This course covers optimal control and reinforcement learning for dynamical systems, with a strong emphasis on robotic applications such as quadrupeds and humanoids. The first half focuses on optimal control for systems with known, potentially nonlinear dynamics. Students will learn the fundamentals of dynamic programming and the linear quadratic regulator (LQR) before delving into trajectory optimization and model predictive control (MPC) for nonlinear systems, which emphasizes numerical optimization techniques for synthesizing complex motions.

The second half explores reinforcement learning (RL) for systems with unknown dynamics. Topics include both model-free and model-based RL algorithms such as proximal policy optimization (PPO), actor-critic methods, and model-based policy optimization, with a focus on continuous state and action spaces. Additional topics may include Lyapunov analysis, vision-based feedback control, and advanced convex optimization. The course prioritizes computational algorithms over theoretical analysis, equipping students with practical tools for solving complex control problems.

Assignments involve programming in Python and MATLAB to control simulated dynamical systems in MuJoCo and other environments.

ES 201/AM 231 is a course in statistical inference and estimation from a signal processing perspective. The course will emphasize the entire pipeline from writing a model, estimating its parameters and performing inference utilizing real data. The first part of the course will focus on linear and nonlinear probabilistic generative/regression models (e.g. linear, logistic, Poisson regression), and algorithms for optimization (ML/MAP estimation) and Bayesian inference in these models. We will play particular attention to sparsity-induced regression models, because of their relation to artificial neural networks, the topic of the second part of the course. The second part of the course will introduce students to the nascent and exciting research area of model-based deep learning. At present, we lack a principled way to design artificial neural networks, the workhorses of modern AI systems. Moreover, modern AI systems lack the ability to explain how they reach their decisions. In other words, we cannot yet call AI explainable or interpretable which, as a society, poses important questions as to the responsible use of such technology. Model-based deep learning provides a framework to develop and constrain neural-network architectures in a principled fashion. We will see, for instance, how neural-networks with ReLU nonlinearites arise from sparse probabilistic generative models introduced in the first part of the course. This will form the basis for a rigorous recipe we will teach you to build interpretable deep neural networks, from the ground up. We will invite an exciting line up of speakers. Time permitting, we will provide a model-based pespective of the building blocks of modern language and image generative models.

This graduate level course studies dynamic systems in time domain with inputs and outputs. Students will learn how to design estimator and controller for a system to ensure desirable properties (e.g., stability, performance, robustness) of the dynamical system. In particular, the course will focus on systems that can be modeled by linear ordinary differential equations (ODEs) and that satisfy time-invariance conditions. The course will introduces the fundamental mathematics of linear spaces, linear operator theory, and then proceeds with the analysis of the response of linear time-variant systems. Advanced topics such as robust control, model predictive control, linear quadratic games and distributed control will be presented based on allowable time and interest from the class. The material learned in this course will form a valuable foundation for further work in systems, control, estimation, identification, detection, signal processing, and communications.

This course introduces students to fundamental results and recently developed techniques in high-dimensional probability theory and statistical physics that have been successfully applied to the analysis of information processing and machine learning problems. Discussions will be focused on studying such problems in the high-dimensional limit, on analyzing the emergence of phase transitions, and on understanding the scaling limits of efficient algorithms. This course seeks to start from basics, assuming just a solid understanding of undergraduate probability theory. Students will take an active role by exploring and applying what they learn from the course to their own research problems.

Microorganisms produce a diverse array of specialized small molecules as part of their metabolic processes. In this course we will study the production, properties, and characterization of these molecules through the lens of food fermentation. In particular, we will focus on the small molecules that contribute taste and aroma in fermented foods. Students will experience the scientific inquiry process in a creative way by designing and implementing their own research project based on a fermented food of their choosing. Still a field with much potential for discovery, interested students are invited to continue their research project in the summer.

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

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

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

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

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

The main course objectives are to introduce students to the exciting and powerful world of electrical engineering and to explain how gadgets that we use every day actually work. After taking ES 50, you will be able to leverage the power of electricity to build systems that sense, control and program the physical world around you. Examples include intelligent and autonomous systems (robots), audio amplifiers (e.g. guitar amp), interactive art installations, light-shows, mind-controlled machines, and so on.

Guided reading and research.

Guided reading and research.

Entrepreneurship is increasingly transforming our society and economy. This course aims to provide for undergraduates an introduction to entrepreneurship and its implications for innovation. The class will primarily consist of case study discussions but will also include some traditional lecture sessions to provide necessary background for the case discussions. It draws primarily on materials from the introductory MBA course at Harvard Business School, The Entrepreneurial Manager (TEM). It is designed for students interested in entrepreneurship, as well as those interested in studying business from a case study perspective.

Entrepreneurship is increasingly transforming our society and economy. This course aims to provide for undergraduates an introduction to entrepreneurship and its implications for innovation. The class will primarily consist of case study discussions but will also include some traditional lecture sessions to provide necessary background for the case discussions. It draws primarily on materials from the introductory MBA course at Harvard Business School, The Entrepreneurial Manager (TEM). It is designed for students interested in entrepreneurship, as well as those interested in studying business from a case study perspective.

Students do field-based work in entrepreneurship to develop their existing startup and explore new ideas and opportunities for startup creation. The course is for student-founders seeking to advance their innovation experience in a supportive community of peer founders. Students may work individually; teams with a working history are preferred. Requires self-directed, independent work and active outreach to mentors, customers, and partners for guidance and feedback in addition to that provided by the instructor and teaching staff.  Students share their work regularly and engage in a peer-to-peer feedback forum. Coursework is customized to the needs of each student and their startup role and includes development of product, technology, market, business, organization and leadership. See: https://tech.seas.harvard.edu/rad to apply for instructor permission to enroll.

Students do field-based work in entrepreneurship to develop their existing startup and explore new ideas and opportunities for startup creation. The course is for student-founders seeking to advance their innovation experience in a supportive community of peer founders. Students may work individually; teams with a working history are preferred. Requires self-directed, independent work and active outreach to mentors, customers, and partners for guidance and feedback in addition to that provided by the instructor and teaching staff.  Students share their work regularly and engage in a peer-to-peer feedback forum. Coursework is customized to the needs of each student and their startup role and includes development of product, technology, market, business, organization and leadership. See: https://tech.seas.harvard.edu/rad to apply for instructor permission to enroll.

Semester-long team-based project providing experience working with clients on complex multi-stakeholders real problems. Course provides exposure to problem definition, problem framing, qualitative and quantitative research methods, modeling, generation and co-design of creative solutions, engineering design trade-offs, and documentation/communication skills. Ordinarily taken in the junior year.

Semester-long team-based project providing experience working with clients on complex multi-stakeholders real problems. Course provides exposure to problem definition, problem framing, qualitative and quantitative research methods, modeling, generation and co-design of creative solutions, engineering design trade-offs, and documentation/communication skills. Ordinarily taken in the junior year.

Individual engineering design projects which demonstrate mastery of engineering knowledge and techniques. Each student will pursue an appropriate capstone project which involves both engineering design and quantitative analysis. This culminates in a final oral presentation and final report/thesis. Students must complete both parts of this course, fall and spring, in order to receive credit.

Individual engineering design projects which demonstrate mastery of engineering knowledge and techniques. Each student will pursue an appropriate capstone project which involves both engineering design and quantitative analysis. This culminates in a final oral presentation and final report/thesis. Students must complete both parts of this course, fall and spring, in order to receive credit.

Multi-year long team projects that provide an engineering experience working with partner communities on real-world problems. Projects provide exposure to problem definition, quantitative analysis, modeling, generation of creative solutions utilizing appropriate technology, engineering design trade-offs, and documentation/communication skills. These projects will be implemented with our project partners after the appropriate design and approvals have been obtained.

Multi-year long team projects that provide an engineering experience working with partner communities on real-world problems. Projects provide exposure to problem definition, quantitative analysis, modeling, generation of creative solutions utilizing appropriate technology, engineering design trade-offs, and documentation/communication skills. These projects will be implemented with our project partners after the appropriate design and approvals have been obtained.

This class integrates perspectives from leading innovators with collaborative practice and theory of innovation to teach and inspire you to be more innovative in your life and career. Our approach is to engage with leaders and learn their perspectives and align this with innovation sprints where you learn the best tools, processes, and methods to innovate. You can see a course overview here https://youtu.be/CqfvXf33TCE.  Find out more information on Instagram @engsci139 or https://www.instagram.com/engsci139/

An introduction to the mathematical, optical, and computational foundations of computer vision, with a focus on applications in augmented reality and robotic perception. Topics include: camera optics, digital color photography pipelines, multi-camera geometry, image processing and manipulation, simultaneous localization and mapping, lighting and material estimation, and 3D scanning. Emphasis on combining mathematical modeling with robust algorithms for solving ill-posed problems.

This course introduces the fundamentals of probability theory for parameter estimation and decision making under uncertainty. It considers applications to information systems as well as other physical and biological systems. Topics include: discrete and continuous random variables, conditional expectations, Bayes’ rules, laws of large numbers, central limit theorems, Markov chains, Bayesian statistical inferences, and parameter estimations.

Electromagnetism and its applications in science and technology. Topics: Maxwell's equations; electromagnetic waves (e.g., light, microwaves, etc.); wave propagation through media discontinuity; transmission lines, waveguides, and microwave circuits; radiation and antennae; interactions between electromagnetic fields and matters; optics of solids; optical devices; origin of colors; interference and diffraction; lasers and masers; nuclear magnetic resonance and MRI; radio astronomy; wireless networking; plasmonic wave (charge density wave).

This course introduces the fundamentals of circuit theory for the analysis of electrical circuits and the fundamentals of semiconductor devices for the understanding of transistors circuits and other useful actuators and sensors (i.e., transducers). Building on the principles from these two core fundamental areas of electrical engineering, the analog behavior of electronic circuits and physical devices will be modelled, analyzed, and applied. Lab assignments will focus on the design, implementation, and measurement of analog electronic circuits using real electrical components which interface to the physical world. This course complements and forms the basis for many of the abstractions that are used in digital computing systems such as in COMPSCI 1410 (formerly 141), COMPSCI 1411 (formerly 146), and COMPSCI 1480 (formerly 148).

This course and its follow-on course ENG-SCI 156 concern the fundamentals of information systems in the real world. Together they provide a comprehensive foundation in signal processing, systems design and analysis, control, and communications, while also introducing key linear-algebraic concepts in the context of authentic applications. The first course, ENG-SCI 155, focuses on the basic principles of feedback and its use as a tool for inferring and/or altering the dynamics of systems under uncertainty. Topics include linear algebra, the elemental representations of dynamic systems, stability analysis, the design of estimators (e.g., Kalman Filter) and feedback controllers (e.g., PID and Optimal Controller). The class includes both the practical and theoretical aspects of the topic.

This course is a follow-on to ENG-SCI 155 and continues to develop the fundamentals of information systems in the real world. It focuses on the analysis and manipulation of signals in the time and frequency domains in the context of authentic applications. Topics include: the sampling theorem, convolution, and linear input-output systems in continuous and discrete time. Further, students are introduced to transforms—including Fourier, discrete cosine, wavelet, and PCA / SVD ‘transforms’—that map between vector spaces via matrix multiplication as a method to ease analysis provided conditionalized knowledge. Randomness, noise, and filtering. Waves and interference in the context of communications; antennae, phasors, modulation, multiplexing. Applications in communications and data science.

This is the first course on Biological Signal Processing, the science of collection, representation, manipulation, transformation, storing of biological signals, and the use of modern scientific computing tools (Python, Jupyter notebooks) to interpret biological signals and tell engaging and informative stories using biological data. The signals of interest can be deterministic, semi-periodic, transient, random, stationary, non-stationary, etc., depending on their source and generation mechanism. We will use EEG, EKG, temperature data, neural spiking data, and data from Covid-19 as examples. Our focus will be on foundational signal processing concepts that can be applied in a variety of biological applications. Examples include the Fourier Transform, Principal Component Analysis, Clustering, etc. Applications include those to patient monitoring, diagnostics, patient prognostics, online monitoring, and the computation of wellness measures. For many of us, one frustrating aspect of Covid-19 is our inability to understand figures that are reported, such as infection rates and numbers. We will introduce you to a powerful suite of mathematical and scientific computing tools will enable you to evaluate and make decisions based on evidence and data.

This course covers optimal control and reinforcement learning for dynamical systems, with a strong emphasis on robotic applications such as quadrupeds and humanoids. The first half focuses on optimal control for systems with known, potentially nonlinear dynamics. Students will learn the fundamentals of dynamic programming and the linear quadratic regulator (LQR) before delving into trajectory optimization and model predictive control (MPC) for nonlinear systems, which emphasizes numerical optimization techniques for synthesizing complex motions.

The second half explores reinforcement learning (RL) for systems with unknown dynamics. Topics include both model-free and model-based RL algorithms such as proximal policy optimization (PPO), actor-critic methods, and model-based policy optimization, with a focus on continuous state and action spaces. Additional topics may include Lyapunov analysis, vision-based feedback control, and advanced convex optimization. The course prioritizes computational algorithms over theoretical analysis, equipping students with practical tools for solving complex control problems. 

Assignments involve programming in Python and MATLAB to control simulated dynamical systems in MuJoCo and other environments.

This course will focus on physical principles underlying semiconductor devices: electrons and holes in semiconductors , energies and bandgaps, transport properties of electrons and holes, p-n junctions, transistors, light emitting diodes, lasers, solar cells and thermoelectric devices.

The course provides introduction to micro- and nano-fabrication processes used to realize photonic, electronic and mechanical devices. Lectures will introduce the state-of-the-art semiconductor fabrication processes, including lithography, deposition of metals and dielectrics, etching, oxidation, implantation, and diffusion of dopants. The fabrication component of the course will be carried out in a state-of-the-art cleanroom in the Center for Nanoscale Systems, where students will fabricate several electronic and photonic devices, including transistors, light-emitting diodes (LEDs), lasers and optical resonators.  Device characterization will be performed in a state-of-the-art teaching labs in SEC in Allston.  

ES 201/AM 231 is a course in statistical inference and estimation from a signal processing perspective. The course will emphasize the entire pipeline from writing a model, estimating its parameters and performing inference utilizing real data. The first part of the course will focus on linear and nonlinear probabilistic generative/regression models (e.g. linear, logistic, Poisson regression), and algorithms for optimization (ML/MAP estimation) and Bayesian inference in these models. We will play particular attention to sparsity-induced regression models, because of their relation to artificial neural networks, the topic of the second part of the course. The second part of the course will introduce students to the nascent and exciting research area of model-based deep learning. At present, we lack a principled way to design artificial neural networks, the workhorses of modern AI systems. Moreover, modern AI systems lack the ability to explain how they reach their decisions. In other words, we cannot yet call AI explainable or interpretable which, as a society, poses important questions as to the responsible use of such technology. Model-based deep learning provides a framework to develop and constrain neural-network architectures in a principled fashion. We will see, for instance, how neural-networks with ReLU nonlinearites arise from sparse probabilistic generative models introduced in the first part of the course. This will form the basis for a rigorous recipe we will teach you to build interpretable deep neural networks, from the ground up. We will invite an exciting line up of speakers. Time permitting, we will provide a model-based pespective of the building blocks of modern language and image generative models.

This graduate level course studies dynamic systems in time domain with inputs and outputs. Students will learn how to design estimator and controller for a system to ensure desirable properties (e.g., stability, performance, robustness) of the dynamical system. In particular, the course will focus on systems that can be modeled by linear ordinary differential equations (ODEs) and that satisfy time-invariance conditions. The course will introduces the fundamental mathematics of linear spaces, linear operator theory, and then proceeds with the analysis of the response of linear time-variant systems. Advanced topics such as robust control, model predictive control, linear quadratic games and distributed control will be presented based on allowable time and interest from the class. The material learned in this course will form a valuable foundation for further work in systems, control, estimation, identification, detection, signal processing, and communications.

This course provides a graduate-level introduction to the global hydrologic cycle and relevant terrestrial and atmospheric processes. It covers the concepts of water and energy balance; atmospheric radiation, composition and circulation; precipitation formation; evaporation and vegetation transpiration; dynamics of the atmospheric boundary layer (ABL), and its coupling with the land surface; boundary layer clouds; atmospheric chemistry within the ABL; and groundwater flow and unsaturated zone processes.

This class integrates perspectives from leading innovators with collaborative practice and theory of innovation to teach and inspire you to be more innovative in your life and career. Our approach is to engage with leaders and learn their perspectives and align this with innovation sprints where you learn the best tools, processes, and methods to innovate. You can see a course overview here https://youtu.be/CqfvXf33TCE.  Find out more information on Instagram @engsci139 or https://www.instagram.com/engsci139/

Students are expected to meet all the requirements of Engineering Sciences 139 and in addition are required to prepare an individual term project with significant analytic emphasis in an area of scientific or technological innovation.

Fundamental concepts of information theory, Entropy, Kullback-Leibler divergence, Mutual information; typical sequences and their applications, Loss-less data compression, Huffman codes, Elias Codes, Arithmetic Codes, Discrete Memory-less Channels, Channel Coding and Capacity, Differential Entropy, Gaussian Channels, rate distortion theory, Multi-user Information Theory, Connections between information theory and statistics.

This course introduces students to fundamental results and recently developed techniques in high-dimensional probability theory and statistical physics that have been successfully applied to the analysis of information processing and machine learning problems. Discussions will be focused on studying such problems in the high-dimensional limit, on analyzing the emergence of phase transitions, and on understanding the scaling limits of efficient algorithms. This course seeks to start from basics, assuming just a solid understanding of undergraduate probability theory. Students will take an active role by exploring and applying what they learn from the course to their own research problems.

This course will discuss electro-optics and nonlinear physics in nanophotonic devices. Topics include key building blocks of integrated photonics such as interferometers, microresonators, Bragg gratings, and photonic crystals; device physics and design of silicon photonics-based electro-optic modulators; second-order nonlinear photonics including parametric oscillation/ amplification, electro-optic modulation/ combs, harmonic generation, quasi-phase matching, and frequency mixing; third-order nonlinear photonics including supercontinuum generation, parametric oscillation, soliton frequency combs, and techniques for dispersion engineering and pulse shaping; Brillouin lasing and Raman scattering.

The course provides introduction to micro- and nano-fabrication processes used to realize photonic, electronic and mechanical devices. Lectures will introduce the state-of-the-art semiconductor fabrication processes, including lithography, deposition of metals and dielectrics, etching, oxidation, implantation, and diffusion of dopants. The fabrication component of the course will be carried out in a state-of-the-art cleanroom in the Center for Nanoscale Systems, where students will fabricate several electronic and photonic devices, including transistors, light-emitting diodes (LEDs), lasers and optical resonators.  Device characterization will be performed in a state-of-the-art teaching labs in SEC in Allston. 

This class leads students to develop their skills in the critical reading and writing of science and engineering. Genres will include research articles, grant proposals, school/fellowship/job applications, or lay abstracts & press releases for the non-scientific public. Crucially, students will be empowered not only to achieve their own writing goals, but also to break down these learned skills and impart them to others, as effective collaborators and mentors of younger students.

This class leads students to develop their skills in the critical reading and writing of science and engineering. Genres will include research articles, grant proposals, school/fellowship/job applications, or lay abstracts & press releases for the non-scientific public. Crucially, students will be empowered not only to achieve their own writing goals, but also to break down these learned skills and impart them to others, as effective collaborators and mentors of younger students.

This is a SAT/UNSAT seminar course focused on design thinking, analysis, planning, and executing the development of engineered systems. Weekly meetings will include discussions and assigned readings of case studies and examples of the systems surrounding the developing technical system. Organizing and executing research, innovation, and product design at the scales from academic group, to startup, to major industry will be discussed. The course is designed to allow the engineer and designer to integrate technical knowledge into an executable framework as an individual or leader of a design team.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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