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 project-based course will introduce the physical concepts that can be applied to various human athletic endeavors. Students will focus on analyzing the dynamics of a specific sport/ physical activity through a project that they develop. This will allow students to construct physical models with an increasing level of realism that can used to analyze sporting events. Mathematics is the language of physics, and its use will be ever-present throughout the semester. However, we will focus more on the application of the laws of physics to understand the world of athletics. Students will learn the use of motion trackers and sensors to analyze motion in its dynamical and kinematic aspects.

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 include some traditional lecture sessions that build on academic papers to provide more frameworks. As such, it draws primarily on materials from the introductory MBA course at Harvard Business School, “The Entrepreneurial Manager” (TEM). Students will be expected to come to class prepared to discuss the cases.

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 include some traditional lecture sessions that build on academic papers to provide more frameworks. As such, it draws primarily on materials from the introductory MBA course at Harvard Business School, “The Entrepreneurial Manager” (TEM). Students will be expected to come to class prepared to discuss the cases.

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/

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 141, COMPSCI 146, and COMPSCI 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 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.  

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

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 focuses on state-of-the-art electronic-photonic integrated circuits for high-speed communication and computation. It emphasizes the importance of electronic-photonic co-design: maximizing overall performance by holistically co-optimizing electronic and photonic circuits together. Topics span multiple layers of the computing stack, including materials (group IV, III-V, II-VI semiconductors), electro-optic devices (modulators, lasers, photodetectors, semiconductor optical amplifiers), circuits (transceivers, data converters), architectures (distributed computing systems, network switches), and integration techniques (three-dimensional integration of electronics and photonics, optical interposers, monolithic integration). Advanced topics include active optical metamaterials, non-linear optical devices, and digital signal processing in the optical domain. 

This course teaches how to create original robotic devices made of light, compliant – informal – materials.

New fabrication techniques are transforming the field of robotics. Rather than rigid parts connected by mechanical connectors, robots can now be made of folded paper, carbon laminates or soft gels. They can be formed fully integrated from a 3D printer rather than assembled from individual components. Informal Robotics draws on cutting-edge research from leading labs, in particular, Harvard’s Micro Robotics Laboratory which has created unique designs for ambulatory and flying robots, end-effectors, medical instruments and other applications.

We will explore informal robotics from multiple perspectives, culminating with the design of original devices displaying animated intelligence in real-time. Going beyond traditional engineering approaches, we will also explore new opportunities for design at the product, architectural, and urban scales.

Techniques:
Hands-on:  Working with the GSD’s Fab Lab we are creating a kit of parts that will be available to all enrolled students. With the kit, you can create a wide range of folding mechanisms controlled by on-board miniature electronics.
Software / Simulation: Software workshops will be offered on Fusion 360 and Grasshopper to simulate robotic performance within a virtual environment.

Topics:
- Kinematics: design techniques for pop-ups, origami, and soft mechanisms.
- Fabrication: methods: for composite materials, laminated assembly, self-folding, and integrated flexures - the kit of parts will allow for hands-on exploration.
- Controls: how to actuate movement and program desired behavior. Topics include servos, linear actuators, and use of Arduino actuator control.
- Applications: takes us beyond purely technological concerns, contextualizing Informal Robotics within larger trends where materials, manufacturing and computation are starting to merge

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.

Supervision of experimental or theoretical research on acceptable problems in engineering and applied science and supervision of reading on topics not covered by regular courses of instruction.

Supervision of experimental or theoretical research on acceptable problems in engineering and applied science and supervision of reading on topics not covered by regular courses of instruction.