Many of tomorrow’s innovations in fields such as fast computing, renewable energy generation, batteries, and transportation will rely on the unique and novel properties of materials. The development of such materials requires integrated knowledge in physics, chemistry, and biology, along with advanced mathematics and computation. Material Science/Physics introduces students to atomic structure, macroscopic elastic and thermodynamic properties, electric and magnetic properties, and fabrication methods and applications.

The fundamental concepts and tools of calculus, probability, and linear algebra are essential to modern sciences, from the theories of physics and chemistry that have long been tightly coupled to mathematical ideas, to the collection and analysis of data on complex biological systems. Given the emerging technologies for collecting and sharing large data sets, some familiarity with computational and statistical methods is now also essential for modeling biological and physical systems and interpreting experimental results. MF1 is an introduction to differential and integral calculus that focuses on the concepts necessary for understanding the meaning of differential equations and their solutions. It includes an introduction to a software package for numerical solution of ordinary differential equations.

This course focuses on the concept of energy and its relevance for explaining the behavior of natural systems. The conservation of energy and the transformations of energy from one form to another are crucial to the function of all systems, including familiar mechanical devices, molecular structures and reactions, and living organisms and ecosystems. By integrating perspectives from physics, chemistry, and biology, this course helps students see both the elegant simplicity of universal laws governing all physical systems and the intricate mechanisms at play in the biosphere. Topics include kinetic energy, potential energy, quantization of energy, energy conservation, cosmological and ecological processes.

The fundamental concepts and tools of calculus, probability, and linear algebra are essential to modern sciences, from the theories of physics and chemistry that have long been tightly coupled to mathematical ideas, to the collection and analysis of data on complex biological systems. Given the emerging technologies for collecting and sharing large data sets, some familiarity with computational and statistical methods is now also essential for modeling biological and physical systems and interpreting experimental results. MF2 is an introduction to probability and statistics with an emphasis on concepts relevant for the analysis of complex data sets. It includes an introduction to the fundamental concepts of matrices, eigenvectors, and eigenvalues.

This course focuses on the collective behavior of systems composed of many interacting components. The phenomena of interest range from the simple relaxation of a gas into an equilibrium state of well-defined pressure and temperature to the emergence of ever increasing complexity in living organisms and the biosphere. The course provides an overview of some fundamental differences between traditional disciplines as well as indications of how they complement each other some important contexts. Topics include thermodynamic (statistical mechanical) equilibrium, fundamental concepts of temperature, entropy, free energy, and chemical equilibrium, driven systems, fundamentals of biological and ecological systems.

Integrated Science 3 emphasizes the physics and chemistry concepts of oscillating systems, waves, and fields, and includes applications to human perception. In addition to their fundamental importance to physics and chemistry proper, these ideas are essential for developing an awareness of the principles employed by engineers in the construction of the electrical and optical devices that are ubiquitous in modern civilization. Topics include harmonic oscillators, sound waves, light, and reaction-diffusion patterns.

Integrated Science 4 has more of a chemistry/biology emphasis, with physics brought to bear as needed. It treats topics relevant to understanding organisms, biochemical engineering, and the environment. Topics include evolution, modern biology, ecosystems, hydrology, and climate.

Scientific Writing and Presentations cover some of the areas of scientific communication that a scientist needs to know and to master in order to successfully promote his or her research and career. Students will learn to recognize and construct logical arguments and become familiar with the structure of common publication formats. It will help students to advance their skills in communicating findings in textual, visual and verbal formats for a variety of audiences.

This course is an introduction to topics fundamental to materials science: structure, bonding, and thermodynamics. Bonding is the foundation of structure, and the structure provides constraints on the thermo-dynamic properties of materials. These topics are intimately related and are required for a full understanding of materials’ synthesis, fabrication, and processing.

This lab course is designed to expose student to synthesis and characterization methods commonly used in materials science. Solution based methods, chemical vapor deposition, solid-solid reaction, SEM, TEM, x-ray diffraction RAMAN, IR, and electrochemical characterization will be the topics with which students will have hands-on experience.

This course focuses on providing students with mathematical knowledge to understand structure-property relationship in materials. The course will be based on “Advanced Calculus for Applications”, which is a textbook designed for undergraduate students with interests in materials science and engineering. Topics include: Number Systems and Algebra of Complex Numbers, Elementary Complex Functions, Analytic Functions, Complex Integrals, Taylor Series, Laurent Series, Differential Equations, etc.

The course will discuss the origin of mechanical properties in materials, mostly solid-state materials. Topics will include: continuum elasticity and plasticity, Slip geometry and dislocation theory, Strengthening mechanisms in metals and alloys, Thermal effects, creep, fracture and fatigue etc. This course will include basic mechanisms and engineering analysis.

This course discusses the electronic, optical and magnetic properties of materials, and how the properties are related to their electronic and molecular structures. Specific examples of important materials will be discussed in the class, including materials for electronic devices, materials for electro-optical devices, optical fibers, solar cells and other devices. How the chemical composition and physical structure changes the properties at nanoscale will also be a major topic of discussion.

Introductory treatments of special relativity and quantum mechanics. Topics include: wave mechanics and interference; relativistic kinematics, energy and momentum; the Schrodinger equation and its interpretation; quantum particles in one-dimension; spin; fermions and bosons; the hydrogen spectrum. Applications to crystallography, semiconductors, atomic physics and optics, particle physics, and cosmology.

Newtonian mechanics at the intermediate level, Lagrangian mechanics, linear oscillations, chaos, dynamics of continuous media, motion in non-inertial reference frames.

This course focuses on the basics of equilibrium thermodynamics and introduces the concepts of temperature, internal energy, and entropy using ideal gases and ideal paramagnets as models. The chemical potential is defined and the three thermodynamic potentials are discussed with use of Legendre transforms. It will also cover topics including the power of thermodynamics in gases and condensed matter, phase transitions, probability theory, and quantum statistics.

Experiments involving the fields of electricity, magnetism, heat, optics, and modern physics. Written and oral presentations of results. Instructor consent required.

Introduction to the non-relativistic quantum description of matter. Topics include experimental foundations, wave-particle duality, Schrodinger wave equation, interpretation of the wave function, the state vector, Hilbert space, Dirac notation, Heisenberg uncertainty principle, one-dimensional quantum problems, tunneling, the harmonic oscillator, three-dimensional quantum problems, angular momentum, the hydrogen atom, spin, angular momentum addition, identical particles, elementary perturbation theory, fine/hyperfine structure of hydrogen, dynamics of two-level systems, and applications to atoms, molecules, and other systems.

Courses listed below are recommended electives for the major. Students can also select other courses in different divisions as electives.

Partial differentiation, multiple integrals, and topics in differential and integral vector calculus, including Green’s theorem, the divergence theorem, and Stokes’s theorem.

Systems of linear equations and elementary row operations, Euclidean n-space and subspaces, linear transformations and matrix representations, Gram-Schmidt orthogonalization process, determinants, eigenvectors and eigenvalues; applications.

This course is intended to provide an introduction to the physics of solids and soft materials. It will discuss topics including properties of static (crystal structure) and dynamic (lattice vibrations) arrangements of atoms; electrons in solids; key features in metals, insulators and semiconductors; semiconductor devices; structure and assembly of a variety of soft materials including liquid crystals, polymers, colloidal systems and surfactants; special properties of materials in nanoscale; etc.

Introductory survey course on nuclear and particle physics. Phenomenology and experimental foundations of nuclear and particle physics; fundamental forces and particles, composites. Interaction of particles with matter and detectors. SU(2), SU(3), models of mesons and baryons. Weak interactions and neutrino physics. Lepton-nucleon scattering, form factors and structure functions. QCD, gluon field and color. W and Z fields, electro-weak unification, the CKM matrix, Nucleon-nucleon interactions, properties of nuclei, single and collective particle models. Electromagnetic and hadronic interactions with nuclei. Nuclear reactions and nuclear structure, nuclear astrophysics. Relativistic heavy ion collisions.

Introduction to the study of temporal patterns in nonequilibrium systems. Theoretical, computational, and experimental insights used to explain phase space, bifurcations, stability theory, universality, attractors, fractals, chaos, and time-series analysis. Each student carries out an individual research project on a topic in nonlinear dynamics and gives a formal presentation of the results.

Frontiers of 21st Century physics explores the major subdisciplines of modern physics and their impact on society. Students learn why society invests so much in physics and what it gets in return, from the origins of electronic devices and computational systems to the large scale structure of our universe. This course explores the things that things are made of and the mechanisms scientists use to change the behavior of things. Computing machinery has existed for less than a century and in every decade the capacity of information technologies has improved by an order of magnitude or more. This course explores the understanding of physical reality that has enabled this revolution and considers how far the revolution may yet proceed.

This major prepares graduates for advanced study in material science, physics, computer science, math and other areas and for careers in fields such as nanotechnology, electronics, biomedical sciences, and automotive and aerospace industries and others.