APHY 5060a, Basic Quantum Mechanics  John Sous

Basic concepts and techniques of quantum mechanics essential for solid state physics and quantum electronics. Topics include the Schrödinger treatment of the harmonic oscillator, atoms and molecules and tunneling, matrix methods, and perturbation theory.
TTh 2:30pm-3:45pm

APHY 5220b, Theory of Electromagnetic Waves, Radiation, and Scattering  A Douglas Stone

This is a graduate-level course on electromagnetic theory, focusing on electromagnetic wave phenomena in a variety of contexts. Electrostatics and magnetostatics are reviewed briefly and then the full time-dependent Maxwell equations are studied to derive the fundamentals of wave propagation, the wave equation, plane waves, polarization, energy and momentum flow in EM waves, conservation laws, gauge transformation, and Green functions for the wave equations. Dielectric media and Fresnel reflection and refraction, total internal reflection, group velocity, wave packets and dispersion. Beam propagation and gaussian optics, optical birefringence. Waves in confined structures, waveguides, optical fibers, resonant cavities. Radiating sources, electric and magnetic dipolar radiation, multipolar radiation, near and far-field solutions, radiating antennas. Scattering theory, scalar and vector diffraction, Rayleigh scattering, scattering matrix and temporal coupled mode theory, scattering resonances, multiple scattering, systems with gain and lasing. Time permitting: relativistic kinematics, covariance of Maxwell's equations, Lorentz transformation of electric and magnetic fields, relativistic mechanics of charged particles. Prerequisites: an undergraduate course on electricity and magnetism and graduate-level vector calculus and differential equations.
TTh 1pm-2:15pm

APHY 5260a, Explorations in Physics and Computation  Logan Wright

Computation has taken on an important, often central, role in both the practice and conception of physical science and engineering physics. This relationship is intricate and multifaceted, including computation for physics, computation with physics, and computation as a lens through which to understand physical processes. This course takes a more or less random walk within this space, surveying ideas and technologies that either apply computation to physics, that understand physical phenomena through the lens of computation, or that use physics to perform computation. Given the extent to which machine learning methods are currently revolutionizing this space of ideas, we focus somewhat more on topics related to modern machine learning, as opposed to other sorts of algorithms and computation. Since it is covered more deeply in other courses, we do not extensively cover error-corrected/fault tolerant quantum information processing, but we do frequently consider quantum physics. The course does not provide a systematic overview of any one topic, but rather a sampling of ideas and concepts relevant to modern research challenges. It is therefore intended for graduate students in early years of their program or research-inclined senior undergraduate students contemplating a research career. As a result, in addition to the scientific topics at hand, key learning goals include the basics of literature review, presentation, collegial criticism (peer review), and synthesizing new research ideas. Evaluation is primarily through two projects, one a lecture reviewing a topic area of interest and one a tutorial notebook providing worked numerical examples/code meant to develop or introduce a concept. Prior experience with Python is ideal, but can be learned as part of the coursework. Students should ideally be familiar with quantum mechanics, including density matrices and some phase-space methods, but this applies to only small fraction of the course. The course is primarily a survey-level overview of many topics, not a deep dive into any one topic. As a result, students who have extensive background on many of the topics described in the syllabus are welcome to participate but should speak with the instructor beforehand so we can determine if their learning goals can be met.
MW 11:35am-12:50pm

APHY 5480a / PHYS 5480a, Solid State Physics I  Yu He

A two-term sequence (with APHY 549) covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity.
HTBA

APHY 5490b / ENAS 851 / PHYS 5490b, Solid State Physics II  Vidvuds Ozolins

A two-term sequence (with APHY 548) covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity.
HTBA

APHY 5750b, Physics of AI  John Sous

A introduction to current research in AI from a physics perspective, i.e. one that emphasizes the mechanisms through which various AI architectures learn. Topics include, linear regression, neural nets, transformers, diffusion, etc. Prerequisites: linear algebra, calculus.
M 1:30pm-3:20pm

APHY 5760a, Topics in Applied Physics Research  Peter Rakich

The course introduces the fundamentals of applied physics research to graduate students in the Department of Applied Physics in order to introduce them to resources and opportunities for research activities. The content of the class includes overview presentations from faculty and other senior members of the department and related departments about their research and their career trajectories. The class also includes presentations from campus experts who offer important services that support Applied Physics graduate students in their successful degree completion.
F 1:30pm-3:20pm

APHY 5900b / PHYS 5900b, Responsible Conduct in Research for Physical Scientists  Staff

A review and discussion of best practices of conduct in research including scientific integrity and misconduct; mentorship; data management; and diversity, equity, and inclusion in science.
F 10am-11:15am

APHY 6070b, Modern Topics in Optics and Quantum Electronics  Peter Rakich

This course provides a survey of modern topics involving integrated photonics, optomechanics, nonlinear optics, and laser physics for students interested in contemporary experimental optics research. Subjects include nonlinear wave phenomena, optomechanical interactions, phonon physics, light scattering, light emission and detection, cavities, systems of cavities, traveling-wave devices and interactions, perturbation theory, reciprocal and nonreciprocal systems, parametric interactions, laser oscillators and related technologies. Students are encouraged to explore these and related research topics through independent study and classroom presentations.
MW 4pm-5:15pm

APHY 6100a / PHYS 6100a, Quantum Many-Body Theory  Yoram Alhassid

Identical particles and second quantization. Electron tunneling and spectral function. General linear response theory. Approximate methods of quantum many-body theory. Dielectric response, screening of long-range interactions, electric conductance, collective modes, and photon absorption spectra. Fermi liquid; Cooper and Stoner instabilities; notions of superconductivity and magnetism. BCS theory, Josephson effect, and Majorana fermions in condensed matter; superconducting qubits. Bose-Einstein condensation; Bogoliubov quasiparticles and solitons.
TTh 11:35am-12:50pm

APHY 6280a / PHYS 6120a, Statistical Physics II  Nicholas Read

An advanced course in statistical mechanics. Topics may include mean field theory of and fluctuations at continuous phase transitions; critical phenomena, scaling, and introduction to the renormalization group ideas; topological phase transitions; dynamic correlation functions and linear response theory; quantum phase transitions; superfluid and superconducting phase transitions; cooperative phenomena in low-dimensional systems.
TTh 2:30pm-3:45pm

APHY 6330b / PHYS 6330b, Introduction to Superconductivity  Yu He

The fundamentals of superconductivity, including both theoretical understandings of basic mechanism and description of major applications. Topics include historical overview, Ginzburg-Landau (mean field) theory, critical currents and fields of type II superconductors, BCS theory, Josephson junctions and microelectronic and quantum-bit devices, and high-Tc oxide superconductors.
MW 11:35am-12:50pm

APHY 6600a / PHYS 6010a, Quantum Information and Computation  Shruti Puri

This course focuses on the theory of quantum information and computation. We cover the following tentative list of topics: overview of postulates of quantum mechanics and measurements, quantum circuits, physical implementation of quantum operations, introduction to computational complexity, quantum algorithms (DJ, Shor’s, Grover’s, and others as time permits), decoherence and noisy quantum channels, quantum error-correction and fault-tolerance, stabilizer formalism, error-correcting codes (Shor, Steane, surface-code, and others as time permits), quantum key distribution, quantum Shannon theory, entropy, and data compression.
TTh 11:35am-12:50pm

APHY 6610b, Fault Tolerance and Quantum Error Correction  Aleksander Kubica

This course focuses on the theory of fault tolerance and quantum error correction. We cover the following tentative list of topics: criteria for quantum error correction, classical linear codes and quantum CSS codes, stabilizer codes, existence of good codes, concatenated codes, threshold theorems, topological codes, decoding algorithms, statistical-mechanical mappings, logical gates and fault-tolerant quantum computing, resource overheads, limitations and no-go theorems, quantum LDPC codes, approximate quantum error correction, experimental realizations of quantum error correction, and open research problems. Prerequisite: APHY 660 or CPSC 547 (or equivalent).
W 3:30pm-5:20pm

APHY 6700a, Statistical Methods with Applications in Science and Finance  Sohrab Ismail-Beigi

Introduction to key methods in statistical physics with examples drawn principally from the sciences (physics, chemistry, astronomy, statistics, biology) as well as added examples from finance. Students learn the fundamentals of Monte Carlo, stochastic random walks, and analysis of covariance analytically as well as via numerical exercises. Prerequisites: ENAS 1940, MATH 2220, ENAS 1300 or equivalents.
HTBA

APHY 6750a / PHYS 6750a, Principles of Optics with Applications  Hui Cao

Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, nanophotonics, plasmonics, and metamaterials. Topics include propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence.
HTBA

APHY 6760a / PHYS 6760a, Introduction to Light-Matter Interactions  Peter Rakich

Optical properties of materials and a variety of coherent light-matter interactions are explored through the classical and quantum treatments. The role of electronic, phononic, and plasmonic interactions in shaping the optical properties of materials is examined using generalized quantum and classical coupled-mode theories. The dynamic response of media to strain, magnetic, and electric fields is also treated. Modern topics are explored, including optical forces, photonic crystals, and metamaterials; multi-photon absorption; and parametric processes resulting from electronic, optomechanical, and Raman interactions.
MW 4pm-5:15pm

APHY 6790b / PHYS 6790b, Nonlinear Optics and Lasers  Logan Wright

Properties and origins of the nonlinear susceptibility; Sum-freq, diff-freq and 2nd-harmonic generation; Intensity-dependent refractive index; Optical phase conjugation; Self-focusing, self-phase modulation, solitons; Stimulated light scattering; Fixed points, bifurcations; Amplification; Rate equations; Relaxation oscillations, frequency pulling; Hole burning; Q-switching; Semiconductor and DFB lasers; Mode-locking; Injection-locking; Intense-field NLO and QM laser theory (time permitting)
MW 1pm-2:15pm

APHY 7260a, Advanced Thin Film Synthesis and Characterization  Charles Ahn

This course covers principles of thin film growth and characterization for advanced electronic and quantum materials applications. Topics include physical vapor deposition and related techniques for achieving state-of-the-art thin films and heterostructures, along with atomic-scale and spectroscopic characterization of thin film structures, including scanning probe microscopies, electron microscopies, diffraction techniques, and photon-based spectroscopies.
MW 1pm-2:15pm

APHY 7270b, Circuit Quantum Electrodynamics  Michael Hatridge and Robert Schoelkopf

Circuit quantum electrodynamics, or circuit QED, is the field of quantum optics with microwave photons, and is the basis of most solid-state quantum computing technologies. In the microwave domain, we can engineer the properties of “artificial atoms” constructed from circuits containing Josephson junctions and couple them strongly to stationary photons trapped in a cavity or resonant circuit and to traveling photons in a waveguide or transmission line. With this approach, one can access regions of strong coupling between “light” and “matter” that are not accessible in atomic physics. This course is an introduction to the concepts and techniques of circuit QED, aimed for the beginning graduate student or advanced undergraduate with a solid background in classical electricity and magnetism and also basic quantum mechanics. The course is intended to provide an important base of knowledge that can prepare the student for research in quantum information processing with superconducting circuits. Topics to be covered include the basics of superconducting qubits, the Jaynes-Cummings model and the strong dispersive regime, and the use of light-matter interactions for measurement, control, and quantum computing with quantum circuits. Extra work for graduate students: The last homework set is optional for undergrads and required for grads. Prerequisites: one semester QM and one semester E&M at advanced undergrad or higher.
TTh 2:30pm-3:45pm

BENG 5200a / C&MP 5500a / MCDB 5500a / PHAR 5500 / PTB 5500, Physiological Systems  W. Mark Saltzman and Stuart Campbell

The course develops a foundation in human physiology by examining the homeostasis of vital parameters within the body, and the biophysical properties of cells, tissues, and organs. Basic concepts in cell and membrane physiology are synthesized through exploring the function of skeletal, smooth, and cardiac muscle. The physical basis of blood flow, mechanisms of vascular exchange, cardiac performance, and regulation of overall circulatory function are discussed. Respiratory physiology explores the mechanics of ventilation, gas diffusion, and acid-base balance. Renal physiology examines the formation and composition of urine and the regulation of electrolyte, fluid, and acid-base balance. Organs of the digestive system are discussed from the perspective of substrate metabolism and energy balance. Hormonal regulation is applied to metabolic control and to calcium, water, and electrolyte balance. The biology of nerve cells is addressed with emphasis on synaptic transmission and simple neuronal circuits within the central nervous system. The special senses are considered in the framework of sensory transduction. Weekly discussion sections provide a forum for in-depth exploration of topics. Graduate students evaluate research findings through literature review and weekly meetings with the instructor.
MWF 9:25am-10:15am

BENG 5270b / C&MP 5560 / MCDB 5600b / PHAR 5600, Cellular and Molecular Physiology: Molecular Machines in Human Disease  Emile Boulpaep

The course focuses on understanding the processes that transfer molecules across membranes at the cellular, molecular, biophysical, and physiological levels. Students learn about the different classes of molecular machines that mediate membrane transport, generate electrical currents, or perform mechanical displacement. Emphasis is placed on the relationship between the molecular structures of membrane proteins and their individual functions. The interactions among transport proteins in determining the physiological behaviors of cells and tissues are also stressed. Molecular motors are introduced and their mechanical relationship to cell function is explored. Students read papers from the scientific literature that establish the connections between mutations in genes encoding membrane proteins and a wide variety of human genetic diseases.
MWF 9:25am-10:15am

BENG 5350b / PATH 5630, Biomaterial-Tissue Interactions  Themis Kyriakides

Study of the interactions between tissues and biomaterials, with an emphasis on the importance of molecular- and cellular-level events in dictating the performance and longevity of clinically relevant devices. Attention to specific areas such as biomaterials for tissue engineering and the importance of stem/progenitor cells, as well as biomaterial-mediated gene and drug delivery.
TTh 9am-10:15am

BENG 5410a, Physical and Chemical Basis of Bioimaging and Biosensing  Douglas Rothman and Daniel Coman

Basic principles and technologies for imaging and sensing the chemical, electrical, and structural properties of living tissues and biological macromolecules. Topics include magnetic resonance spectroscopy, MRI, positron emission tomography, and molecular imaging with MRI and fluorescent probes.
MW 1pm-2:15pm

BENG 5415a, Practical Applications of Bioimaging and Biosensing  Daniel Coman and Evelyn Lake

Detecting, measuring, and quantifying the structural and functional properties of tissue is of critical importance in both biomedical research and medicine. This course focuses on the practicalities of generating quantitative results from raw bioimaging and biosensing data to complement other courses focus on the theoretical foundations which enable the collection of these data. Participants in the course work with real, cutting-edge data collected here at Yale. They become familiar with an array of current software tools, denoising and processing techniques, and quantitative analysis methods that are used in the pursuit of extracting meaningful information from imaging data. The subject matter of this course ranges from bioenergetics, metabolic pathways, molecular processes, brain receptor kinetics, protein expression and interactions to wide spread functional networks, long-range connectivity, and organ-level brain organization. The course provides a unique hands-on experience with processing and analyzing in vitro and in vivo bioimaging and biosensing data that is relevant to current research topics. The specific imaging modes which are covered include in vivo magnetic resonance spectroscopy (MRS) and spectroscopic imaging (MRSI), functional, structural, and molecular imaging (MRI), wide-field fluorescent optical imaging, and positron emission tomography (PET). The course provides the necessary background in biochemistry, bioenergetics, and biophysics for students to motivate the image manipulations which they learn to perform. Prerequisites: Math through first order differential equations, PHYS 180/181, CHEM 161, BIOL 101/102, BENG 249 or other experience with scientific software like MATLAB, BENG 350 and BENG 410 (both of which can be taken at the same time as this course)  0 Course cr
F 1pm-2:15pm

BENG 5420a, Biophotonics  Cristina Rodriguez

This course provides an introduction to biophotonics, with a strong emphasis on optical microscopy and the fundamental principles governing how light interacts with biological matter. Students learn key optical concepts, including diffraction, interference, Fourier optics, and fluorescence, as well as advanced techniques such as multiphoton microscopy and harmonic generation imaging. The course covers the physics underlying imaging systems, the design and function of modern optical microscopes, and their applications in biomedical research. This course is designed for students in biomedical engineering, physics, biology, and related fields who seek to understand the optical foundations of modern imaging technologies.
TTh 2:30pm-3:45pm

BENG 5440a, Fundamentals of Medical Imaging  Chi Liu, Dana Peters, and Gigi Galiana

Review of basic engineering and physical principles of common medical imaging modalities including X-ray, CT, PET, SPECT, MRI, and echo modalities (ultrasound and optical coherence tomography). Additional focus on clinical applications and cutting-edge technology development.
MW 11:35am-12:50pm

BENG 5450a, Biomedical Image Processing and Analysis  Lawrence Staib and James Duncan

This course is an introduction to biomedical image processing and analysis, covering image processing basics and techniques for image enhancement, feature extraction, compression, segmentation, registration, and motion analysis including traditional and machine-learning techniques. Students learn the fundamentals behind image processing and analysis methods and algorithms with an emphasis on biomedical applications.
TTh 11:35am-12:50pm

BENG 5482a, Physics of Magnetic Resonance Spectroscopy in Vivo  Graeme Mason

The physics of chemical measurements performed with nuclear magnetic resonance spectroscopy, with special emphasis on applications to measurement studies in living tissue. Concepts that are common to magnetic resonance imaging are introduced. Topics include safety, equipment design, techniques of spectroscopic data analysis, and metabolic modeling of dynamic spectroscopic measurements.
MW 11:35am-12:50pm

BENG 5485b / INP 9585b, Fundamentals of Neuroimaging  Fahmeed Hyder, Elizabeth Goldfarb, and Douglas Rothman

The neuroenergetic and neurochemical basis of several dominant neuroimaging methods, including fMRI. Topics range from technical aspects of different methods to interpretation of the neuroimaging results. Controversies and/or challenges for application of fMRI and related methods in medicine are identified.
W 3:30pm-5:20pm

BENG 5550b, Vascular Mechanics  Jay Humphrey

This course is designed to enable students to apply methods of continuum biomechanics to study diverse vascular conditions and treatments, including aging, atherosclerosis, aneurysms, effects of hypertension, design of tissue-engineered constructs, and vein grafts from an engineering perspective. Emphasis is placed on ensuring that the mechanics is driven by advances in the vascular mechanobiology.
TTh 1pm-2:15pm

BENG 5560b, Molecular and Cellular Biomechanics  Michael Murrell

The basic mechanical principles at the molecular and cellular level that underlie the major physical behaviors of the cell, from cell division to cell migration. Basic cellular physiology, methodology for studying cell mechanical behaviors, models for understanding the cellular response under mechanical stimulation, and the mechanical impact on cell differentiation and proliferation.
W 3:30pm-5:20pm

BENG 5570b, Computational Mechanics  Martin Pfaller

This course integrates fundamental concepts from nonlinear continuum mechanics and finite element methods applied to solid and fluid mechanics, focusing on theoretical understanding and numerical techniques. Topics covered are fundamentals of tensor calculus, kinematics, balance equations, constitutive relationships, geometric and material nonlinearities, nonlinear solution strategies, stability, nonlinear dynamics, errors, convergence, and adaptivity. Applications in biomedical engineering are stressed throughout the course. Prerequisites: fundamentals in calculus, differential equations, and linear algebra.
TTh 9am-10:15am

BENG 5611b, BioMEMS & Biomedical Microdevices  Rong Fan

Principles and applications of micro- and nanotechnologies for biomedicine. Approaches to fabricating micro- and nanostructures. Fluid mechanics, electrokinetics, and molecular transport in microfluidic systems. Integrated biosensors and microTAS for laboratory medicine and point-of-care uses. High-content technologies including DNA, protein microarrays, and cell-based assays for differential diagnosis and disease stratification. Emerging nanobiotechnology for systems medicine. Prerequisites: CHEM 112a, 114a, or 118a, and ENAS 194a or b.
TTh 2:30pm-3:45pm

BENG 5630a, Immunoengineering  Tarek Fahmy

An advanced class that introduces immunology principles and methods to engineering students. The course focuses on biophysical principles and biomaterial applications in understanding and engineering immunity. The course is divided into three parts. The first part introduces the immune system: organs, cells, and molecules. The second part introduces biophysical characterization and quantitative modeling in understanding immune system interactions. The third part focuses on intervention, modulation, and techniques for studying the immune system with emphasis on applications of biomaterials for intervention and diagnostics.
TTh 11:35am-12:50pm

BENG 5680b, Topics in Immunoengineering  Tarek Fahmy

This course addresses the intersection of immunobiology with engineering and biophysics. It invokes engineering tools, such as biomaterials, solid-state devices, nanotechnology, biophysical chemistry, and chemical engineering, toward developing newer and effective solutions to cancer immunotherapy, autoimmune therapy, vaccine design, transplantation, allergy, asthma, and infections. The central theme is that dysfunctional immunity is responsible for a wide range of disease states and that engineering tools and methods can forge a link between the basic science and clinically translatable solutions that will potentially be “modern cures” to disease. This course is a follow-up to ENAS 553 and focuses more on the clinical translation aspect as well as new understandings in immunology and how they can be translated to the clinic and eventually to the market. Prerequisites: ENAS 553, differential equations, and advanced calculus.
MW 4pm-5:15pm

BENG 5690a, Single-Cell Biology, Technologies, and Analysis  Rong Fan

This course teaches the principles of single-cell heterogeneity in human health and disease as well as the cutting-edge wet-lab and computational techniques for single-cell analysis, with a particular focus on omics-level profiling and data analysis. Topics covered include single-cell-level morphometric analysis, genomic alteration analysis, epigenomic analysis, mRNA transcriptome sequencing, small RNA profiling, surface epitope, intracellular signaling protein and secreted protein analysis, metabolomics, multi-omics, and spatially resolved single-cell omics mapping. We also teach computational methods for quantification of cell types, states, and differentiation trajectories using single-cell high-dimensional data. Finally, case studies are provided to show the power of single-cell analysis in therapeutic target discovery, biomarker research, clinical diagnostics, and personalized medicine. Prerequisite: physiological systems, molecular biology, or biochemistry.
TTh 2:30pm-3:45pm

BENG 5724b, Topics in Computational and Systems Biology  Purushottam Dixit

This course covers topics related to modeling biological networks across time and length scales. Specifically, the course covers models of intracellular signaling networks, transcriptional regulation networks, cellular metabolic networks, and ecological networks in microbial consortia. For each type of network, we cover the biological basics, standard mathematical treatments including deterministic and stochastic modeling, methods to infer model parameters from data, and new machine-learning based inference approaches. The required mathematical methods are briefly covered. The course assignments involve coding in MATLAB.
MW 2:30pm-3:45pm

BENG 5767b, Systems Biology of Cell Signaling  Andre Levchenko

This course designed for graduate and advanced undergraduate students is focused on systems biology approaches to the fundamental processes underlying the sensory capability of individual cells and cell-cell communication in health and disease. The course is designed to provide deep treatment of both the biological underpinnings and mathematical modeling of the complex events involved in signal transduction. As such, it can be attractive to students of biology, bioengineering, biophysics, computational biology, and applied math. The class is part of the planned larger track in systems biology, being one of its final, more specialized courses. In spite of this, each lecture has friendly introduction to the specific topic of interest, aiming to provide sufficient refreshment of the necessary knowledge. The topics have been selected to represent both cutting-edge directions in systems analysis of signaling processes and exciting settings to explore, making learning complex notions more enjoyable. Prerequisites: basic knowledge of biochemistry and cell biology, as well as programming experience and basic notions from probability theory and differential equations.
MW 4pm-5:15pm

BENG 5823b, Data and Clinical Decision-Making  John Onofrey and Michael Choma

Data and computation are reshaping medicine and clinical decision-making. Examples include acute states of physiological failure such as shock and sepsis as well as failure modes associated with aging (e.g., delirium/acute brain failure, falls). This seminar provides (1) a modern, clinically facing view of physiological failure and (2) a survey of how data and computation are reshaping clinical concepts and practice, including decision-making. Key topics and concepts include medical data types (e.g., imaging, lab values, oximetry); nonlinearity and complexity in physiological resilience and failure; clinically relevant AI/ML methods; data-driven definitions of medical disease; predictive modeling as a distinct field in AI/ML; and clinical decision-making using modern data and computational tools. The course is led by two instructors with complementary backgrounds that include AI/ML, statistics/data science, medical physiology, clinical medicine, and digital health. Guest lecturers from both clinical practice and industry provide additional context. Course work includes scientific literature review, written reports, oral presentations, and a final project. Students interested in AI/ML in medicine in both academic and industry settings with an engineering/medical background would benefit from this course. The course provide the requisite background for physiology and assumes a basic understanding of AI/ML but has no strict prerequisites.
HTBA

BENG 5849b, Biomedical Data Analysis  Cristina Rodriguez and Richard Carson

The course focuses on the analysis of biological and medical data associated with applications of biomedical engineering. It provides basics of probability and statistics, and analytical approaches for determination of quantitative biological parameters from noisy, experimental data. Programming in MATLAB to achieve these goals is a major portion of the course. Applications include Michaelis-Menten enzyme kinetics, Hodgkin-Huxley, neuroreceptor assays, receptor occupancy, MR spectroscopy, PET neuroimaging, brain image segmentation and reconstruction, and molecular diffusion.
TTh 1pm-2:15pm

BENG 5910b, Effective Fellowship Grant Writing: From Concept to Submission  Fadi Akar

This course is designed to equip participants with the essential skills and strategies needed to prepare successful fellowship grant applications. It covers the entire grant writing process, from understanding funding opportunities and requirements to developing a compelling proposal. Participants learn how to clearly define research goals, align their projects with funding criteria, and craft persuasive narratives that effectively communicate their ideas. The course also emphasizes the importance of strong supporting documents, including CVs, budgets, and letters of recommendation. Through practical exercises, peer reviews, and expert feedback, participants refine their writing techniques, enhance proposal clarity, and increase their chances of securing funding. The course is intended for seniors and graduate students in Biomedical Engineering or a related Biomedical Sciences department.  0 Course cr
TTh 1pm-2:15pm

BENG 5990a or b, Special Investigations  Kathryn Miller-Jensen

Faculty-supervised individual projects with emphasis on research, laboratory, or theory. Students must define the scope of the proposed project with the faculty member who has agreed to act as supervisor, and submit a brief abstract to the director of graduate studies for approval.
HTBA

CENG 5210b, Classical and Statistical Thermodynamics  Peijun Guo

A unified approach to bulk-phase equilibrium thermodynamics, bulk-phase irreversible thermodynamics, and interfacial thermodynamics in the framework of classical thermodynamics, and an introduction to statistical thermodynamics. Both the activity coefficient and the equations of state are used in the description of bulk phases. Emphasis on classical thermodynamics of multicomponents, including concepts of stability and criticality, curvature effect, and gravity effect. The choice of Gibbs free energy function covers applications to a broad range of problems in chemical, environmental, biomedical, and petroleum engineering. The introduction includes theory of Gibbs canonical ensembles and the partition functions, fluctuations; Boltzmann statistics; Fermi-Dirac and Bose-Einstein statistics. Application to ideal monatomic and diatomic gases is covered.
MW 9am-10:15am

CENG 6020a, Chemical Reaction Engineering  Eric Altman

Applications of physical-chemical and chemical-engineering principles to the design of chemical process reactors. Ideal reactors treated in detail in the first half of the course, practical homogeneous and catalytic reactors in the second.
TTh 1pm-2:15pm

CENG 6030b, Energy, Mass, and Momentum Processes  Amir Haji-Akbari

Application of continuum mechanics approach to the understanding and prediction of fluid flow systems that may be chemically reactive, turbulent, or multiphase.
TTh 1pm-2:15pm

CENG 6050a, Colloid Science and Engineering  Paul Van Tassel

A graduate-level introduction is given to modern colloid science as practiced by engineers. Topics include thermodynamics of surfaces, transport in colloidal systems, the electric double layer, colloidal forces, self-assembly in solution and at interfaces, and adsorption. Applications to problems frequently encountered by chemical, biomedical, and environmental engineers are stressed throughout.
TTh 11:35am-12:50pm

CENG 6090a, Principles and Design of Energy Devices  Shu Hu

This is a comprehensive course with content at the intersection of nanoscale science, engineering, and technology, including application areas and nanofabrication technique. Topics include nanoscaled photovoltaic cells, hydrogen storage, fuel cells, and nanoelectronics; layer-by-layer assembly; organic-inorganic mesostructures; colloidal crystals, organic monolayers, proteins, DNA and abalone shells; synthesis of carbon nanotubes, nanowire, and nanocrystals; microelectromechanical systems (MEMs) devices; photolithography, electron beam lithography, and scanning probe lithography; lithium-based batteries; and nanomanufacturing (roll to roll, nanoimprint lithography, inkjet printing).
MW 2:30pm-3:45pm

CENG 6140b, Surface and Thin Film Characterization  Eric Altman

Fundamental and practical aspects of spectroscopy, diffraction, and microscopy related to the structural and chemical characterization of surfaces and thin films. Emphasis on identification of adsorbed species by vibrational spectroscopy, determination of the chemical state of the surface by photoelectron spectroscopy, quantitative methods in surface analysis, determination of surface structure by scanning probe microscopy techniques and diffraction methods, and recent advances in surface characterization.
TTh 9am-10:15am

CENG 6150a, Synthesis of Nanomaterials  Lisa Pfefferle

This course focuses on the synthesis and engineering of nanomaterials. We also introduce different types of nanomaterials, unique properties at the nanoscale, measurement, and important applications of nanomaterials (including biomedical, electronic, and energy applications). Synthesis methods covered include gas phase and high vacuum techniques (CVD, MOCVD) as well as wet chemistry techniques such as reduction of metal salts, sonochemistry, and sol gel methods. Taking sample applications, we discuss the properties necessary for each, and how to control these properties through synthesis control, such as by using templating methods.
MW 9am-10:15am

CENG 6200a, Fundamentals of Molecular Modeling  Amir Haji-Akbari

This is an elective course for graduate students in engineering and sciences that familiarizes them with basics of molecular modeling. The course commences with a brief overview of classical thermodynamics and statistical mechanics. Subsequently, the theoretical foundations and the algorithmic implementation aspects of the following techniques are covered: Monte Carlo simulations, molecular dynamics simulations, thermostats and barostats, estimation of static and dynamic properties, long-ranged interactions and Ewald-based methods, free energy calculations, constrained MD, biased simulations (Landau free energies, umbrella sampling, metadynamics), and rare events and rate calculations. Students are expected to be proficient in calculus, probability theory, thermodynamics and statistical mechanics. They should also have basic familiarity with computer programming (preferably in C or C++).
TTh 2:30pm-3:45pm

CPSC 5130b, Computer System Security  Timothy Barron

Overview of the principles and practice behind analyzing, designing, and implementing secure computer systems. The course covers problems that have continued to plague computer systems for years as well as recent events and research in this rapidly evolving field. Students learn to think from the perspective of an adversary, to understand systems well enough to see how their flaws could be exploited, and to consequently defend against such exploitation. The course offers opportunities for hands-on exploration of attacks and defenses in the contexts of web applications, networks, and system-level software. It also addresses ethical considerations and responsibilities associated with security research and practice.
HTBA

CPSC 5150b, Law and Large Language Models  Ruzica Piskac and Scott Shapiro

This course is intended for computer science and law students interested in how artificial intelligence can be applied to legal reasoning. It combines basic AI theory with practical project work, focusing on using tools like large language models (LLMs) and other AI technologies for tasks common in legal practice. Students learn how to automate case summarization, draft legal memos and briefs, simulate oral arguments for better argumentation skills, and assist in the preparation of pro-se motions for self-represented litigants. The course emphasizes hands-on experience, helping students build real-world skills in applying AI in legal settings. Our goal is to bring together students from computer science and from law and match them together in the teams. Each team works on a project that automates a specific aspect of the legal process or legal reasoning, focusing on practical, real-world applications. In addition to all standard course requirements, graduate students need to present a recent, relevant research paper in class. Prerequisites: basic coding skills, including knowledge of Python; interest in Large Language Models (LLMs); basic understanding of linear algebra and calculus; familiarity with basic probability (e.g., likelihood, averages) and simple statistical concepts (like mean and variance).
HTBA

CPSC 5160a, Lattices and Post-Quantum Cryptography  Katerina Sotiraki

This course explores the role of lattices in modern cryptography. In the last decades, novel computational problems, whose hardness is related to lattices, have been instrumental in cryptography by offering: (a) a basis for "post-quantum" cryptography, (b) cryptographic constructions based on worst-case hard problems, and (c) numerous celebrated cryptographic protocols unattainable from other cryptographic assumptions. This course covers the foundations of lattice-based cryptography from fundamental definitions to advanced cryptographic constructions. More precisely, we introduce the Learning with Error (LWE) and the Short Integer Solutions (SIS) problems and study their unique properties, such as the fact that their average-case hardness is based on the worst-case hardness of lattice problems. Next, we cover lattice constructions of advanced cryptographic primitives, such as fully homomorphic encryption and signature schemes. Finally, we introduce some notions of quantum cryptography and explore the role of lattices in this area. Overall, this course offers insights on the foundations and recent advancements in lattice-based cryptography. Prerequisites: CPSC 467/567 or equivalent and linear algebra.
MW 4pm-5:15pm

CPSC 5190a or b, Full Stack Web Programming  Alan Weide

This course introduces students to a variety of advanced software engineering and programming techniques in the context of full-stack web programming. The focus of the course includes both client- and server-side programming (and database programming), client/server communication, user interface programming, and parallel programming.
HTBA

CPSC 5200b, Computer Architecture  Abhishek Bhattacharjee

This course offers a treatment of computer architectures for high-performance and power/energy-efficient computer systems. Topics include the foundations of general-purpose computing, including instruction set architectures, pipelines, superscalar and out-of-order execution, speculation, support for precise exceptions, and simultaneous multi-threading. We also cover domain-specific hardware (e.g., graphics processing units), and ongoing industry efforts to elevate them to the status of first-class computing units. In tandem, we cover topics relevant to both general-purpose and domain-specific computing, including memory hierarchies, address translation and virtual memory, on-chip networks, machine learning techniques for resource management, and coherence techniques. If time permits, we study the basics of emerging non-classical computing paradigms like neuromorphic computing. Overall, this course offers insights on how the computing industry is combating the waning of traditional technology scaling via acceleration and heterogeneity. Prerequisites: Courses similar to CPSC 323, 223, and 202. This is a programming-intensive course, so comfort with large programming projects is essential.
HTBA

CPSC 5210a, Compilers and Interpreters  Zhong Shao

Compiler organization and implementation: lexical analysis, formal syntax specification, parsing techniques, execution environment, storage management, code generation and optimization, procedure linkage, and address binding. The effect of language-design decisions on compiler construction.
MW 2:30pm-3:45pm

CPSC 5230b, Operating Systems  Anurag Khandelwal

The design and implementation of operating systems. Topics include synchronization, deadlocks, process management, storage management, file systems, security, protection, and networking.
HTBA

CPSC 5240b, Parallel Programming Techniques  Quanquan Liu

Practical introduction to parallel programming, emphasizing techniques and algorithms suitable for scientific and engineering computations. Aspects of processor and machine architecture. Techniques such as multithreading, message passing, and data parallel computing using graphics processing units. Performance measurement, tuning, and debugging of parallel programs. Parallel file systems and I/O.
HTBA

CPSC 5261a, Building AI Infra Systems  Y. Richard Yang

This course covers the design, deployment, operations, and optimization of infrastructure systems that power large-scale modern AI systems such as large-language models (LLMs). It takes an all-resources view, considering AI infrastructure components spanning compute, memory, storage, network, data, and energy resources. Focusing on core AI infrastructure design goals including efficiency, scalability, and stability, the course studies not only the basic mechanisms but also the complete systems to realize the goals. Labs and a capstone project form the core of the course. Prerequisite: CPSC 323, or an equivalent course in systems programming. A background in AI is highly recommended.
TTh 1pm-2:15pm

CPSC 5270a, C++ Programming for Stability, Security, and Speed  Michael Fischer

Computer programming involves both abstraction and practice. Lower-level programming courses focus on learning how to correctly implement algorithms for carrying out a task.  This course treats a computer program as an artifact with additional attributes of practical importance including execution efficiency, clarity and readability, redundancy, safety in the face of unexpected or malicious environments, and longevity—the ability to evolve over time as bugs are discovered and requirements change. This course is taught using modern C++.
MW 1pm-2:15pm

CPSC 5310a, Computer Music: Algorithmic and Heuristic Composition  Scott Petersen

Study of the theoretical and practical fundamentals of computer-generated music. Music and sound representations, acoustics and sound synthesis, scales and tuning systems, algorithmic and heuristic composition, and programming languages for computer music. Theoretical concepts are supplemented with pragmatic issues expressed in a high-level programming language.
MW 11:35am-12:50pm

CPSC 5320b, Computer Music: Sound Representation and Synthesis  Scott Petersen

Study of the theoretical and practical fundamentals of computer-generated music, with a focus on low-level sound representation, acoustics and sound synthesis, scales and tuning systems, and programming languages for computer music generation. Theoretical concepts are supplemented with pragmatic issues expressed in a high-level programming language. Prerequisite: ability to read music.
HTBA

CPSC 5330b, Computer Networks  Y. Richard Yang

An introduction to the design, implementation, analysis, and evaluation of computer networks and their protocols. Topics include layered network architectures, applications, transport, congestion, routing, data link protocols, local area networks, performance analysis, multimedia networking, network security, and network management. Emphasis on protocols used in the Internet.
HTBA

CPSC 5350b, Building an Internet Router  Robert Soule

Over the course of the term, students build a fully functioning Internet router. Students design the control plane in Python on a Linux host and design the data plane in the new P4 language on the bmv2 software switch. To provide context and background for the design of their router, students read a selection of papers to get both a historical perspective and exposure to current research in networking. Prerequisite: CPSC 533.
HTBA

CPSC 5370a, Database Systems  Avi Silberschatz

An introduction to database systems. Data modeling. The relational model and the SQL query language. Relational database design, integrity constraints, functional dependencies, and natural forms. Object-oriented databases. Implementation of databases: file structures, indexing, query processing, transactions, concurrency control, recovery systems, and security.
TTh 9am-10:15am

CPSC 5380a, Big Data Systems: Trends and Challenges  Anurag Khandelwal

Today’s Internet-scale applications and cloud services generate massive amounts of data. At the same time, the availability of inexpensive storage has made it possible for these services and applications to collect and store every piece of data they generate, in the hopes of improving their services by analyzing the collected data. This introduces interesting new opportunities and challenges designing systems for collecting, analyzing, and serving the so-called big data. This course looks at technology trends that have paved the way for big data applications, surveys state-of-the-art systems for storage and processing of big data, and considers future research directions driven by open research problems. Our discussions span topics such as cluster architecture, big data analytics stacks, scheduling and resource management, batch and stream analytics, graph processing, ML/AI frameworks, and serverless platforms and disaggregated architectures.
MW 4pm-5:15pm

CPSC 5390a, Software Engineering  Timos Antonopoulos

Introduction to building a large software system in a team. Learning how to collect requirements and write a specification. Project planning and system design. Increasing software reliability: debugging, automatic test generation. Introduction to type systems, static analysis, and model checking.
TTh 11:35am-12:50pm

CPSC 5391b, Advanced Software Engineering  Timos Antonopoulos

This course builds on CPSC 439/539, Software Engineering, with a focus on (a) building systems that scale well and (b) the technical infrastructure and approaches that would guide or inform entrepreneurship/business decisions. During the whole semester, teams work on a term-length software project of students’ design, most often a continuation of the project they worked on during CPSC 439/539. There is an extra seminar for the graduate students, where they are assigned topics based on relevant recent research papers published at the top conferences. The topics closely correspond to the lectures covered in the course. The graduate students prepare twenty-minute presentations of those papers and present them in the class. Grading also reflects an expectation of additional sophistication. Prerequiste: After CPSC 539 or similar. Students have to have a working product they built during CPSC 539 or similar course to further develop during this course.
HTBA

CPSC 5410a, Verifiable, Private, Decentralized Computing in the Age of AI  Ben Fisch

You type your question into ChatGPT and get back a response. How do you trust its accuracy? Perhaps you have reviewed the latest published benchmark results for GPT-4, or trust that others have. But how do you know the response you are getting from OpenAI’s servers is the true output of GPT-4? Perhaps due to a bug or system overload your question was handled by a weaker AI model. Or worse, perhaps the servers were hacked by someone maliciously giving you incorrect results. And, how do you trust that the sensitive questions you are sending to ChatGPT will not be leaked or used against you? This is a course in cryptographic proof systems. In the digital world today, we trust services to perform many kinds of computations on our data, from managing financial ledgers and databases to complex analytics, such as large-language model (LLM) inference. We trust these services not only to operate correctly, but also to keep our information private. Cryptographic systems allow us to remove this trust. A “succinct” cryptographic proof enables a service to attach a small certificate on the correctness of its computation which can be verified easily on a low-power device, even if the original computation was extremely complex. The proof of some ML computation that was run for hours on a GPU farm can fit in an email and take just milliseconds to verify on a mobile device! Beyond correctness, a “zero-knowledge” proof system enables us to prove knowledge of secret information, including hidden inputs to a computation that achieves a certain output. For instance, OpenAI could prove that the response is the true output of GPT-4 (a proprietary model) without revealing sensitive details about the model itself. In industry, the market for cryptographic proofs is currently around $75 million and projected to reach $10 billion by 2030, according to some estimates. Cryptographic proofs have become the leading technology for scaling blockchains and achieving privacy in cryptocurrencies. Verifiable and zero-knowledge computing also create an important foundation for decentralizing AI services. Training and serving large models currently require vast resources, leading to centralization. Decentralized ML networks offer a compelling alternative—letting many independent operators contribute incremental work to the overall task using their own resources big or small, from a single GPU to a server cluster, and earn a share of the payments clients make to use the service. In such a setting it is critical to verify that operators contribute incremental work correctly. Or, they may use private data to jointly train an ML model. Succinct zero-knowledge proofs would enable these operators to prove correctness of their work without revealing sensitive data. We cover some of the other challenges and directions in decentralized model training and inference, such as reducing the amount of data that needs to be communicated between physically distributed islands of hardware and the potential role of reinforcement learning.
TTh 1pm-2:15pm

CPSC 5420a, Theory of Computation  Dylan McKay

This course first introduces core, traditional ideas from the theory of computation with more modern ideas used in the process, including basic ideas of languages and automata. Building on the core ideas, the course then covers a breadth of topics in modular units, where each unit examines a new model and potentially a new perspective on computation. Topics may include: basic notions of Complexity Theory, provability and logic, circuits and non-uniform computation, randomized computation, quantum computation, query-based computation, notions of machine learning, compression, and algebraic models of computation. Additional topics might be introduced in lectures or student projects, according to student interests, including mechanism design, voting schemes, cryptography, biological computation, distributed computation, and pseudorandomness. Prerequisite: One of CPSC 365, 366, or 368 is required. This course is a proof-based theory course and mathematical maturity is expected.
TTh 4pm-5:15pm

CPSC 5440b, Real-World Cryptography  Fan Zhang

Cryptography provides strong security and privacy guarantees in well-defined mathematical models, but applying it to real-world systems is an art—one that must account for performance, cost, evolving adversarial threats, and even user behavior. This course aims to impart the art of designing and applying cryptography in the real world, by examining select advanced cryptographic tools used in practice. Topics include secure channels, identity and credentials, anonymity, end-to-end encrypted messaging, and Trusted Execution Environments (TEEs). Graduate students undertake a semester-long research project and present at the end of the semester. Students are expected to be familiar with concepts in computer security and cryptography (e.g., from CPSC 4130, CPSC 4670, or similar courses). To set the stage, we go over the content of Katz and Lindell (https://www.cs.umd.edu/~jkatz/imc.html) in the first few lectures at a quick pace.
HTBA

CPSC 5460a, Data and Information Visualization  Holly Rushmeier

Visualization is a powerful tool for understanding data and concepts. This course provides an introduction to the concepts needed to build new visualization systems, rather than to use existing visualization software. Major topics are abstracting visualization tasks, using visual channels, spatial arrangements of data, navigation in visualization systems, using multiple views, and filtering and aggregating data. Case studies to be considered include a wide range of visualization types and applications in humanities, engineering, science, and social science. Prerequisite: CPSC 223.
MW 1pm-2:15pm

CPSC 5470a, Introduction to Quantum Computing  Yongshan Ding

This course introduces the fundamental concepts in the theory and practice of quantum computing. Topics covered include information processing, quantum programming, quantum compilation, quantum algorithms, and error correction. The objective of the course is to engage students in applying fresh thinking to what computers can do. We establish an understanding of how quantum computers store and process data, and we discover how they differ from conventional digital computers. We anticipate this course will be of interest to students working in computer science, electrical engineering, physics, or mathematics. Students must be comfortable with programming, discrete probability, and linear algebra. Prior experience in quantum computing is useful but not required.
MW 11:35am-12:50pm

CPSC 5490b, Quantum Information Systems  Yongshan Ding

Quantum information systems encompass the hardware, software, and networking systems that are designed to encode, store, process, and distribute quantum information. In this course, students get a complete view of such information systems and explore the current advancement associated with building practical quantum computers and networks. This course is structured as four modules: quantum information theory, quantum processor, quantum memory, and quantum network. Students are asked to read and discuss selected research papers. Prerequisite: CPSC 547, PHYS 345 or equivalent. This course is intended for advanced undergraduates who are familiar with basic quantum computation and information. We anticipate this course will be of interest to students working in computer science, electrical engineering, or physics.
HTBA

CPSC 5510b, The User Interface  David Gelernter

The user interface (UI) in the context of modern design, where tech has been a strong and consistent influence from the Bauhaus and U.S. industrial design of the 1920s and 1930s through the IBM-Eames design project of the 1950s to 1970s. The UI in the context of the windows-menus-mouse desktop, as developed by Alan Kay and Xerox in the 1970s and refined by Apple in the early 1980s. Students develop a detailed design and simple implementation for a UI.
HTBA

CPSC 5520b / AMTH 5520b / CB&B 6663b / GENE 6630b, Deep Learning Theory and Applications  Smita Krishnaswamy

Deep neural networks have gained immense popularity within the past decade due to their success in many important machine-learning tasks such as image recognition, speech recognition, and natural language processing. This course provides a principled and hands-on approach to deep learning with neural networks. Students master the principles and practices underlying neural networks, including modern methods of deep learning, and apply deep learning methods to real-world problems including image recognition, natural language processing, and biomedical applications. Course work includes homework, a final exam, and a final project—either group or individual, depending on enrollment—with both a written and oral (i.e., presentation) component. The course assumes basic prior knowledge in linear algebra and probability. Prerequisites: CPSC 202 and knowledge of Python programming.
HTBA

CPSC 5540a, Software Analysis and Verification  Ruzica Piskac

Introduction to concepts, tools, and techniques used in the formal verification of software. State-of-the-art tools used for program verification; detailed insights into algorithms and paradigms on which those tools are based, including model checking, abstract interpretation, decision procedures, and SMT solvers.
TTh 2:30pm-3:45pm

CPSC 5550a, Algorithmic Game Theory  Manolis Zampetakis

A mathematically rigorous investigation of the interplay of economic theory and computer science, with an emphasis on the relationship of incentive-compatibility and algorithmic efficiency. Particular attention to the formulation and solution of mechanism-design problems that are relevant to data networking and Internet-based commerce.
MW 2:30pm-3:45pm

CPSC 5580b, Automated Decision Systems  Stephen Slade

People make dozens of decisions every day in their personal and professional lives. What would it mean for you to trust a computer to make those decisions for you? It is likely that many of those decisions are already informed, mediated, or even made by computer systems. Explicit examples include dating sites like match.com or recommendation systems such as Amazon or Netflix. Most Internet ads on sites like Google or Facebook are run by real-time-bidding (RTB) systems that conduct split-second auctions in the hopes of getting your attention. Driverless cars offer the promise of safer highways. Corporations and other enterprises invest in decision support systems to improve the quality of their products and services. This course considers the spectrum of automated decision models and tools, examining their costs and effectiveness. Examples come from a variety of fields including finance, risk management, credit-card fraud, robotics, medicine, and politics.
HTBA

CPSC 5590a, Building Interactive Machines  Marynel Vazquez

This advanced course brings together methods from machine learning, computer vision, robotics, and human-computer interaction to enable interactive machines to perceive and act in a variety of environments. Part of the course examines approaches for perception with different sensing devices and algorithms; the other part focuses on methods for decision-making and applied machine learning for control. The course is a combination of lectures, state-of-the-art reading, presentations and discussions, programming assignments, and a final team project. Prerequisites: CPSC 570 and understanding of probability, differential calculus, linear algebra, and planning (in Artificial Intelligence). Programming assignments require proficiency in Python and high-level familiarity with C++. Students who do not fit this profile may be allowed to enroll with the permission of the instructor.
MW 11:35am-12:50pm

CPSC 5626a, Scalable and Private Graph Algorithms  Quanquan Liu

What techniques can we use to deal with modern real-world data with billions of data points? How do we account for strong adversaries that violate the privacy of users providing this data? This course provides students with the knowledge to tackle research questions in these domains. We propose answers and techniques to these broad questions from an algorithmic standpoint, presenting foundational topics such as: (1) the parallel, distributed, and streaming models and algorithmic techniques commonly used within these models; (2) differential privacy and mechanisms for private data analysis; and (3) implementation techniques, tools, and examples that demonstrate the practicality of these algorithms in real-world systems. This course focuses on advanced topics in practical graph algorithms with provable guarantees beyond the sequential model used in most introductory algorithms classes. Specific topics include local graph techniques for problems such as maximal matching, independent set, k-core decomposition, densest subgraphs, and coloring as well as global techniques for problems like connectivity, shortest paths, and spanners. Introductory lectures also feature techniques used beyond graph algorithms. Students are asked to read and present influential recent research papers on these topics. Papers come from prominent CS theory conferences such as STOC, FOCS, SODA as well as database and data mining conferences like VLDB, PODS, and WWW. In addition to these presentations, students also work on a final project which may be theoretical or implementation-based. The course also features voluntary open problem sections where we discuss (known) practice problems and open-ended research questions related to the topics in this course in a collaborative group setting.
TTh 1pm-2:15pm

CPSC 5630b / ECON 5565b, Algorithms via Convex Optimization  Nisheeth Vishnoi

Convex optimization has played a major role in the recent development of fast algorithms for problems arising in areas such as theoretical computer science, discrete optimization, and machine learning. The approach is to first formulate the problem as a continuous (convex) optimization problem, even if the problem may be over a discrete domain, adapt or develop deterministic or randomized continuous-time dynamical systems to solve it, and then design algorithms for the problem via appropriate discretizations. The goal of this course is to design state-of-the-art algorithms for various classical discrete problems through the use of continuous optimization/sampling. The algorithmic applications include maximum flow in graphs, maximum matching in bipartite graphs, linear programming, submodular function minimization, and counting problems involving discrete objects such as matroids. We present approaches gradient descent, mirror descent, interior-point methods, and cutting plane methods. A solid background in calculus, linear algebra, and probability is recommended. It is intended for students who are comfortable with proofs.
HTBA

CPSC 5640a, Algorithms and their Societal Implications  Nisheeth Vishnoi

Today’s society comprises humans living in an interconnected world that is intertwined with a variety of sensing, communicating, and computing devices. Human-generated data is being recorded at unprecedented rates and scales, and powerful AI and ML algorithms, which are capable of learning from such data, are increasingly controlling various aspects of modern society: from social interactions. These data-driven decision-making algorithms have a tremendous potential to change our lives for the better, but, via the ability to mimic and nudge human behavior, they also have the potential to be discriminatory, reinforce societal prejudices, violate privacy, polarize opinions, and influence democratic processes. Thus, designing effective tools to govern modern society which reinforce its cherished values such as equity, justice, democracy, health, privacy, etc. has become paramount and requires a foundational understanding of how humans, data, and algorithms interact. This course is for students who would like to understand and address some of the key challenges and emerging topics at the aforementioned interplay between computation and society. On the one hand, we study human decision-making processes and view them through the lens of computation, and on the other hand we study and address the limitations of artificial decision-making algorithms when deployed in various societal contexts. The focus is on developing solutions through a combination of foundational work such as coming up with the right definitions, modeling, algorithms, and empirical evaluation. The current focus is on bias and privacy, with additional topics including robustness, polarization, and democratic representation. The grade will be based on class participation and a project. The project grade will be determined by a midterm and endterm report/presentation. The course has four primary modules: (1) Data: human-generated data; data collection and aggregation; (2) Decision-Making Algorithms: human decision-making algorithms; traditional algorithmic decision-making models and methods; machine learning-based decision-making models and methods; (3) Bias: socio-technical contexts and underlying computational problems; definitions of fairness; interventions for ensuring fairness; human biases through the lens of computation; privacy; need for definitions of privacy; differential privacy; beyond differential privacy; (4) Other topics: robustness; polarization; elections and social choice. Solid mathematical and programming background is necessary to enroll in this course. CPSC 365 and S&DS 251 are recommended.
T 9:25am-11:15am

CPSC 5650b, Theory of Distributed Systems  James Aspnes

Models of asynchronous distributed computing systems. Fundamental concepts of concurrency and synchronization, communication, reliability, topological and geometric constraints, time and space complexity, and distributed algorithms.
HTBA

CPSC 5660b, Web3, Blockchains, and Cryptocurrencies  Ben Fisch

This course is an introduction to blockchain systems, such as Bitcoin and Ethereum. We begin with a brief history of blockchains and an overview of how they are being used today before launching into foundational topics, including distributed consensus, smart contracts, cryptographic building blocks from signatures to authenticated datastructures, and the economics of blockchains. We then cover advanced topics including the scalability and interoperability of blockchain systems and applications such as “decentralized finance” (DeFi). The lectures and assignments engage students in both theoretical and applied aspects of blockchain systems. The course assumes background in various fundamental areas of CS, including discrete math, probability, algorithms, data structures, cryptography, and networks.
HTBA

CPSC 5670a, Introduction to Cryptography  Charalampos Papamanthou

This course introduces modern symmetric and public-key cryptography as well as their broad applications, both from a theoretical and practical perspective. There is an initial emphasis on fundamental cryptographic primitives (e.g., block ciphers, pseudorandom functions, pseudorandom generators, one-way functions), their concrete efficiency and implementation, as well as their security definitions and proofs. Ways of combining such primitives that lead to more complex objects used to secure today’s internet (e.g., via TLS), such as key exchange, randomized encryption, message authentication codes, and digital signatures are also studied. The last part of the course is devoted to modern and more advanced applications of cryptography (some of which are deployed at scale today), such as authenticated data structures, zero-knowledge proofs, oblivious RAM, private information retrieval, secret sharing, distributed consensus, and cryptocurrencies. (e.g, Bitcoin).
TTh 11:35am-12:50pm

CPSC 5671b, Advanced Topics in Cryptography: Cryptography and Computation  Charalampos Papamanthou

Traditional cryptography is mostly concerned with studying the foundations of securing communication via, for example, encryption and message authentication codes. This class studies the applications of cryptography in securing computation. Topics include, but not limited to, fundamental results and most recent progress in oblivious computation and private information retrieval (PIR), zero-knowledge proofs, secure computation, consensus algorithms, searchable encryption, and lattice-based cryptography. The class focuses both on theory and applications. This is an advanced course, which requires mathematical maturity as well as comfort with programming. The course also assumes prior knowledge of fundamental notions in cryptography. Prerequisite: CPSC 4670 or equivalent.
HTBA

CPSC 5680b, Computational Complexity  Dylan McKay

Introduction to the theory of computational complexity. Basic complexity classes, including polynomial time, nondeterministic polynomial time, probabilistic polynomial time, polynomial space, logarithmic space, and nondeterministic logarithmic space. The roles of reductions, completeness, randomness, and interaction in the formal study of computation.
HTBA

CPSC 5690a, Randomized Algorithms  James Aspnes

Beginning with an introduction to tools from probability theory including some inequalities like Chernoff bounds, the course covers randomized algorithms from several areas: graph algorithms, algorithms in algebra, approximate counting, probabilistically checkable proofs, and matrix algorithms.
MW 2:30pm-3:45pm

CPSC 5700a, Artificial Intelligence  Tesca Fitzgerald

Introduction to artificial intelligence research, focusing on reasoning and perception. Topics include knowledge representation, predicate calculus, temporal reasoning, vision, robotics, planning, and learning.
TTh 11:35am-12:50pm

CPSC 5710a, Trustworthy Deep Learning  Rex Ying

In recent years, deep learning has seen applications in many fields, from science and technology, to finance, humanity, and businesses. However, real-world, high-impact machine learning applications demand more than just model performance. In particular, deep learning models are often required to be “trustworthy,” so that domain experts can trust that the models consistently behave in a way that corresponds to their domain knowledge. For example, medical experts would expect a deep learning diagnosis model to be able to explicitly utilize medical domain knowledge in its prediction; an insurance company would expect a decision on insurance price to be explainable in terms of risk factors; a financial company would expect its fraud detection model to be robust to adversarial attacks; a physicist would expect models to provide consistency with the underlying laws. This course introduces various fields of trustworthy deep learning, including model robustness, defenses for adversarial attacks, interpretability, explainability, fairness, privacy, domain adaptation, rules, and constraints. The course covers some of these aspects in the context of graph neural networks but also covers many other ML models in general deep learning, natural language processing, and computer vision. Prerequisites: a course in linear algebra and multi-variable calculus and familiarity with PyTorch and other common Python libraries such as Numpy, Sklearn. Deep learning courses such as CPSC 452 or 453 are recommended.
TTh 4pm-5:15pm

CPSC 5740a, Computational Intelligence for Games  James Glenn

A seminar on current topics in computational intelligence for games, including developing agents for playing games, procedural content generation, and player modeling. Students read, present, and discuss recent papers and competitions, and complete a term-long project that applies some of the techniques discussed during the term to a game of their choice.
MW 1pm-2:15pm

CPSC 5750a / ECE 5750a / INP 7575a, Computational Vision and Biological Perception  Steven Zucker

An overview of computational vision with a biological emphasis. Suitable as an introduction to biological perception for computer science and engineering students, as well as an introduction to computational vision for mathematics, psychology, and physiology students.
MW 2:30pm-3:45pm

CPSC 5770b, Natural Language Processing  Arman Cohan

This course provides a deep dive into modern Natural Language Processing (NLP), with a strong focus on Language Modeling. The curriculum spans both foundational concepts and cutting-edge developments in the field. The course begins with core neural network concepts in NLP, covering word embeddings, sequence modeling, and attention mechanisms. Building on these foundations, we explore transformer architectures and their evolution, including early transformer language models like BERT, GPT and T5. The course examines how these models enable sophisticated language understanding and generation through pre-training and transfer learning. The latter portion covers contemporary advances: Large Language Models (LLMs), multi-modal integration, parameter-efficient fine-tuning, evaluation, multi-agent systems, reasoning, and model compression. We'll analyze the capabilities and limitations of current systems while discussing emerging research directions.
HTBA

CPSC 5780b, Computer Graphics  Theodore Kim

Introduction to the basic concepts of two- and three-dimensional computer graphics. Topics include affine and projective transformations, clipping and windowing, visual perception, scene modeling and animation, algorithms for visible surface determination, reflection models, illumination algorithms, and color theory.
HTBA

CPSC 5790b, Advanced Topics in Computer Graphics  Julie Dorsey

An in-depth study of advanced algorithms and systems for rendering, modeling, and animation in computer graphics. Topics vary and may include reflectance modeling, global illumination, subdivision surfaces, NURBS, physically based fluids systems, and character animation.
HTBA

CPSC 5791a, Building Game Engines  Michael Shah

This course teaches the fundamentals of building a reusable software architecture by building games. This is a programming-intensive course where the end product of this course is a data-driven game engine that students work in small teams to implement in a systems programming language (e.g. C, C++, D, etc.). Students apply data structures, algorithms, and systems programming skills in the domain of games. Discussion and implementation of the components of a game engine may include: resource management (allocators, resource managers, serialization), abstraction (design patterns, game objects, scripting, graphics layers), graphics management algorithms (scene graphs, level of detail), physics (linear algebra, collision detection and resolution algorithms), artificial intelligence (e.g. pathfinding,decision making), and performance (concurrency, parallelism, math). Students work on a final course project for their portfolio. Prerequisite: previous experience with data structures and systems programming comparable to CPSC 223 and CPSC 323.
MW 4pm-5:15pm

CPSC 5792b, Real-Time 3D Computer Graphics Programming  Michael Shah

This course teaches the fundamentals of real-time 3D computer graphics programming using a systems programming language (e.g. C, C++, D, etc.). Students interested in making 3D games, virtual reality applications, simulations, medical visualizations, and other interactive applications are the target audience. Throughout the course students also learn about co-processors (e.g. GPUs) for hardware accelerated graphics, and program in a graphics API enabling hardware accelerated graphics. Students apply a sampling of mathematics in the domain of geometry, trigonometry, linear algebra, and calculus in order to generate photo and non-photorealistic images in real-time. Additional topics may include: geometry processing, scene organization, texturing techniques, advanced lighting techniques, compute shaders, and topics in performance.
HTBA

CPSC 5800a, Introduction to Computer Vision  Alex Wong

This course focuses on fundamental topics in computer vision. We begin with the image formation process and discuss the role of camera models and intrinsic calibration in perspective projection. Basic image processing techniques (i.e. filtering) is introduced. After which, we discuss techniques to describe an image, from edges to feature descriptors and methods to establish correspondences between different images of the same scene. The course additionally covers topics in recognition (i.e. image classification, segmentation, detection, etc.) and reconstruction (i.e. stereo, structure-from-motion, optical flow). Machine learning and deep learning based methods in a subset of the topics covered are also introduced. Students get hands-on experience in implementing the techniques covered in the class and applying them to real world datasets and applications. Students taking this course must have successfully passed courses in data structures and object-oriented programming (e.g. CPSC 223a or equivalent courses) and foundational mathematical tools such as discrete math and linear algebra (e.g. CPSC 202 or equivalent courses). It is recommended that students have taken or successfully passed calculus (e.g. MATH 112, MATH 115, MATH 120, or equivalent courses) and linear algebra (e.g. MATH 225, or equivalent courses). A background in statistics, machine learning and deep learning is useful but not required. Experience in programming with Python is preferable, as we use it for assignments and projects. Familiarity with Google Colab and numerical and image processing packages (i.e. NumPy, SciPy, and Sci-kit Image) is helpful throughout the course.
TTh 1pm-2:15pm

CPSC 5810b, Introduction to Machine Learning  Alex Wong

This course focuses on fundamental topics in machine learning. We begin with an overview of different components of machine learning and types of learning paradigms. We introduce a linear function, discuss how one can train a linear function on a given dataset, and utilize it to tackle classification and regression problems. We then consider kernel methods to enable us to solve nonlinear problems. Additionally, we introduce the concept of generalization error and overfitting. We discuss the role of regularization and extend linear regression to ridge regression. We also cover topics in optimization, beginning from gradient descent and extending it to stochastic gradient descent and its momentum variant. We also cover the concept of alternating optimization and topics within it. We introduce the curse of dimensionality and discuss topics on dimensionality reduction. Finally, we conclude the course with neural networks: how to build them using the topics discussed, how to optimize them, and how to apply them to solve a range of machine learning tasks. Prerequisites: Courses in data structures and object-oriented programming (e.g. CPSC 223a or equivalent courses), foundational mathematical tools such as discrete math and linear algebra (e.g. CPSC 202 or equivalent courses), calculus (e.g. MATH 112, MATH 115, MATH 120, or equivalent courses), linear algebra (e.g. MATH 225, or equivalent courses), and artificial intelligence (e.g. CPSC 370/570). A background in statistics is useful but not required. Experience in programming with Python and familiarity with Google Colab and numerical and image processing packages (i.e. NumPy, SciPy) is helpful.
HTBA

CPSC 5830b, Deep Learning on Graph-Structured Data  Rex Ying

Graph structure emerges in many important domain applications, including but not limited to computer vision, natural sciences, social networks, languages, and knowledge graphs. This course offers an introduction to deep learning algorithms applied to such graph-structured data. The first part of the course is an introduction to representation learning for graphs and covers common techniques in the field, including distributed node embeddings, graph neural networks, deep graph generative models, and non-Euclidean embeddings. The first part also touches upon topics of real-world significance, including auto-ML and explainability for graph learning. The second part of the course covers important applications of graph machine learning. We learn ways to model data as graphs and apply graph learning techniques to problems in domains including online recommender systems, knowledge graphs, biological networks, physical simulations and graph mining. The course covers many deep techniques (graph neural networks, graph deep generative models) catered to graph structures. We cover basic deep learning tutorials in this course. Knowledge of graphs as a data structure, and understanding of basic graph algorithms are essential for applying machine learning to graph-structured data. Familiarity with Python and important libraries such as Numpy and Pandas are helpful. A foundation of deep neural networks is highly recommended. Experience in machine Learning and Graph Theory are welcomed as well.
HTBA

CPSC 5840b, Introduction to Human-Computer Interaction  Marynel Vazquez

This course introduces students to the interdisciplinary field of human-computer interaction (HCI), with particular focus on human-robot interaction (HRI). The first part of the course covers principles and techniques in the design, development, and evaluation of interactive systems. It provides students with an introduction to UX design and user-centered research. The second part focuses on the emergent filed of HRI and several other nontraditional interfaces, e.g., AR/VR, tangibles, crowdsourcing. The course is organized as a series of lectures, presentations, a midterm exam, and a term-long group project on designing a new interactive system. Prerequisites: CPSC 201 and CPSC 202 or equivalents. Students who do not fit this profile may be allowed to enroll with permission of the instructor.
HTBA

CPSC 5850a, Applied Planning and Optimization  Daniel Rakita

This course introduces students to concepts, algorithms, and programming techniques pertaining to planning and optimization. At a high level, the course teaches students how to break down a particular problem into a state-space or a state-action space, how to select an effective planning or optimization algorithm given the problem at hand, and how to ultimately apply the selected algorithm to achieve desired outputs. Concepts are solidified through grounded, real-world examples (particularly in robotics, but also including machine learning, graphics, biology, etc.). These examples come in the form of programming assignments, problem sets, and a final project. General topics include discrete planning, sampling-based path planning, optimization via matrix methods, linear programming, computational differentiation, non-linear optimization, and mixed integer programming. After the course, students are able to generalize their knowledge of planning and optimization to any problem domain. Knowledge of linear algebra and calculus is expected. Students should be familiar with matrix multiplication, derivatives, and gradients.
MW 9am-10:15am

CPSC 5860b, Probabilistic Machine Learning  Andre Wibisono

This course provides an overview of the probabilistic frameworks for machine learning applications. The course covers probabilistic generative models, learning and inference, algorithms for sampling, and a survey of generative diffusion models. This course studies the theoretical analysis of the problems and how to design algorithms to solve them. This course familiarizes students with techniques and results in literature and prepares them for research in machine learning. Prerequisites: Knowledge of machine learning, linear algebra, probability, and calculus.
HTBA

CPSC 5870b, 3D Spatial Modeling and Computing  Daniel Rakita

Several areas of computer science and related fields must model and compute how objects are situated in three-dimensional space over time, such as robotics, computer vision, computer graphics, computational physics, computational biology, aerospace engineering, and so on. This course teaches students how to computationally model the spatial configuration of and spatial relationships between objects over time. Topics covered include various methods for representing spatial configurations and transformations (such as transformation matrices, Euler angles, unit quaternions, dual quaternions, etc.), hierarchical chaining of spatial transformations, derivatives of spatial representations with respect to time, computing intersections and penetration depths between objects in space, interpolating over spatial representations (such as using splines), signal processing over spatial transformations, optimizing over spatial representations, and more. To develop these concepts rigorously, we draw from linear algebra, calculus, topology, Lie theory, and geometric algebra. Real-world examples from robotics, computer vision, and computer graphics are utilized to solidify these concepts, with programming assignments, problem sets, and a final project that allows students to apply what they have learned. Interactive visual aids created by the instructor are an integral part of lectures to help students connect mathematical concepts with spatial phenomena. Prerequisites: Undergraduate students should have taken CPSC 202 and CPSC 223. All students should have proficiency in programming with mathematical reasoning. A background in linear algebra and calculus is recommended but not required.
HTBA

CPSC 5890b, Robot Learning  Tesca Fitzgerald

This course explores methods for grounding machine learning algorithms in embodied, interactive robots. We cover topics including learning from demonstration, active learning, inverse reinforcement learning, representations for modeling high-level and low-level task information, and human factors for designing learning interactions. Students are asked to read and present research papers on these topics from top publication venues in AI, machine learning, robotics, and human-robot interaction. Students also complete lab assignments in which they implement and evaluate state-of-the-art methods for interactive robot learning on a physical robot arm. Prerequisite: CPSC 370/470/570 or an equivalent AI course (requires approval by instructor). Recommended: an introductory machine-learning course such as S&DS 265 or CPSC 481.
HTBA

CPSC 6110a, Topics in Computer Science and Global Affairs  Joan Feigenbaum and Ted Wittenstein

This course focuses on “socio-technical” problems in computing and international relations. These are problems that cannot be solved through technological progress alone but rather require legal, political, or cultural progress as well. Examples include but are not limited to cyber espionage, disinformation, ransomware attacks, and intellectual-property theft. This course is offered jointly by the SEAS Computer Science Department and the Jackson School of Global Affairs. It is addressed to graduate students who are interested in socio-technical issues but whose undergraduate course work may not have addressed them; it is designed to bring these students rapidly to the point at which they can do research on socio-technical problems. Prerequisites: Basics of cryptography and computer security (as covered in Yale’s CPSC 467), networks (as covered in Yale’s CPSC 433), and databases (as covered in Yale’s CPSC 437) helpful but not required.
W 3:30pm-5:20pm

CPSC 6120b, Topics in Algorithmic Game Theory  Yang Cai

The course focuses on algorithms and the complexity of equilibrium computation as well as its connection with learning theory and optimization. As many recent machine learning approaches have moved from an optimization perspective to an “equilibration” perspective, where a good model is framed as the equilibrium of a game. The intersection of game theory, learning theory, and optimization is becoming increasingly relevant. The goal of the course is to cover the fundamentals and bring students to the frontier of this active research area. Prerequisites: A course in algorithms (CPSC 365 or 366) and a course in probability theory (MATH/S&DS 241). A course in algorithmic game theory (CPSC 455/555) is helpful but not required.
HTBA

CPSC 6130a, Digital Identity Infrastructure  Michael Fischer

A digital identity system establishes a connection between a real person and an internet platform such as an online banking site or a social media platform. Current digital identity systems utilize an ad hoc collection of password-based and multi-factor authentication methods. The inconsistency of these methods leads to user confusion, inconvenience, lack of interoperability, poor privacy properties, and degraded security. Data breaches, account takeovers, and privacy violations have become the norm. Efforts to combat these abuses have only been marginally effective. This course presents design principles for an internet-wide digital identity standard to ameliorate most of these problems. It is based on established principles of commerce and law from the non-digital world such as isolation of sensitive data, distributed trust, rules of evidence, and dispute-resolution procedures. A network of trusted agents maintain a distributed blockchain of transactions that provide evidence of authorization of internet transactions and assign responsibility for breaches of trust. Helpful but not required: basics of cryptography and computer security (as covered in Yale’s CPSC 4670), distributed computing (as covered in Yale's CPSC 4650), and networks (as covered in Yale’s CPSC 4330). Instructor permission required.
MW 2:30pm-3:45pm

CPSC 6400b / AMTH 640b / MATH 6400b, Topics in Numerical Computation  Vladimir Rokhlin

This course discusses several areas of numerical computing that often cause difficulties to non-numericists, from the ever-present issue of condition numbers and ill-posedness to the algorithms of numerical linear algebra to the reliability of numerical software. The course also provides a brief introduction to “fast” algorithms and their interactions with modern hardware environments. The course is addressed to Computer Science graduate students who do not necessarily specialize in numerical computation; it assumes the understanding of calculus and linear algebra and familiarity with (or willingness to learn) either C or FORTRAN. Its purpose is to prepare students for using elementary numerical techniques when and if the need arises.
HTBA

CPSC 6440a / MATH 7440, Geometric and Topological Methods in Machine Learning  Smita Krishnaswamy

This course provides an introduction to geometric and topological methods in data science. Our starting point is the manifold hypothesis: that high dimensional data live on or near a much lower dimensional smooth manifold. We introduce tools to study the geometric and topological properties of this manifold in order to reveal relevant features and organization of the data. Topics include: metric space structures, curvature, geodesics, diffusion maps, eigenmaps, geometric model spaces, gradient descent, data embeddings and projections, and topological data analysis (TDA) in the form of persistence homology and their associated “barcodes.” We see applications of these methods in a variety of data types. Prerequisites: MATH 225 or 226; MATH 255 or 256; MATH 302 and CPSC 112. Students who completed MATH 231 or 250 may substitute another analysis course level 300 or above in place of MATH 302. Familiarity with algorithms/programming is beneficial.
TTh 11:35am-12:50pm

CPSC 6900a, Independent Project I  Lin Zhong

Independent Project I. By arrangement with faculty.
HTBA

CPSC 6910a, Independent Project II  Staff

By arrangement with faculty.
HTBA

CPSC 6920a, Independent Project  Staff

Individual research for students in the M.S. program. Requires a faculty supervisor and the permission of the director of graduate studies.
HTBA

CPSC 6930a, MS Thesis Research I  Holly Rushmeier

First term of thesis research for students in the two-year MS program in Computer Science None
HTBA

CPSC 6940a, MS Thesis Research II  Holly Rushmeier

Second term of thesis research for students in the two-year MS program in Computer Science.
HTBA

CPSC 7520b / CB&B 7520b / MB&B 7520b / MB&B 753 / MB&B 754 / MCDB 7520b, Biomedical Data Science: Mining and Modeling  Mark Gerstein and Matthew Simon

Biomedical data science encompasses the analysis of gene sequences, macromolecular structures, and functional genomics data on a large scale. It represents a major practical application for modern techniques in data mining and simulation. Specific topics to be covered include sequence alignment, large-scale processing, next-generation sequencing data, comparative genomics, phylogenetics, biological database design, geometric analysis of protein structure, molecular-dynamics simulation, biological networks, normalization of microarray data, mining of functional genomics data sets, and machine-learning approaches to data integration. Prerequisites: biochemistry and calculus, or permission of the instructor.
MW 1pm-2:15pm

CPSC 7760b, Topics in Industrial AI Applications  Xiuye (Sue) Chen

This seminar aims to familiarize students with cutting-edge topics in industrial AI research and their practical applications. We will explore a broad range of topics such as large language models, image generation, ML/AI systems considerations, autonomous vehicles, robotics, recommender systems, ambient intelligence, and AI applications in the life sciences and healthcare. Most sessions will be devoted to in-depth discussions of one to two key papers on modern AI applications. We will also feature a series of industry guest speakers, providing students with the opportunity to learn directly from practicing experts. In this seminar, students are expected to present papers, actively participate in class discussions, and work either individually or in groups on a final project that emphasizes the practical implementation of AI techniques. Students should be familiar enough with ML/AI concepts to read academic papers, and comfortable with programming to run open source code in the ML/AI space.
HTBA

CPSC 9900a, Ethical Conduct of Research for Master’s Students  Yoehan Oh

This course forms a vital part of research ethics training, aiming to instill moral research codes in graduate students of computer science, math, and applied math. By devling into case studies and real-life examples related to research misconduct, students will grasp core ethical principles in research and academia. The course also offers an opportunity to explore the societal impacts of research in computer science, math, and applied math. This course is designed specifically for first-year graduate students in computer science/applied math/math. Successful completion of the course necessitates in-person attendance on eight occasions; virtual participation will not fulfill this requirement. In cases where illness, job interviews, or unforeseen circumstances prevent attendance, makeup sessions will be offered. This course is 0 credits for YC students.  0 Course cr
F 1:30pm-2:20pm

CPSC 9910a / MATH 9910a, Ethical Conduct of Research  Yoehan Oh

This course forms a vital part of research ethics training, aiming to instill moral research codes in graduate students of computer science, math, and applied math. By delving into case studies and real-life examples related to research misconduct, students grasp core ethical principles in research and academia. The course also offers an opportunity to explore the societal impacts of research in computer science, math, and applied math. This course is designed specifically for first-year graduate students in computer science, applied math, and math. Successful completion of the course necessitates in-person attendance on eight occasions; virtual participation does not fulfill this requirement. In cases where illness, job interviews, or unforeseen circumstances prevent attendance, makeup sessions are offered.  0 Course cr
F 2:30pm-3:20pm

CPSC 9920a or b, Academic Writing  Staff

This course is an intensive analysis of the principles of excellent writing for Ph.D. students and scientists preparing a range of texts including research papers, conference posters, technical reports, research statements, grant proposals, correspondence, science and industry blogs, and other relevant documents. We look at the components of rhetorical positioning in the development of a clear, interesting, and rigorous science research paper. Some of the sub-genres we analyze and practice include the introduction, literature review, methodology, data commentary, results/discussion, conclusion, and abstract. In addition to the research paper, we practice other types of texts including research statements, requests for funding, bio-data statements, and blogs. We also discuss how writers can develop content and fluency as well as strategies for redrafting and editing. Students receive detailed feedback on their writing with a focus on clarity, precision, tone, and readability.  0 Course cr
T 10am-11:50am

ECE 4061b / ECE 8061b, Photovoltaic Energy  Fengnian Xia

Electricity from photovoltaic solar cells is receiving increasing attention due to growing world demand for clean power sources. This course primarily emphasizes device physics of photovoltaics; statistics of charge carriers in and out of equilibrium; design of solar cells; and optical, electrical, and structural properties of semiconductors relevant to photovoltaics. Two laboratory sessions and a final project aid students in understanding both the applications and limitations of photovoltaic technology. The main objectives of this course are to equip students with the necessary background and analytical skills to understand and assess established and emerging photovoltaic technologies; to familiarize students with the diverse range of photovoltaic materials; and to connect materials properties to aspects of cell design, processing, and performance.
MW 1pm-2:15pm

ECE 5021b / S&DS 5510b, Stochastic Processes  Ilias Zadik

Introduction to the study of random processes, including Markov chains, Markov random fields, martingales, random walks, Brownian motion, and diffusions. Techniques in probability such as coupling and large deviations. Applications chosen from image reconstruction, Bayesian statistics, finance, probabilistic analysis of algorithms, genetics, and evolution.
MW 1pm-2:15pm

ECE 5750a / CPSC 5750a / INP 7575a, Computational Vision and Biological Perception  Steven Zucker

An overview of computational vision with a biological emphasis. Suitable as an introduction to biological perception for computer science and engineering students, as well as an introduction to computational vision for mathematics, psychology, and physiology students.
MW 2:30pm-3:45pm

ECE 7181b, Advanced Electronic Devices  Mengxia Liu

The science and technology of semiconductor electron devices. Topics include compound semiconductor material properties and growth techniques; heterojunction, quantum well, and superlattice devices; quantum transport; graphene and other 2-D material systems.
TTh 11:35am-12:50pm

ECE 8061b / ECE 4061b, Photovoltaic Energy  Fengnian Xia

Electricity from photovoltaic solar cells is receiving increasing attention due to growing world demand for clean power sources. This course primarily emphasizes device physics of photovoltaics; statistics of charge carriers in and out of equilibrium; design of solar cells; and optical, electrical, and structural properties of semiconductors relevant to photovoltaics. Two laboratory sessions and a final project aid students in understanding both the applications and limitations of photovoltaic technology. The main objectives of this course are to equip students with the necessary background and analytical skills to understand and assess established and emerging photovoltaic technologies; to familiarize students with the diverse range of photovoltaic materials; and to connect materials properties to aspects of cell design, processing, and performance.
MW 1pm-2:15pm

ECE 8400a, Detection and Estimation  Dionysis Kalogerias

Detection and Estimation refers to the development and study of statistical theory and methods in settings involving stochastic signals and, more generally, stochastic processes or stochastic data, where the goal is (optimal) testing of possibly multiple hypotheses regarding the generative model of the data, (optimal) signal estimation from potentially noisy measurements/observations, and parameter estimation whenever parametric signal/data models are available. Although these problems often come up in the context of signal processing and communications, the concepts are fundamental to the basic statistical methodologies used broadly across science, medicine, and engineering. The course has been designed from a contemporary perspective, and includes new and cutting-edge topics such as risk-aware statistical estimation and intrinsic links with stochastic optimization and statistical learning.
TTh 2:30pm-3:45pm

ECE 8680a, Emerging Materials and Technologies toward Sustainability  Liangbing Hu

The goal of this course is to demonstrate the role of new materials and emerging technologies in solving one of the most critical socio-economic issues of our time—sustainability. The course focuses on electrochemical, electrical, optical, thermal, and mechanically functional materials and their use in energy devices. Topics to be covered include electrochemical energy conversion and storage (fuel cells and batteries), catalysts and membrane separations (fossil fuel and biomass energy conversion), electrified heating (Joule, plasma, microwave), solar thermal and fuel, thermoelectrics, energy efficient lighting, and building energy savings (light, thermal).
TTh 1pm-2:15pm

ECE 8750a, Introduction to VLSI System Design  Rajit Manohar

Chip design. Provides background in integrated devices, circuits, and digital subsystems needed for design and implementation of silicon logic chips. Historical context, scaling, technology projections, physical limits. CMOS fabrication overview, complementary logical circuits, design methodology, computer-aided design techniques, timing, and area estimation. Case studies of recent research and commercial chips. Objectives of the course are (1) to give students the ability to complete the course project (design of a digital CMOS subsystem chip through layout), and (2) to understand the directions that future chip technologies may take. Selected projects are fabricated and packaged for testing by students. Prerequisite: circuits at the level of introductory physics and computer programming.
MW 11:35am-12:50pm

ECE 8880a, FPGA-Based Accelerator Design and Implementation  Linghao Song

The goal of this course is to equip students with the skills to design and implement FPGA-based accelerators and deploy the generated bitstreams for real applications. Topics include FPGA programing using high level synthesis (HLS), dataflows, on-chip and off-chip memories, frequency tuning, and performance modeling and analysis of accelerator architectures. The course includes hands-on labs that cover both computation-intensive and memory-intensive workloads. It also introduces recent developments in FPGA technology and accelerator design. Prerequisites: coding skills and basic knowledge of computer systems.
TTh 11:35am-12:50pm

ECE 9001b, Decisions and Computations across Networks  A Stephen Morse

Within the field of network science there has long been interest in distributed computation and distributed decision-making problems of many types. Among these are consensus and flocking problems, the multi-robot rendezvous problem, distributed averaging, distributed solutions to linear algebraic equations, social networking problems, localization of sensors in a multisensor network, and the distributed management of robotic formations. The aim of this course is to explain what these problems are and to discuss their solutions. Related concepts from spectral graph theory, rigid graph theory, non-homogeneous Markov chain theory, stability theory, and linear system theory are covered. Prerequisite: although most of the mathematics needed are covered in the lectures, students taking this course should have a working understanding of basic linear algebra.
MW 2:30pm-3:45pm

ECE 9020a, Linear Systems  A Stephen Morse

Background linear algebra; finite-dimensional, linear-continuous, and discrete dynamical systems; state equations, pulse and impulse response matrices, weighting patterns, transfer matrices. Stability, Lyapunov’s equation, controllability, observability, system reduction, minimal realizations, equivalent systems, McMillan degree, Markov matrices. Recommended for all students interested in feedback control, signal and image processing, robotics, econometrics, and social and biological networks.
MW 1pm-2:15pm

ECE 9051a, Applied Digital Signal Process  Roman Kuc

Random variables, central limit theorem estimations, and cost and risk functions. Processing techniques including estimating autocorrelation sequences, variance reduction and spectrum estimation and filter design.
TTh 1pm-2:15pm

ECE 9100a / MATH 7120a, Topics in Denoising and Structure Recovery from Data  Boris Landa

Recovering signals and underlying structure from noisy observations is a fundamental problem in many areas of science and engineering. Over the past few decades, a rich body of work has emerged to address this challenge across diverse settings. A common guiding principle is to leverage structural assumptions—such as smoothness, sparsity, or low-rankness in the data—alongside models of the noise to enable effective recovery. This course explores both classical and modern approaches to denoising and structural data recovery, blending theoretical foundations with algorithmic and applied perspectives. Particular emphasis is placed on high-dimensional regimes relevant to modern data analysis, where noise can behave in counterintuitive ways, yet also exhibit predictable patterns that can be exploited for denoising. The course introduces tools and results from high-dimensional probability and random matrix theory that underpin many recent advances in this area.
TTh 2:30pm-3:45pm

ECE 9500a, How to Wirelessly Sense Almost Anything  Staff

This seminar course introduces graduate students and senior undergraduates in EE/CS to wireless sensing. We explore various signals and sensing modalities, including radio frequency, mmWave, acoustics, and visible light. We cover fundamental principles such as battery-free computing, wireless localization, sensor security, health sensing, and backscatter networking. In this course, we examine wireless sensing applications such as seeing through walls, contactless vital sign monitoring, smart homes, ocean IoT, and smart agriculture, as well as multi-modal sensing for augmented reality headsets and robotics. Lectures introduce fundamental technologies through research paper discussions and readings. Additionally, students undertake a semester-long research project.
T 1:30pm-3:20pm

ECE 9520a, Internet Engineering

Introduction to basic Internet protocols and architectures. Topics include packet-switch and multi-access networks, routing, flow control, congestion control, Internet protocols (IP, TCP, BGP), the client-server model, IP addressing and the domain name system, wireless access networks, and mobile communications.
TTh 2:30pm-3:45pm

ECE 9631b, Network Algorithms and Stochastic Optimization  Leandros Tassiulas

This course focuses on resource allocation models as well as associated algorithms and design and optimization methodologies that capture the intricacies of complex networking systems in communications computing as well as transportation, manufacturing, and energy systems. Max-weight scheduling, back-pressure routing, wireless opportunistic scheduling, time-varying topology network control, and energy-efficient management are sample topics to be considered, in addition to Lyapunov stability and optimization, stochastic ordering, and notions of fairness in network resource consumption.
MW 11:35am-12:50pm

ECE 9909a or b, Special Investigations  Staff

Faculty-supervised individual projects with emphasis on research, laboratory, or theory. Students must define the scope of the proposed project with the faculty member who has agreed to act as supervisor, and submit a brief abstract to the director of graduate studies for approval.
HTBA

ENAS 5000a, Mathematical Methods I  Martin Pfaller

A beginning, graduate-level introduction to ordinary and partial differential equations, vector analysis, linear algebra, and complex functions. Laplace transform, series expansion, Fourier transform, and matrix methods are given particular attention. Applications to problems frequently encountered in engineering practice are stressed throughout.
TTh 9am-10:15am

ENAS 5041b / MENG 5041b, Applied Numerical Methods for Differential Equations

The derivation, analysis, and implementation of numerical methods for the solution of ordinary and partial differential equations, both linear and nonlinear. Additional topics such as computational cost, error estimation, and stability analysis are studied in several contexts throughout the course. ENAS 747 is not a prerequisite.
MW 2:30pm-3:45pm

ENAS 5080b, Responsible Conduct of Research  Staff

Required of first-year students. Presentation and discussion of topics and best practices relevant to responsible conduct of research including academic fraud and misconduct, conflict of interest and conflict of commitment, data acquisition and human subjects, use and care of animals, publication practices and responsible authorship, mentor/trainee responsibilities and peer review, and collaborative science.  0 Course cr
HTBA

ENAS 5170b / MB&B 5170b / MCDB 5170b / PHYS 5170b, Methods and Logic in Interdisciplinary Research  Corey O'Hern and Emma Carley

This full PEB class is intended to introduce students to integrated approaches to research. Each week, the first of two sessions is student-led, while the second session is led by faculty with complementary expertise and discusses papers that use different approaches to the same topic (for example, physical and biological or experiment and theory).
TTh 4pm-5:30pm

ENAS 5180a / CBIO 635 / MB&B 6350a, Quantitative Methods in Biophysics  Nikhil Malvankar, Julien Berro, and Yong Xiong

An introduction to quantitative methods relevant to analysis and interpretation of biological data. Topics include statistical testing, data presentation, and error analysis; introduction to artificial intelligence-based data analysis tools, Alpha Fold Tutorial, introduction to mathematical modeling of biological dynamics; and Fourier analysis in signal/image processing and macromolecular structural studies. Instruction in basic programming skills and data analysis using MATLAB; study of real data from MB&B research groups. Prerequisites: MATH 120 and MB&B 600 or equivalents, or permission of the instructors.
TTh 9am-10:15am

ENAS 5190b, Responsible Conduct of Research  Staff

Required of first-year students in Chemical & Environmental Engineering, Electrical Engineering, and Mechanical Engineering & Materials Science. Presentation and discussion of topics and best practices relevant to responsible conduct of research including academic fraud and misconduct, conflict of interest and conflict of commitment, data acquisition and human subjects, use and care of animals, publication practices and responsible authorship, mentor/trainee responsibilities and peer review, and collaborative science.  0 Course cr
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ENAS 5620b / AMTH 765b / CB&B 5620b / INP 562b / INP 7562b / MB&B 5620b / PHYS 5620b, Modeling Biological Systems II  Thierry Emonet, Jing Yan, and Damon Clark

This course covers advanced topics in computational biology. How do cells compute, how do they count and tell time, how do they oscillate and generate spatial patterns? Topics include time-dependent dynamics in regulatory, signal-transduction, and neuronal networks; fluctuations, growth, and form; mechanics of cell shape and motion; spatially heterogeneous processes; diffusion. This year, the course spends roughly half its time on mechanical systems at the cellular and tissue level, and half on models of neurons and neural systems in computational neuroscience. Prerequisite: a 200-level biology course or permission of the instructor.
HTBA

ENAS 5710b / MB&B 5910b / MCDB 5910b / PHYS 5710b, Integrated Workshop  Corey O'Hern

This required course for students in the PEB graduate program involves a series of modules, co-taught by faculty, in which students from different academic backgrounds and research skills collaborate on projects at the interface of physics, engineering, and biology. The modules cover a broad range of PEB research areas and skills. The course starts with an introduction to MATLAB, which is used throughout the course for analysis, simulations, and modeling.
TTh 9am-10:15am

ENAS 6240b, Finding Yourself in the Future of Creativity  John Kao

This course is for would-be entrepreneurs, future leaders wanting to drive creative agendas, and all of us who wish to harness and amplify our innate creativity to make a difference. It describes a set of driving forces that require a re-evaluation of how creativity works and how it can be practiced. These include expanded views of creative cognition and its relationship to advanced brain science, the growing connections between human creativity and machine intelligence, the role of culture and politics in shaping the gameboard for creativity’s global spread, and finally an emerging ethical perspective on creativity. Courses on creativity, entrepreneurship, and leadership usually focus on the externalities—what to do, and how to analyze. This course by contrast embraces the internalities, the critical human and cognitive factors that drive creative outcomes. To clarify these internalities, the course has been designed to balance didactic and experiential learning and is meant for students who have an appetite for self-assessment and engaging in personal exploration. Accordingly, the course integrates presentations, hands-on self-assessment exercises, directed readings, and collaborative projects.
M 9:25am-11:15am

ENAS 8000a, Smart City Engineering with IoT  Andrei Khurshudov

A smart city is one that employs technology to gather data from various sources such as sensors, people, devices, vehicles, and buildings. This data is then used for optimal decision-making and control. Cities around the world are adopting “smart” technology, thereby transforming urban life. Utilizing the Internet of Things (IoT), cities like Barcelona, London, and Singapore aim to improve living standards, boost the economy, and enhance sustainability. They achieve this through innovations like intelligent streetlights, smart electric grids, and advanced traffic systems. The Internet of Things, a global network consisting of connected sensors, machines, devices, communication networks, and decision-making algorithms is facilitating a new wave of the industrial revolution. This course is designed for both graduate and undergraduate students and offers a comprehensive overview of the key technologies shaping contemporary and future smart cities. It delves into the foundational elements of IoT devices and applications, covering topics such as: data analytics using ML and AI (which will be used to address practical problems); smart sensors and interconnected devices; IoT data: formats, transmission, and storage; Cloud and Edge computing, and the associated trade-offs; connectivity and wireless communication technologies; device failure prevention and reliability modeling; and other relevant subjects.
MW 9am-10:15am

MENG 5020b, Mechatronics Laboratory  Madhusudhan Venkadesan

Hands-on synthesis of control systems, electrical engineering, and mechanical engineering. Review of Laplace transforms, transfer functions, software tools for solving ODEs. Review of electronic components and introduction to electronic instrumentation. Introduction to sensors, mechanical power transmission elements, programming microcontrollers, and PID control.
HTBA

MENG 5041b / ENAS 5041b, Applied Numerical Methods for Differential Equations  Beth Anne Bennett

The derivation, analysis, and implementation of numerical methods for the solution of ordinary and partial differential equations, both linear and nonlinear. Additional topics such as computational cost, error estimation, and stability analysis are studied in several contexts throughout the course. ENAS 747 is not a prerequisite.
MW 2:30pm-3:45pm

MENG 5050a, Computer-Aided Engineering  Omer Subasi

Aspects of computer-aided design and manufacture (CAD/CAM). The computer’s role in the mechanical design and manufacturing process; commercial tools for two- and three-dimensional drafting and assembly modeling; finite-element analysis software for modeling mechanical, thermal, and fluid systems.
TTh 11:35am-12:50pm

MENG 5359a, Neuromuscular Biomechanics  Madhusudhan Venkadesan

Mechanics and control of animal movement, including skeletal muscle mechanics, systems-level neural and sensory physiology, elements of feedback control, and optimal control. Deriving equations of motion for multibody mechanical systems that are actuated by muscles or muscle-like motors; incorporating sensory feedback; analyzing system properties such as stability and energetics.
MW 4pm-5:15pm

MENG 6278a, Advanced Robotic Mechanisms  Aaron Dollar

TBD
TTh 1pm-2:15pm

MENG 7465a, Chemical Propulsion Systems  Alessandro Gomez

Study of chemical propulsion systems. Topics include review of propulsion fundamentals; concepts of compressible fluid flow; development and application of relations for Fanno and Rayleigh flows; normal and oblique shock systems to various propulsion system components; engine performance characteristics; fundamentals of turbomachinery; liquid and solid rocket system components and performance.
MW 1pm-2:15pm

MENG 7469a, Aerodynamics  Juan de la Mora

Review of fluid dynamics. Inviscid flows over airfoils; finite wing theory; viscous effects and boundary layer theory. Compressible aerodynamics: normal and oblique shock waves and expansion waves. Linearized compressible flows. Some basic knowledge of thermodynamics is expected.
TTh 9am-10:15am

MENG 7475a, Fluid Mechanics of Natural Phenomena  Amir Pahlavan

This course draws inspiration from nature and focuses on utilizing the fundamental concepts of fluid mechanics and soft matter physics to explain these phenomena. We study a broad range of problems related to (1) nutrient transport in plants, slime molds, and fungi and the adaptation of their networks in dynamic environments, (2) collective behavior and chemotaxis of swimming microorganisms, and (3) pattern formation in nature, e.g. icicles, mud cracks, salt polygons, dendritic crystals, and Turing patterns. We also discuss how our understanding of these problems could be used to develop sustainable solutions for the society, e.g. designing synthetic trees to convert CO2 to oxygen, developing micro/nano robots for biomedical applications, and utilizing pattern formation and self-assembly to make new materials.
MW 11:35am-12:50pm

MENG 8664b, Forces on the Nanoscale  Udo Schwarz

Modern materials science often exploits the fact that atoms located at surfaces or in thin layers behave differently from bulk atoms to achieve new or greatly altered material properties. The course provides an in-depth discussion of intermolecular and surface forces, which determine the mechanical and chemical properties of surfaces. In the first part, we discuss the fundamental principles and concepts of forces between atoms and molecules. Part two generalizes these concepts to surface forces. Part three then gives a variety of examples. The course is of interest to students studying thin-film growth, surface coatings, mechanical and chemical properties of surfaces, soft matter including biomembranes, and colloidal suspensions.
MW 11:35am-12:50pm

MENG 8672b, Electronic and Optical Properties of Energy Materials  Diana Qiu

This course explores the electronic and optical properties of materials from the perspective of electronic and molecular structure with a special focus on the microscopic origin and design of properties of interest for energy harvesting, storage, and transport. The course begins by briefly introducing concepts in quantum mechanics, such as wave functions and the time-independent Schrödinger equations. Then, we explore electronic structure in the context of designing materials for energy harvesting and generation, such as photovoltaics, thermoelectrics, and piezoelectrics. We also study dynamical processes, such as hot electron relaxation, multi-exciton generation, charge transport, and energy transport at a phenomenological level. Finally, we overview common energy storage materials, with a focus on solid-state batteries and solar fuels.
TTh 9am-10:15am

MENG 8673a, Introduction to Nanomaterials and Nanotechnology  Cong Su

Survey of nanomaterial synthesis methods and current nanotechnologies. Approaches to synthesizing nanomaterials; characterization techniques; device applications that involve nanoscale effects.
MW 1pm-2:15pm

MENG 8675b, Thermodynamics, Kinetics, and Structure of Materials  Jan Schroers

This advanced-level course focuses on the thermodynamic and kinetic aspects of materials and how they define structure and properties. We first discuss thermodynamics relevant to materials. This includes thermodynamic laws, auxiliary functions to develop convenient equations of state to describe equilibrium, Gibbs Free Energy (G), experimental determination of G, model calculations of G such as ideal solutions and regular solutions, using G curves to construct equilibrium conditions, phase diagram constructions, reading of phase diagrams. We then focus on solidification which we develop from the phenomena of undercooling, nucleation and growth. Combining both allows us to predict microstructures formed during solidification far and close to equilibrium. We also discuss glass formation, the case when nucleation and growth can be suppressed, and the liquid freezes upon cooling into a glass.
TTh 9am-10:15am

MENG 9000a, Research Seminars in Mechanical Engineering & Materials Science  Jan Schroers

The purpose of this course is to introduce graduate students to state-of-the-art research in all areas of Mechanical Engineering & Materials Science (MEMS), as well as related disciplines, so that students understand the range of current research questions that are being addressed. An important goal is to encourage students to explore research topics beyond their particular field of study and develop the ability to contextualize their work in terms of larger research questions in MEMS. We therefore require that MEMS Ph.D. students enrolled in this course attend at least eight research seminars during the term: six must be part of the official MEMS seminar series, and two can be from any other relevant Yale graduate department/program seminar series. This course is graded Sat/Unsat with sign-in sheets used to monitor attendance. Required of first- and second-year MEMS Ph.D. students.  0 Course cr
HTBA

MENG 9900a, Special Investigations  Staff

Faculty-supervised individual projects with emphasis on research, laboratory, or theory. Students must define the scope of the proposed project with the faculty member who has agreed to act as supervisor, and submit a brief abstract to the director of graduate studies for approval.
HTBA