Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It revolves around complex analytic functions—functions that have a complex derivative. Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Applications reviewed in this class include harmonic functions, two dimensional fluid flow, easy methods for computing (seemingly) hard integrals, Laplace transforms, and Fourier transforms with applications to engineering and physics.

6.844 is a graduate introduction to programming theory, logic of programming, and computability, with the programming language Scheme used to crystallize computability constructions and as an object of study itself. Topics covered include: programming and computability theory based on a term-rewriting, "substitution" model of computation by Scheme programs with side-effects; computation as algebraic manipulation: Scheme evaluation as algebraic manipulation and term rewriting theory; paradoxes from self-application and introduction to formal programming semantics; undecidability of the Halting Problem for Scheme; properties of recursively enumerable sets, leading to Incompleteness Theorems for Scheme equivalences; logic for program specification and verification; and Hilbert's Tenth Problem.

6.004 offers an introduction to the engineering of digital systems. Starting with MOS transistors, the course develops a series of building blocks — logic gates, combinational and sequential circuits, finite-state machines, computers and finally complete systems. Both hardware and software mechanisms are explored through a series of design examples.
6.004 is required material for any EECS undergraduate who wants to understand (and ultimately design) digital systems. A good grasp of the material is essential for later courses in digital design, computer architecture and systems. The problem sets and lab exercises are intended to give students "hands-on" experience in designing digital systems; each student completes a gate-level design for a reduced instruction set computer (RISC) processor during the semester.

Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments.
This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.472J. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.158J.

This course examines wave equations for fluid and visco-elastic media, wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides, and Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media. Also covered are Seismo-Acoustic modeling of seabeds and ice covers, seismic interface and surface waves in a stratified seabed, Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides, numerical modeling of target scattering and reverberation clutter in ocean waveguides, and ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research.
This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.853. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.068.

This course provides the fundamental computational toolbox for solving science and engineering problems. Topics include review of linear algebra, applications to networks, structures, estimation, finite difference and finite element solutions of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, the discrete Fourier transform, and convolution. We will also explore many topics in AI and machine learning throughout the course.

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Note: This course was previously called "Mathematical Methods for Engineers I."

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.

This course explores statistical modeling and control in manufacturing processes. Topics include the use of experimental design and response surface modeling to understand manufacturing process physics, as well as defect and parametric yield modeling and optimization. Various forms of process control, including statistical process control, run by run and adaptive control, and real-time feedback control, are covered. Application contexts include semiconductor manufacturing, conventional metal and polymer processing, and emerging micro-nano manufacturing processes.

This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms. The aim is to develop the core analytical and algorithmic issues of continuous optimization, duality, and saddle point theory using a handful of unifying principles that can be easily visualized and readily understood.

Course Description: This course will assist learners to find the math that is used in the real-world. Learners will learn how to solve real-life problems using mathematical stills they will acquire as they work through these lessons. By the end of this course, learners will be able to design their own project and discuss the math in it with their classmates.

Are you ready to leave the sandbox and go for the real deal? Have you followed Data Analysis: Take It to the MAX() and Data Analysis: Visualization and Dashboard Design and are ready to carry out more robust data analysis?

In this project-based course you will engage in a real data analysis project that simulates the complexity and challenges of data analysts at work. Testing, data wrangling, Pivot Tables, sparklines? Now that you have mastered them you are ready to apply them all and carry out an independent data analysis.

For your project, you will pick one raw dataset out of several options, which you will turn into a dashboard. You will begin with a business question that is related to the dataset that you choose. The datasets will touch upon different business domains, such as revenue management, call-center management, investment, etc.

This course introduces methods for harnessing data to answer questions of cultural, social, economic, and policy interest. We will start with essential notions of probability and statistics. We will proceed to cover techniques in modern data analysis: regression and econometrics, design of experiments, randomized control trials (and A/B testing), machine learning, and data visualization.
We will illustrate these concepts with applications drawn from real-world examples and frontier research. Finally, we will provide instruction on the use of the statistical package R, and opportunities for students to perform self-directed empirical analyses.
MITx Online
This course draws materials from 14.310x Data Analysis for Social Scientists, which is part of the MicroMasters Program in Data, Economics, and Design of Policy offered by MITx Online. The MITx Online course is entirely free to audit, though learners have the option to pay a fee, which is based on the learner’s ability to pay, to take the proctored exam and earn a course certificate. To access that course, create an MITx Online account and enroll in the course 14.310x Data Analysis for Social Scientists.

This course is designed to introduce first-year Sloan MBA students to the fundamental techniques of using data. In particular, the course focuses on various ways of modeling, or thinking structurally about decision problems in order to make informed management decisions.

This page shares five units of youcubed lessons for grades 6-10 that introduce students (and teachers) to data science. The units start with an introduction to the concept of data and move to lessons that invite students to explore their own data sets. These lessons teach important content through a pattern-seeking, exploratory approach, and are designed to engage students actively.







Data Science LessonsThis page shares five units of youcubed lessons for grades 6-10 that introduce students (and teachers) to data science. The units start with an introduction to the concept of data and move to lessons that invite students to explore their own data sets.  These lessons teach important content through a pattern-seeking, exploratory approach, and are designed to engage students actively. The culminating unit is a citizen science project that gives students an opportunity to conduct a data inquiry. The lessons accompany a new online course for teachers, where some of the lessons are featured, along with other lesson ideas. These lessons are offered with ideas for in-person or online teaching, and can be taught at any time of year.









LessonsTeacher Online Course: 21st Century Teaching and LearningUnit 1: Data Is EverywhereUnit 2: Working With Data Analysis ToolsUnit 3: Measures of Center & SpreadUnit 4: Understanding VariabilityUnit 5: A Community Data Collection Project

ResourcesHigh School Data Science CourseCODAPWhat's Going On In This Graph?Data Science Initiative VideoThe Data Science K-12 MovementData Talks



Cool Extras




What are Data Talks?






A Picture Book Introduction to Data Science






Measures of Center and Spread Animated Movies






Stanford News Press Release

In an increasingly data-driven world, data and its use aren’t always all it’s cracked up to be. This course aims to address the critical lack of any or appropriate data in many areas where complex decisions need to be made.

For instance, how can you predict volcano activity when no eruptions have been recorded over a long period of time? Or how can you predict how many people will be resistant to antibiotics in a country where there is no available data at national level? Or how about estimating the time needed to evacuate people in flood risk areas?

In situations like these, expert opinions are needed to address complex decision-making problems. This course, aimed at researchers and professionals from any academic background, will show you how expert opinion can be used for uncertainty quantification in a rigorous manner.

Various techniques are used in practice. They vary from the informal and undocumented opinion of one expert to a fully documented and formal elicitation of a panel of experts, whose uncertainty assessments can be aggregated to provide support for complex decision making.

In this course you will be introduced to state-of-the-art expert judgment methods, particularly the Classical Model (CM) or Cooke’s method, which is arguably the most rigorous method for performing Structured Expert Judgment.

CM, developed at TU Delft by Roger Cooke, has been successfully applied for over 30 years in areas as diverse as climate change, disaster management, epidemiology, public and global health, ecology, aeronautics/aerospace, nuclear safety, environment and ecology, engineering and many others.

This course is an introduction to the theory and application of large-scale dynamic programming. Topics include Markov decision processes, dynamic programming algorithms, simulation-based algorithms, theory and algorithms for value function approximation, and policy search methods. The course examines games and applications in areas such as dynamic resource allocation, finance and queueing networks.

Foundations and philosophical applications of Bayesian decision theory, game theory and theory of collective choice. Why should degrees of belief be probabilities? Is it always rational to maximize expected utility? If so, why and what is its utility? What is a solution to a game? What does a game-theoretic solution concept such as Nash equilibrium say about how rational players will, or should, act in a game? How are the values and the actions of groups, institutions and societies related to the values and actions of the individuals that constitute them?

This is an intermediate algorithms course with an emphasis on teaching techniques for the design and analysis of efficient algorithms, emphasizing methods of application. Topics include divide-and-conquer, randomization, dynamic programming, greedy algorithms, incremental improvement, complexity, and cryptography.