Engineering & Applied Science

17 Hillhouse Avenue, 203.432.4220
http://seas.yale.edu
M.S., M.Phil., Ph.D.

Dean
Jeffrey Brock

Deputy Dean
Vincent Wilczynski

Assistant Dean
Sarah M. Miller

Assistant Dean for Faculty Affairs
Kristin Flower

Assistant Dean for Faculty Development
Julie Dorsey

Assistant Dean for Research
Rajit Manohar

Assistant Dean for Innovation and Entrepreneurship
W. Mark Saltzman

Applied Physics

Chair
Vidvuds Ozolins

Director of Graduate Studies
Peter Schiffer (BCT 329; 203.432.2647; peter.schiffer@yale.edu)

Professors Charles Ahn, Sean Barrett (Physics), Hui Cao, Michel Devoret, Paul Fleury (Emeritus), Steven Girvin (Physics), Leonid Glazman (Physics), Jack Harris (Physics), Victor Henrich (Emeritus), Sohrab Ismail-Beigi, Marshall Long (Mechanical Engineering & Materials Science), Simon Mochrie, Corey O’Hern (Mechanical Engineering & Materials Science), Vidvuds Ozolins, Daniel Prober, Nicholas Read, Peter Schiffer, Robert Schoelkopf, Ramamurti Shankar (Physics), Mitchell Smooke (Mechanical Engineering & Materials Science), A. Douglas Stone, Hong Tang (Electrical Engineering), Robert Wheeler (Emeritus), Werner Wolf (Emeritus)

Associate Professors Michael Choma (Biomedical Engineering), Peter Rakich

Assistant Professors Yu He, Owen Miller, Shruti Puri

Biomedical Engineering

Chair
James Duncan

Director of Graduate Studies
Richard Carson (richard.carson@yale.edu)

Professors Helene Benveniste,* Joerg Bewersdorf,* Richard Carson,† Nicholas Christakis,* Todd Constable,* Robin de Graaf,* James Duncan,† Rong Fan, Jay Humphrey, Fahmeed Hyder,† Farren Isaacs,* Themis Kyriakides,† Francis Lee,* Andre Levchenko, Graeme Mason,* Evan Morris,* Xenophon Papademetris,* Douglas Rothman,† W. Mark Saltzman, Martin Schwartz,* Fred Sigworth,* Albert Sinusas,* Brian Smith,* Lawrence Staib,† Hemant Tagare,* John Tsang,* Paul Van Tassel,* Steven Zucker†

Associate Professors Fadi Akar,* Stuart Campbell, Tarek Fahmy, Gigi Galiana,* Anjelica Gonzalez, Michelle Hampson,* Michael Higley,* Henry Hsia,* Chenxiang Lin,* Chi Liu,* Kathryn Miller-Jensen, Michael Murrell, Dana Peters,* Yibing Qyang,* Jiangbing Zhou*

Assistant Professors Sanjay Aneja,* Julius Chapiro,* Daniel Coman,* Nicha Dvornek,* Ansel Hillmer,* Michael Mak, John Onofrey, Cristina Rodriguez, Dustin Scheinost,* Gregory Tietjen*

Chemical & Environmental Engineering

Chair
Jordan Peccia

Director of Graduate Studies
Michael Loewenberg (michael.loewenberg@yale.edu) [F]
Mingjiang Zhong (mingjiang.zhong@yale.edu) [Sp]

Professors Eric Altman, Paul Anastas,* Michelle Bell,* Menachem Elimelech, John Fortner, Gary Haller (Emeritus), Edward Kaplan, Jaehong Kim, Michael Loewenberg, Andrew Miranker,* Jordan Peccia, Lisa Pfefferle, Daniel Rosner (Emeritus), W. Mark Saltzman,* Udo Schwarz,* T. Kyle Vanderlick, Paul Van Tassel, Julie Zimmerman†

Associate Professor Drew Gentner

Assistant Professors Nicole Deziel,* Peijun Guo, Amir Haji-Akbari, Shu Hu, Krystal Pollitt,* Lea Winter, Yuan Yao,* Mingjiang Zhong

Lecturer Yehia Khalil 

Computer Science

Chair
Zhong Shao

Director of Graduate Studies
Lin Zhong (lin.zhong@yale.edu)

Professors Dana Angluin (Emerita), James Aspnes, Dirk Bergemann,* Ronald Coifman,* Aaron Dollar,* Julie Dorsey, Joan Feigenbaum, Michael Fischer, Robert Frank,* David Gelernter, Mark Gerstein,* John Lafferty,* Rajit Manohar,* Vladimir Rokhlin,† Holly Rushmeier, Brian Scassellati, Martin Schultz (Emeritus), Zhong Shao, Avi Silberschatz, Daniel Spielman, Phillipp Strack,* Leandros Tassiulas,* Nisheeth Vishnoi, Y. Richard Yang, Lin Zhong, Steven Zucker†

Associate Professors Abhishek Bhattacharjee, Yang Cai, Theodore Kim, Smita Krishnaswamy,* Sahand Negahban,* Charalampos Papamanthou, Ruzica Piskac, Robert Soule, Jakub Szefer*

Assistant Professors Kim Blenman,* Arman Cohan, Yongshan Ding, Benjamin Fisch, Tesca Fitzgerald, Wenjun Hu,* Julian Jara-Ettinger,* Anurag Khandelwal, Daniel Rakita, Katerina Sotiraki, David van Dijk,* Marynel Vázquez, Andre Wibisono, Alex Wong, Zhitao Ying, Manolis Zampetakis, Fan Zhang

Senior Lecturers James Glenn, Andrew Sherman, Stephen Slade

Lecturers Timos Antonopoulos, Timothy Barron, Ozan Erat, Kyle Jensen,* Janet Kayfetz, Jay Lim, Dylan McKay, Cody Murphey, Sohee Park, Scott Petersen, Brad Rosen, Andrew Sherman,* Inyoung Shin, Alan Weide, Cecillia Xie

Electrical Engineering

Chair
Jung Han

Director of Graduate Studies
Hong Tang (hong.tang@yale.edu)

Professors Hui Cao,* James Duncan,† Jung Han, Roman Kuc, Rajit Manohar, A. Stephen Morse, Kumpati Narendra (Emeritus), Daniel Prober,† Lawrence Staib,† Hemant Tagare,* Hong Tang, Leandros Tassiulas, J. Rimas Vaisnys (Emeritus), Fengnian Xia, Y. Richard Yang†

Associate Professors Amin Karbasi, Jakub Szefer

Assistant Professors Dionysis Kalogerias, Mengxia Liu, Priyadarshini Panda

Mechanical Engineering & Materials Science

Chair
Udo Schwarz

Director of Graduate Studies
Jan Schroers (jan.schroers@yale.edu)

Professors Charles Ahn,† Ira Bernstein (Emeritus), Juan Fernández de la Mora, Aaron Dollar, Alessandro Gomez, Sohrab Ismail-Beigi,* Shun-Ichiro Karato,* Marshall Long (Emeritus), Corey O’Hern, Vidvuds Ozolins,* Brian Scassellati,* Jan Schroers, Udo Schwarz, Mitchell Smooke

Associate Professors Rebecca Kramer-Bottiglio, Madhusudhan Venkadesan

Assistant Professors Ian Abraham, Yimin Luo, Amir Pahlavan, Diana Qiu, Cong Su, Daniel Wiznia*

Senior Lecturer Beth Anne Bennett

Lecturers Joran Booth, Lawrence Wilen, Joseph Zinter

Programs of study are offered in the areas of applied mechanics, applied physics, computer science, mechanical engineering and materials science, chemical and environmental engineering, electrical engineering, biomedical engineering, and personalized medicine and applied engineering. All programs are under the School of Engineering & Applied Science.

Applied PHysics

Fields of Study

Fields include areas of theoretical and experimental condensed-matter and materials physics, optical and laser physics, quantum engineering, and nanoscale science. Specific programs include surface and interface science, first principles electronic structure methods, photonic materials and devices, complex oxides, magnetic and superconducting artificially engineered systems, quantum computing and superconducting device research, quantum transport and nanotube physics, quantum optics, and random lasers.

Biomedical Engineering

Fields of Study

Biological and medical devices, biological signals and sensors, biomaterials, biophotonics, cellular biomechanics, computational biomechanics, computational medicine, computer vision, digital image analysis and processing, drug delivery, energy metabolism, experimental biomechanics, gene delivery, gene therapy, image analysis, Magnetic Resonance Imaging (MRI), Magnetic Resonance Spectroscopy (MRS), modeling in mechanobiology, molecular biomechanics, nanomedicine, network analysis, neuroreceptors, physics of image formation (MRI, optics, ultrasound, nuclear medicine, and X-ray), physiology and human factors engineering, Positron Emission Tomography (PET), regenerative medicine, signaling pathways, Single Photon Emission Computed Tomography (SPECT), systems biology, systems medicine, tissue engineering, tracer kinetic modeling, and vascular biology.

Chemical & Environmental Engineering

Fields of Study

Fields include nanomaterials, soft matter, interfacial phenomena, energy, water and air quality, and sustainability.

Computer Science

Fields of Study

Algorithms and computational complexity, artificial intelligence, data networking, databases, graphics, machine learning, programming languages, robotics, scientific computing, security and privacy, and systems.

Electrical Engineering

Fields of Study

Fields include biomedical sensory systems, communications and signal processing, neural networks, control systems, wireless networks, sensor networks, microelectromechanical and nanomechanical systems, nanoelectronic science and technology, optoelectronic materials and devices, semiconductor materials and devices, quantum and nonlinear photonics, quantum materials and engineering, computer engineering, computer architecture, hardware security, neuromorphic computing, and VLSI design.

Mechanical Engineering & Materials Science

Fields of Study

Fluids and thermal sciences Electrospray theory and characterization; electrical propulsion applications; aerodynamic instrumentation for separation of clusters and aerosol particles; heterogeneous nucleation in the gas phase; combustion and flames; computational methods for fluid dynamics and reacting flows; interfacial flows and instabilities and transport phenomena in disordered media.

Soft matter/complex fluids Jamming and slow dynamics in gels, glasses, and granular materials; mechanical properties of soft and biological materials; rheology and statistical mechanics of muscle; structure and dynamics of proteins and other macromolecules and wetting of soft solids, elastocapillarity, and poroelasticity.

Materials science Studies of structure-property-processing relationships; thin films; nanoscale effects on electronic, optical, and emergent properties of two-dimensional layered materials; picoscale characterization and engineering; correlated electron systems; molecular beam epitaxy; metallic glasses; sustainable metallurgy; data centered research approaches; nanomaterials; characterization of crystallization and other phase transformations; nanoimprinting; atomic-scale investigations of surface interactions and properties; classical and quantum nanomechanics; nanostructured energy applications; combinatorial materials science; data science in materials science; materials genome; scanning probe microscopy; theoretical spectroscopy and computational materials science; and halide perovskites.

Robotics/mechatronics Machine and mechanism design; dynamics and control; robotic grasping and manipulation; legged locomotion; multi-agent search and exploration; optimal control for learning; model-predictive control; reinforcement learning; human-machine interface; rehabilitation robotics; haptics; soft robotics; flexible and stretchable electronics; soft material manufacturing; responsive material actuators; artificial muscle; soft-bodied control; electromechanical energy conversion; biomechanics of human movement and human-powered vehicles.

Bioengineering Engineering sciences of living systems; biomolecular structure; biomechanics; motor control; animal locomotion; cell and tissue mechanics; biomaterials and therapeutics; human health and orthopaedics; bio-inspired computation and design.

Integrated Graduate Program in Physical and Engineering Biology (PEB)

Students applying to the Ph.D. program in Applied Physics, Biomedical Engineering, Chemical & Environmental Engineering, and Mechanical Engineering & Materials Science may also apply to be part of the PEB program. See the description under Non-Degree-Granting Programs, Councils, and Research Institutes for course requirements, and http://peb.yale.edu for more information about the benefits of this program and application instructions.

Special Requirements for the Ph.D. Degree

The online publication Qualification Procedure for the Ph.D. Degree describes in detail all requirements in Biomedical Engineering, Chemical & Environmental Engineering, Electrical Engineering, and Mechanical Engineering & Materials Science. The student is strongly encouraged to read it carefully; key requirements are briefly summarized below. See Computer Science’s departmental entry in this bulletin for special requirements for the Ph.D. in Computer Science and the Applied Physics departmental entry for special requirements for the Ph.D. in Applied Physics.

Students plan their course of study in consultation with faculty advisers (the student’s advisory committee). A minimum of ten term courses is required, to be completed in the first two years. Well-prepared students may petition for course waivers based on courses taken in a previous graduate degree program. Similarly, students may place out of certain ENAS courses via an examination prepared by the course instructor. Placing out of the course will not reduce the total number of required courses. Core courses, as identified by each department, should be taken in the first year unless otherwise noted by the department. With the permission of the departmental director of graduate studies (DGS), students may substitute more advanced courses that cover the same topics. During the first year, students are required to register for two Special Investigations; any additional terms of Special Investigations will not count toward the degree. At least two elective courses must be outside the area of the dissertation. All students must complete a one-term course, Responsible Conduct of Research, in the first year of study.

Each term, the faculty review the overall performance of the student and report their findings to the DGS who, in consultation with the associate dean, determines whether the student may continue toward the Ph.D. degree. By the end of the second term, it is expected that a faculty member has agreed to accept the student as a research assistant, and it is required that by the beginning of the third term, the faculty adviser provides the financial support indicated in the admissions offer letter, barring the award of external funding. By December 5 of the third year, an area examination must be passed and a written prospectus submitted before dissertation research is begun. These events result in the student’s admission to candidacy. Subsequently, the student will report orally each year to the full advisory committee on progress. When the research is nearing completion, but before the thesis writing has commenced, the full advisory committee will advise the student on the thesis plan. A final oral presentation of the dissertation research is required to be given during term time. There is no foreign language requirement.

Teaching experience is regarded as an integral part of the graduate training program at Yale University, and all Engineering graduate students are required to serve as teaching fellows for up to two terms, typically during year two. Teaching duties normally involve assisting in laboratories or discussion sections and grading papers and are not expected to require more than ten hours per week. Students are not permitted to teach during their first year of study.

If a student was admitted to the program having earned a score of less than 26 on the Speaking Section of the Internet-based TOEFL, the student will be required to take an English as a Second Language (ESL) course each term at Yale until the Graduate School’s Oral English Proficiency standard has been met. This must be achieved by the end of the third year for the student to remain in good standing.

Core Course Requirements for the Ph.D. Degree

Applied Physics See the departmental entry for Applied Physics in this bulletin.

Biomedical Engineering ENAS 510, ENAS 550. One of these courses may be taken in the second year. In addition, there is a math requirement that must be met by taking ENAS 500, ENAS 505, or ENAS 549 in the first year. Students enrolled in IGPPEB may also meet the math requirement by taking ENAS 541 or ENAS 561.

Chemical & Environmental Engineering (Chemical track) ENAS 500, and two of the following three courses: ENAS 521, ENAS 602, ENAS 603.

Chemical & Environmental Engineering (Environmental track) ENAS 640ENAS 641, ENAS 642. In addition, there is a math requirement that must be met by taking one of the following courses in the first year: ENAS 500, ENAS 748, ENV 758, or S&DS 530. Any other mathematics or statistics class can be taken as an elective in addition to one of these core classes.

Computer Science See the departmental entry for Computer Science in this bulletin.

Electrical Engineering Courses will be assigned by the adviser in coordination with the research committee, and are subject to approval by the DGS.

Mechanical Engineering & Materials Science Students must demonstrate competence in one of five areas: Fluid and Thermal Sciences, Soft Matter/Complex Fluids, Materials Science, Robotics/Mechatronics, or Bioengineering. As a minimum requirement, students must take at least one of the following courses in the first year of study: CPSC 559, CPSC 570CPSC 572, CPSC 573, CPSC 585ENAS 521, ENAS 541, ENAS 559, ENAS 606, ENAS 615, ENAS 703, ENAS 704, ENAS 708, ENAS 752, ENAS 755, ENAS 770, ENAS 773ENAS 778, ENAS 787, ENAS 848, ENAS 850, ENAS 851, ENAS 902 (if not used to satisfy the math requirement), ENAS 994PHYS 628. There is a math requirement that must be met by taking CPSC 553ENAS 500, ENAS 902, or PHYS 506, depending on the research area. In addition, students must take two terms of ENAS 700 during the first two years of study; this course does not count toward the ten-course requirement.

Honors Requirement

Students must meet the Honors requirement in at least two term courses (excluding Special Investigations) by the end of the second term of full-time study. An extension of one term may be granted at the discretion of the DGS. An average grade of at least High Pass must be maintained through all courses that count toward the Ph.D.

M.D./Ph.D. Students

M.D./Ph.D. students affiliate with the Department of Biomedical Engineering via the School of Medicine. M.D./Ph.D. students officially affiliate with Biomedical Engineering after selecting a thesis adviser and consulting with the DGS.

The academic requirements for M.D./Ph.D. students entering Biomedical Engineering are modified from the normal requirements for Ph.D. students. Other than the modifications listed here, M.D./Ph.D. students in Biomedical Engineering are subject to all of the same requirements as the other graduate students in the department.

Courses Seven graduate-level courses taken for a grade must be completed during the first two years of the Ph.D. program. (One Yale graduate-level course taken for a grade during medical school may be counted toward this requirement at the discretion of the DGS.) There are three required courses: ENAS 510 and two terms of ENAS 990. All students are expected to present their Special Investigation work at a department symposium held on the last day of the reading period. In addition, there is a math requirement, which may be met by taking any one of the following courses: ENAS 500, ENAS 505, or ENAS 549. Among the three electives, one must be in engineering or a closely related field. Students must obtain a grade of Honors in any two of these courses, excluding ENAS 990, and maintain an average of at least High Pass.

Teaching Students are required to serve as a teaching fellow for up to two terms but are not permitted to teach during their first year of graduate study.

Prospectus and qualifying exam M.D./Ph.D. students must complete and submit their thesis prospectus by the end of the fifth term as an affiliated graduate student. Students who affiliate at the customary point of year three must submit the approved prospectus before the end of the fall term of the fifth year (at the beginning of year three as an affiliated Ph.D. student). After submitting the prospectus, students present their results to date and their proposed research to their thesis committee in an area examination. Students are given two opportunities to pass this exam.

Candidacy M.D./Ph.D. students will be admitted to candidacy once they have completed their course requirements, passed their qualifying exam, and had their dissertation prospectus approved by their advisory committee.

Further requirements M.D./Ph.D. students who are admitted to candidacy are required to have an annual Thesis Committee meeting. In the first year after admission to candidacy, students are expected to present their research work at a departmental seminar. Attendance at weekly Biomedical Engineering Seminars is mandatory. A final oral presentation of the dissertation research is required before students may submit to the Dissertation Office.

Master’s Degrees

M.Phil. See Degree Requirements under Policies and Regulations.

M.S. (en route to the Ph.D.) To qualify for the M.S., the student must pass eight term courses; no more than two may be Special Investigations. An average grade of at least High Pass is required, with at least one grade of Honors.

Terminal Master’s Degree Program Students may also be admitted directly to a terminal master’s degree program. The requirements are the same as for the M.S. en route to the Ph.D., although there are no core course requirements for students in this program. This program is normally completed in one year, but a part-time program may be spread over as many as four years. Some courses are available in the evening, to suit the needs of students from local industry.

The Master’s of Science in Personalized Medicine and Applied Engineering Directed and taught jointly by faculty in the School of Engineering & Applied Sciences and the School of Medicine, this program prepares biomedical, mechanical, and electrical engineers, as well as computer science majors and medical students, with the tools to develop innovative 3D solutions for personalized medicine. The program trains graduate students to develop and apply 3D technology to address surgical and medical conditions, with the goal of personalizing healthcare treatments to improve patient clinical outcomes. Additional societal benefits include lower healthcare costs and improved patient quality of life. Prospective students should apply through the Graduate School of Arts and Sciences (https://gsas.yale.edu/admissions/degree-program-application-process). 

The program is one full year: summer through spring. Students are required to participate in an eight-week, summer clinical immersion session prior to registration in fall term sequence courses. Although course credit is not awarded for the clinical program, completion of the requirement will be noted on the transcript.

Students have flexibility in selecting the focus of their special investigation projects as well as an optional biomedical engineering industry collaboration project (“internal internship”) tailored to their specific academic backgrounds and interests. For example, students with a strong engineering background may want to focus on medical school-focused classes, while medical students may want to focus on engineering-related courses. Students must take a total of eight courses, of which six courses are required of all students in the program: ENAS 526, ENAS 527, ENAS 528, ENAS 529, and two terms of ENAS 532 or ENAS 990. In rare exceptions, students may be allowed to take both with approval from the program director and DGS. With the approval of the program's DGS, the final two courses may be chosen from Yale-wide graduate-level technical electives, which must be approved by the program’s DGS. An average grade of at least High Pass is required, with at least one grade of Honors.

Joint Master’s Degree Program (School of Engineering & Applied Science and School of the Environment) The joint master’s degree program offered by the School of the Environment (YSE) and the School of Engineering & Applied Science (SEAS) provides environmental engineers and environmental managers with the opportunity to develop knowledge and tools to address the complex relationship between technology and the environment. This joint-degree program will train graduate students to design and manage engineered and natural systems that address critical societal challenges, while considering the complex technical, economic, and sociopolitical systems relationships. Each joint program leads to the simultaneous award of two graduate professional degrees: either the Master of Environmental Management (M.E.M.) or the Master of Environmental Science (M.E.Sc.) from YSE, and a Master of Science (M.S.) from SEAS. Students can earn the two degrees concurrently in 2.5 years, less time than if they were pursued sequentially. Candidates spend the first year at YSE, the second year at SEAS, and their final term at YSE. Joint-degree students are guided in this process by advisers in both YSE and SEAS. Candidates must submit formal applications to both YSE and SEAS and be admitted separately to each School, i.e., each School makes its decision independently. It is highly recommended that students apply to and enter a joint-degree program from the outset, although it is possible to apply to the second program once matriculated at Yale. Prospective students to the joint-degree program apply to the YSE master’s degree through YSE (https://apply.environment.yale.edu/apply) and to the SEAS master’s degree in Chemical & Environmental Engineering through the Graduate School of Arts and Sciences (https://gsas.yale.edu/admissions/degree-program-application-process).

The following six courses are required of all joint-degree YSE/SEAS master’s students completing their M.S. in Environmental Engineering: ENAS 641, ENAS 642, ENAS 660, ENV 773, ENV 838, and either ENV 712 or ENV 724. Two additional Yale-wide technical electives approved by the DGS (or faculty in an equivalent role in Environmental Engineering) are required. These courses may be cross-listed with or administered by YSE with prior approval from the DGS. For the joint-degree requirements for completion of the M.E.M. or M.E.Sc. in YSE, see the bulletin of the Yale School of the Environment at https://bulletin.yale.edu.


Program information is available via email to engineering@yale.edu or at our website, http://seas.yale.edu.

Courses

The list of courses may be slightly modified by the time term begins. Please visit https://courses.yale.edu for the most updated course listing.

ENAS 500b, Mathematical Methods IPaul Van Tassel

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 508b, Responsible Conduct of ResearchStaff

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 510a, Physical and Chemical Basis of Bioimaging and BiosensingDouglas Rothman, Ansel Hillmer, and Fahmeed Hyder

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

ENAS 511b, Photonics and Optical ElectronicsJung Han

A survey of the enabling components and devices that constitute modern optical communication systems. Focus on the physics and principles of each functional unit, its current technological status, design issues relevant to overall performance, and future directions.
TTh 2:30pm-3:45pm

ENAS 517b / MB&B 517b / MCDB 517b / PHYS 517b, Methods and Logic in Interdisciplinary ResearchCorey O'Hern

This half-term 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). Counts as 0.5 credit toward graduate course requirements.  ½ Course cr
MW 6pm-7:15pm

ENAS 518a / MB&B 635a, Quantitative Approaches in Biophysics and BiochemistryJulien Berro and Yong Xiong

The course offers an introduction to quantitative methods relevant to analysis and interpretation of biophysical and biochemical data. Topics covered include statistical testing, data presentation, and error analysis; introduction to dynamical systems; analysis of large datasets; and Fourier analysis in signal/image processing and macromolecular structural studies. The course also includes an introduction to basic programming skills and data analysis using MATLAB. Real data from research groups in MB&B are used for practice. Prerequisites: MATH 120 and MB&B 600 or equivalents, or permission of the instructors.
TTh 9am-10:15am

ENAS 519b, Responsible Conduct of ResearchVincent Wilczynski

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
HTBA

ENAS 522a, Engineering and Biophysical Approaches to CancerMichael Mak

This course examines the current understanding of cancer as a complex disease and the advanced engineering and biophysical methods developed to study and treat this disease. All treatment methods are covered. Basic quantitative and computational backgrounds are required. Prerequisites: BENG 249 or equivalent and MATH 120 or equivalent.
W 3:30pm-5:20pm

ENAS 523b, Data and Clinical Decision-MakingJohn 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.
M 9:25am-11:15am

ENAS 526a, Clinical Knowledge for an EngineerSteven Tommasini and Daniel Wiznia

An eight-week summer clinical immersion session provides students with early hands-on learning and shadowing of the current 3D innovation landscape. Students are assigned to a clinical mentor. They shadow their mentor in the clinics and operating rooms, observing how they incorporate personalized medicine into the treatments of patients. This course is only open to graduate students enrolled in the M.S. in Personalized Medicine and Applied Engineering.
HTBA

ENAS 527a, Personalized Medicine SeminarSanjay Aneja, Kimberly Hieftje, Asher Marks, and Frank Buono

Students learn about the healthcare legal landscape, anatomy and pathology, medical imaging modalities, image acquisition and 3D model creation, surgical planning tools, computer navigation, robotics. Topics explored include PACS, DICOM, model creation, model validation, use of CAD with 3D models, image processing algorithm development. In addition, there is an introduction to surgical suite and clinical environment, sterile processing, and YSM simulation center. This course is only open to graduate students enrolled in the M.S. in Personalized Medicine and Applied Engineering.
T 1:30pm-3:20pm

ENAS 528a, Advanced Personalized Medicine TechniquesSteven Tommasini, Julius Chapiro, and Daniel Wiznia

This course incorporates an apprenticeship in the Yale Orthopaedics 3D Printing Lab or in a bioprinting lab within Biomedical Engineering or YSM assisting the in-house clinical engineer with the development and production of clinician requested patient specific 3D prints, custom surgical guides and molds. The curriculum explores 3D printing technologies (pros/cons, post processing requirements), FDA regulation, quality management, common 3D printer design and setup, preparing parts for the printer, printer maintenance and troubleshooting, post-processing, 3D printer validation. Students have a bioprinting lab in which they 3D print tissues and learn about 4D printing and incorporation of biologics. This course is only open to graduate students enrolled in the M.S. in Personalized Medicine and Applied Engineering.
Th 7pm-8:50pm

ENAS 529b, Medical Device Design and InnovationDaniel Wiznia and Steven Tommasini

The engineering design, project planning, prototype creation, and fabrication processes for medical devices that improve patient conditions, experiences, and outcomes. Students develop viable solutions and professional-level working prototypes to address clinical needs identified by practicing physicians. Some attention to topics such as intellectual property, the history of medical devices, documentation and reporting, and regulatory affairs.  0 Course cr
MW 4pm-5:15pm

ENAS 532a or b, Industry-Sponsored 3D Design ProjectStaff

Teams of two to three students are paired to work on 3D medical innovation projects with biomedical engineering companies, industry leaders of personalized medicine. This course serves as a potential “route to employment” by providing students with a year-long internship / “internal interview” with a biomedical technology company’s engineering teamThese projects may involve the student developing novel software, hardware, manufacturing validations, medical devices, surgical instruments, or 3D printing modalities. This course is only open to graduate students enrolled in the M.S. in Personalized Medicine and Applied Engineering.
HTBA

ENAS 535b / PATH 630b, Biomaterial-Tissue InteractionsThemis 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

ENAS 541a / CB&B 523a / MB&B 523a / PHYS 523a, Biological PhysicsYimin Luo

The course has two aims: (1) to introduce students to the physics of biological systems and (2) to introduce students to the basics of scientific computing. The course focuses on studies of a broad range of biophysical phenomena including diffusion, polymer statistics, protein folding, macromolecular crowding, cell motion, and tissue development using computational tools and methods. Intensive tutorials are provided for MATLAB including basic syntax, arrays, for-loops, conditional statements, functions, plotting, and importing and exporting data.
TTh 1pm-2:15pm

ENAS 544a, Fundamentals of Medical ImagingChi 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

ENAS 549b, Biomedical Data AnalysisRichard 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

ENAS 550a / C&MP 550a / MCDB 550a / PHAR 550a / PTB 550a, Physiological SystemsW. 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

ENAS 551b, Biotransport and KineticsKathryn Miller-Jensen

Creation and critical analysis of models of biological transport and reaction processes. Topics include mass and heat transport, biochemical interactions and reactions, and thermodynamics. Examples from diverse applications, including drug delivery, biomedical imaging, and tissue engineering.
MW 9am-10:15am

ENAS 553a, ImmunoengineeringTarek 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

ENAS 554b, Continuum BiomechanicsJay Humphrey

This course is designed to enable students to learn advanced and state-of-the-art methods of continuum and computational biomechanics, especially related to the need to formulate new theories of soft tissue growth, remodeling, disease progression, healing, and aging. Emphasis is placed on ensuring that the mechanics is driven by advances in the vascular mechanobiology.
TTh 1pm-2:15pm

ENAS 556b, Molecular and Cellular BiomechanicsMichael 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

ENAS 558a, Introduction to BiomechanicsMichael Murrell

An introduction to the biomechanics used in biosolid mechanics, biofluid mechanics, biothermomechanics, and biochemomechanics. Diverse aspects of biomedical engineering, from basic mechanobiology to characterization of materials behaviors and the design of medical devices and surgical interventions.
TTh 9am-10:15am

ENAS 561b / AMTH 765b / CB&B 562b / INP 562b / MB&B 562b / MCDB 562b / PHYS 562b, Modeling Biological Systems IIJoe Howard

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.
TTh 2:30pm-3:45pm

ENAS 565a, Practical Applications of Bioimaging and BiosensingDaniel Coman, Ansel Hillmer, 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

ENAS 567b, Systems Biology of Cell SignalingAndre 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

ENAS 568b, Topics in ImmunoengineeringTarek 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

ENAS 569a, Single-Cell Biology, Technologies, and AnalysisRong 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

ENAS 570b / C&MP 560b / MCDB 560b / PHAR 560b, Cellular and Molecular Physiology: Molecular Machines in Human DiseaseEmile 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

ENAS 575a / CPSC 575a / INP 575a, Computational Vision and Biological PerceptionSteven 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

ENAS 576b / AMTH 667b / CPSC 576b, Advanced Computational VisionSteven Zucker

Advanced view of vision from a mathematical, computational, and neurophysiological perspective. Emphasis on differential geometry, machine learning, visual psychophysics, and advanced neurophysiology. Topics include perceptual organization, shading, color, and texture.
HTBA

ENAS 585b / INP 585b, Fundamentals of NeuroimagingFahmeed 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

ENAS 600a or b, Computer-Aided EngineeringStaff

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.
HTBA

ENAS 602b, Chemical Reaction EngineeringEric 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.
MW 9am-10:15am

ENAS 603a, Energy, Mass, and Momentum ProcessesAmir 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

ENAS 638b, Environmental Organic ChemistryJohn Fortner

This course examines the major physical and chemical attributes and processes affecting the behavior of organic compounds in environmental systems, including volatilization, sorption/attachment, diffusion, and reactions. Emphasis is on anthropogenic hydrophobic organic compounds (e.g., TCE, PCBs, DDT) and less hydrophobic emerging contaminants of concern (e.g., pharmaceuticals, explosives, etc.). The course reviews basic concepts from physical chemistry and examines the relationships between chemical structure, properties, and environmental behavior of organic compounds. Physical and chemical processes important to the fate, treatment, and transformation of specific organic compounds are addressed, including solubility, volatilization, partitioning, sorption/attachment, bioaccumulation, and bulk environmental transformation pathways. Equilibrium and kinetic models based on these principles are used to predict the fate and transport of organic contaminants in the environment.
TTh 1pm-2:15pm

ENAS 640b / ENV 708b, Aquatic ChemistryJordan Peccia

A detailed examination of the principles governing chemical reactions in water. Emphasis is on developing the ability to predict the aqueous chemistry of natural and perturbed systems based on a knowledge of their biogeochemical setting. Focus is on inorganic chemistry, and topics include elementary thermodynamics, acid-base equilibria, alkalinity, speciation, solubility, mineral stability, redox chemistry, and surface complexation reactions. Illustrative examples are taken from the aquatic chemistry of estuaries, lakes, rivers, wetlands, soils, aquifers, and the atmosphere. A standard software package used to predict chemical equilibria may also be presented.
MW 1pm-2:15pm

ENAS 642a, Environmental Physicochemical ProcessesJaehong Kim

Fundamental and applied concepts of physical and chemical (“physicochemical”) processes relevant to water quality control. Topics include chemical reaction engineering, overview of water and wastewater treatment plants, colloid chemistry for solid-liquid separation processes, physical and chemical aspects of coagulation, coagulation in natural waters, filtration in engineered and natural systems, adsorption, membrane processes, disinfection and oxidation, disinfection by-products.
TTh 1pm-2:15pm

ENAS 648a, Environmental Transport ProcessesMenachem Elimelech

Analysis of transport phenomena governing the fate of chemical and biological contaminants in environmental systems. Emphasis on quantifying contaminant transport rates and distributions in natural and engineered environments. Topics include distribution of chemicals between phases; diffusive and convective transport; interfacial mass transfer; contaminant transport in groundwater, lakes, and rivers; analysis of transport phenomena involving particulate and microbial contaminants.
MW 2:30pm-3:45pm

ENAS 660b, Green Engineering and SustainabilityJulie Zimmerman

This hands-on course highlights the key approaches to advancing sustainability through engineering design. The class begins with discussions on sustainability, metrics, general design processes, and challenges to sustainability. The current approach to design, manufacturing, and disposal is discussed in the context of examples and case studies from various sectors. This provides a basis for what and how to consider when designing products, processes, and systems to contribute to furthering sustainability. The fundamental engineering design topics to be addressed include toxicity and benign alternatives, pollution prevention and source reduction, separations and disassembly, material and energy efficiencies and flows, systems analysis, biomimicry, and life cycle design, management, and analysis. Students tackle current engineering and product design challenges in a series of class exercises and a final design project.
MW 1pm-2:15pm

ENAS 700a or b, Research Seminars in Mechanical Engineering & Materials ScienceJan 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

ENAS 703b, Introduction to Nanomaterials and NanotechnologyCong Su

Survey of nanomaterial synthesis methods and current nanotechnologies. Approaches to synthesizing nanomaterials; characterization techniques; device applications that involve nanoscale effects.
TTh 9am-10:15am

ENAS 704b, Theoretical Fluid DynamicsJuan de la Mora

Derivation of the equations of fluid motion from basic principles. Potential theory, viscous flow, flow with vorticity. Topics in hydrodynamics, gas dynamics, stability, and turbulence.
TTh 11:35am-12:50pm

ENAS 711b, BioMEMS & Biomedical MicrodevicesRong 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

ENAS 713a, AcousticsStaff

Wave propagation in strings, membranes, plates, ducts, and volumes; plane, cylindrical, and spherical waves; reflection, transmission, and absorption characteristics; sources of sound. Introduction to special topics such as architectural, underwater, psychological, nonlinear, and musical acoustics, noise, and ultrasonics.
MW 7pm-8:15pm

ENAS 718b, Advanced Electron DevicesMengxia 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

ENAS 748a, Applied Numerical Methods for Differential EquationsBeth 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 9am-10:15am

ENAS 755b, Electronic and Optical Properties of Energy MaterialsDiana 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.
MW 9am-10:15am

ENAS 773a, Fundamentals of Robot Modeling and ControlIan Abraham

This course introduces fundamental concepts for modeling and controlling robotic systems. The course is divided into two components: Part 1 introduces mathematical tools for modeling and simulating complex robot dynamics, and Part 2 formulates various ways to control robots through comprehensive analysis of dynamics and a deep dive into control theory. Specific lecture topics cover an introduction to variational calculus, state representation, kinematics and dynamics, manipulator equations, contact dynamics and collision detection, observability and controllability, control of fully actuated and underactuated robots, model-based methods for control, and control for manipulation and locomotion. The course focuses on connecting mathematical topics with concrete algorithmic implementation where the mid-term project assignment has students model the dynamics of a robot of their choosing. Coding assignments throughout the term provide experience setting up and interfacing with URDF’s, automatic differentiation math libraries in python, and algorithmic implementation of state-of-the-art control methods. Students finish with a codebase and foundational knowledge for simulating and controlling general robotic systems. Special topic lectures focus on recent developments in the field of robotics and highlight core research areas. A final class project takes place instead of a final exam where students leverage the mid-term robot simulation to control the robot to perform a task of their choosing. Prerequisites: The course is designed for incoming graduate students (and advanced senior undergraduates). Experience with differential equations, linear algebra, PID control, and numerical methods for solving ordinary differential equations is required. Functional and object-oriented coding experience in e.g., python, C/C++ is also required.
TTh 4pm-5:15pm

ENAS 776a, Fluid Mechanics of Natural PhenomenaAmir 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

ENAS 778a, Advanced Robotic MechanismsAaron Dollar


MW 1pm-2:15pm

ENAS 787b, Forces on the NanoscaleUdo 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

ENAS 788b, Thermodynamics, Kinetics, and Structure of MaterialsJan 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

ENAS 800a, Science and Technology of the Internet of ThingsAndrei Khurshudov

The Internet of Things refers to a global network of connected machines, devices, sensors, communication networks and protocols, and decision-making algorithms that enable a new wave of the industrial revolution. IoT is the foundation for a new world of connected and intelligent devices operating together to improve our lives. This course covers underlying technologies found in IoT devices and applications, major IoT applications and their practical implementations, the origin and types of IoT data and IoT Big Data Analytics, main technological and economic drivers, as well as inhibitors, of past, present, and future IoT trends and directions. It also discusses how the world's leading corporations adopt IoT. The course also addresses the following subjects: how startups work and what can make them successful, how corporations work and how to succeed in the corporate world, what skills can help you advance your corporate career, and many similar topics.
MW 9am-10:15am

ENAS 820b / CPSC 520b, Computer ArchitectureAbhishek 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

ENAS 825a, Physics of Magnetic Resonance Spectroscopy in VivoGraeme 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

ENAS 840a, Detection and EstimationDionysis 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

ENAS 850a / APHY 548a / PHYS 548a, Solid State Physics IYu 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.
TTh 1pm-2:15pm

ENAS 851b / APHY 549b / PHYS 549b, Solid State Physics IISohrab Ismail-Beigi

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.
TTh 11:35am-12:50pm

ENAS 902a, Linear SystemsA 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

ENAS 912a, Biomedical Image Processing and AnalysisJames Duncan and Lawrence Staib

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

ENAS 924b, Computer Hardware SecurityJakub Szefer

This course provides an in-depth examination of computers and their hardware-based security issues. The operation of the hardware, from transistors to processor microarchitectures, has intimate impact on the security of the whole system. Often, software or algorithms executing on a computer have no control over, or detailed access to, the underlying hardware. Yet, the operation of the hardware and different types of side-effects, such as changing timing, changing power consumption, EM emanations, or different types of crosstalk effects lead to information leakage. To understand the hardware-based security issues, and how to prevent them, the course focuses on classical microprocessors, accelerators such as Field Programmable Gate Arrays, as well as emerging technologies such as Quantum Computers. For the different types of computers, the course teaches students about the various hardware security issues, and students are able to experiment and perform hands-on exercises to demonstrate different types of information leaks. Students also learn about latest research through reading and presenting research papers in class.
TTh 11:35am-12:50pm

ENAS 940a, Neural Networks and Learning SystemsPriya Panda

Neural networks (NNs) have become all-pervasive, giving us self-driving cars, Siri voice assistant, Alexa, and many more. While deep NNs deliver state-of-the-art accuracy on many artificial intelligence tasks, it comes at the cost of high computational complexity. Accordingly, designing efficient hardware architectures for deep neural networks is an important step toward enabling the wide deployment of NNs, particularly in low-power computing platforms, such as mobiles, embedded Internet of Things (IoT), and drones. This course aims to provide a thorough overview of deep learning techniques, while highlighting the key trends and advances toward efficient processing of deep learning in hardware systems, considering algorithm-hardware co-design techniques. Prerequisite: prior exposure to probability/linear algebra/matrix operations at basic undergraduate level is expected. Prior knowledge of programming language like Python NumPy is useful. Familiarity with digital system design with basic understanding of logic, memory, and related design components is expected.
MW 11:35am-12:50pm

ENAS 963b, Network Algorithms and Stochastic OptimizationLeandros 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

ENAS 968a, Cloud Computing with FPGAsJakub Szefer

This course is an intermediate- to advanced-level course focusing on digital design and use of Field Programmable Gate Arrays (FPGAs). The course centers around the new cloud computing paradigm of using FPGAs that are hosted remotely by cloud providers and accessed remotely by users. The theoretical aspects of the course focus on digital system modeling and design using the Verilog Hardware Description Language (Verilog HDL). In the course, students learn about logic synthesis, behavioral modeling, module hierarchies, combinatorial and sequential primitives, and implementing and testing the designs in simulation and real FPGAs. Students learn about topics ranging from high-level ideas about cloud computing to low-level details of interfacing servers to FPGAs, PCIe protocol, AXI protocol, and other common communication protocols between hardware modules or between AXI protocols, and how to write software that runs on the cloud servers and leverages the FPGAs and the host computer, including Serial, SPI, and I2C. Students also learn about and use FPGA tools from Xilinx, but course also touches on tools available from Intel (formerly Altera) as well as open-source tools. The practical aspects of the course include semester-long projects leveraging commercial or in-lab remote FPGAs, based on the project selected by students. Students should be familiar with digital design basics and have some experience with Hardware Description Languages such as Verilog or VHDL.
TTh 11:35am-12:50pm

ENAS 990a or b, Special InvestigationsStaff

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 991a / MB&B 591a / MCDB 591a / PHYS 991a, Integrated WorkshopCorey 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.
MW 2:30pm-3:45pm

ENAS 994b, Mechatronics LaboratoryMadhusudhan 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; PID control.
F 10:30am-1:30pm, MW 1pm-2:15pm