Faculty of Arts & Sciences

This course explores the Internet as a central component of modern scientific data processing and computation. We will examine the architecture of the Internet and the models of computation and data with which it is compatible. Through readings and exercises, students will explore the trade-offs of these various models and gain an appreciation for successful Internet-oriented system design for modern, federated, data- and compute-intensive scientific research. Students will complete a team project to develop an Internet-based system for scientific data processing. Python will be used for examples.

The course will describe major computational techniques for fluid flows, as described by the Navier-Stokes equations of continuum mechanics. In addition, the course will cover a new class of mesoscale techniques for complex flows and soft matter systems, which do not fit within the continuum Navier-Stokes description. The latter encompass a broad class of flowing materials of special interest to micro-nano engineering and biology.

The CSE capstone project is intended to integrate and apply the skills and ideas CSE students acquire in their core courses and electives. By requiring students to complete a substantial and challenging collaborative project, the capstone course will prepare students for the professional world and ensure that they are trained to conduct research. There will be no homework or lectures. Students will be dealing with real-world problems, messy data sets, and the chance to work on an end-to-end solution to a problem using computational methods.

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

Linear algebra: matrices, determinants, eigenvalues, eigenvectors, Markov processes. Optimization and least-squares analysis. Ordinary differential equations. Infinite series and Fourier series. Orthogonality and completeness. Introduction to partial differential equations. Applications in electrical and mechanical engineering.

An individual project of guided reading and research culminating in a substantial paper or other piece of work which can be meaningfully evaluated to assign a letter grade; may not be taken on a PA/FL basis. Students engaged in preparation of a senior thesis ordinarily should take Applied Mathematics 99r instead.

Introductory statistical methods for students in the applied sciences and engineering. Random variables and probability distributions; the concept of random sampling, including random samples, statistics, and sampling distributions; the Central Limit Theorem and its role in statistical inference; parameter estimation, including point estimation and maximum likelihood methods; confidence intervals; hypothesis testing; simple linear regression; and multiple linear regression. Introduction to more advanced techniques as time permits.

Ordinary differential equations: power series solutions; special functions; eigenfunction expansions. Review of vector calculus. Elementary partial differential equations: separation of variables and series solutions; diffusion, wave and Laplace equations. Brief introduction to nonlinear dynamical systems and to numerical methods.

Topics in combinatorial mathematics that find frequent application in computer science, engineering, and general applied mathematics. Specific topics taken from graph theory, enumeration techniques, optimization theory, combinatorial algorithms, and discrete probability.

Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problems without the prejudice of trying to apply a particular method of solution. Topics drawn from biology, economics, engineering, physical and social sciences.

Introduction to basic mathematical ideas and computational methods for solving deterministic and stochastic optimization problems. Topics covered: linear programming, integer programming, branch-and-bound, branch-and-cut, Markov chains, Markov decision processes. Emphasis on modeling. Examples from business, society, engineering, sports, e-commerce. Exercises in AMPL, complemented by Maple or Matlab.

An inquiry based and hands on exploration in computational geometry. Topics include: projective geometry (duality between points/lines, symmetry among spheric/planar/hyperbolic geometry), linear algebra (vectors, matrices, symmetry groups) and recursion. We will draw pretty pictures (fractals, tesselations, algebraic curves, etc.). We will write computer programs in Mathematica (and possibly Java, if time permits).

An introduction to nonlinear dynamical phenomena, covering the behavior of systems described by ordinary differential equations. Topics include: stability; bifurcations; chaos; routes to chaos and universality; approximations by maps; strange attractors; fractals. Techniques for analyzing nonlinear systems are introduced with applications to physical, chemical, and biological systems such as forced oscillators, chaotic reactions, and population dynamics.

Theory and techniques for finding exact and approximate analytical solutions of partial differential equations: eigenfunction expansions, Green functions, variational calculus, transform techniques, perturbation methods, characteristics, integral equations, selected nonlinear PDEs including pattern formation and solitons, introduction to numerical methods.

An examination of the mathematical foundations of a range of well-established numerical algorithms, exploring their use through practical examples drawn from a range of scientific and engineering disciplines. Emphasizes theory and numerical analysis to elucidate the concepts that underpin each algorithm. There will be a significant programming component. Students will be expected to implement in Matlab a range of numerical methods through individual and group-based project work to get hands-on experience with modern scientific computing.

Develops skills for computational research with focus on stochastic approaches, emphasizing implementation and examples. Stochastic methods make it feasible to tackle very diverse problems when the solution space is too large to explore systematically, or when microscopic rules are known, but not the macroscopic behavior of a complex system. Methods will be illustrated with examples from a wide variety of fields, ranging from simulating the immune system to strategies for investing in financial markets.

This is a graduate level course on optimization which provides a foundation for applications such as statistical machine learning, signal processing, finance, and approximation algorithms. The course will cover fundamental concepts in optimization theory, modeling, and algorithmic techniques for solving large-scale optimization problems. Topics include elements of convex analysis, linear programming, Lagrangian duality, optimality conditions, and discrete and combinatorial optimization. Exercises and the class project will involve developing and implementing optimization algorithms.

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

AP 50a is the first half of a one-year, team-based and project-based introduction to physics. This course teaches students to develop scientific reasoning and problem-solving skills. AP50a topics include: kinematics; linear and rotational motion; relativity; conservation of momentum and energy; forces; gravitation; and oscillations and waves. Multivariable and vector calculus is introduced and used extensively in the course. Students work in teams on three, month-long projects, each culminating in a project fair. The twice-weekly class periods are all inclusive: there are no separate labs or discussion sections.

Fundamental physical properties of crystalline solids discussed in terms of the basic principles of quantum physics. Crystal structure, energy band structure of metals, semiconductors and insulators. Fermi gas, phonons, thermal properties, electronic transport, optical properties. Low dimensional solids including quantum nanostructures and graphene. Magnetism, superconductivity. Spintronic and photonic applications.

Optical systems and lasers have recently revolutionized both technology and basic research. We cover simple models of light-matter interactions, Fourier optics and holography, light scattering, and optics in biology: single-molecule studies, optical coherence tomography, nonlinear imaging techniques.

Introduction to the physics of soft matter, also called complex fluids or squishy physics, includes the study of capillarity, thin films, polymers, polymer solutions, surfactants, and colloids,. Emphasis is on physical principles which scale bulk behavior. Students will understand the concepts, experimental techniques, and, especially, the open questions. Lecture notes are supplied in place of a textbook.

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

This course will provide the background and an extensive set of examples showing how computational methods are applied to modern design of materials with desired functionality. The methods will span multiple length and time scales, including molecular dynamics simulations, first-principles approaches, stochastic methods for optimization and sampling, and continuum elasticity theory. Examples will include problems in electronic and photonic devices, materials for energy conversion, storage, and environmental protection, and those related to mechanical strength of materials.

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

Kinetic principles underlying atomic motions, transformations, and other atomic transport processes in condensed phases. Application to atomic diffusion, continuous phase transformations, nucleation, growth, coarsening and mechanisms of plastic deformation.

Special topics in materials science.

Theory of the electron liquid, Fermi liquid theory. Ferromagnetism of metals, BCS theory of superconductivity. Lattice models of correlated electrons: antiferromagnetism. Graphene: semi metals and quantum phase transitions. Non-fermi liquids in correlated metals.

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

A survey of systems theory with applications from bioengineering and physiology. Analysis: differential equations, linear and nonlinear systems, stability, the complementary nature of time and frequency domain methods, feedback, and biological oscillations. Applications: nerve function, muscle dynamics, cardiovascular regulation. Laboratory: neural models, feedback control systems, properties of muscle, cardiovascular function.

Fundamental engineering and biological principles underlying field of tissue engineering, along with examples and strategies to engineer specific tissues for clinical use. Students will prepare a paper in the field of tissue engineering, and participate in a weekly laboratory in which they will learn and use methods to fabricate materials and perform 3-D cell culture.

This course will introduce bioelectricity and bioelectromagnetics starting with Maxwell Equations, which will quickly be simplified to the quasi-static form typically applicable in physiology. We will introduce the basics of membrane electrical biophysics, which we will use to study action potentials and action potential propagation. Applications will include electro-cardiograms (ECGs), electro-myograms (EMGs), electro-oculograms (EOGs), and electro-encephalograms (EEGs). EEG investigations will include analyses of spatial resolution as well as dynamic properties. A course project will allow students to choose an area of specific interest for more in-depth investigation and analysis.

A biomaterial is any form of matter that is produced by or interacts with biological systems. One of the pillars of biomedical engineering is to use naturally derived and synthetic biomaterials to treat, augment, or replace human tissues. This course examines the structure, properties and processing of biomaterials.

The Internet operates in layers, and so does much of the technology that hooks up to it: PCs, mobile phones, tablets. Nearly two decades ago those platforms were conceptually simple: a "generative" base offered by one manufacturer, on which any third party could build. (Think: Windows and the programs that run on it.) Some efforts by platform makers to tip the scales in their favor in the layer above resulted in extended controversy and regulatory efforts, such as over Windows coming bundled with Internet Explorer. Today platforms are just as vital but far more complex. We have hybrids like the iOS and Android operating systems or the Facebook and Twitter platforms, where the platform makers offer their systems as services rather than products, influencing and sometimes outright limiting connection between users and independent developers for those platforms. How should we think about these new platforms? What counts as a "level playing field," and what responsibility, if any, is there for public authorities to enforce it? What lessons, if any, do the prior tangles offer for today?

Introduction to the intellectual enterprises of computer science and the art of programming. This course teaches students how to think algorithmically and solve problems efficiently. Topics include abstraction, algorithms, data structures, encapsulation, resource management, security, software engineering, and web development. Languages include C, PHP, and JavaScript plus SQL, CSS, and HTML. Problem sets inspired by real-world domains of biology, cryptography, finance, forensics, and gaming. Designed for concentrators and non-concentrators alike, with or without prior programming experience.

Abstraction and design in computation. Topics include functional and object-oriented styles of programming, software engineering in the small, and models of computation. Our main goal is to understand how to design large programs to make them readable, maintainable, elegant, and efficient. Exercises in OCaml.

This seminar will examine the individuals and institutions that control the Internet, and how the Internet affects the distribution and operation of power, broadly conceived. We will examine technologies of control (such as surveillance, censorship, propaganda, and use control) and of evading control, the individuals and institutions that seek to regulate the Internet (such as governments, the IETF, and hackers), the relationship between cybersecurity, national security, and Internet governance, the economics of Internet communications, and more.

Cooperative design, development, and testing of a sizable and realistic computer system. Students work as a group with a client on a real-world open-ended problem, and gain experience in problem definition, software development, and system lifecycle issues, and in the area of application. Students work in groups; both student participation in the classroom and effective group cooperation outside the classroom are stressed.

Learning from data in order to gain useful predictions and insights. This course introduces methods for five key facets of an investigation: data wrangling, cleaning, and sampling to get a suitable data set; data management to be able to access big data quickly and reliably; exploratory data analysis to generate hypotheses and intuition; prediction based on statistical methods such as regression and classification; and communication of results through visualization, stories, and interpretable summaries. Built around three modules: prediction and elections, recommendation and business analytics, and sampling and social network analysis.

Design and analysis of efficient algorithms and data structures. Algorithm design methods, graph algorithms, approximation algorithms, and randomized algorithms are covered.

Algorithms to guarantee privacy and authenticity of data during communication and computation. Proofs of security based on precise definitions and assumptions. Topics may include one-way functions, private-key and public-key encryption, digital signatures, pseudorandom generators, zero-knowledge proofs, fully homomorphic encryption, and the role of cryptography in network and systems security.

Networking has enabled the emergence of mobile and cloud computing, creating the most important technological paradigm shift in computing of the past decade. Further advancements in networking are expected to similarly transform the technological landscape over the next decade through the emergence of the Internet of Things and gigabit wireless networks. In order to play a role in this era of new network-powered advancements, students must have a thorough understanding of emerging networking topics. Rather than teaching the basic networking protocols, which have become very mature and can be treated as a black box, in CS 143, we will teach the new issues and topics of interest which will power important emerging applications. This focus on upcoming applications is the motivation for CS 143 this semester. The class will be organized into the following nine modules: Basic Networking Concepts: Protocol Layering; Internet of Things: All-service Bluetooth Low Energy (BLE); Data Center Networking: Software Defined Networking; Web-scale Networking: Distributed Cloud Computing and Virtual Machine Migration; Content Networks: Video Streaming; Network Security: Defense Against Protocol Exploitation; Wireless Networking: Wireless Mesh, Geographic Routing; Machine Learning Assisted Networking: End-to-end Application Adaptive Protocols; Cyber-physical Networks: Vehicular Networking. Students will have the opportunity to implement the concepts learned in the course through programming assignments, read and discuss the latest networking literature, and design and implement a final project.

Review of the fundamental structures in modern processor design. Topics include computer organization, memory system design, pipelining, and other techniques to exploit parallelism. Emphasis on a quantitative evaluation of design alternatives and an understanding of timing issues.

Comprehensive introduction to the principal features and overall design of both traditional and modern programming languages, including syntax, formal semantics, abstraction mechanisms, modularity, type systems, naming, polymorphism, closures, continuations, and concurrency. Provides the intellectual tools needed to design, evaluate, choose, and use programming languages.

The fundamental principles of resource management and abstraction in modern operating systems. Control abstractions: threads, processes, scheduling, synchronization. Storage abstractions: dynamic memory allocation, virtual memory, file system design. Communication abstractions: interprocess communication, networking. Case studies. Design and implementation of parts of a multiuser multitasking virtual-memory operating system.

We are in the big data era and data systems sit in the critical path of everything we do, i.e., in businesses, in sciences, as well as in everyday life. This course will be a comprehensive introduction to modern data systems. The primary focus of the course will be on modern trends that are shaping the data management industry right now such as column-store and hybrid systems, shared nothing architectures, cache conscious algorithms, hardware/software codesign, main memory systems, adaptive indexing, stream processing, scientific data management, and key value stores. We will also study the history of data systems and traditional and seminal concepts and ideas such as the relational model, row-store database systems, optimization, indexing, concurrency control, recovery and SQL in order to understand both how data systems have evolved over the years and why, as well as how these concepts apply today and how data systems might evolve in the future.

This course covers the fundamentals of 3D computer graphics using a modern shader-based version of OpenGL. Main topics include: geometric coordinate systems and transformations, keyframe animation and interpolation, camera simulation, triangle rasterization, material simulation, texture mapping, image sampling and color theory. The course also touches on ray tracing, geometric modeling and simulation-based animation.

Introduction to machine learning, providing a probabilistic view on artificial intelligence and reasoning under uncertainty. Topics include: supervised learning, ensemble methods and boosting, neural networks, support vector machines, kernel methods, clustering and unsupervised learning, maximum likelihood, graphical models, hidden Markov models, inference methods, and computational learning theory. Students should feel comfortable with multivariate calculus, linear algebra, probability theory, and complexity theory. Students will be required to produce non-trivial programs in Python.

The interplay between economic thinking and computational thinking as it relates to electronic commerce, social networks, collective intelligence and networked systems. Topics covered include: game theory, peer production, reputation and recommender systems, prediction markets, crowd sourcing, network influence and dynamics, auctions and mechanisms, privacy and security, matching and allocation problems, computational social choice and behavioral game theory. Emphasis will be given to core methodologies, with students engaged in theoretical, computational and empirical exercises.

Building autonomous robotic systems requires understanding how to make robots that observe, reason, and act. Each component uses many engineering principles: how to fuse, multiple, noisy sensors; how to balance short-term versus long-term goals; how to control one's actions and how to coordinate with others. This year, we will study these questions in the context of a project to develop autonomous robot soccer teams. The class format will mix seminar and lab formats.

This is a project-based course emphasizing designing, building, testing, maintaining and modifying software for scientific computing. Students will work in groups on a number of projects, ranging from small data-transformation utilities to large-scale systems. Students will learn to use a variety of tools and languages, as well as various techniques for organizing teams. Most important, students will learn to fit tools and approaches to the problem being solved.

Covers topics related to algorithms for big data, especially related to networks. Themes include compression, cryptography, coding, and information retrieval related to the World Wide Web. Requires a major final project.

Advanced algorithm design, including but not limited to amortization, randomization, online algorithms, graph algorithms, approximation algorithms, linear programming, and data structures.

Topics in cryptography and data privacy drawn from the theoretical computer science research literature. Focus for 2014-15: Differential Privacy -- a mathematical framework for privacy-preserving analysis of datasets, which enables aggregate computations while preventing the leakage of individual-level information.

Biology abounds with step by step processes, whether in evolution, neural activity, development, or protein circuits. In many of these neither the actual steps taken nor the outcomes are well understood. Computer science is the study of step by step processes and offers an approach to understanding them as they occur in biology. Students will read, present, and critically evaluate research papers in this area.

The contents and course requirements are similar to those of Computer Science 146, with the exception that students enrolled in Computer Science 246 are expected to undertake a substantial course project.

The contents and course requirements are similar to those of Computer Science 148, with the exception that students enrolled in Computer Science 248 are expected to do a substantial design project and paper discussions on advanced topics.

Seminar course exploring recent research in programming languages. Topics vary from year to year. Students read and present research papers, undertake a research project.

An introduction to operating systems research. Paper-based seminar course that introduces students to the state of the art in systems research through historical and quantitative lenses. Students will read and discuss research papers and complete a final research project.

Big data is everywhere. A fundamental goal across numerous modern businesses and sciences is to be able to exploit as many machines as possible, to consume as much information as possible and as fast as possible. The big challenge is "how to turn data into useful knowledge". This is far from a simple task and a moving target as both the underlying hardware and our ability to collect data evolve. In this class, we will discuss how to design data systems and algorithms that can "scale up" and "scale out". Scale up refers to the ability to use a single machine to all its potential, i.e., to exploit properly the memory hierarchy and the multiple CPU and GPU cores. Scale out refers to the ability to use more than 1 machines (typically 100s or 1000s) effectively. This is a research oriented class. Every week we will read two modern research papers; one from the scale up area and one from the scale out area. We will use examples from several areas, including relational systems and distributed databases, graph processing systems (i.e., for social networks), key value stores, noSQL and newSQL systems as well as mobile computing. Each student will work on a semester long data systems research project (in groups of 2-4 students) which can be in any of the above areas and will be based on an open research problem.

Advanced course in computer graphics focusing on image rendering and processing. Topics include: light transport, efficient rendering, image based rendering, texture processing, interactive image processing.

Seminar course exploring research directions in artificial intelligence (AI), typically combining two or more of such areas as multi-agent systems, natural-language processing, machine learning, reasoning under uncertainty, representation systems. Topic for Spring 2015: Multi-agent systems teamwork and plan management.

The focus of the Spring 2015 course will be reinforcement learning, a framework for solving problems involving a sequence of decisions with uncertain outcomes. This course will cover the fundamental theory through readings of classic papers and build practical intuition through coding assignments. Topics will include Markov decision process and partially observable Markov decision processes, planning under uncertainty, model-free and model-based reinforcement learning, function approximation in reinforcement learning, and batch reinforcement learning.

Topics on the design and analysis of algorithms, processes, and systems related to crowds and social networks. Readings in AI, theoretical CS, machine learning, social science theory, economic theory, and operations research.

Interplay between computation and economics. Topics in electronic commerce, computational social choice, computational mechanism design, peer production, prediction markets and reputation systems. Readings in AI, theoretical CS, multi-agent systems, economic theory, and operations research.

Seminar course exploring recent research in computer vision. Topics vary from year to year, typically including object recognition; activity recognition; and visual surveillance. Students read and present research papers and undertake a research project.

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

An integrative introduction to engineering sciences. Combines classroom discussion with activity-based learning, and emphasizes concepts that span multiple disciplines. Covers topics having direct societal impact, and presents them in historical context. Involves qualitative and quantitative analysis, mathematical modeling, and design. Introduces common engineering software and hardware tools.

This course teaches students to generate, develop and realize breakthrough ideas for social and cultural change. Students form groups of four to five around one of four seed ideas. Over the course of the semester students mold their idea, learn idea translation skills, and develop idea proposals they pitch at the end of the semester. Students have the opportunity to apply for Idea Translation Fellowships, funded by the Wyss Institute and the Harvard Global Health Institute. Winners are funded to develop their ideas further over the course of the summer starting with a week long workshop with students from around the world at Le Laboratoire Cambridge. Students brainstorm, give public presentations, and write final group reports. Students also engage in studio practice with artists, designers, technologists, and scientists. Case study and conceptual readings will complement student idea exploration.

Multi-disciplinary course for students interested in designing products and services that are simple, irresistible, delightful, cool, covetable, viral, and, in today's competitive market, increasingly much more likely to be successful. Students study real world cases of exceptionally designed products and services (from Apple, Gucci, Zipcar and more) strategically design for desirability (via status, belonging, usability, etc.). In weekly design challenges, students use analogical transfer to apply these insights to diverse industries and target markets (e.g., health literacy campaigns, declining technologies, the future of luxury). Each week we prototype using different software and constraints, helping students to flexibly work across tools, with weekly prototyping workshops help supplement students' skills across prototyping areas. Weekly critiques enable students to develop their own design point of view and to finish with a diverse design portfolio.

This Seminar/Workshop will look into the design and technical challenges involved in the development of web based interfaces for collaborative and participatory design scenarios where more than one agents are involved. The designer in a sense is given the chance to design and experiment with the communication architecture and temporality of the design process itself. Students will be introduced to web technologies for front end and back end development [javascript, webGL, nodeJS, MongoDB].

This is an introductory course to computational design and the prerequisite for a spring course that deals with more advanced topics in the field. This course is primarily intended for designers with little background in programming who are interested in developing their skills in order to be able to better understand, interface with and customize the digital tools they are using, or develop their own software and interactive applications. The course introduces students to fundamental concepts and techniques in computational design. By the term "computational design" we mean an ad hoc set of methods borrowed from computer science, computational geometry and other fields, and adapted to specific design problems such as design development, fabrication, analysis, interaction and communication.

A first course in the design and construction of mechanical and electromechanical devices. Engineering graphics and sketching; dimensions and tolerances. Introduction to materials selection and structural design. Machine elements and two-dimensional mechanisms; DC motors. Design methodology. Emphasis on laboratory work and design projects using professional solid modeling CAD software and numerically controlled machine tools.

A foundation in human organ systems physiology, including cardiac, respiratory, renal, gastrointestinal, and neural systems. Quantitative description of organ systems function and control in terms of physical principles and physiologic mechanisms. Simple mathematical models representing key aspects of organ systems function. Emphasis will be given to understanding the ways in which dysfunction in these systems gives rise to common human disease processes.

Students do field-based work in entrepreneurship to develop their existing startup and explore new ideas and opportunities for startup design. The course is for students seeking innovation experience as a founder of a startup. Students may work individually; teams 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. Students will share their work regularly and engage in a peer-to-peer feedback forum. The coursework is customized to the needs of each student and their startup role and includes development of product, technology, market, business, organization and leadership.

Individual engineering design projects which demonstrate mastery of engineering knowledge and techniques. During the year, each student will pursue an appropriate capstone project which involves both engineering design and quantitative analysis and culminating in a final oral presentation and final report/thesis.

Introduces the fundamental statistical and mapping tools needed for analysis of environmental systems. Topics will be linked by environmental and social themes and will include GIS concepts; data models; spatial statistics; density mapping; buffer zone analysis; surface estimation; map algebra; suitability modeling. Students will acquire technical skills in both mapping and spatial analysis. Software packages used will include ArcGis. There will be guest lectures by researchers and practitioners who use GIS for spatial analysis.

Many complex physical problems defy simple analytical solutions or even accurate analytical approximations. Scientific computing can address certain of these problems successfully, providing unique insight. This course introduces some of the widely used techniques in scientific computing through examples chosen from physics, chemistry, and biology. The purpose of the course is to introduce methods that are useful in applications and research and to give the students hands-on experience with these methods.

Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problems without the prejudice of trying to apply a particular method of solution. Topics drawn from biology, economics, engineering, physical and social sciences.

Introduction to basic mathematical ideas and computational methods for solving deterministic and stochastic optimization problems. Topics covered: linear programming, integer programming, branch-and-bound, branch-and-cut, Markov chains, Markov decision processes. Emphasis on modeling. Examples from business, society, engineering, sports, e-commerce. Exercises in AMPL, complemented by Maple or Matlab.

Modeling and analysis of mechanical and electromechanical systems. Topics include 3D rigid body dynamics, resonance, damping, frequency response, Laplace transform methods, Lagrange's equations, multiple degree-of-freedom systems and an introduction to nonlinear vibration, continuous systems, and control. Analytical modeling will be supplemented with numerical simulations and lab experiments. Laboratory exercises will explore vibration, stabilization, and nonlinear systems using data acquisition systems.

Basic observations and theoretical understanding of ocean phenomena from local surface beach waves to the effects of the oceans on global climate. Observations and dynamics of ocean waves, currents, turbulence, temperature and salinity distributions; basic fluid dynamics equations; the ocean's role in climate: wind-driven circulation and the Gulf Stream, thermohaline circulation and the potential instability of Europe's climate, El Nino, the oceans and global warming.

Physical and chemical processes determining the composition of the atmosphere and its implications for climate, ecosystems, and human welfare. Construction of atmospheric composition models. Atmospheric transport. Nitrogen, oxygen, and carbon cycles. Climate forcing by greenhouse gases and aerosols. Stratospheric ozone. Oxidizing power of the atmosphere. Surface air pollution: aerosols and ozone. Deposition to ecosystems: acid rain, nitrogen, mercury.

This course provides a systematic introduction to the energy system for students in engineering and applied sciences. Students should gain a working understanding of the some of the most important energy technologies, from prime movers--gas turbines, steam cycles, and reciprocating engines--to secondary energies including fuel production and refining technologies and the electricity transmission and distribution system. The course aims at a systematic understanding of the energy system's environmental footprint as a tool to help students who will work to reduce it. Energy is a commodity. One cannot hope to re-shape the energy system to meet environmental constrains without a rough working understanding of energy markets--costs, prices and elasticities of supply and demand. So the course will integrate engineering economics and other applied social sciences into the treatment of energy technologies to enable a system's view of energy.

This course introduces students to probability theory and statistics, and their applications to physical, biological and information systems. Topics include: random variables, distributions and densities, conditional expectations, Bayes' rules, laws of large numbers, central limit theorems, Markov chains, Bayesian statistical inferences and parameter estimations. The goal of this course is to prepare students with adequate knowledge of probability theory and statistical methods, which will be useful in the study of several advanced undergraduate/graduate courses and in formulating and solving practical engineering problems.

A lab-intensive introduction to electronic circuit design. Develops circuit intuition and debugging skills through daily hands-on lab exercises, each preceded by class discussion, with minimal use of mathematics and physics. Moves quickly from passive circuits, to discrete transistors, then concentrates on operational amplifiers, used to make a variety of circuits including integrators, oscillators, regulators, and filters. The digital half of the course treats analog-digital interfacing, emphasizes the use of microcontrollers and programmable logic devices (PLDs).

General properties of common biosignals, Bioelectrical (electrophysiological), Biomechanical, Biomagnetic , and Biochemical signals, Bioelectrical acquisition process. Brief discussion of bio-signals obtained from tomography and inverse imaging. Brief introduction to underlying principles of MRI, Ultrasound, CT-Scan, PET, and SPECT, and their associated signals, inverse imaging, ill-posed problems and regularization. Non-transformed and transformed methods for biosignal processing. Structural and Graphical descriptions. Overview of Fourier transforms, Sine and cosine transform, Wavelet transform, Principle Component Analysis, dimension reduction techniques. Blind Source Separation, Representation models based on the statistical independence of the underlying sources, Independent component analysis (ICA), Dependent component analysis, Independent Subspace separation, Pattern Recognition, neural networks, clustering, and genetics algorithms. Applications to Biosignal Processing, and Human computer interaction.

This course provides an introduction to feedback and control in physical, biological, engineering, information, financial, and social sciences. The focus is on the basic principles of feedback and its use as a tool for inferring and/or altering the dynamics of systems under uncertainty. Key themes throughout the course will include linear system analysis, state/output feedback, frequency response, reference tracking, PID controller, dynamic programming, and limit of performance. This includes both the practical and theoretical aspects of the topic.

This course will examine the theory and practical application of environmental chemistry and toxicology for assessing the behavior, toxicity and human health risks of chemical contaminants in the environment. The goals of the course are to: (a) illustrate how various sub-disciplines in environmental toxicology are integrated to understand the behavior of pollutants; (b) demonstrate how scientific information is applied to inform environmental management decisions and public policy through several case studies; and (c) provide an introduction to the legislative framework in which environmental toxicology is conducted. This course will be directed toward undergraduate students with a basic understanding of chemistry and calculus and an interest in applied science and engineering to address environmental management problems.

This course is focused on aspects of environmental engineering related to the fate, transport, and control of pollution in aquatic ecosystems. The course will cover human impacts to water resources; the sources and ecological impacts of environmental contaminants; quantitative models of the fate and transport of pollutants in natural aquatic ecosystems; best management practices for the prevention and control of pollution; and sustainable natural treatment systems for water quality improvement.

Introduces the fundamentals of water biology, chemistry, physics and transport processes needed to understand water quality and water purification technologies. Practical instruction in basic water analyses concluding with a final water treatment project in place of exam.

Quantum mechanics provides not only an essential tool for engineers, material scientists and biologists to study and control objects in nano and atomic scales but also radical ways to do information processing, sensing, and fabrication. Advances in nanotechnology and quantum information processing raise growing interests in engineering students to learn applied quantum mechanics that is also essential for understanding modern devices and systems in electronics photonics. Topics of this course will cover topics ranging from solution of Schrodinger equation in quantum confined nano-structures and most recent topics such as quantum circuits and entanglement. Examples, problems and numerical simulation are designed to address the applications of the course contents to real problems in semiconductor electronics, optoelectronics, photonics, quantum information processing and superconducting electronics.

The course will provide an overview of the solid state device physics and p-n junction operation necessary to understand the operation. Several different solar architectures will be discussed including crystalline and amorphous silicon, multijunction, CdTe, CIGS, organic, dye sensitized as well as additional related topics light management, building integrated devices, and policy and economic issues relating to adoption.

Introduction to micro- and nanofabrication processes used for photonic and electronic devices. Students use state-of-the-art cleanroom in Center for Nanoscale Systems to fabricate transistors and light-emitting diodes (LEDs). Lectures on fabrication processes, including lithography, deposition, etching, oxidation, implantation, diffusion and electrical characterization.

The macroscopic description of the fundamentals of heat transfer and applications to practical problems in energy conversion, electronics and living systems with an emphasis on developing a physical and analytical understanding of conductive, convective and radiative heat transfer. Emphasis will also be given to problem solving skills based on applying governing principles, mathematical models and physical intuition. Includes laboratory sessions and semester-long projects.

Introductory statistical methods for students in the applied sciences and engineering with a focus on social networks. Random variables and probability distributions; the concept of random sampling, including random samples, statistics, and sampling distributions; role of statistics in social network analysis; mathematical interpretation of social networks; connections and homophily, propinquity, mutuality/reciprocity, multiplexity, network closure; distributions and bridges, distance, centrality, density; segmentation and cliques, cohesion, clustering; graph theory and adjacency matrices; Erdos-Renyi model; Watts-Strogatz Small World model; Barabasi -Albert (BA) Preferential Attachment model; special topics in social network analysis.

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.

Climate change, health insurance reform, space exploration, the teaching of science and a host of other issues - today Americans confront more and more important public debates in which the argument hangs on technical issues. On the whole, however, they have difficulty dealing with these issues, in large part because the scientists and engineers who could help them are missing from the debate. This course is designed for graduate students in engineering and the biological and physical sciences who are interested in learning how to engage with the public on these and other issues. It also offers useful guidance on how to explain their own work - writing, speaking and online - intelligently and intelligibly.

A sophisticated perspective on the design, construction, and testing of model physiological systems recapitulated with tissue engineering and lab on a chip technologies. Topics include organ and multiorgan physiology and pathophysiology; in vitro disease models; and design tools and fabrication techniques for lab on a chip technologies.

Continuum mechanics; conservation of mass and momentum, energy; stress, kinematics, and constitutive equations; vector and tensor calculus. Dimensional analysis and scaling. Navier-Stokes equations, Reynolds number. Solutions for simple flow states. Low Reynolds number flows; porous media flows; lubrication theory; gravity currents. Inviscid flows, Kelvin circulation theorem, Bernoulli integrals, Vortical flows. Waves in fluids; acoustics, shocks, water waves. Airfoil theory. Boundary layers. Flow instabilities. Mixing, and turbulence in unbounded and bounded flows.

This is a combined introductory graduate/upper-level undergraduate course that focuses on examining modern techniques for manipulating cellular behavior and the application of these techniques to problems in the biomedical and biotechnological arenas. Topics will include expanding the genetic code, genetic circuits, rewiring signaling pathways, controlling behavior through cell-matrix interactions, and directed differentiation of stem cells. Lectures will review fundamental concepts in cell biology before delving into topical examples from current literature. Students will work individually and in teams to determine the boundaries of existing cellular engineering techniques using scientific literature and propose original research to address unmet technological needs.

Project-based course on the design of medical devices to address needs identified by hospital-based clinicians. Students work in teams with physicians to develop a novel device. The design process includes: needs finding; problem identification; prior art searches; strategy and concept generation; estimation; sketching; sketch modeling; machine elements, ergonomics and prototyping.

Principles governing energy generation and interconversion. Current and projected world energy use. Selected important current and anticipated future technologies for energy generation, interconversion, storage, and end usage.

Principles governing energy generation and interconversion. Current and projected world energy use. Selected important current and anticipated future technologies for energy generation, interconversion, storage, and end usage.

This is a field study course in which students undertake significant external research in the in-depth development of a business plan for a health-care and technology business venture. Students will learn to develop such a business plan, evaluate and select appropriate technologies, define a new technology based product in the health-care space, and develop appropriate prototypes for presentation to customers and investors.

This course is designed for those who want to understand the role of start-ups and venture capital in the creation of new products and services in the for-profit and not-for-profit sectors. It is intended to help students identify areas in which changes in science and technology, consumer and social attitudes, or political and regulatory processes support the creation of new businesses and organizations in independent ventures or within established organizations. Margo Seltzer and Bill Anderson are supporting the course by supervising course projects in their respective areas of expertise.

Foundations of continuum mechanics, development of elasticity theory, and introduction to plasticity and creep. Elastic waves. Basic elasticity solutions. Variational principles.

Finite elements for analysis and design. The key goal of this class is the application of the finite element method to classical and state-of-the-art modeling and design problems. We introduce a commercial finite element program - ABAQUS - and demonstrate how to use it in modeling and analysing design problems. Topics include the implementations of user-defined subroutines (UMAT and VUMAT), instability analyses, analysis of waves propagation, fluid-structure interactions.

Fundamentals of fracture with applications in materials and structural mechanics. Micromechanics of fracture in ceramics, metals, and polymers. Fracture of composite materials. Interfacial fracture mechanics. Fatigue crack propagation.

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 will introduce bioelectricity and bioelectromagnetics starting with Maxwell Equations, which will quickly be simplified to the quasi-static form typically applicable in physiology. We will introduce the basics of membrane electrical biophysics, which we will use to study action potentials and action potential propagation. Applications will include electro-cardiograms (ECGs), electro-myograms (EMGs), electro-oculograms (EOGs), and electro-encephalograms (EEGs). EEG investigations will include analyses of spatial resolution as well as dynamic properties. A course project will allow students to choose an area of specific interest for more in-depth investigation and analysis.

Today, robotic devices are being made from folded paper, carbon laminates or soft gels. Rather than assembled, they can be formed directly from 2D or 3D printer. These Informal robots are light, flexible, compliant, highly customized, and demonstrate programmable behavior that is closely coupled with material composition. Taught in collaboration with the Wyss Institute, the course will focus on techniques to create original robotic devices. Lectures will be organized along four primary topics: Kinematics, Fabrication, Controls and Applications. There will be assignments to produce test mechanisms and CAD models, followed by semester-long group projects.

The course focuses on the engineering, infrastructure and institutions needed to manage water on a basin and city scale. The course does this using the case study method. All cases are presented by practitioners who have had deep engagement with the cases.

Physics and chemistry of aerosol particles. Concepts: size, shape, and density; number size distributions; uniform, accelerated, and Brownian motion; electrical properties; measurement instrumentation; condensation/evaporation; coagulation; and optical properties. Taught by reference to topical problems.

Introduces students to the environmental aspects of nanoscience and nanotechnology. We will study the fundamental physical chemical properties, characterization, environmental implications, and environmental applications of nanoparticles and nanomaterials. Case studies from recent publications on engineered carbon nanomaterials such as fullerenes, carbon nanotubes, and graphene will be discussed.

Design of RF and high speed integrated communication circuits at both transistor and system levels.

Electronic structure of crystals. Semiconductor heterostructures: bandstructure engineering. Low-dimensional solids: quantum wells, wires and dots; superlattices; 2D electron gas; carbon nanotubes, nanowires, graphene. Tunneling and resonant tunneling, superlattice transport. Quantum point contacts. Interband and intersubband optical transistions. Quantum confined Stark effect. Device concepts (diodes, transistors, lasers). Quantum well lasers, modulators and detectors. Resonant tunneling devices. Quantum cascade lasers.

This course introduces student to the rapidly emerging, multi-disciplinary and exciting field of MicroElectroMechanical Systems (MEMS). It teaches fundamentals of micro machining and Micro fabrication techniques, including planar thin-film process technologies, photolithography and soft-lithography techniques, deposition and etching techniques, and surface, bulk, and electroplating micro machining technologies.

Unpacking the dynamics of getting transformational policy reforms over the line. An examination of case studies in the design and implementation of successful reforms in water, fishery, natural resource and environmental management.

This course explores research methods and techniques through the analyses of emerging energy-efficient materials and systems and their applications in buildings. It serves as an interdisciplinary platform for engineers, materials and computer scientists to interact with the design students and develop new products. The course introduces ideas-to-innovation processes in a hands-on, project/product focused manner that balance engineering concepts with promising, real-world opportunities. Switching back and forth between guided discovery and focused development, between bottom-up and top-down thinking, and market analyses, the course helps students establish generalizable frameworks as researchers and innovators with a focus on new and emerging technologies.

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