Systems EngineeringOpen learning
2nd Summer Introduction to Design
Introduce students to the creative design process, based on the scientific method and peer review, by application of fundamental principles and learning to complete projects according to schedule and within budget. Subject relies on active learning through a major team-based design-and-build project focused on the need for a new consumer product identified by each team. Topics to be learned while teams create, design, build, and test their product ideas include formulating strategies, concepts and modules, and estimation, concept selection, machine elements, design for manufacturing, visual thinking, communication, teamwork, and professional responsibilities.
Dept 22.971+january-iap_2003
Science & MathOpen learning
7.03x Genetics
In this course, you will learn the principles of genetics with application to the study of biological function at the level of molecules, cells, and multicellular organisms, including humans. We will cover structure and function of genes, chromosomes, and genomes; biological variation resulting from recombination, mutation, and selection; population genetics; and the use of genetic methods to modify genes and genomes and analyze protein function, gene regulation, and inherited disease. This course, based on the MIT course 7.03 Genetics taken by enrolled MIT students, was organized as a three-part series offered through the MITx program by MIT’s Department of Biology. It is self-paced and free as long as you enroll in the Audit Track option, which you can select after creating a free account on MITx Online.
Dept 7RES.7-006+spring_2023
BiologyOpen learning
7.06x Cell Biology
In this course, you will engage in the biology of cells of higher organisms. You will study 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. This course emphasizes the current molecular knowledge of cell biological processes as well as the genetic, biochemical, and other experimental approaches that resulted in these discoveries. This course, based on the MIT course 7.06 Cell Biology taken by enrolled MIT students, was organized as a three-part series offered through the MITx program by MIT’s Department of Biology. It is self-paced and free as long as you enroll in the Audit Track option, which you can select after creating a free account on MITx Online.
Dept 7RES.7-007+spring_2023
BiologyOpen learning
7.28x Molecular Biology
This course is an in-depth adventure through the molecular mechanisms that control the maintenance, expression, and evolution of prokaryotic and eukaryotic genomes. Through lectures and readings of relevant literature, students will explore gene regulation, DNA replication, genetic recombination, transcription, and mRNA translation. The quizzes are designed to build students’ experimental design and data analysis skills. This course, based on the MIT course 7.28/7.58 Molecular Biology taken by enrolled MIT students, was organized as a three-part series offered through the MITx program by MIT’s Department of Biology. It is self-paced and free as long as you enroll in the Audit Track option, which you can select after creating a free account on MITx Online.
Dept 7RES.7-008+spring_2023
Pedagogy and CurriculumOpen learning
7.InT: Inclusive Teaching Module
The Inclusive Teaching Module is both a standalone online resource for those looking to explore materials related to inclusive teaching as well as an integral part of a blended workshop available to use at your own institution. If you are looking to facilitate a blended workshop using this material, please download the Facilitation Guide and Appendix files to get started! As part of the Open Learning Library (OLL), this course is free to use. You have the option to sign up and enroll if you want to track your progress, or you can view and use all the materials without enrolling. Resources on OLL allow learners to learn at their own pace while receiving immediate feedback through interactive content and exercises.
Dept 7RES.7-009+fall_2022
BiologyOpen learning
A Clinical Approach to the Human Brain
This course is designed to provide an understanding of how the human brain works in health and disease, and is intended for both the Brain and Cognitive Sciences major and the non-Brain and Cognitive Sciences major. Knowledge of how the human brain works is important for all citizens, and the lessons to be learned have enormous implications for public policy makers and educators. The course will cover the regional anatomy of the brain and provide an introduction to the cellular function of neurons, synapses and neurotransmitters. Commonly used drugs that alter brain function can be understood through a knowledge of neurotransmitters. Along similar lines, common diseases that illustrate normal brain function will be discussed. Experimental animal studies that reveal how the brain works will be reviewed. Throughout the seminar we will discuss clinical cases from Dr. Byrne’s experience that illustrate brain function; in addition, articles from the scientific literature will be discussed in each class.
Dept 9, HST9.22J+fall_2006
Computer ScienceOpen learning
A Gentle Introduction to Programming Using Python
This course will provide a gentle introduction to programming using Python™ for highly motivated students with little or no prior experience in programming computers. The course will focus on planning and organizing programs, as well as the grammar of the Python programming language. Lectures will be interactive featuring in-class exercises with lots of support from the course staff. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.
Dept 66.189+january-iap_2008
EngineeringOpen learning
A Gentle Introduction to Programming Using Python
This course will provide a gentle, yet intense, introduction to programming using Python for highly motivated students with little or no prior experience in programming. The course will focus on planning and organizing programs, as well as the grammar of the Python programming language. The course is designed to help prepare students for 6.01 Introduction to EECS I . 6.01 assumes some knowledge of Python upon entering; the course material for 6.189 has been specially designed to make sure that concepts important to 6.01 are covered. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.
Dept 66.189+january-iap_2011
Art, Design & ArchitectureOpen learning
A Global History of Architecture Writing Seminar
This course will study the question of Global Architecture from the point of view of producing a set of lectures on that subject. The course will be run in the form of a writing seminar, except that students will be asked to prepare for the final class an hour-long lecture for an undergraduate survey course. During the semester, students will study the debates about where to locate “the global” and do some comparative analysis of various textbooks. The topic of the final lecture will be worked on during the semester. For that lecture, students will be asked to identify the themes of the survey course, and hand in the bibliography and reading list for their lecture.
Dept 44.696+spring_2008
Health & MedicineOpen learning
A Hands-On Introduction to Nuclear Magnetic Resonance
Hands-on introduction to NMR presenting background in classical theory and instrumentation. Each lecture is followed by lab experiments to demonstrate ideas presented during the lecture and to familiarize students with state-of-the-art NMR instrumentation. Experiments cover topics ranging from spin dynamics to spectroscopy, and include imaging.
Dept 2222.920+january-iap_1997
Media StudiesOpen learning
A Passage to India: Introduction to Modern Indian Culture and Society
This course is an introduction to modern Indian culture and society through films, documentaries, short stories, novels, poems, and journalistic writing. The principal focus is on the study of major cultural developments and social debates in the last sixty five years of history through the reading of literature and viewing of film clips. The focus will be on the transformations of gender and class issues, representation of nationhood, the idea of regional identities and the place of the city in individual and communal lives. The cultural and historical background will be provided in class lectures. The idea is to explore the “other Indias” that lurk behind our constructed notion of a homogeneous national culture.
Dept 21G21G.040+spring_2012
Adaptation and ResilienceOpen learning
A Sustainable Transportation Plan for MIT
This seminar-style class will focus on evaluating and recommending alternative commuter and business-related transportation policies for the MIT campus. Emphasis will be placed on reducing transportation-related energy usage in a sustainable manner in response to President Hockfield’s “Walk the Talk” energy initiative. Students will explore the relative roles of MIT and the MBTA as transportation providers, as well as the efficiency and effectiveness of related subsidy policies currently in place for all modes of transportation.
Dept 11.963+spring_2007
Science & MathOpen learning
A Vision of Linear Algebra
This collection of videos presents Professor Strang’s updated vision of how linear algebra could be taught. It starts with six brief videos, recorded in 2020, containing many ideas and suggestions about the recommended order of topics in teaching and learning linear algebra. Topics include A New Way to Start Linear Algebra , The Column Space of a Matrix, The Big Picture of Linear Algebra, Orthogonal Vectors, Eigenvalues and Eigenvectors, and Singular Values and Singular Vectors. An additional brief video, recorded in 2021, Finding the Nullspace: Solving Ax = 0 by Elimination , computes the nullspace of any matrix A . In 2023, Professor Strang recorded a new one-hour video, Five Factorizations of a Matrix, providing an overall look at linear algebra by highlighting five different ways that a matrix gets factored. Two more videos were added in 2024: The Four Fundamental Subspaces and Least Squares and Elimination and Factorization A = CR
Dept 18RES.18-010+spring_2020
PhysicsOpen learning
A WikiTextBook for Introductory Mechanics
This e-Book is a first step toward a shift in the role of the printed textbook from authoritative serial repository to modular, customizable, linkable, interactive hub. The ideal modern textbook should provide a clear overview of the domain, short summaries of key content, links to more detailed online source material, embedded self-assessment, and a vehicle for instant student feedback. This open-source e-Book for introductory mechanics uses ideas from modeling physics to encourage strategic, concept-based problem solving and employs a wiki format to enable multiple parallel organizations of the material, links to resources and student comments. Online Publication
Dept 8RES.8-002+fall_2009
EngineeringOpen learning
A Workshop on Geographic Information Systems
This class uses lab exercises and a workshop setting to help students develop a solid understanding of the planning and public management uses of geographic information systems (GIS). The goals are to help students: acquire technical skills in the use of GIS software; acquire qualitative methods skills in data and document gathering, analyzing information, and presenting results; and investigate the potential and practicality of GIS technologies in a typical planning setting and evaluate possible applications. The workshop teaches GIS techniques and basic database management at a level that extends somewhat beyond the basic thematic mapping and data manipulation skills included in the MCP core classes (viz. 11.204 and 11.220). Instead of focusing on one thematic map of a single variable, students will concentrate on more open-ended planning questions that invite spatial analysis but will require judgment and exploration to select relevant data and mapping techniques; involve mixing and matching new, local data with extracts from official records (such as census data, parcel data and regional employment and population forecasts); utilize spatial analysis techniques such as buffering, address matching, overlays; use other modeling and visualization techniques beyond thematic mapping; and raise questions about the skills, strategy, and organizational support needed to sustain such analytic capability within a variety of local and regional planning settings. Students seeking graduate credit should enroll in the subject 11.520; undergraduates should enroll in the subject 11.188. The subjects meet together and have nearly identical content. ArcGIS/ArcMap/ArcInfo Graphical User Interface is the intellectual property of ESRI and is used herein with permission. Copyright © ESRI. All rights reserved.
Dept 1111.520+fall_2005
Health Care ManagementOpen learning
Abnormal Language
Introduction to the linguistic study of language pathology, concentrating on experimental approaches and theoretical explanations. Discussion of Specific Language Impairment, autism, Down syndrome, Williams syndrome, normal aging, Parkinson’s disease, Alzheimer’s disease, hemispherectomy and aphasia. Focuses on the comparison of linguistic abilities among these syndromes, while drawing clear comparisons with first and second language acquisition. Topics include the lexicon, morphology, syntax, semantics and pragmatics. Relates the lost linguistic abilities in these syndromes to properties of the brain.
Dept 9, 249.56J+fall_2004
HumanitiesOpen learning
Accelerated Introductory Portuguese for Spanish Speakers
Accelerated Introductory Portuguese for Spanish Speakers covers the basics of Portuguese grammar and presents selected cultural aspects of the Lusophone world, with special emphasis on Brazil. Designed as an intensive introductory course equivalent to Portuguese I and II, it is a Portuguese course for native speakers of Spanish or speakers of other languages who have a native-like command of Spanish.
Dept 21G21G.880+fall_2013
Science & MathOpen learning
Acoustical Oceanography
This course will begin with brief overview of what important current research topics are in oceanography (physical, geological, and biological) and how acoustics can be used as a tool to address them. Three typical examples are climate, bottom geology, and marine mammal behavior. Will then address the acoustic inverse problem, reviewing inverse methods (linear and nonlinear) and the combination of acoustical methods with other measurements as an integrated system. Last part of course will concentrate on specific case studies, taken from current research journals. This course is taught on campus at MIT and with simultaneous video at Woods Hole Oceanographic Institution.
Dept 22.682+spring_2012
Electrical EngineeringOpen learning
Acoustics of Speech and Hearing
The Acoustics of Speech and Hearing is an H-Level graduate course that reviews the physical processes involved in the production, propagation and reception of human speech. Particular attention is paid to how the acoustics and mechanics of the speech and auditory system define what sounds we are capable of producing and what sounds we can sense. Areas of discussion include: the acoustic cues used in determining the direction of a sound source, the acoustic and mechanical mechanisms involved in speech production and the acoustic and mechanical mechanism used to transduce and analyze sounds in the ear.
Dept 6, HST6.551J+fall_2004
EngineeringOpen learning
Adaptive Antennas and Phased Arrays
The 16 lectures in this course cover the topics of adaptive antennas and phased arrays. Both theory and experiments are covered in the lectures. Part one (lectures 1 to 7) covers adaptive antennas. Part two (lectures 8 to 16) covers phased arrays. Parts one and two can be studied independently (in either order). The intended audience for this course is primarily practicing engineers and students in electrical engineering. This course is presented by Dr. Alan J. Fenn, senior staff member at MIT Lincoln Laboratory. Online Publication
Dept MITRES.LL-002+spring_2010
MarketingOpen learning
Adaptive Markets: Financial Market Dynamics and Human Behavior
Economists can’t agree on whether investors and markets are rational and efficient, as modern financial theory assumes, or irrational and inefficient, as behavioral economists believe. Drawing on psychology, evolutionary biology, neuroscience, artificial intelligence, and other fields, Prof. Lo cuts through the debate in this course with a new framework—the Adaptive Markets Hypothesis—in which rationality and irrationality coexist. Topics: Introduction and Financial Orthodoxy Rejecting the Random Walk and Efficient Markets Behavioral Biases and Psychology The Neuroscience of Decision-Making Evolution and the Origin of Behavior The Adaptive Markets Hypothesis Hedge Funds: The Galapagos Islands of Finance Applications of Adaptive Markets The Financial Crisis Ethics and Adaptive Markets The Finance of the Future and the Future of Finance As part of the Open Learning Library (OLL), this course is free to use. You have the option to sign up and enroll if you want to track your progress, or you can view and use all the materials without enrolling. Resources on OLL allow learners to learn at their own pace while receiving immediate feedback through interactive content and exercises.
Dept 1515.481X+fall_2022
Computer ScienceOpen learning
Advanced Algorithms
This is a graduate course on the design and analysis of algorithms, covering several advanced topics not studied in typical introductory courses on algorithms. It is especially designed for doctoral students interested in theoretical computer science.
Dept 6, 186.854J+fall_2008
EngineeringOpen learning
Advanced Algorithms
This course is a first-year graduate course in algorithms. Emphasis is placed on fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Techniques to be covered include amortization, randomization, fingerprinting, word-level parallelism, bit scaling, dynamic programming, network flow, linear programming, fixed-parameter algorithms, and approximation algorithms. Domains include string algorithms, network optimization, parallel algorithms, computational geometry, online algorithms, external memory, cache, and streaming algorithms, and data structures.
Dept 6, 186.854J+fall_2005
MathematicsOpen learning
Advanced Analytic Methods in Science and Engineering
Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.
Dept 1818.305+fall_2004
Cognitive ScienceOpen learning
Advanced Animal Behavior
The course includes survey and special topics designed for graduate students in the brain and cognitive sciences. It emphasizes ethological studies of natural behavior patterns and their analysis in laboratory work, with contributions from field biology (mammology, primatology), sociobiology, and comparative psychology. It stresses mammalian behavior but also includes major contributions from studies of other vertebrates and of invertebrates. It covers some applications of animal-behavior knowledge to neuropsychology and behavioral pharmacology.
Dept 99.201+spring_2000
MathematicsOpen learning
Advanced Calculus for Engineers
This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.
Dept 1818.075+fall_2004
Electrical EngineeringOpen learning
Advanced Circuit Techniques
Following a brief classroom discussion of relevant principles, each student in this course completes the paper design of several advanced circuits such as multiplexers, sample-and-holds, gain-controlled amplifiers, analog multipliers, digital-to-analog or analog-to-digital converters, and power amplifiers. One of each student’s designs is presented to the class, and one may be built and evaluated. Associated laboratory assignments emphasize the use of modern analog building blocks. This course is worth 12 Engineering Design Points.
Dept 66.331+spring_2002
ManagementOpen learning
Advanced Communication for Leaders
This course introduces interactive oral and interpersonal communication skills critical to leaders, including strategies for presenting to a hostile audience, running effective and productive meetings, active listening, and contributing to group decision-making. There are team-run classes on chosen communication topics, and an individual analysis of leadership qualities and characteristics. Students deliver an oral presentation and an executive summary, both aimed at a business audience.
Dept 1515.281+spring_2016
MathematicsOpen learning
Advanced Complexity Theory
This graduate-level course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.
Dept 6, 1818.405J+spring_2016
EngineeringOpen learning
Advanced Data Structures
Data structures play a central role in modern computer science. You interact with data structures even more often than with algorithms (think Google, your mail server, and even your network routers). In addition, data structures are essential building blocks in obtaining efficient algorithms. This course covers major results and current directions of research in data structure. Acknowledgments Thanks to videographers Martin Demaine and Justin Zhang.
Dept 66.851+spring_2012
PhysicsOpen learning
Advanced Electromagnetism
In 6.635, topics covered include: special relativity, electrodynamics of moving media, waves in dispersive media, microstrip integrated circuits, quantum optics, remote sensing, radiative transfer theory, scattering by rough surfaces, effective permittivities, random media, Green’s functions for planarly layered media, integral equations in electromagnetics, method of moments, time domain method of moments, EM waves in periodic structures: photonic crystals and negative refraction.
Dept 66.635+spring_2003
EngineeringOpen learning
Advanced Fluid Dynamics of the Environment
Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.
Dept 11.63+fall_2002
EngineeringOpen learning
Advanced Fluid Mechanics
This course is a survey of principal concepts and methods of fluid dynamics. Topics include mass conservation, momentum, and energy equations for continua; Navier-Stokes equation for viscous flows; similarity and dimensional analysis; lubrication theory; boundary layers and separation; circulation and vorticity theorems; potential flow; introduction to turbulence; lift and drag; surface tension and surface tension driven flows.
Dept 22.25+fall_2013
Civil EngineeringOpen learning
Advanced Geotechnical Engineering
1.364 examines site characterization and geotechnical aspects of the design and construction of foundation systems. Topics include: site investigation (with emphasis on in situ testing), shallow (footings and raftings) and deep (piles and caissons) foundations, excavation support systems, groundwater control, slope stability, soil improvement (compaction, soil reinforcement, etc.), and construction monitoring. This course is a core requirement for the Geotechnical Master of Engineering program at MIT.
Dept 11.364+fall_2003
LanguageOpen learning
Advanced German Literature & Culture: Madness, Murder, Mysteries
This course provides the opportunity to discuss, orally and in writing, cultural, ethical, and social issues on a stylistically sophisticated level. It explores representative and influential works from the nineteenth century to the present, through literary texts (prose, drama, poetry), radio plays, art, film, and architecture, as well as investigates topics such as the human and the machine, science and ethics, representation of memory, and issues of good and evil. Taught in German.
Dept 21G21G.412+fall_2014
LanguageOpen learning
Advanced German: Professional Communication
This course exposes students to current issues and language use in German technology, business, and international industrial relations, and discusses ramifications of these issues in a larger social and cultural context. We seek to prepare students who wish to work or study in a German-speaking country by focusing on specialized vocabulary and systematic training in speaking and writing skills to improve fluency and style and emphasizing communicative strategies that are crucial in a working environment. Discussion and analysis of newspaper and magazine articles, modern expository prose, and extensive use of online material are included. Taught in German.
Dept 21G21G.410+spring_2017
Earth ScienceOpen learning
Advanced Igneous Petrology
Advanced Igneous Petrology covers the history of and recent developments in the study of igneous rocks. Students review the chemistry and structure of igneous rock-forming minerals and proceed to study how these minerals occur and interact in igneous rocks. The course focuses on igneous processes and how we have learned about them through studying a number of significant sites worldwide.
Dept 1212.490+fall_2005
EconomicsOpen learning
Advanced Macroeconomics I
14.461 is an advanced course in macroeconomics that seeks to bring students to the research frontier. The course is divided into two sections. The first half is taught by Prof. Iván Werning and covers topics such as how to formulate and solve optimal problems. Students will study fiscal and monetary policy, among other issues. The second half, taught by Prof. George-Marios Angeletos, covers recent work on multiple equilibria, global games, and informational fictions.
Dept 1414.461+fall_2012
EconomicsOpen learning
Advanced Macroeconomics II
Professor Blanchard will discuss shocks, labor markets and unemployment, and dynamic stochastic general equilibrium models (DSGE models). Professor Lorenzoni will cover demand shocks, macroeconomic effects of news (with or without nominal rigidities), investment with credit constraints, and liquidity with its aggregate effects.
Dept 1414.462+spring_2007
EconomicsOpen learning
Advanced Macroeconomics II
14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information
Dept 1414.462+spring_2004
HumanitiesOpen learning
Advanced Natural Language Processing
This course is a graduate introduction to natural language processing - the study of human language from a computational perspective. It covers syntactic, semantic and discourse processing models, emphasizing machine learning or corpus-based methods and algorithms. It also covers applications of these methods and models in syntactic parsing, information extraction, statistical machine translation, dialogue systems, and summarization. The subject qualifies as an Artificial Intelligence and Applications concentration subject.
Dept 66.864+fall_2005
ChemistryOpen learning
Advanced Organic Chemistry
This course deals with the application of structure and theory to the study of organic reaction mechanisms: Stereochemical features including conformation and stereoelectronic effects; reaction dynamics, isotope effects and molecular orbital theory applied to pericyclic and photochemical reactions; and special reactive intermediates including carbenes, carbanions, and free radicals.
Dept 55.43+spring_2007
MathematicsOpen learning
Advanced Partial Differential Equations with Applications
The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.
Dept 1818.306+fall_2009
LinguisticsOpen learning
Advanced Phonology
This course focuses on phonological phenomena that are sensitive to morphological structure, including base-reduplicant identity, cyclicity, level ordering, derived environment effects, opaque rule interactions, and morpheme structure constraints. In the recent OT literature, it has been claimed that all of these phenomena can be analyzed with a single theoretical device: correspondence constraints, which regulate the similarity of lexically related forms (such as input and output, base and derivative, base and reduplicant).
Dept 2424.962+spring_2005
Visual ArtsOpen learning
Advanced Projects in the Visual Arts: Personal Narrative
This advanced video class serves goes into greater depth on the topics covered in 4.351 Introduction to Video. It also will explore the nature and function of narrative in cinema and video through exercises and screenings culminating in a final project. Starting with a brief introduction to the basic principles of classical narrative cinema, we will proceed to explore strategies designed to test the elements of narrative: story trajectory, character development, verisimilitude, time-space continuity, viewer identification, suspension of disbelief, and closure.
Dept 44.366+spring_2004
LinguisticsOpen learning
Advanced Semantics
This course is the second of the three parts of our graduate introduction to semantics. The others are 24.970 Introduction to Semantics and 24.954 Pragmatics in Linguistic Theory . Like the other courses, this one is not meant as an overview of the field and its current developments. Our aim is to help you to develop the ability for semantic analysis, and we think that exploring a few topics in detail together with hands-on practical work is more effective than offering a bird’s-eye view of everything. Once you have gained some experience in doing semantic analysis, reading around in the many recent handbooks and in current issues of major journals and attending our seminars and colloquia will give you all you need to prosper. Because we want to focus, we need to make difficult choices as to which topics to cover. This year, we will focus on topics having to do with modality, conditionals, tense, and aspect.
Dept 2424.973+spring_2009
BiologyOpen learning
Advanced Seminar in Geology and Geochemistry: Organic Geochemistry
12.491 is a seminar focusing on problems of current interest in geology and geochemistry. For Fall 2005, the topic is organic geochemistry. Lectures and readings cover recent research in the development and properties of organic matter.
Dept 1212.491+fall_2005
Urban StudiesOpen learning
Advanced Seminar: Urban Nature and City Design
This course will explore the mutual influences of ideas of nature, theories of city design and planning, and practices of urban design, construction, and management. We will investigate how natural processes shape urban landscapes (from the scale of street corner to region) and how to intervene strategically in those processes in order to achieve certain goals. We will examine cases of cities that adapted successfully to natural processes and those that did not. Students will then have the opportunity to research a case of their choice and to present their findings for discussion. The subject may be historical or an an example of contemporary theory and practice.
Dept 4, 1111.308J+fall_2012
Earth ScienceOpen learning
Advanced Soil Mechanics
This class presents the application of principles of soil mechanics. It considers the following topics: the origin and nature of soils; soil classification; the effective stress principle; hydraulic conductivity and seepage; stress-strain-strength behavior of cohesionless and cohesive soils and application to lateral earth stresses; bearing capacity and slope stability; consolidation theory and settlement analysis; and laboratory and field methods for evaluation of soil properties in design practice.
Dept 11.361+fall_2004
LanguageOpen learning
Advanced Spanish Conversation and Composition
En este curso el estudiante perfeccionará su comunicación oral y escrita mediante el estudio y la discusión de temas relacionados al impacto social y cultural de la ciencia y la tecnología en ciertas sociedades hispanas. Algunos de los temas a tratar son los efectos de los cambios tecnológicos en la estructura familiar y comunitaria, en las relaciones entre los sexos, en la identidad personal y cultural, en el mundo natural y en los sistemas de valores, la religión, la educación y el trabajo. También se examinan y discuten diversas actitudes hacia la innovación tecnológica y científica así como las ramificaciones éticas de las decisiones tecnológicas.
Dept 21G21G.711+spring_2014
LanguageOpen learning
Advanced Speaking and Critical Listening Skills (ELS)
This course is for advanced students who wish to build confidence and skills in spoken English. It focuses on the appropriate oral presentation of material in a variety of professional contexts: group discussions, classroom explanations and interactions, and theses/research proposals. It is valuable for those who intend to teach or lecture in English and includes language laboratory assignments. The goal of the workshop is to develop effective speaking and listening skills for academic and professional contexts.
Dept 21G21G.232+spring_2007
MathematicsOpen learning
Advanced Stochastic Processes
This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.
Dept 6, 1515.070J+fall_2013
EntrepreneurshipOpen learning
Advanced Strategy
This course draws on a wide range of perspectives to explore the roots of long term competitive advantage in unusually successful firms. Using a combination of cases, simulations, readings and, most importantly, lively discussion, the course will explore the ways in which long term advantage is built from first mover advantage, increasing returns, and unique organizational competencies. We will focus particularly on the ways in which the actions of senior management build competitive advantage over time, and on the strategic implications of understanding the roots of a firm’s success.
Dept 1515.963+spring_2008
PhysicsOpen learning
Advanced Structural Dynamics and Acoustics (13.811)
This course begins with the foundations of 3D elasticity, fluid and elastic wave equations, elastic and plastic waves in rods and beams, waves in plates, and dynamics and acoustics of cylindrical shells. The course considers acoustic fluids effects such as radiation and scattering by submerged plates and shells, and interaction between structural elements. Finally, it covers the response of plates and shells to high-intensity loads, dynamic plasticity and fracture, and structural damage caused by implosive and impact loads. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.811. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.067.
Dept 22.067+spring_2004
Environmental EngineeringOpen learning
Advanced Studio on the Production of Space
This class is developed around the concept of disobedient interference within the existing models of production of space and knowledge. Modeling is the main modus operandi of the class as students will be required to make critical diagrammatic cuts through processes of production in different thematic registers – from chemistry, law and economy to art, architecture and urbanism – in order to investigate the sense of social responsibility and control over the complex agendas embedded in models that supports production of everyday objects and surroundings. Students will be encouraged to explore relations between material or immaterial aspects and agencies of production, whether they emerged as a consequence of connection of mind, body and space, or the infrastructural, geographical and ecological complexities of the Anthropocene. These production environments will be taken as modeling settings.
Dept 44.313+fall_2016
LinguisticsOpen learning
Advanced Syntax
This course is a continuation of 24.951. This semester the course topics of interest include movement, phrase structure, and the architecture of the grammar.
Dept 2424.952+spring_2007
Business & ManagementOpen learning
Advanced System Architecture
This course provides a deep understanding of engineering systems at a level intended for research on complex engineering systems. It provides a review and extension of what is known about system architecture and complexity from a theoretical point of view while examining the origins of and recent developments in the field. The class considers how and where the theory has been applied, and uses key analytical methods proposed. Students examine the level of observational (qualitative and quantitative) understanding necessary for successful use of the theoretical framework for a specific engineering system. Case studies apply the theory and principles to engineering systems.
Dept ESDESD.342+spring_2006
Science & MathOpen learning
Advanced Thermodynamics
This course is a self-contained concise review of general thermodynamics concepts, multicomponent equilibrium properties, chemical equilibrium, electrochemical potentials, and chemical kinetics, as needed to introduce the methods of nonequilibrium thermodynamics and to provide a unified understanding of phase equilibria, transport, and nonequilibrium phenomena useful for future energy and climate engineering technologies. Applications include second-law efficiencies and methods to allocate primary energy consumptions and CO₂ emissions in cogeneration and hybrid power systems, minimum work of separation, maximum work of mixing, osmotic pressure and membrane equilibria, metastable states, spinodal decomposition, and Onsager’s near-equilibrium reciprocity in thermodiffusive, thermoelectric, and electrokinetic cross effects.
Dept 22.43+spring_2024
Computer ScienceOpen learning
Advanced Topics in Cryptography
The topics covered in this course include interactive proofs, zero-knowledge proofs, zero-knowledge proofs of knowledge, non-interactive zero-knowledge proofs, secure protocols, two-party secure computation, multiparty secure computation, and chosen-ciphertext security.
Dept 6, 186.876J+spring_2003
Data Science, Analytics & Computer TechnologyOpen learning
Advanced Topics in Cryptography
This course is about the evolution of proofs in computer science. We will learn about the power of interactive proofs, multi-prover interactive proofs, and probabilistically checkable proofs. We will then show how to use cryptography to convert these powerful proof systems into computationally sound non-interactive arguments (SNARGs).
Dept 66.5630+fall_2023
Art, Design & ArchitectureOpen learning
Advanced Topics in Hispanic Literature and Film: The Films of Luis Buñuel
This course considers films spanning the entire career of pioneering Spanish filmmaker Luis Buñuel (1900–1983), from his silent surrealist classic of 1929, Un perro andaluz , to his last film, Ese oscuro objeto del deseo (1977). We pay special attention to his Mexican period, in exile, and the films he made in, and about, Spain, including his work in documentary. It explores Buñuel’s early friendship with painter Salvador Dalí and poet Federico García Lorca, surrealist aesthetics, the influence of Freud’s ideas on dreams and sexuality, and the director’s corrosive criticism of bourgeois society and the Catholic church. We will focus on historical contexts and relevant film criticism. About This Course on OpenCourseWare The instructor of this course, Elizabeth Garrels, is a Professor Emeritus at MIT. She retired in 2014 after 35 years at the Institute. Professor Garrels taught this course for over 15 years, and it evolved over this time period. Normally, a course on OCW represents the version of a course taught during a specific semester and year. However, for this course we hope to represent the evolution of the course during the main years it was taught. The materials you see here are not from a particular iteration of the course, but are drawn from all of the years the course was taught.
Dept 21G21G.735+fall_2013
Real EstateOpen learning
Advanced Topics in Real Estate Finance
This half-semester course introduces and surveys a selection of cutting-edge topics in the field of real estate finance and investments. The course follows an informal “seminar” format to the maximum degree possible, with students expected to take considerable initiative. Lectures and discussions led by the instructors will be supplemented by several guest speakers from the real estate investment industry, who will present perspectives on current trends and important developments in the industry.
Dept 15, 1111.434J+spring_2007
Media StudiesOpen learning
Advanced Topics: Plotting Terror in European Culture
This interdisciplinary course surveys modern European culture to disclose the alignment of literature, opposition, and revolution. Reaching back to the foundational representations of anarchism in nineteenth-century Europe (Kleist, Conrad) the curriculum extends through the literary and media representations of militant organizations in the 1970s and 80s (Italy’s Red Brigade, Germany’s Red Army Faction, and the Real Irish Republican Army). In the middle of the term students will have the opportunity to hear a lecture by Margarethe von Trotta, one of the most important filmmakers who has worked on terrorism. The course concludes with a critical examination of the ways that certain segments of European popular media have returned to the “radical chic” that many perceive to have exhausted itself more than two decades ago.
Dept 21G21G.061+spring_2004
EconomicsOpen learning
Advanced Urban Public Finance: Collective Action and Provisions of Local Public Goods
In analyzing fiscal issues, conventional public finance approaches focus mainly on taxation and public spending. Policymakers and practitioners rarely explore solutions by examining the fundamental problem: the failure of interested parties to act collectively to internalize the positive externalities generated by public goods. Public finance is merely one of many possible institutional arrangements for assigning the rights and responsibilities to public goods consumption. This system is currently under stress because of the financial crisis. The first part of the class will focus on collective action and its connection with local public finance. The second part will explore alternative institutional arrangements for mediating collective action problems associated with the provision of local public goods. The objective of the seminar is to broaden the discussion of local public finance by incorporating collective action problems into the discourse. This inclusion aims at exploring alternative institutional arrangements for financing local public services in the face of severe economic downturn. Applications of emerging ideas to the provision of public health, education, and natural resource conservation will be discussed.
Dept 1111.902+spring_2009
HumanitiesOpen learning
Advanced Workshop in Writing for Science and Engineering (ELS)
This course offers analysis and practice of various forms of scientific and technical writing, from memos to journal articles, in addition to strategies for conveying technical information to specialist and non-specialist audiences. Comparable to 21W.780 Communicating in Technical Organizations , but methods in this course are designed to deal with special problems of advanced ELS or bilingual students. The goal of the workshop is to develop effective writing skills for academic and professional contexts. Models, materials, topics and assignments vary from term to term.
Dept 21G21G.225+spring_2016
LanguageOpen learning
Advanced Workshop in Writing for Social Sciences and Architecture (ELS)
This workshop is designed to help you write clearly, accurately and effectively in both an academic and a professional environment. In class, we analyze various forms of writing and address problems common to advanced speakers of English. We will often read one another’s work.
Dept 21G21G.228+spring_2007
LiteratureOpen learning
Advanced Writing Seminar
The purpose of this seminar is to expose the student to a number of different types of writing that one may encounter in a professional career. The class is an opportunity to write, review, rewrite and present a point of view both orally and in written form.
Dept 1111.229+spring_2004
AIOpen learning
Advances in Computer Vision
This course dives into advanced concepts in computer vision. A first focus is geometry in computer vision, including image formation, representation theory for vision, classic multi-view geometry, multi-view geometry in the age of deep learning, differentiable rendering, neural scene representations, correspondence estimation, optical flow computation, and point tracking. Next, we explore generative modeling and representation learning including image and video generation, guidance in diffusion models, and conditional probabilistic models, as well as representation learning in the form of contrastive and masking-based methods. Finally, we will explore the intersection of robotics and computer vision with “vision for embodied agents,” investigating the role of vision for decision-making, planning and control.
Dept 66.8300+spring_2025
Computer ScienceOpen learning
Adventures in Advanced Symbolic Programming
This course covers concepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers, computer-algebra systems, deductive systems, and some artificial intelligence applications. Topics include combinators, generic operations, pattern matching, pattern-directed invocation, rule systems, backtracking, dependencies, indeterminacy, memoization, constraint propagation, and incremental refinement. Substantial weekly programming assignments are an integral part of the subject. There will be extensive programming assignments, using MIT/GNU Scheme. Students should have significant programming experience in Scheme, Common Lisp, Haskell, CAML or some other “functional” language.
Dept 66.945+spring_2009
Aerospace EngineeringOpen learning
Aerodynamics
This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem.
Dept 1616.100+fall_2005
Aerospace EngineeringOpen learning
Aerodynamics of Viscous Fluids
The major focus of 16.13 is on boundary layers, and boundary layer theory subject to various flow assumptions, such as compressibility, turbulence, dimensionality, and heat transfer. Parameters influencing aerodynamic flows and transition and influence of boundary layers on outer potential flow are presented, along with associated stall and drag mechanisms. Numerical solution techniques and exercises are included.
Dept 1616.13+fall_2003
EngineeringOpen learning
Aerospace Biomedical and Life Support Engineering
This course introduces students to a quantitative approach to studying the problems of physiological adaptation in altered environments, especially microgravity and partial gravity environments. The course curriculum starts with an Introduction and Selected Topics, which provides background information on the physiological problems associated with human space flight, as well as reviewing terminology and key engineering concepts. Then curriculum modules on Bone Mechanics, Muscle Mechanics, Musculoskeletal Dynamics and Control, and the Cardiovascular System are presented. These modules start out with qualitative and biological information regarding the system and its adaptation, and progresses to a quantitative endpoint in which engineering methods are used to analyze specific problems and countermeasures. Additional course curriculum focuses on interdisciplinary topics, suggestions include extravehicular activity and life support. The final module consists of student term project work.
Dept 16, HST, IDS16.423J+spring_2006
Aerospace EngineeringOpen learning
Aerospace Dynamics
This undergraduate course builds upon the dynamics content of Unified Engineering, a sophomore course taught in the Department of Aeronautics and Astronautics at MIT. Vector kinematics are applied to translation and rotation of rigid bodies. Newtonian and Lagrangian methods are used to formulate and solve equations of motion. Additional numerical methods are presented for solving rigid body dynamics problems. Examples and problems describe applications to aircraft flight dynamics and spacecraft attitude dynamics.
Dept 1616.61+spring_2003
BiologyOpen learning
Affect: Neurobiological, Psychological and Sociocultural Counterparts of "Feelings"
This course studies the relations of affect to cognition and behavior, feeling to thinking and acting, and values to beliefs and practices. These connections will be considered at the psychological level of organization and in terms of their neurobiological and sociocultural counterparts.
Dept 99.68+spring_2013
Cognitive ScienceOpen learning
Affective Computing
This course instructs students on how to develop technologies that help people measure and communicate emotion, that respectfully read and that intelligently respond to emotion, and have internal mechanisms inspired by the useful roles emotions play.
Dept MASMAS.630+fall_2015
BiologyOpen learning
Affective Priming at Short and Extremely Short Exposures
This course is an investigation of affective priming and creation of rigorously counterbalanced, fully computerized testing paradigm. Includes background readings, study design, counterbalancing, study execution, data analysis, presentation of poster, and final paper.
Dept 99.51+spring_2003
ImagingOpen learning
AFNI Training Bootcamp
This training course is an introduction to the use of the AFNI software suites for the analysis of functional MRI (fMRI) data. It is not intended as an introduction to how fMRI works but is aimed at people who are already doing fMRI data analysis, or those who will be in the near future. AFNI (Analysis of Functional NeuroImages) is a leading software suite of C, Python, and R programs and shell scripts, primarily developed for the analysis and display of anatomical and fMRI data. It is freely available for research purposes. This event was organized by the Center for Brains, Minds, and Machines (CBMM) Trainee Leadership Council. CBMM is a multi-institutional NSF Science and Technology Center headquartered at MIT that is dedicated to developing a computationally based understanding of human intelligence and establishing an engineering practice based on that understanding. CBMM brings together computer scientists, cognitive scientists, and neuroscientists to create a new field—the science and engineering of intelligence.
Dept 9RES.9-006+spring_2018
HistoryOpen learning
Africa and the Politics of Knowledge
This course considers how, despite its immense diversity, Africa continues to hold purchase as both a geographical entity and meaningful knowledge category. It examines the relationship between articulations of “Africa” and projects like European imperialism, developments in the biological sciences, African de-colonization and state-building, and the imagining of the planet’s future. Readings in anthropology and history are organized around five themes: space and place, race, representation, self-determination, and time.
Dept 21G21G.025+spring_2019
LiteratureOpen learning
After Columbus
Sometime after 1492, the concept of the New World or America came into being, and this concept appeared differently - as an experience or an idea - for different people and in different places. This semester, we will read three groups of texts: first, participant accounts of contact between native Americans and French or English speaking Europeans, both in North America and in the Caribbean and Brazil; second, transformations of these documents into literary works by contemporaries; third, modern texts which take these earlier materials as a point of departure for rethinking the experience and aftermath of contact. The reading will allow us to compare perspectives across time and space, across the cultural geographies of religion, nation and ethnicity, and finally across a range of genres - reports, captivity narratives, essays, novels, poetry, drama, and film. Some of the earlier authors we will read are Michel Montaigne, William Shakespeare, Jean de Léry, Daniel Defoe and Mary Rowlandson; more recent authors include Derek Walcott, and J. M. Coetzee.
Dept 21G, 21L21L.007J+fall_2003
EngineeringOpen learning
AI 101
Machine vision. Data wrangling. Reinforcement learning. What do these terms even mean? In AI 101, MIT researcher Brandon Leshchinskiy offers an introduction to artificial intelligence that’s designed specifically for those with little to no background in the subject. The workshop starts with a summary of key concepts in AI, followed by an interactive exercise where participants train their own algorithm. Finally, it closes with a summary of key takeaways and Q/A. All are welcome!
Dept 6RES.6-013+fall_2021
International DevelopmentOpen learning
AIDS and Poverty in Africa
This is a discussion-based interactive seminar on the two major issues that affect Sub-Saharan Africa: HIV/AIDS and Poverty. AIDS and Poverty, seemingly different concepts, are more inter-related to each other in Africa than in any other continent. As MIT students, we feel it is important to engage ourselves in a dynamic discussion on the relation between the two - how to fight one and how to solve the other.
Dept ESES.253+spring_2005
Urban StudiesOpen learning
Air Traffic Control
This course introduces the various aspects of present and future Air Traffic Control systems. Among the topics in the present system that we will discuss are the systems-analysis approach to problems of capacity and safety, surveillance, including the National Airspace System and Automated Terminal Radar Systems, navigation subsystem technology, aircraft guidance and control, communications, collision avoidance systems and sequencing and spacing in terminal areas. The class will then talk about future directions and development and have a critical discussion of past proposals and of probable future problem areas.
Dept 1616.72+fall_2006
EngineeringOpen learning
Air Transportation Systems Architecting
This course addresses the architecting of air transportation systems. The focus is on the conceptual phase of product definition, including technical, economic, market, environmental, regulatory, legal, manufacturing, and societal factors. It centers on a realistic system case study and includes a number of lectures from industry and government. Past examples include: the Very Large Transport Aircraft, a Supersonic Business Jet, and a Next Generation Cargo System. The course identifies the critical system level issues and analyzes them in depth via student team projects and individual assignments. The overall goal of the semester is to produce a business plan and a system specifications document that can be used to assess candidate systems.
Dept 1616.886+spring_2004
Aerospace EngineeringOpen learning
Aircraft Stability and Control
This class includes a brief review of applied aerodynamics and modern approaches in aircraft stability and control. Topics covered include static stability and trim; stability derivatives and characteristic longitudinal and lateral-directional motions; and physical effects of the wing, fuselage, and tail on aircraft motion. Control methods and systems are discussed, with emphasis on flight vehicle stabilization by classical and modern control techniques; time and frequency domain analysis of control system performance; and human-pilot models and pilot-in-the-loop controls with applications. Other topics covered include V/STOL stability, dynamics, and control during transition from hover to forward flight; parameter sensitivity; and handling quality analysis of aircraft through variable flight conditions. There will be a brief discussion of motion at high angles-of-attack, roll coupling, and other nonlinear flight regimes.
Dept 1616.333+fall_2004
EngineeringOpen learning
Aircraft Systems Engineering
16.885J offers a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams retrospectively analyze an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Oral and written versions of the case study are delivered. For the Fall 2005 term, the class focuses on a systems engineering analysis of the Space Shuttle. It offers study of both design and operations of the shuttle, with frequent lectures by outside experts. Students choose specific shuttle systems for detailed analysis and develop new subsystem designs using state of the art technology.
Dept 16, ESD16.885J+fall_2005
Aerospace EngineeringOpen learning
Aircraft Systems Engineering
Aircraft are complex products comprised of many subsystems which must meet demanding customer and operational lifecycle value requirements. This course adopts a holistic view of the aircraft as a system, covering: basic systems engineering; cost and weight estimation; basic aircraft performance; safety and reliability; lifecycle topics; aircraft subsystems; risk analysis and management; and system realization. Small student teams “retrospectively analyze” an existing aircraft covering: key design drivers and decisions; aircraft attributes and subsystems; and operational experience. Finally, the student teams deliver oral and written versions of the case study.
Dept 16, ESD16.885J+fall_2004
ManagementOpen learning
Airline Management
This course provides an overview of airline management decision processes with a focus on economic issues and their relationship to operations planning models and decision support tools. It emphasizes the application of economic models of demand, pricing, costs, and supply to airline markets and networks, and it examines industry practice and emerging methods for fleet planning, route network design, scheduling, pricing and revenue management.
Dept 16, 116.75J+spring_2006
Urban StudiesOpen learning
Airline Schedule Planning
Explores a variety of models and optimization techniques for the solution of airline schedule planning and operations problems. Schedule design, fleet assignment, aircraft maintenance routing, crew scheduling, passenger mix, and other topics are covered. Recent models and algorithms addressing issues of model integration, robustness, and operations recovery are introduced. Modeling and solution techniques designed specifically for large-scale problems, and state-of-the-art applications of these techniques to airline problems are detailed.
Dept 16, 1, ESD1.206J+spring_2003
MathematicsOpen learning
Algebra I
This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.
Dept 1818.701+fall_2010
MathematicsOpen learning
Algebra I Student Notes
Algebra I is the first semester of a year-long introduction to modern algebra. Algebra is a fundamental subject, used in many advanced math courses and with applications in computer science, chemistry, etc. The focus of this class is studying groups, linear algebra, and geometry in different forms. These notes, which were created by students in a recent on-campus 18.701 Algebra I class, are offered here to supplement the materials included in OCW’s version of 18.701. They have not been checked for accuracy by the instructors of that class or by other MIT faculty members.
Dept 18RES.18-011+fall_2021
MathematicsOpen learning
Algebra II
This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.
Dept 1818.702+spring_2011
MathematicsOpen learning
Algebra II Student Notes
Algebra II is the second semester of a year-long introduction to modern algebra. The course focuses on group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. These notes, which were created by students in a recent on-campus 18.702 Algebra II class, are offered here to supplement the materials included in OCW’s version of 18.702. They have not been checked for accuracy by the instructors of that class or by other MIT faculty members.
Dept 18RES.18-012+spring_2022
MathematicsOpen learning
Algebraic Combinatorics
This course covers the applications of algebra to combinatorics. Topics include enumeration methods, permutations, partitions, partially ordered sets and lattices, Young tableaux, graph theory, matrix tree theorem, electrical networks, convex polytopes, and more.
Dept 1818.212+spring_2019
MathematicsOpen learning
Algebraic Geometry
This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.
Dept 1818.725+fall_2015
MathematicsOpen learning
Algebraic Geometry
This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also analyzes the relations between complex algebraic varieties and complex analytic varieties.
Dept 1818.725+fall_2003
MathematicsOpen learning
Algebraic Geometry
This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.
Dept 1818.726+spring_2009
