Fundamentals of linear systems, and abstraction modeling of multi-physics lumped and distributed systems using lumped electrical circuits. Linear networks involving independent and dependent sources, resistors, capacitors, and inductors. Extensions to include operational amplifiers and transducers. Dynamics of first- and second-order networks; analysis and design in the time and frequency domains; signal and energy processing applications. Design exercises. Weekly laboratory with microcontroller and transducers.

Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design.

Introduction to computer science and programming. Students develop skills to program and use computational techniques to solve problems. Topics include: the notion of computation, Python, simple algorithms and data structures, object-oriented programming, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of 6.100A and 6.100B (or 16.C20) counts as REST subject.

Provides an introduction to the design of digital systems and computer architecture. Emphasizes expressing all hardware designs in a high-level hardware description language and synthesizing the designs. Topics include combinational and sequential circuits, instruction set abstraction for programmable hardware, single-cycle and pipelined processor implementations, multi-level memory hierarchies, virtual memory, exceptions and I/O, and parallel systems.

Lab-intensive subject that investigates digital systems with a focus on FPGAs. Lectures and labs cover logic, flip flops, counters, timing, synchronization, finite-state machines, digital signal processing, communication protocols, and modern sensors. Prepares students for the design and implementation of a large-scale final project of their choice: games, music, digital filters, wireless communications, video, or graphics. Extensive use of System/Verilog for describing and implementing and verifying digital logic designs.

A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression, and identification). Concepts are introduced with lectures and online problems, and then mastered during weekly labs. In lab, students model, design, test, and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g., optimizing thrust-driven positioners or stabilizing magnetic levitators). Students taking graduate version complete additional problems and labs.

Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design. Enrollment may be limited.

Introduces the design and construction of power electronic circuits and motor drives. Laboratory exercises include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating. Basic electric machines introduced include DC, induction, and permanent magnet motors, with drive considerations. Provides instruction in written and oral communication. Students taking independent inquiry version 6.2221 expand the scope of their laboratory project. Enrollment limited.

Study of electromagnetics and electromagnetic energy conversion leading to an understanding of devices, including electromagnetic sensors, actuators, motors and generators. Quasistatic Maxwell's equations and the Lorentz force law. Studies of the quasistatic fields and their sources through solutions of Poisson's and Laplace's equations. Boundary conditions and multi-region boundary-value problems. Steady-state conduction, polarization, and magnetization. Charge conservation and relaxation, and magnetic induction and diffusion. Extension to moving materials. Electric and magnetic forces and force densities derived from energy, and stress tensors. Extensive use of engineering examples. Students taking graduate version complete additional assignments.

Provides an introduction to using computation to build models that can be used to help understand real-world phenomena. Topics include optimization problems, simulation models, and statistical models. Requires experience programming in Python as a prerequisite. Combination of 6.100A and 6.100B counts as REST subject.

Provides instruction in aspects of effective technical oral presentations and exposure to communication skills useful in a workplace setting. Students create, give and revise a number of presentations of varying length targeting a range of different audiences.

An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments.

Fosters deep understanding and intuition that is crucial in innovating analog circuits and optimizing the whole system in bipolar junction transistor (BJT) and metal oxide semiconductor (MOS) technologies. Covers both theory and real-world applications of basic amplifier structures, operational amplifiers, temperature sensors, bandgap references. Covers topics such as noise, linearity and stability. Homework and labs give students access to CAD/EDA tools to design and analyze analog circuits. Provides practical experience through lab exercises, including a broadband amplifier design and characterization. Students taking graduate version complete additional assignments.

Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem. Credit cannot also be received for 6.041A or 6.041B.

Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful.

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Mechanical vibrations and waves; simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations, and normal modes; vibrations of continuous systems; reflection and refraction; phase and group velocity. Optics; wave solutions to Maxwell's equations; polarization; Snell's Law, interference, Huygens's principle, Fraunhofer diffraction, and gratings.

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Instruction in effective undergraduate research, including choosing and developing a research topic, surveying previous work and publications, research topics in EECS and the School of Engineering, industry best practices, design for robustness, technical presentation, authorship and collaboration, and ethics. Students engage in extensive written and oral communication exercises, in the context of an approved advanced research project. A total of 12 units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult EECS SuperUROP website for more information.

Introduces the fundamentals of applied quantum mechanics, materials science, and fabrication skills needed to design, engineer, and build emerging nanodevices with diverse applications in energy, memory, display, communications, and sensing. Focuses on the application and outlines the full progression from the fundamentals to the implemented device and functional technology. Closely integrates lectures with design-oriented laboratory modules. 

Individual research project arranged with appropriate faculty member or approved advisor. Forms and instructions for the final report are available in the EECS Undergraduate Office.

Vector spaces, linear operators, and matrix representations.  Inner products and adjoint operators. Commutator identities. Dirac's Bra-kets. Uncertainty principle and energy-time version. Spectral theorem and complete set of commuting observables. Schrodinger and Heisenberg pictures.  Axioms of quantum mechanics. Coherent states and nuclear magnetic resonance. Multiparticle states and tensor products. Quantum teleportation, EPR and Bell inequalities. Angular momentum and central potentials. Addition of angular momentum. Density matrices, pure and mixed states, decoherence.

Introduction to C and assembly language for students coming from a Python background (6.100A). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions.

Introduces the fundamentals of machine tools use and fabrication techniques. Students work with a variety of machine tools including the bandsaw, milling machine, and lathe. Mechanical Engineering students are advised to take this subject in the first IAP after declaring their major. Enrollment may be limited due to laboratory capacity. Preference to Course 2 majors and minors.

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems.

First in a two-term advanced laboratory sequence in modern physics focusing on the professional and personal development of the student as a scientist through the medium of experimental physics. Experimental options cover special relativity, experimental foundations of quantum mechanics, atomic structure and optics, statistical mechanics, and nuclear and particle physics. Uses modern physics experiments to develop laboratory technique, systematic troubleshooting, professional scientific attitude, data analysis skills and reasoning about uncertainty. Provides extensive training in oral and written communication methods.

Exposes students to the models and methods of engineering leadership within the contexts of conceiving, designing, implementing and operating products, processes and systems. Introduces the Capabilities of Effective Engineering Leaders, and models and theories related to the capabilities. Discusses the appropriate times and reasons to use particular models to deliver engineering success. Includes occasional guest speakers or panel discussions. May be repeated for credit once with permission of instructor. Preference to first-year students in the Gordon Engineering Leadership Program.

Advances students' leadership, teamwork, and communication skills through further exposure to leadership frameworks, models, and cases within an engineering context in an interactive, practice-based environment. Students coach others, assess performance, and lead guided reflections on individual and team successes, while discovering opportunities for improvement. Students assist with programmatic planning and implementation of role-play simulations, small group discussions, and performance and peer assessments by and of other students and by instructors. Includes frequent engineering industry-guest participation and involvement. Content is frequently student-led. Second year Gordon Engineering Leadership Program (GEL) Program students register for 6.9130. Preference to students enrolled in the second year of the Gordon-MIT Engineering Leadership Program.

Introduction to computer science and programming. Students develop skills to program and use computational techniques to solve problems. Topics include: the notion of computation, Python, simple algorithms and data structures, object-oriented programming, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of 6.100A and 6.100B (or 16.C20) counts as REST subject.

Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design. Enrollment may be limited.

Fundamentals of linear systems, and abstraction modeling of multi-physics lumped and distributed systems using lumped electrical circuits. Linear networks involving independent and dependent sources, resistors, capacitors, and inductors. Extensions to include operational amplifiers and transducers. Dynamics of first- and second-order networks; analysis and design in the time and frequency domains; signal and energy processing applications. Design exercises. Weekly laboratory with microcontroller and transducers.

Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited.

Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful.

Provides an introduction to the design of digital systems and computer architecture. Emphasizes expressing all hardware designs in a high-level hardware description language and synthesizing the designs. Topics include combinational and sequential circuits, instruction set abstraction for programmable hardware, single-cycle and pipelined processor implementations, multi-level memory hierarchies, virtual memory, exceptions and I/O, and parallel systems.

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design.

Lab-intensive subject that investigates digital systems with a focus on FPGAs. Lectures and labs cover logic, flip flops, counters, timing, synchronization, finite-state machines, digital signal processing, communication protocols, and modern sensors. Prepares students for the design and implementation of a large-scale final project of their choice: games, music, digital filters, wireless communications, video, or graphics. Extensive use of System/Verilog for describing and implementing and verifying digital logic designs.

Provides an introduction to using computation to build models that can be used to help understand real-world phenomena. Topics include optimization problems, simulation models, and statistical models. Requires experience programming in Python as a prerequisite. Combination of 6.100A and 6.100B counts as REST subject.

A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression, and identification). Concepts are introduced with lectures and online problems, and then mastered during weekly labs. In lab, students model, design, test, and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g., optimizing thrust-driven positioners or stabilizing magnetic levitators). Students taking graduate version complete additional problems and labs.

Provides instruction in aspects of effective technical oral presentations and exposure to communication skills useful in a workplace setting. Students create, give and revise a number of presentations of varying length targeting a range of different audiences.

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.

Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem. Credit cannot also be received for 6.041A or 6.041B.

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments.

Introduction to C and assembly language for students coming from a Python background (6.100A). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions.

Instruction in effective undergraduate research, including choosing and developing a research topic, surveying previous work and publications, research topics in EECS and the School of Engineering, industry best practices, design for robustness, technical presentation, authorship and collaboration, and ethics. Students engage in extensive written and oral communication exercises, in the context of an approved advanced research project. A total of 12 units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult EECS SuperUROP website for more information.

Design and implementation of operating systems, and their use as a foundation for systems programming. Topics include virtual memory, file systems, threads, context switches, kernels, interrupts, system calls, interprocess communication, coordination, and interaction between software and hardware. A multi-processor operating system for RISC-V, xv6, is used to illustrate these topics. Individual laboratory assignments involve extending the xv6 operating system, for example to support sophisticated virtual memory features and networking.

Exposes students to the models and methods of engineering leadership within the contexts of conceiving, designing, implementing and operating products, processes and systems. Introduces the Capabilities of Effective Engineering Leaders, and models and theories related to the capabilities. Discusses the appropriate times and reasons to use particular models to deliver engineering success. Includes occasional guest speakers or panel discussions. May be repeated for credit once with permission of instructor. Preference to first-year students in the Gordon Engineering Leadership Program.

Advances students' leadership, teamwork, and communication skills through further exposure to leadership frameworks, models, and cases within an engineering context in an interactive, practice-based environment. Students coach others, assess performance, and lead guided reflections on individual and team successes, while discovering opportunities for improvement. Students assist with programmatic planning and implementation of role-play simulations, small group discussions, and performance and peer assessments by and of other students and by instructors. Includes frequent engineering industry-guest participation and involvement. Content is frequently student-led. Second year Gordon Engineering Leadership Program (GEL) Program students register for 6.9130. Preference to students enrolled in the second year of the Gordon-MIT Engineering Leadership Program.

Provides students with skills to prepare for and excel in the world of industry. Emphasizes practical application of career theory and professional development concepts. Introduces students to relevant and timely resources for career development, provides students with tools to embark on a successful internship search, and offers networking opportunities with employers and MIT alumni. Students work in groups, led by industry mentors, to improve their resumes and cover letters, interviewing skills, networking abilities, project management, and ability to give and receive feedback. Objective is for students to be able to adapt and contribute effectively to their future employment organizations. A total of two units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult UPOP website for more information.

Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design. Enrollment may be limited.

Introduction to computer science and programming. Students develop skills to program and use computational techniques to solve problems. Topics include: the notion of computation, Python, simple algorithms and data structures, object-oriented programming, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of 6.100A and 6.100B (or 16.C20) counts as REST subject.

Provides an introduction to the design of digital systems and computer architecture. Emphasizes expressing all hardware designs in a high-level hardware description language and synthesizing the designs. Topics include combinational and sequential circuits, instruction set abstraction for programmable hardware, single-cycle and pipelined processor implementations, multi-level memory hierarchies, virtual memory, exceptions and I/O, and parallel systems.

Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited.

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.

Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful.

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Provides an introduction to using computation to build models that can be used to help understand real-world phenomena. Topics include optimization problems, simulation models, and statistical models. Requires experience programming in Python as a prerequisite. Combination of 6.100A and 6.100B counts as REST subject.

Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem. Credit cannot also be received for 6.041A or 6.041B.

Provides instruction in aspects of effective technical oral presentations and exposure to communication skills useful in a workplace setting. Students create, give and revise a number of presentations of varying length targeting a range of different audiences.

A rapid introduction to the theoretical foundations of statistical methods that are useful in many applications. Covers a broad range of topics in a short amount of time with the goal of providing a rigorous and cohesive understanding of the modern statistical landscape. Mathematical language is used for intuition and basic derivations but not proofs. Main topics include: parametric estimation, confidence intervals, hypothesis testing, Bayesian inference, and linear and logistic regression. Additional topics may include: causal inference, nonparametric estimation, and classification.

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Introduction to C and assembly language for students coming from a Python background (6.100A). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions.

Provides design-focused instruction on how to build complex software applications. Presents key skills in product design and human-computer interaction (identifying authentic demand, prototyping, visual design, and user testing), software concept design (achieving clarity, modularity, and focus in structuring functionality), and analyzing social and ethical implications. Implementation topics include client/server web apps, reactive front-ends, and databases. Students work on both individual projects and a larger team project, and are taught to make effective and intentional use of LLMs in design and coding.

Design and implementation of operating systems, and their use as a foundation for systems programming. Topics include virtual memory, file systems, threads, context switches, kernels, interrupts, system calls, interprocess communication, coordination, and interaction between software and hardware. A multi-processor operating system for RISC-V, xv6, is used to illustrate these topics. Individual laboratory assignments involve extending the xv6 operating system, for example to support sophisticated virtual memory features and networking.

A more extensive and theoretical treatment of the material in 6.1400J/18.400J, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

Introduces the study of human language from a computational perspective, including syntactic, semantic and discourse processing models. Emphasizes machine learning methods and algorithms. Uses these methods and models in applications such as syntactic parsing, information extraction, statistical machine translation, dialogue systems. Instruction and practice in oral and written communication provided.

18.701-18.702 is more extensive and theoretical than the 18.700-18.703 sequence. Experience with proofs necessary. 18.701 focuses on group theory, geometry, and linear algebra.

Fundamentals of deep learning, including both theory and applications. Topics include neural net architectures (MLPs, CNNs, RNNs, graph nets, transformers), geometry and invariances in deep learning, backpropagation and automatic differentiation, learning theory and generalization in high-dimensions, and applications to computer vision, natural language processing, and robotics.

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space.

Introduction to computer science and programming. Students develop skills to program and use computational techniques to solve problems. Topics include: the notion of computation, Python, simple algorithms and data structures, object-oriented programming, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of 6.100A and 6.100B (or 16.C20) counts as REST subject.

Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design. Enrollment may be limited.

Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited.

Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful.

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.

Provides an introduction to using computation to build models that can be used to help understand real-world phenomena. Topics include optimization problems, simulation models, and statistical models. Requires experience programming in Python as a prerequisite. Combination of 6.100A and 6.100B counts as REST subject.

A rapid introduction to the theoretical foundations of statistical methods that are useful in many applications. Covers a broad range of topics in a short amount of time with the goal of providing a rigorous and cohesive understanding of the modern statistical landscape. Mathematical language is used for intuition and basic derivations but not proofs. Main topics include: parametric estimation, confidence intervals, hypothesis testing, Bayesian inference, and linear and logistic regression. Additional topics may include: causal inference, nonparametric estimation, and classification.

An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments.

Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem. Credit cannot also be received for 6.041A or 6.041B.

Introduces the study of human language from a computational perspective, including syntactic, semantic and discourse processing models. Emphasizes machine learning methods and algorithms. Uses these methods and models in applications such as syntactic parsing, information extraction, statistical machine translation, dialogue systems. Instruction and practice in oral and written communication provided.

Introduction to fundamentals of modern data-driven decision-making frameworks, such as causal inference and hypothesis testing in statistics as well as supervised and reinforcement learning in machine learning. Explores how these frameworks are being applied in various societal contexts, including criminal justice, healthcare, finance, and social media. Emphasis on pinpointing the non-obvious interactions, undesirable feedback loops, and unintended consequences that arise in such settings. Enables students to develop their own principled perspective on the interface of data-driven decision making and society. Students taking graduate version complete additional assignments.

A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression, and identification). Concepts are introduced with lectures and online problems, and then mastered during weekly labs. In lab, students model, design, test, and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g., optimizing thrust-driven positioners or stabilizing magnetic levitators). Students taking graduate version complete additional problems and labs.

Fundamentals of deep learning, including both theory and applications. Topics include neural net architectures (MLPs, CNNs, RNNs, graph nets, transformers), geometry and invariances in deep learning, backpropagation and automatic differentiation, learning theory and generalization in high-dimensions, and applications to computer vision, natural language processing, and robotics.

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Provides students with skills to prepare for and excel in the world of industry. Emphasizes practical application of career theory and professional development concepts. Introduces students to relevant and timely resources for career development, provides students with tools to embark on a successful internship search, and offers networking opportunities with employers and MIT alumni. Students work in groups, led by industry mentors, to improve their resumes and cover letters, interviewing skills, networking abilities, project management, and ability to give and receive feedback. Objective is for students to be able to adapt and contribute effectively to their future employment organizations. A total of two units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult UPOP website for more information.

Introduction to the methods and applications of optimization. Topics include linear optimization, duality, non-linear optimization, integer optimization, and optimization under uncertainty. Instruction provided in modeling techniques to address problems arising in practice, mathematical theory to understand the structure of optimization problems, computational algorithms to solve complex optimization problems, and practical applications. Covers several examples and in-depth case studies based on real-world data to showcase impactful applications of optimization across management and engineering. Computational exercises based on the Julia-based programming language JuMP. Includes a term project. Basic competency in computational programming and linear algebra recommended. Students taking graduate version complete additional assignments. This subject was previously listed as 6.7201.

Introduces the study of computational models of human language, covering classical statistical methods, representation learning, and modern deep network models through the lens of language modeling. Students complete a substantial final project, applying or extending these methods. Instruction and practice in oral and written communication provided.

Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design.

A more extensive and theoretical treatment of the material in 6.1400J/18.400J, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

Principles, techniques, and algorithms in machine learning from the point of view of statistical inference; representation, generalization, and model selection; and methods such as linear/additive models, active learning, boosting, support vector machines, non-parametric Bayesian methods, hidden Markov models, Bayesian networks, and convolutional and recurrent neural networks. Recommended prerequisite: 6.3900 or other previous experience in machine learning. Enrollment may be limited.

Provides an introduction to the design of digital systems and computer architecture. Emphasizes expressing all hardware designs in a high-level hardware description language and synthesizing the designs. Topics include combinational and sequential circuits, instruction set abstraction for programmable hardware, single-cycle and pipelined processor implementations, multi-level memory hierarchies, virtual memory, exceptions and I/O, and parallel systems.

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space.

18.701-18.702 is more extensive and theoretical than the 18.700-18.703 sequence. Experience with proofs necessary. 18.701 focuses on group theory, geometry, and linear algebra.

Provides instruction in aspects of effective technical oral presentations and exposure to communication skills useful in a workplace setting. Students create, give and revise a number of presentations of varying length targeting a range of different audiences.

Introduction to computational theories of human cognition. Focus on principles of inductive learning and inference, and the representation of knowledge. Computational frameworks covered include Bayesian and hierarchical Bayesian models; probabilistic graphical models; nonparametric statistical models and the Bayesian Occam's razor; sampling algorithms for approximate learning and inference; and probabilistic models defined over structured representations such as first-order logic, grammars, or relational schemas. Applications to understanding core aspects of cognition, such as concept learning and categorization, causal reasoning, theory formation, language acquisition, and social inference. Graduate students complete a final project.

Highlights common principles that permeate the functioning of diverse technological, economic and social networks. Utilizes three sets of tools for analyzing networks -- random graph models, optimization, and game theory -- to study informational and learning cascades; economic and financial networks; social influence networks; formation of social groups; communication networks and the Internet; consensus and gossiping; spread and control of epidemics; control and use of energy networks; and biological networks. Students taking graduate version complete additional assignments.

Introduction to C and assembly language for students coming from a Python background (6.100A). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions.

Introduces probabilistic modeling for problems of inference and machine learning from data, emphasizing analytical and computational aspects. Distributions, marginalization, conditioning, and structure, including graphical and neural network representations. Belief propagation, decision-making, classification, estimation, and prediction. Sampling methods and analysis. Introduces asymptotic analysis and information measures. Computational laboratory component explores the concepts introduced in class in the context of contemporary applications. Students design inference algorithms, investigate their behavior on real data, and discuss experimental results.

Introduction to finance from the perspective of business people and finance professionals. Designed to build effective decision-making skills based on sound financial knowledge, focusing on areas such as day-to-day operational issues and management, launching a startup, or negotiating option bonuses. Provides a firm grounding in the modern financial analysis underlying any decision, through three core themes: determining the value of a project, deciding how to finance a project, and managing its risk. Students also hone their ability to negotiate skillfully and speak intelligently about finance. Meets with 15.417 when offered concurrently. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Some sections are restricted to graduate students only without the permission of the instructor. See syllabus url for further details.

Introduction to computer science and programming. Students develop skills to program and use computational techniques to solve problems. Topics include: the notion of computation, Python, simple algorithms and data structures, object-oriented programming, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of 6.100A and 6.100B (or 16.C20) counts as REST subject.

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Fundamentals of linear systems, and abstraction modeling of multi-physics lumped and distributed systems using lumped electrical circuits. Linear networks involving independent and dependent sources, resistors, capacitors, and inductors. Extensions to include operational amplifiers and transducers. Dynamics of first- and second-order networks; analysis and design in the time and frequency domains; signal and energy processing applications. Design exercises. Weekly laboratory with microcontroller and transducers.

Introduction to C and assembly language for students coming from a Python background (6.100A). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions.

Provides an introduction to the design of digital systems and computer architecture. Emphasizes expressing all hardware designs in a high-level hardware description language and synthesizing the designs. Topics include combinational and sequential circuits, instruction set abstraction for programmable hardware, single-cycle and pipelined processor implementations, multi-level memory hierarchies, virtual memory, exceptions and I/O, and parallel systems.

Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited.

Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design. Enrollment may be limited.

Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design.

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful.

Provides an introduction to using computation to build models that can be used to help understand real-world phenomena. Topics include optimization problems, simulation models, and statistical models. Requires experience programming in Python as a prerequisite. Combination of 6.100A and 6.100B counts as REST subject.

An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments.

Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design. Enrollment may be limited.

Introduction to computer science and programming. Students develop skills to program and use computational techniques to solve problems. Topics include: the notion of computation, Python, simple algorithms and data structures, object-oriented programming, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of 6.100A and 6.100B (or 16.C20) counts as REST subject.

Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited.

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Presents the biology of cells of higher organisms. Studies the structure, function, and biosynthesis of cellular membranes and organelles; cell growth and oncogenic transformation; transport, receptors, and cell signaling; the cytoskeleton, the extracellular matrix, and cell movements; cell division and cell cycle; functions of specialized cell types. Emphasizes the current molecular knowledge of cell biological processes as well as the genetic, biochemical, and other experimental approaches that resulted in these discoveries.

Provides an introduction to using computation to build models that can be used to help understand real-world phenomena. Topics include optimization problems, simulation models, and statistical models. Requires experience programming in Python as a prerequisite. Combination of 6.100A and 6.100B counts as REST subject.

Introduces the experimental concepts and methods of molecular biology. Covers basic principles of experimental design and data analysis, with an emphasis on the acquisition of practical laboratory experience. Satisfies 6 units of Institute Laboratory credit. Satisfies biology laboratory credit for pre-health professions. Enrollment limited.

The principles of genetics with application to the study of biological function at the level of molecules, cells, and multicellular organisms, including humans. Structure and function of genes, chromosomes, and genomes. Biological variation resulting from recombination, mutation, and selection. Population genetics. Use of genetic methods to analyze protein function, gene regulation, and inherited disease.

Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful.

Equilibrium properties of macroscopic and microscopic systems. Basic thermodynamics: state of a system, state variables. Work, heat, first law of thermodynamics, thermochemistry. Second and third law of thermodynamics: entropy and its statistical basis, Gibbs function. Chemical equilibrium of reactions in gas and solution phase. Macromolecular structure and interactions in solution. Driving forces for molecular self-assembly. Binding cooperativity, solvation, titration of macromolecules.

Laboratory-based exploration of modern experimental molecular biology. Specific experimental system studied may vary from term to term, depending on instructor. Emphasizes concepts of experimental design, data analysis and communication in biology and how these concepts are applied in the biotechnology industry. Satisfies 6 units of Institute Laboratory credit. Enrollment limited; admittance may be controlled by lottery.

Provides instruction in aspects of effective technical oral presentations and exposure to communication skills useful in a workplace setting. Students create, give and revise a number of presentations of varying length targeting a range of different audiences.

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.

Focuses on synthesis, structure determination, mechanism, and the relationships between structure and reactivity. Selected topics illustrate the role of organic chemistry in biological systems and in the chemical industry.

Basic thermodynamics: state of a system, state variables. Work, heat, first law of thermodynamics, thermochemistry. Second and third law of thermodynamics: entropy and free energy, including the molecular basis for these thermodynamic functions. Equilibrium properties of macroscopic systems. Special attention to thermodynamics related to global energy issues and biological systems. Combination of 5.601 and 5.602 counts as a REST subject.

Introduction to organic chemistry. Development of basic principles to understand the structure and reactivity of organic molecules. Emphasis on substitution and elimination reactions and chemistry of the carbonyl group. Introduction to the chemistry of aromatic compounds.

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Covers the algorithmic and machine learning foundations of computational biology, combining theory with practice. Principles of algorithm design, influential problems and techniques, and analysis of large-scale biological datasets. Topics include (a) genomes: sequence analysis, gene finding, RNA folding, genome alignment and assembly, database search; (b) networks: gene expression analysis, regulatory motifs, biological network analysis; (c) evolution: comparative genomics, phylogenetics, genome duplication, genome rearrangements, evolutionary theory. These are coupled with fundamental algorithmic techniques including: dynamic programming, hashing, Gibbs sampling, expectation maximization, hidden Markov models, stochastic context-free grammars, graph clustering, dimensionality reduction, Bayesian networks.

Undergraduate research opportunities in the Department of Biology.

Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem. Credit cannot also be received for 6.041A or 6.041B.

Students carry out independent literature research. Journal club discussions are used to help students evaluate and write scientific papers. Instruction and practice in written and oral communication is provided. 

Emphasizes direct and active involvement in laboratory research in bioengineering or environmental health. May be extended over multiple terms.

Instruction in effective undergraduate research, including choosing and developing a research topic, surveying previous work and publications, research topics in EECS and the School of Engineering, industry best practices, design for robustness, technical presentation, authorship and collaboration, and ethics. Students engage in extensive written and oral communication exercises, in the context of an approved advanced research project. A total of 12 units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult EECS SuperUROP website for more information.

Introduces experimental chemistry for students who are not majoring in Course 5. Principles and applications of chemical laboratory techniques, including preparation and analysis of chemical materials, measurement of pH, gas and liquid chromatography, visible-ultraviolet spectrophotometry, infrared spectroscopy, kinetics, data analysis, and elementary synthesis, are described, in addition to experimental design principles. Includes instruction and practice in written and oral communication to multiple audiences. Enrollment limited.

Provides a comprehensive introduction to the fundamentals of cancer biology and cancer treatment. Topics include cancer genetics, genomics, and epigenetics; familial cancer syndromes; signal transduction, cell cycle control, and apoptosis; cancer metabolism; stem cells and cancer; metastasis; cancer immunology and immunotherapy; conventional and molecularly-targeted therapies; and early detection and prevention. Students taking graduate version complete additional assignments.

Introduces experimental biochemical and molecular techniques from a quantitative engineering perspective. Experimental design, data analysis, and scientific communication form the underpinnings of this subject. In this, students complete discovery-based experimental modules drawn from current technologies and active research projects of BE faculty. Generally, topics include DNA engineering, in which students design, construct, and use genetic material; parts engineering, emphasizing protein design and quantitative assessment of protein performance; systems engineering, which considers genome-wide consequences of genetic perturbations; and biomaterials engineering, in which students use biologically-encoded devices to design and build materials. Enrollment limited; priority to Course 20 majors.

Focuses on fundamental principles of developmental biology by which cells build organs and organisms. Analyzes the pivotal role of stem cells in tissue maintenance or repair, and in treatment of disease. Explores how to integrate this knowledge with engineering tools to construct functional tissue structures. Students taking graduate version complete additional assignments

Free energy and chemical potential. Phase equilibrium and properties of solutions. Chemical equilibrium of reactions. Rates of chemical reactions. Special attention to thermodynamics related to global energy issues and biological systems. Combination of 5.601 and 5.602 counts as a REST subject.

Students carry out an experiment that builds skills in how to rationally design macromolecules for drug delivery based on fundamental principles of physical organic chemistry. Begins with conjugation of a drug molecule to a polymerizable group through a cleavable linker to generate a prodrug monomer. Continues with polymerization of monomer to produce macromolecular (i.e., polymer) prodrug; monomer and polymer prodrugs are fully characterized. Rate of drug release is measured and correlated to the size of the macromolecule as well as the structure of the cleavable linker. Satisfies 4 units of Institute Laboratory credit.

Students carry out an experiment that provides an introduction to the synthesis of simple coordination compounds and chemical kinetics. Illustrates cobalt coordination chemistry and its transformations as detected by visible spectroscopy. Students observe isosbestic points in visible spectra, determine the rate and rate law, measure the rate constant at several temperatures, and derive the activation energy for the aquation reaction. Satisfies 5 units of Institute Laboratory credit.

Students carry out an experiment that introduces fundamental principles of the most common types of spectroscopy, including UV-visible absorption and fluorescence, infrared, and nuclear magnetic resonance. Emphasizes principles of how light interacts with matter, a fundamental and hands-on understanding of how spectrometers work, and what can be learned through spectroscopy about prototype molecules and materials. Students record and analyze spectra of small organic molecules, native and denatured proteins, semiconductor quantum dots, and laser crystals. Satisfies 4 units of Institute Laboratory credit.

Focuses on physiomimetics: transforming therapeutic strategy and development. Overview of development of therapies for complex diseases, including disease mechanisms in heterogeneous patient populations, developing therapeutic strategies, modeling these in vitro, and testing the therapies. Explores the five essential technological contributions to this process: computational systems biology, synthetic biology, immuno-engineering, microphysiological systems devices/tissue engineering, and microfluidic device engineering for in vitro models and analysis. Introduces disease modeling, patient stratification, and drug development processes, includes extensive examples from industry, and provides context for choosing a concentration track in the Living Machines thread. Weekly lectures from experts in the field supplemented with structured, short projects in each topic area. Limited to 24; preference to students in the NEET Living Machines thread.

Interactive introduction to the discipline of Biological Engineering through presentations by alumni practitioners, with additional panels and discussions on skills for professional development. Presentations emphasize the roles of communication through writing and speaking, building and maintaining professional networks, and interpersonal and leadership skills in building successful careers. Provides practical advice about how to prepare for job searches and graduate or professional school applications from an informed viewpoint. Prepares students for UROPs, internships, and selection of BE electives. Subject can count toward the 6-unit discovery-focused credit limit for first-year students.  

Provides students with skills to prepare for and excel in the world of industry. Emphasizes practical application of career theory and professional development concepts. Introduces students to relevant and timely resources for career development, provides students with tools to embark on a successful internship search, and offers networking opportunities with employers and MIT alumni. Students work in groups, led by industry mentors, to improve their resumes and cover letters, interviewing skills, networking abilities, project management, and ability to give and receive feedback. Objective is for students to be able to adapt and contribute effectively to their future employment organizations. A total of two units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult UPOP website for more information.

Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited.

Introduction to computer science and programming. Students develop skills to program and use computational techniques to solve problems. Topics include: the notion of computation, Python, simple algorithms and data structures, object-oriented programming, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of 6.100A and 6.100B (or 16.C20) counts as REST subject.

Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful.

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Equips students with the strategies, tactics, and tools to use quantitative information to inform and persuade others. Emphasizes effective communication skills as the foundation of successful careers. Develops the skills to communicate quantitative information in a business context to drive people and organizations toward better decisions. Focuses heavily on the cycle of practicing, reflecting, and revising. Students receive extensive, personalized feedback from teaching team and classmates. Limited to 25.

Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. Lab component consists of software design, construction, and implementation of design. Enrollment may be limited.

Provides an introduction to using computation to build models that can be used to help understand real-world phenomena. Topics include optimization problems, simulation models, and statistical models. Requires experience programming in Python as a prerequisite. Combination of 6.100A and 6.100B counts as REST subject.

Introduces regression and other tools for causal inference and descriptive analysis in empirical economics. Topics include analysis of randomized experiments, instrumental variables methods and regression discontinuity designs, differences-in-differences estimation, and regression with time series data. Develops the skills needed to conduct — and critique — empirical studies in economics and related fields. Empirical applications are drawn from published examples and frontier research. Familiarity with statistical programming languages is helpful. Students taking graduate version complete an empirical project leading to a short paper. No listeners. Limited to 70 total for versions meeting together.

Introduces core concepts in data-driven modeling that inform and optimize business decisions under uncertainty. Covers models and frameworks, such as machine learning, time series forecasting, dynamic programming, stochastic optimization, and multi-armed bandits. Draws on real-world applications, with several examples from retail, healthcare, logistics, supply chain, and public sector.

Preparation and analysis of financial statements. Focuses on why financial statements take the form they do, and how they can be used in evaluating corporate performance and solvency and in valuation of corporate securities. Introduces concepts from finance and economics (e.g., cash flow discounting and valuation) and explains their relation to, and use in, accounting. Students taking the graduate version complete additional assignments.

Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem. Credit cannot also be received for 6.041A or 6.041B.

Introduction to finance from the perspective of business people and finance professionals. Designed to build effective decision-making skills based on sound financial knowledge, focusing on areas such as day-to-day operational issues and management, launching a startup, or negotiating option bonuses. Provides a firm grounding in the modern financial analysis underlying any decision, through three core themes: determining the value of a project, deciding how to finance a project, and managing its risk. Students also hone their ability to negotiate skillfully and speak intelligently about finance. Meets with 15.417 when offered concurrently. Expectations and evaluation criteria differ for students taking graduate version; consult syllabus or instructor for specific details. Some sections are restricted to graduate students only without the permission of the instructor. See syllabus url for further details.

Exposes students to the process of conducting independent research in empirical economics and effectively communicating the results of the research. Emphasizes econometric analysis of an assigned economic question and culminates in each student choosing an original topic, performing appropriate analysis, and delivering oral and written project reports. Limited to 20 per section.

A rapid introduction to the theoretical foundations of statistical methods that are useful in many applications. Covers a broad range of topics in a short amount of time with the goal of providing a rigorous and cohesive understanding of the modern statistical landscape. Mathematical language is used for intuition and basic derivations but not proofs. Main topics include: parametric estimation, confidence intervals, hypothesis testing, Bayesian inference, and linear and logistic regression. Additional topics may include: causal inference, nonparametric estimation, and classification.

Develops appreciation for organizational dynamics and competence in navigating social networks, working in a team, demystifying rewards and incentives, leveraging the crowd, understanding change initiatives, and making sound decisions. Provides instruction and practice in written and oral communication through presentations, and interpersonal and group exercises.

Broad introduction to the various aspects of management including analytics, accounting and finance, operations, marketing, entrepreneurship and leadership, organizations, economics, systems dynamics, and negotiation and communication. Introduces the field of management through a variety of experiences as well as discussions led by faculty or industry experts. Also reviews the three undergraduate majors offered by Sloan as well as careers in management. Subject can count toward the 6-unit discovery-focused credit limit for first year students. Limited to undergraduates; preference to first years.

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Provides students with skills to prepare for and excel in the world of industry. Emphasizes practical application of career theory and professional development concepts. Introduces students to relevant and timely resources for career development, provides students with tools to embark on a successful internship search, and offers networking opportunities with employers and MIT alumni. Students work in groups, led by industry mentors, to improve their resumes and cover letters, interviewing skills, networking abilities, project management, and ability to give and receive feedback. Objective is for students to be able to adapt and contribute effectively to their future employment organizations. A total of two units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult UPOP website for more information.

Introduces the theoretical and empirical literature of behavioral economics. Examines important and systematic departures from the standard models in economics by incorporating insights from psychology and other social sciences. Covers theory and evidence on time, risk, and social preferences; beliefs and learning; emotions; limited attention; and frames, defaults, and nudges. Studies applications to many different areas, such as credit card debt, procrastination, retirement savings, addiction, portfolio choice, poverty, labor supply, happiness, and government policy. Students participate in surveys and experiments in class, review evidence from lab experiments, examine how the results can be integrated into models, and test models using field and lab data. Students taking graduate version complete additional assignments.

Self-contained introduction to probability and statistics with applications in economics and the social sciences.  Covers elements of probability theory, statistical estimation and inference, regression analysis, causal inference, and program evaluation. Couples methods with applications and with assignments involving data analysis. Uses basic calculus and matrix algebra.  Students taking graduate version complete additional assignments. May not count toward HASS requirement.

Introduction to corporate finance. Classroom portion primarily uses case studies to introduce financial analytical tools needed to make real-world value-enhancing business decisions across many industries: how to decide which projects to invest in, how to finance those investments, and how to manage the cash flows of the firm. Laboratory sessions are organized around team valuation projects, such as valuation of an oil field and analysis of a potential merger between two public firms proposed by student teams. Projects require extensive use of financial databases. Laboratory sessions also provide instruction on writing and speaking on financial topics. Meets with 15.402 when offered concurrently.