwork and the steps of the engineering design process.

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 article attempts to bring out ‘The Superultramodern Unification’. It is basically the idea that the mysterious phenomena underlying most of the most challenging problems in modern / ultramodern science / philosophy are, in fact, multiple aspects of a singular structure, which the NSTP (Non – Spatial Thinking Process) theory (a major component of superultramodern science / philosophy) is the unique theoretical representation of. The NSTP theory thus unifies and demystifies the phenomena, and solves the problems. The first part of this article presents the solutions to two of the problems viz. Zeno’s paradoxes and the problem of quantum non-locality. The second part states the remaining problems. And the third, and the last, part states some other challenging problems, solvable with the NSTP theory, which are not directly connected to the aforementioned structure.

The lesson begins by introducing Olympics as the unit theme. The purpose of this lesson is to introduce students to the techniques of engineering problem solving. Specific techniques covered in the lesson include brainstorming and the engineering design process. The importance of thinking out of the box is also stressed to show that while some tasks seem impossible, they can be done. This introduction includes a discussion of the engineering required to build grand, often complex, Olympic event centers.

Introduction to organic chemistry. Development of basic principles to understand the structure and reactivity of organic molecules. Emphasis on substitution and elimination reactions and chemistry of the carbonyl group. Introduction to the chemistry of aromatic compounds.

Instructional expert Jim Knight visits first year middle school teacher Aisha Santos to discuss pacing and structure of her lessons.

The difference between an architect and an engineer is sometimes confusing because their roles in building design can be similar. Students experience a bit of both professions by following a set of requirements and meeting given constraints as they create a model parking garage. They experience the engineering design process first-hand as they design, build and test their models. They draw a blueprint for their design, select the construction materials and budget their expenditures. They also test their structures for strength and find their maximum loads.

In this Design Challenge activity students will explore how structure relates to function as they design devices to save Fido.

Student teams investigate biomedical engineering and the technology of prosthetics. Students create a model prosthetic lower leg using various materials. Each team demonstrate its prosthesis' strength and consider its pros and cons, giving insight into the characteristics and materials biomedical engineers consider in designing artificial limbs.

In this video segment adapted from NOVA scienceNOW, learn how RNAi, a mechanism that has evolved in cells to prevent viral infection, was discovered and how it works.

Using scientific animations and illustrated metaphors, this interactive activity from NOVA scienceNOW explains RNAi and how it works.

Reading Fiction is designed to sharpen your skills as a critical reader. As we explore both short stories and novels focusing on the theme of "the city in literature," we will learn about the various elements that shape the way we read texts - structure, narrative voice, character development, novelistic experimentation, historical and political contexts and reader response.

The student practices their reading comprehension and vocabulary by means of texts concerning the training of pilots. He/she exercise structuring details by comparing data from several websites.

Rocks cover the earth's surface, including what is below or near human-made structures. With rocks everywhere, breaking rocks can be hazardous and potentially disastrous to people. Students are introduced to three types of material stress related to rocks: compressional, torsional and shear. They learn about rock types (sedimentary, igneous and metamorphic), and about the occurrence of stresses and weathering in nature, including physical, chemical and biological weathering.

General study of modern architecture as a response to important technological, cultural, environmental, aesthetic, and theoretical challenges after the European Enlightenment. Focus on the theoretical, historiographic, and design approaches to architectural problems encountered in the age of industrial and post-industrial expansion across the globe, with specific attention to the dominance of European modernism in setting the agenda for the discourse of a global modernity at large. Explores modern architectural history through thematic exposition rather than as simple chronological succession of ideas.

The purpose of this work is to describe that ‘it is self-evident that consciousness is non-spatial’; that is, ‘consciousness can be represented by no spatial structure’. It considers the example of the consciousness of bodily pain, which is stated to be conceptually distinct from its bodily counterpart, i.e. identification of some electrochemical signal in brain, as a self-evident fact. This example is just a matter of illustration and is not meant to be the justification/basis of the self-evident non-spatiality of consciousness, as no self-evident truth needs justification. Further it is argued that a reader’s possible denial of the self-evident non-spatiality of consciousness is, in fact, their inability to understand the truth due to the relatively profound concepts involved in it; as a simple self-evident mathematical proposition, like if p implies q and if p is true then q is true, may not be self-evidently comprehensible to a person of extremely poor intellect. The self-evident proposition that ‘consciousness is non-spatial’ is one of the six self-evident propositions that form the axiomatic/self-evident foundation of the NSTP (Non – Spatial Thinking Process) theory.