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.

This resource provides a variety of information and activities that teachers may like to use with their students to explore the Islamic Middle East collections at the V&A. It can be used to support learning in Maths and Art. Included in this resource are sections on:

Principles of Islamic art and design
Pre-visit activities
Activities to do in the museum
Activities to do back at school
Islamic art explores the geometric systems that depend upon the regular division of the circle and the study of Islamic art increases appreciation and understanding of geometry. The use of these geometric systems creates a harmony among Islamic decorative arts and architecture, which is consistent with the Islamic belief that all creation is harmoniously interrelated.

Approaching an abstract subject in a concrete way provides a means of extending maths into other curriculum areas. The context of the Museum expands and enriches students' appreciation of the application of geometry in a cultural context and develops the sense of different cultural identities. Students have the opportunity to become familiar with the relationship between geometry and design and this can give confidence to students who have never seen themselves as 'good at art'.

Do you like to paint? Watch this step by step video as artist Kristin Farr demonstrates how to paint your very own "Magic Hecksagon," which is a colorful, geometric design inspired by folk art. She uses a plethora of different colors to bring a sense of motion to her work. Watch and learn more in the interview with Kristin Farr: http://youtu.be/OX1r-3-VK-0

In this video segment from Cyberchase, a plant expert shows Bianca the patterns and symmetry found in nature.

Students explore the concepts of center of mass and static equilibrium by seeing how non-symmetrical objects balance. Using a paper cut-out shape of a parrot sitting on a wire coat hanger, they learn that their parrot exists in stable equilibrium — it returns to its balancing point after being disturbed. The weight of its tail makes the parrot balance upright. Give the parrot a push, and she knocks off balance, but swings back and forth until coming to rest in balance again.

Students will discuss works of art that have grotesque elements and symmetry in their design. They will identify symmetry and line in grotesques. Students will create symmetrical designs for a pilgrim bottle and also design a door panel using grotesques. They will then analyze William Blake's poem "The Tiger" and write their own grotesque-inspired poetry.

The concepts of stability and equilibrium are introduced while students learn how these ideas are related to the concept of center of mass. They gain further understanding when they see, first-hand, how equilibrium is closely related to an object's center of mass. In an associated literacy activity, students learn about motion capture technology, the importance of center of gravity in animation and how use the concept of center of gravity in writing an action scene.

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

Meet Bay Area artist Mike Shine, who discusses his carnival-inspired paintings, and his recent large-scale stencil murals. He makes art for people to enjoy, both superficially and in depth, and condemns much of modern art because of the context needed for interpretation. He wants his art to be able to be interpreted, regardless of how it is interpreted. He wants it to transcend cultural and language barriers. Check out how his art is made in this video.

This is the first term of a theoretical treatment of the physics of solids. Topics covered include crystal structure and band theory, density functional theory, a survey of properties of metals and semiconductors, quantum Hall effect, phonons, electron phonon interaction and superconductivity.

To learn about the concept of center of mass, students examine how objects balance. They make symmetrical cut-outs of different "creatures" and experiment with how they balance on a tightrope of string. Students see the concept of center of mass at work as the creatures balance.

After students have complete the associated activity to collect and graph acceleration data from walking human subjects, they learn more about gait analysis---the study of human motion, which is used as biometric data for human medical diagnostics and (non-human) comparative biomechanics. They learn about the steps that comprise the universal process of engineering analysis—data collection, data analysis, mathematical modeling and reporting—and consider how these steps could be applied to analyze a person's gait, which prepares them to conduct the second associated activity.

Through this activity, Bernoulli's principle as it relates to winged flight is demonstrated. Student pairs use computers and an online virtual wind tunnel to see the influence of camber and airfoil angle of attack on lift. Activity and math worksheets are provided.