AP 50A is the first half of a year-long, team- and project-based introduction to physics focusing on the application of physics to real-world problems. The AP 50A and B sequence, designed for engineering and physics concentrators, is equivalent in content and rigor to a standard calculus-based introductory physics course sequence. Lectures and exams are replaced by interactive, hands-on, and collaborative learning activities that will not only help you master physics concepts and hone your scientific reasoning and problem-solving skills, but also grow your capacity for self-directed learning and develop your collaborative skills.

Course Content: Kinematics, mechanics, waves

AP 50B is the second half of a year-long, team- and project-based introduction to physics focusing on the application of physics to real-world problems. The AP 50A and B sequence, designed for engineering and physics concentrators, is equivalent in content and rigor to a standard calculus-based introductory physics course sequence. Lectures and exams are replaced by interactive, hands-on, and collaborative learning activities that will not only help you master physics concepts and hone your scientific reasoning and problem-solving skills, but also grow your capacity for self-directed learning and develop your collaborative skills.

Course Content: Electromagnetism and optics

The physics of crystalline solids and their electric, magnetic, optical, and thermal properties. Designed as a first course in solid-state physics. Topics: free electron model; Drude model; the physics of crystal binding; crystal structure and vibration (phonons); x-ray diffraction; electrons in solids (Bloch theorem) and electronic band structures; metals and insulators; semiconductors (and their applications in pn junctions and transistors); magnetism; superconductivity.

This course provides an introduction to quantum materials and devices, including low-dimensional materials, single and double quantum dots, Josephson junctions, and graphene. Their behavior is explained using quantum and semiclassical transport, the Coulomb blockade, and superconductivity. Quantum devices offer new approaches for electronics and photonics.

The first half of the course will cover the interaction of quantized atoms with electromagnetic fields, introducing a number of basic concepts such as coherent Rabi transitions vs. rate-equation dynamics, stimulated & spontaneous transitions, and energy & phase relaxations. These will be then used to study a range of applications of atom-field interactions, such as nuclear magnetic resonance, molecular beam and paramagnetic masers, passive and active atomic clocks, dynamic nuclear polarization, pulse sequence techniques to coherently manipulate atomic quantum states, and laser oscillators with applications. We will also touch upon the interaction of quantized atoms with quantized fields, discussing the atom + photon (Jaynes-Cummings) Hamiltonian, dressed states, and cavity quantum electrodynamics. The second half will cover the classical interaction of electromagnetic fields with matter, with special attentions to collective electrodynamics in particular, magnetohydrodynamics and plasma physics with applications in astrophysics, space physics, and Bloch electrons in crystalline solids.

This course covers the electrical, optical and magnetic properties of technologically important materials. It provides a quantitative description of their functional properties including dielectric, ferroelectric, and piezoelectric behavior, and their paramagnetic and ferromagnetic states.  Electronic characteristics of semiconductors, dielectric materials, and superconductors will be covered, as well as the optical response including birefringence, Pockels effect, Kerr effect, and photoelasticity. In addition, special topics related to recent research will be addressed. 

This course will present a survey of soft matter physics, providing an overview of the richness and breadth of the field. The emphasis will be on the physics of the systems, rather than on the formalism. It will cover most of the fields of interest within soft matter physics, both current and through the history of the field. The course is intended to be of value to both experimentalists and theorists.

Select topics in materials chemistry, focusing on chemical bonds, crystal chemistry, organic and polymeric materials, hybrid materials, surfaces and interfaces, self-assembly, electrochemistry, biomaterials, and bio-inspired materials synthesis.

This course introduces electrochemical systems through the lens of thermodynamics, kinetics, and transport. We begin by asking what fundamental role an electron plays in a chemical reaction, then we move to methods to treat electrons through traditional chemical kinetic theories, and last, we discuss entire systems and how mass transport affects chemistry. Throughout the course, we will focus on examples from industry, and we will finish by combining all the above into a discussion on electrochemical interfaces in some practical systems.

This course covers theoretical background and practical hands-on applications of modern computational atomistic methods used to understand and design properties of advanced functional materials. Topics include classical interatomic potentials and machine learning methods, quantum first-principles electronic structure models based on wave functions and density functional theory, Monte Carlo sampling and molecular dynamics simulations of phase transitions and free energies, fluctuations and transport properties. Applications include atomistic and electronic effects in materials for energy conversion and storage, catalysis, alloys, polymers, and low-dimensional materials.

The course introduces various aspects of quantum science, including quantum computing, quantum simulation, quantum communication and quantum metrology. It will particularly focus on the presentation of different experimental platforms currently used in the field and include superconducting qubits, trapped ions, neutral atoms, defects in solids, photons, among others. The course will cover an introduction of the general goals and essential prerequisites for these platforms; it will elucidate their operational principles and highlight some of their most significant and recent achievements, as well as the main challenges in their development.

Bonding, crystallography, diffraction, phase diagrams, microstructure, point defects, dislocations, and grain boundaries.

Basic principles of statistical physics with applications including: the equilibrium properties of classical and quantum gases; phase diagrams, phase transitions and critical points, as illustrated by the gas-liquid transition and simple magnetic models; Bose-Einstein condensation.

This course focuses on the modern applications of Statistical Mechanics. We will learn the basics of information theory, coding and compression. We will next learn about Bayesian Inference, priors and maximizing entropy, which will naturally lead us to regularization and compressed sensing. We will then cover learning: support vector machines, vc dimension, supervised, reinforcement and unsupervised learning. These topics, which build on each other, will be taught using examples in the primary literature with an emphasis on applying the framework we develop. Applications will be taught through problems in genomics, neuroscience, geophysics, and engineering.

This course supports new PhD students in finding their research fit, building good research habits, and becoming a researcher. It consists of two 2-unit courses: 290a (spring of G1 year) focuses on adapting to a research group, developing strong reading and writing habits, and preparing students for teaching during their G2 year; 290b (fall of G2 year) focuses on oral communication and on preparing students for the qualifying exam. This course also develops other skills necessary for success in graduate school such as setting goals, peer feedback, research ethics, collaboration and teamwork, and negotiation.

This course supports new PhD students in finding their research fit, building good research habits, and becoming a researcher. It consists of two 2-unit courses: 290a (spring of G1 year) focuses on adapting to a research group, developing strong reading and writing habits, and preparing students for teaching during their G2 year; 290b (fall of G2 year) focuses on oral communication and on preparing students for the qualifying exam. This course also develops other skills necessary for success in graduate school such as setting goals, peer feedback, research ethics, collaboration and teamwork, and negotiation.

Lectures and laboratory instruction on transmission electron microscopy (TEM) and Cs corrected, aberration-correction microscopy and microanalysis. Lab classes include; diffraction, dark field imaging, X-ray spectroscopy, electron energy-loss spectroscopy, atomic imaging, materials sample preparation, polymers, and biological samples.

Lattices and symmetries. Electronic Structure of Crystals. Semiclassical Transport Theory. Semiconductors. Localization. Integer Quantum Hall effect. Topological Insulators. Phonons. Additional topics from the theory of interacting electrons, including introduction to magnetism and superconductivity.

A course on the application of the principles of many-particle quantum mechanics to the properties of solids. The objective is to make students familiar with the tools of second quantization and diagrammatic perturbation theory, while describing the theory of the electron liquid, the BCS theory of superconductivity, and theory of magnetism in metals and insulators. Modern topics on correlated electron systems will occupy the latter part of the course.

Concepts of condensed matter physics are applied to the science and technology of beyond-CMOS devices, in particular, mesoscale, low-dimensional, and superconducting devices. Topics include: quantum dots/wires/wells and two-dimensional (2D) materials; optoelectronics with confined electrons; conductance quantization, Landauer-Buttiker formalism, and resonant tunneling; magneto oscillation; integer and fractional quantum Hall effects; Berry phase and topology in condensed matter physics; various Hall effects (anomalous, spin, valley, etc.); Weyl semimetal; topological insulator; spintronic devices and circuits; collective electron behaviors in low dimensions and applications; Cooper-pair boxes and superconducting quantum circuits.

Experimental or theoretical research project on acceptable problems in applied mathematics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied mathematics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

Experimental or theoretical research project on acceptable problems in applied physics supervised by a SEAS faculty member, and/or supervised reading on topics not covered by regular courses of instruction. The project or reading must be arranged between the student and individual SEAS faculty supervisor prior to enrolling in the course.

The focus of this course is on the basic principles involved in the control of quantum systems and assumes knowledge of undergraduate quantum mechanics. Schrödinger, Heisenberg and interaction representations.  Eigenvalue and time dependent problems, wave packets, coherent states. Harmonic oscillators. Quantization of the EM field. Tunneling; periodic potentials; Bloch’s theorem. Perturbation theory. WKB approximation. Transfer matrix methods. Variational methods. Rotation generators and angular momentum. Magnetic moment and spin; Stern Gerlach experiment. Spin states, Pauli matrices. Pauli equation. Dynamics of spins in a static and a transverse time dependent magnetic field; dynamics in a rotating frame; Rabi oscillations.  Coherent dynamics of two-level atoms. Rotating-wave and dipole approximations. Mixed states and density matrix. T₁ and T₂ relaxation times. Bloch equations. Identical particles: Bosons and Fermions. Slater determinant. Entanglement; singlet and triplet states. Clebsch-Gordan coefficients. Exchange energy. Elements of quantum information (qubits, no-cloning theorem, teleportation, quantum circuits).

The focus is on the foundations of optics/photonics and on some of its most important modern developments and applications. Powerful and widely used computational tools will be developed in the sections. Topics to be covered: Maxwell's equations, Free space optics. Reflection, refraction, polarization (Jones Calculus and Stokes parameters); interference and diffraction. Light-matter interaction, dispersion and absorption. Guided wave optics (including optical fibers). Perturbation and couple mode theory, transfer matrix methods; numerical methods. Optical resonators.  Photonic crystals. Near-field optics. Metal optics and Plasmonics. Metamaterials and Metasurfaces.

This class covers the fundamental principles underlying cryo-electron microscopy applied to Biological and SoftMaterials starting with the basic anatomy of electron microscopes, an introduction to Fourier transforms, and the principles of image formation. Building upon that foundation, the class then covers the sample preparation issues, data collection strategies, and basic image processing workflows.

This course provides students with an understanding of the complexities surrounding today’s most intractable problems and helps them develop methodologies for navigating the challenges they will face. After introducing systems thinking, with a focus on interconnections and feedback loops, the course will address a significant interdisciplinary issue: Artificial Intelligence (AI) and its relationship to human cognition.

The study of AI and human cognition is both timely and dynamic. This expansive domain integrates computer science, statistics, big data, cognitive science, psychology, and philosophy. As a transformative technology, AI has achieved remarkable success in understanding natural language and emulating human reasoning, making it invaluable in augmenting human cognition.

Despite these advances, many questions remain about the nature of AI and its relationship with human thought. This course invites participants to explore these questions through an intellectual journey. Students will engage in discussions on systems and paradigms, the essence of intelligence, computational approaches, mind and machine metaphors, cognitive biases in AI, and the role of AI in creativity and intuition.

The course emphasizes collaborative learning, with students working in teams to learn from each other, as well as from lectures and selected literature. Each lecture will be paired with research papers and books, followed by a discussion session.

The topics covered in the course are listed in the syllabus. Each will include an overview of the issue and its significance. Students will apply systems thinking and a multidisciplinary approach to analyze and critique each topic. By the end of the course, students will have developed a strong framework for multidisciplinary discussions, gained a deep understanding of AI’s power, limitations, and risks, and explored its technical building blocks through hands-on exercises. Additionally, students will experience the value of collaboration and the importance of diversity while working in diverse teams.

This course is an introduction to the foundations of quantum mechanics, with specific focus on the basic principles involved in the control of quantum systems. Experimental foundations of quantum mechanics. Superposition principle, Schrödinger’s equation, eigenvalue and time dependent problems, wave packets, coherent states; uncertainty principle. One dimensional problems: double well potentials, tunneling and resonant tunneling; WKB approximation. Hermitian operators and expectation values; time evolution and Hamiltonian, commutation rules, transfer matrix methods. Crystals, Bloch theorem, superlattices. Angular momentum, spin, Pauli matrices. Coherent interaction of light with two-level systems. Quantization of the EM field, spontaneous and stimulated emission; qubits, entanglement, teleportation.

Taking this course meets the quantum mechanics core course requirement for the Applied Physics model programs.