This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.

6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can’t be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).

This book aims to be an accessible introduction into the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them.

The topics covered include:

The divide and conquer technique.
The use of randomization in algorithms.
The general, but typically inefficient, backtracking technique.
Dynamic programming as an efficient optimization for some backtracking algorithms.
Greedy algorithms as an optimization of other kinds of backtracking algorithms.
Hill-climbing techniques, including network flow.

The goal of the book is to show you how you can methodically apply different techniques to your own algorithms to make them more efficient. While this book mostly highlights general techniques, some well-known algorithms are also looked at in depth. This book is written so it can be read from "cover to cover" in the length of a semester, where sections marked with a * may be skipped.

This is a graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations. The material in this course constitutes a common foundation for work in machine learning, signal processing, artificial intelligence, computer vision, control, and communication. Ultimately, the subject is about teaching you contemporary approaches to, and perspectives on, problems of statistical inference.

This course presents real-world examples in which quantitative methods provide a significant competitive edge that has led to a first order impact on some of today’s most important companies. We outline the competitive landscape and present the key quantitative methods that created the edge (data-mining, dynamic optimization, simulation), and discuss their impact.

This course covers the key quantitative methods of finance: financial econometrics and statistical inference for financial applications; dynamic optimization; Monte Carlo simulation; stochastic (Itô) calculus. These techniques, along with their computer implementation, are covered in depth. Application areas include portfolio management, risk management, derivatives, and proprietary trading.

Esta guía práctica acompaña la serie de videos Poder estadístico y tamaño de muestra en R, de mi canal de YouTube Investigación Abierta, que recomiendo ver antes de leer este documento. Contiene una explicación general del análisis de poder estadístico y cálculo de tamaño de muestra, centrándose en el procedimiento para realizar análisis de poder y tamaños de muestra en jamovi y particularmente en R, usando los paquetes pwr (para diseños sencillos) y Superpower (para diseños factoriales más complejos). La sección dedicada a pwr está ampliamente basada en este video de Daniel S. Quintana (2019).

Python es un lenguaje de programación general que es útil para escribir scripts para trabajar con datos de manera efectiva y reproducible. Esta es una introducción a Python diseñada para participantes sin experiencia en programación. Estas lecciones pueden enseñarse en un día (~ 6 horas). Las lecciones empiezan con información básica sobre la sintaxis de Python, la interface de Jupyter Notebook, y continúan con cómo importar archivos CSV, usando el paquete Pandas para trabajar con DataFrames, cómo calcular la información resumen de un DataFrame, y una breve introducción en cómo crear visualizaciones. La última lección demuestra cómo trabajar con bases de datos directamente desde Python. Nota: los datos no han sido traducidos de la versión original en inglés, por lo que los nombres de variables se mantienen en inglés y los números de cada observación usan la sintaxis de habla inglesa (coma separador de miles y punto separador de decimales).

15.875 is a project-based course that explores how organizations can use system dynamics to achieve important goals. In small groups, students learn modeling and consulting skills by working on a term-long project with real-life managers. A diverse set of businesses and organizations sponsor class projects, from start-ups to the Fortune 500. The course focuses on gaining practical insight from the system dynamics process, and appeals to people interested in system dynamics, consulting, or managerial policy-making.

The textbook is written as a series of Quarto Documents in RStudio and is aimed both as an educational resource on the topic of categorical data analysis and as an aid to the use of the R language for statistical computing. The rendered textbook is interactive with tasks and solution as well as a series of lab questions at the end of each chapter. It also includes OER resources for various introductory math and statistics courses.

This course covers empirical strategies for applied micro research questions. Our agenda includes regression and matching, instrumental variables, differences-in-differences, regression discontinuity designs, standard errors, and a module consisting of 8–9 lectures on the analysis of high-dimensional data sets a.k.a. “Big Data”.

6.728 is offered under the department’s “Devices, Circuits, and Systems” concentration. The course covers concepts in elementary quantum mechanics and statistical physics, introduces applied quantum physics, and emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger’s equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.

Spreadsheets across the Curriculum Activity. Student build spreadsheets that allow them to estimate pi using the same iterative process as Archimedes.

The numerical methods, formulation and parameterizations used in models of the circulation of the atmosphere and ocean will be described in detail. Widely used numerical methods will be the focus but we will also review emerging concepts and new methods. The numerics underlying a hierarchy of models will be discussed, ranging from simple GFD models to the high-end GCMs. In the context of ocean GCMs, we will describe parameterization of geostrophic eddies, mixing and the surface and bottom boundary layers. In the atmosphere, we will review parameterizations of convection and large scale condensation, the planetary boundary layer and radiative transfer.

This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure approaches, molecular dynamics, and Monte Carlo.
This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5107 (Atomistic Computer Modeling of Materials).
Acknowledgements
Support for this course has come from the National Science Foundation’s Division of Materials Research (grant DMR-0304019) and from the Singapore-MIT Alliance.

The Authenticity and Agency rubrics are based on elements from two frameworks: Student as Producer and Social Pedagogies. The rubrics were created for instructors and instructional designers to use as they develop authentic learning experiences in the course design process.

A Software Carpentry lesson to learn how to use Make Make is a tool which can run commands to read files, process these files in some way, and write out the processed files. For example, in software development, Make is used to compile source code into executable programs or libraries, but Make can also be used to: run analysis scripts on raw data files to get data files that summarize the raw data; run visualization scripts on data files to produce plots; and to parse and combine text files and plots to create papers. Make is called a build tool - it builds data files, plots, papers, programs or libraries. It can also update existing files if desired. Make tracks the dependencies between the files it creates and the files used to create these. If one of the original files (e.g. a data file) is changed, then Make knows to recreate, or update, the files that depend upon this file (e.g. a plot). There are now many build tools available, all of which are based on the same concepts as Make.

In the master-equation formalism, a set of differential equations describe the time-evolution of the probability distribution of an ensemble of systems. This can be used, for example, to describe the varied mRNA copy numbers found in individual cells in a population.

The stochastic simulation algorithm (SSA, Kinetic Monte Carlo, Gillespie algorithm) produces an example trajectory for a particular member of a probabilistic ensemble by looping over the following steps. The current state of the system is used to determine the likelihood of each possible chemical reaction in relative comparison to the likelihoods for the other possible reactions, as well as to determine when the next reaction is expected. Pseudo-random numbers are drawn to "roll the dice" to determine exactly when the next reaction will proceed, and which kind of reaction it will happen to be.

This course is a study of Behavior of Algorithms and covers an area of current interest in theoretical computer science. The topics vary from term to term. During this term, we discuss rigorous approaches to explaining the typical performance of algorithms with a focus on the following approaches: smoothed analysis, condition numbers/parametric analysis, and subclassing inputs.