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Description

This class is an applications-oriented course covering the modeling of large-scale systems in decision-making domains and the optimization of such systems using state-of-the-art optimization tools. Application domains include: transportation and logistics planning, pattern classification and image processing, data mining, design of structures, scheduling in large systems, supply-chain management, financial engineering, and telecommunications systems planning. Modeling tools and techniques include linear, network, discrete and nonlinear optimization, heuristic methods, sensitivity and post-optimality analysis, decomposition methods for large-scale systems, and stochastic optimization. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5223 This class is an applications-oriented course covering the modeling of large-scale systems in decision-making domains and the optimization of such systems using state-of-the-art optimization tools. Application domains include: transportation and logistics planning, pattern classification and image processing, data mining, design of structures, scheduling in large systems, supply-chain management, financial engineering, and telecommunications systems planning. Modeling tools and techniques include linear, network, discrete and nonlinear optimization, heuristic methods, sensitivity and post-optimality analysis, decomposition methods for large-scale systems, and stochastic optimization. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5223Subjects

decision making | decision making | management | management | Mathematical optimization | Mathematical optimization | modeling of large-scale system | modeling of large-scale system | optimization software | optimization software | telecommunications system planning | telecommunications system planning | 15.094 | 15.094 | 1.142 | 1.142 | SMA 5223 | SMA 5223License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.316 Building and Leading Effective Teams (MIT) 15.316 Building and Leading Effective Teams (MIT)

Description

This course is an intensive one-week introduction to leadership, teams, and learning communities. The class meets daily for five days. The class serves as an introduction of concepts and uses a variety of experiential exercises to develop individual and team skills, as well as supportive relationships within the Leaders for Manufacturing class. As part of the focus on leadership, it discusses the idea of the "Universe Within", the images, thoughts, and experiences that are internal to all leaders. This course is an intensive one-week introduction to leadership, teams, and learning communities. The class meets daily for five days. The class serves as an introduction of concepts and uses a variety of experiential exercises to develop individual and team skills, as well as supportive relationships within the Leaders for Manufacturing class. As part of the focus on leadership, it discusses the idea of the "Universe Within", the images, thoughts, and experiences that are internal to all leaders.Subjects

leadership | leadership | teambuilding | teambuilding | ladder of inference | ladder of inference | learning communities | learning communities | experiences | experiences | management | management | teams | teams | skill set | skill set | facilitation | facilitation | motivation | motivation | decision making | decision making | planned change | planned change | Universe Within | Universe Within | Fifth Discipline | Fifth Discipline | Peter Senge | Peter Senge | Rick Ross | Rick RossLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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The nuts and bolts of preparing a Business Plan will be explored in this 16th annual course offering. The course is open to members of the MIT Community and to others interested in entrepreneurship. It is particularly recommended for persons who are interested in starting or are involved in a new business. Because some of the speakers will be judges of the MIT $50K Entrepreneurship Competition, persons who are planning to enter the Competition should find the course particularly useful. Historically, the number of students taking the course is 250+, divided approximately 50/50 between Scientist/Engineers and Sloan students. The nuts and bolts of preparing a Business Plan will be explored in this 16th annual course offering. The course is open to members of the MIT Community and to others interested in entrepreneurship. It is particularly recommended for persons who are interested in starting or are involved in a new business. Because some of the speakers will be judges of the MIT $50K Entrepreneurship Competition, persons who are planning to enter the Competition should find the course particularly useful. Historically, the number of students taking the course is 250+, divided approximately 50/50 between Scientist/Engineers and Sloan students.Subjects

preparing a Business Plan | preparing a Business Plan | entrepreneurship | entrepreneurship | new business | new business | MIT $50K Entrepreneurship Competition | MIT $50K Entrepreneurship Competition | seminar | seminarLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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Much of 15.617 focuses on mergers and acquisitions (M&A), and the law-sensitive aspects of financial services and financial markets. The course is designed to be an introduction to business law that covers the fundamentals, including contracts, liability, regulation, employment, and corporations. This class also provides an in-depth treatment of the law of finance. Much of 15.617 focuses on mergers and acquisitions (M&A), and the law-sensitive aspects of financial services and financial markets. The course is designed to be an introduction to business law that covers the fundamentals, including contracts, liability, regulation, employment, and corporations. This class also provides an in-depth treatment of the law of finance.Subjects

corporate finance | corporate finance | financial markets | financial markets | finance law | finance law | corporate law | corporate law | business law | business law | contracts | contracts | liability | liability | regulation | regulation | employment | employment | mergers | mergers | acquisitions | acquisitions | A | A | international financial markets | international financial markets | venture capital | venture capital | private equity | private equity | corporate financial structure | corporate financial structure | antitrust | antitrust | bankruptcy | bankruptcy | reorganization | reorganization | financial products | financial products | financial services | financial services | financial liability | financial liability | courts | courts | legal action | legal action | taxes | taxes | tax law | tax law | deal structures | deal structures | purchase agreement | purchase agreement | buying companies | buying companies | purchasing company | purchasing company | joint ventures | joint ventures | publicly-held corporations | publicly-held corporations | public offerings | public offerings | commercial lending | commercial lending | hedge fund building | hedge fund buildingLicense

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15.014 focuses on using case studies to investigate the macroenvironment in which firms operate. The course is divided in five parts: Basic tools of macroeconomic management Evaluation of different economic development strategies Crises in emerging markets: causes, solutions, and prevention Problems faced by transition economies Challenges of developed countries This course is a full-term version of Applied Macro- and International Economics (15.012), with additional topics. 15.014 focuses on using case studies to investigate the macroenvironment in which firms operate. The course is divided in five parts: Basic tools of macroeconomic management Evaluation of different economic development strategies Crises in emerging markets: causes, solutions, and prevention Problems faced by transition economies Challenges of developed countries This course is a full-term version of Applied Macro- and International Economics (15.012), with additional topics.Subjects

macroeconomics | macroeconomics | international economics | international economics | world economies | world economies | global trade | global trade | economic policy | economic policy | inflation | inflation | interest rates | interest rates | exchange rates | exchange rates | national economic strategies | national economic strategies | developing nations | developing nations | currency crisis | currency crisis | transition economies | transition economies | global markets | global markets | world bank | world bank | IMF | IMF | international monetary fund | international monetary fund | monetary policy | monetary policy | depression | depression | unemployment | unemployment | international financial architecture | international financial architectureLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.063 Communicating With Data (MIT) 15.063 Communicating With Data (MIT)

Description

Communicating With Data has a distinctive structure and content, combining fundamental quantitative techniques of using data to make informed management decisions with illustrations of how real decision makers, even highly trained professionals, fall prey to errors and biases in their understanding. We present the fundamental concepts underlying the quantitative techniques as a way of thinking, not just a way of calculating, in order to enhance decision-making skills. Rather than survey all of the techniques of management science, we stress those fundamental concepts and tools that we believe are most important for the practical analysis of management decisions, presenting the material as much as possible in the context of realistic business situations from a variety of settings. Exer Communicating With Data has a distinctive structure and content, combining fundamental quantitative techniques of using data to make informed management decisions with illustrations of how real decision makers, even highly trained professionals, fall prey to errors and biases in their understanding. We present the fundamental concepts underlying the quantitative techniques as a way of thinking, not just a way of calculating, in order to enhance decision-making skills. Rather than survey all of the techniques of management science, we stress those fundamental concepts and tools that we believe are most important for the practical analysis of management decisions, presenting the material as much as possible in the context of realistic business situations from a variety of settings. ExerSubjects

quantitative | quantitative | data analysis | data analysis | graphs | graphs | charts | charts | factual decisions | factual decisions | statistics | statistics | communication | communication | fact-based | fact-based | information analysis | information analysis | spreadsheets | spreadsheets | models | models | probability | probability | decision analysis | decision analysis | regression | regression | simulation | simulation | linear | linear | nonlinear | nonlinear | optimization | optimization | data | data | analysis | analysis | marketing | marketing | finance | finance | operations management | operations management | strategy | strategy | operations | operations | management | management | diagrams | diagrams | formula | formula | structure | structure | content | contentLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.057 Systems Optimization (MIT) 15.057 Systems Optimization (MIT)

Description

Managers and engineers are constantly attempting to optimize, particularly in the design and operation of complex systems. This course is an application-oriented introduction to (systems) optimization. It seeks to: Motivate the use of optimization models to support managers and engineers in a wide variety of decision making situations; Show how several application domains (industries) use optimization; Introduce optimization modeling and solution techniques (including linear, non-linear, integer, and network optimization, and heuristic methods); Provide tools for interpreting and analyzing model-based solutions (sensitivity and post-optimality analysis, bounding techniques); and Develop the skills required to identify the opportunity and manage the implementation of an optimization-based Managers and engineers are constantly attempting to optimize, particularly in the design and operation of complex systems. This course is an application-oriented introduction to (systems) optimization. It seeks to: Motivate the use of optimization models to support managers and engineers in a wide variety of decision making situations; Show how several application domains (industries) use optimization; Introduce optimization modeling and solution techniques (including linear, non-linear, integer, and network optimization, and heuristic methods); Provide tools for interpreting and analyzing model-based solutions (sensitivity and post-optimality analysis, bounding techniques); and Develop the skills required to identify the opportunity and manage the implementation of an optimization-basedSubjects

system optimization | system optimization | distribution | distribution | production planning | production planning | supply chain managment | supply chain managment | scheduling | inventory | scheduling | inventory | scheduling | scheduling | inventory | inventoryLicense

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See all metadata15.311 Organizational Processes (MIT) 15.311 Organizational Processes (MIT)

Description

Organizational Processes enhances students' ability to take effective action in complex organizational settings by providing the analytic tools needed to analyze, manage, and lead the organizations of the future. Emphasis is placed on the importance of the organizational context in influencing which individual styles and skills are effective. The subject centers on three complementary perspectives, or "lenses", on an organization: political, cultural, and strategic design. Students enrolled in this class are also jointly enrolled in 15.328, Team Project, in order to complete a field study of an organizational change initiative. Organizational Processes also operates in conjunction with 15.280, Communication for Managers, by sharing certain assignments and holding some Organizational Processes enhances students' ability to take effective action in complex organizational settings by providing the analytic tools needed to analyze, manage, and lead the organizations of the future. Emphasis is placed on the importance of the organizational context in influencing which individual styles and skills are effective. The subject centers on three complementary perspectives, or "lenses", on an organization: political, cultural, and strategic design. Students enrolled in this class are also jointly enrolled in 15.328, Team Project, in order to complete a field study of an organizational change initiative. Organizational Processes also operates in conjunction with 15.280, Communication for Managers, by sharing certain assignments and holding someSubjects

optimal organization | optimal organization | corporate structure | corporate structure | bureaucracy | bureaucracy | organizational behavior | organizational behavior | contingency theory | contingency theory | organizational change | organizational change | power | power | politics | politics | culture | culture | strategic design | strategic design | studying organizations | studying organizations | team project | team project | hiring | hiring | decision making | decision making | business ethics | business ethics | corporate incentives | corporate incentives | authority | authority | networks | networks | negotiation | negotiation | bargaining | bargaining | leading change | leading change | complex organizations | complex organizations | organizational analysis | organizational analysis | management | management | leadership | leadership | experiential learning | experiential learning | case studies | case studies | political perspective | political perspective | cultural perspective | cultural perspectiveLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata15.515 Financial Accounting (MIT) 15.515 Financial Accounting (MIT)

Description

Our goal is to help you develop a framework for understanding financial, managerial, and tax reports. The course goal is divided into five subordinate challenges that can help you organize the way you learn accounting: The record keeping and reporting challenge The computation challenge The judgment challenge The usage challenge The search challenge The course adopts a decision-maker perspective of accounting by emphasizing the relation between accounting data and the underlying economic events generating them. Restricted to first-year Sloan MBA students. Acknowledgements Acknowledgment is hereby given to Professor G. Peter Wilson for his authorship of the following content in this course: The Five Challenges (see Syllabus and Lecture 1) "What Do Intel and Accountants Have in Common? Our goal is to help you develop a framework for understanding financial, managerial, and tax reports. The course goal is divided into five subordinate challenges that can help you organize the way you learn accounting: The record keeping and reporting challenge The computation challenge The judgment challenge The usage challenge The search challenge The course adopts a decision-maker perspective of accounting by emphasizing the relation between accounting data and the underlying economic events generating them. Restricted to first-year Sloan MBA students. Acknowledgements Acknowledgment is hereby given to Professor G. Peter Wilson for his authorship of the following content in this course: The Five Challenges (see Syllabus and Lecture 1) "What Do Intel and Accountants Have in Common?Subjects

acquisitions | acquisitions | finances | finances | financial accounting | financial accounting | balancing the books | balancing the books | accountants | accountants | accrual accounting | accrual accounting | cash basis | cash basis | financial statements | financial statements | bookkeeping | bookkeeping | income statement | income statement | balance sheet | balance sheet | retained earnings | retained earnings | fiscal period | fiscal period | statement of cash flows | statement of cash flows | statement of owners' equity | statement of owners' equity | financial ratios | financial ratios | profits and losses | profits and losses | recognizing revenue | recognizing revenue | doubtful accounts | doubtful accounts | income | income | expenses | expenses | analyzing financial records | analyzing financial records | LIFO | LIFO | FIFO | FIFO | cost of goods sold | cost of goods sold | depreciation | depreciation | taxes | taxes | securities | securities | debt | debt | valuation | valuation | valuing a company | valuing a companyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata16.842 Fundamentals of Systems Engineering (MIT) 16.842 Fundamentals of Systems Engineering (MIT)

Description

This course introduces the principles and methods of Systems Engineering. Lectures follow the "V"-model of Systems Engineering, including needs identification, requirements formulation, concept generation and selection, trade studies, preliminary and detailed design, component and subsystem test and integration as well as functional testing and delivery and operations. Additional concepts such as tradeoffs between performance, cost and system operability will be discussed. Systems Engineering standards and selected journal articles serve as a basis for readings, and individual homework assignments will apply the concepts from class. Both aeronautical and astronautical applications are covered. The class serves as preparation for the systems field exam in the Department of Aeronau This course introduces the principles and methods of Systems Engineering. Lectures follow the "V"-model of Systems Engineering, including needs identification, requirements formulation, concept generation and selection, trade studies, preliminary and detailed design, component and subsystem test and integration as well as functional testing and delivery and operations. Additional concepts such as tradeoffs between performance, cost and system operability will be discussed. Systems Engineering standards and selected journal articles serve as a basis for readings, and individual homework assignments will apply the concepts from class. Both aeronautical and astronautical applications are covered. The class serves as preparation for the systems field exam in the Department of AeronauSubjects

fundamentals of systems engineering | fundamentals of systems engineering | stakeholder analysis | stakeholder analysis | requirements definition | requirements definition | system architecture | system architecture | concept generation and selection | concept generation and selection | tradespace exploration | tradespace exploration | multidisciplinary optimization | multidisciplinary optimization | human factors in engineering | human factors in engineering | systems integration | systems integration | verification and validation | verification and validation | system safety | system safety | lifecycle management | lifecycle managementLicense

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See all metadata16.89J Space Systems Engineering (MIT) 16.89J Space Systems Engineering (MIT)

Description

In 16.89 / ESD.352 the students will first be asked to understand the key challenges in designing ground and space telescopes, the stakeholder structure and value flows, and the particular pros and cons of the proposed project. The first half of the class will concentrate on performing a thorough architectural analysis of the key astrophysical, engineering, human, budgetary and broader policy issues that are involved in this decision. This will require the students to carry out a qualitative and quantitative conceptual study during the first half of the semester and recommend a small set of promising architectures for further study at the Preliminary Design Review (PDR).Both lunar surface telescopes as well as orbital locations should be considered.The second half of the class will then pi In 16.89 / ESD.352 the students will first be asked to understand the key challenges in designing ground and space telescopes, the stakeholder structure and value flows, and the particular pros and cons of the proposed project. The first half of the class will concentrate on performing a thorough architectural analysis of the key astrophysical, engineering, human, budgetary and broader policy issues that are involved in this decision. This will require the students to carry out a qualitative and quantitative conceptual study during the first half of the semester and recommend a small set of promising architectures for further study at the Preliminary Design Review (PDR).Both lunar surface telescopes as well as orbital locations should be considered.The second half of the class will then piSubjects

16.89 | 16.89 | ESD.352 | ESD.352 | System Requirements Review | System Requirements Review | Preliminary Design Review | Preliminary Design Review | Critical Design Review | Critical Design Review | Conceptual Design Phase | Conceptual Design Phase | Preliminary Design Phase | Preliminary Design Phase | Detailed Design Phase | Detailed Design Phase | astrophysics | astrophysics | Stakeholder Analysis | Stakeholder Analysis | System Architecture | System Architecture | Radio Astronomy | Radio Astronomy | Space Telescope | Space Telescope | Interferometry | Interferometry | Lunar Logistics | Lunar LogisticsLicense

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This course introduces analysis techniques for complex structures and the role of material properties in structural design, failure, and longevity. Students will learn about the energy principles in structural analysis and their applications to statically-indeterminate structures and solid continua. Additionally, the course will examine matrix and finite-element methods of structured analysis including bars, beams, and two-dimensional plane stress elements. Structural materials and their properties will be considered, as will metals and composites. Other topics include modes of structural failure, criteria for yielding and fracture, crack formation and fracture mechanics, and fatigue and design for longevity. Students are expected to apply these concepts to their own structural design proj This course introduces analysis techniques for complex structures and the role of material properties in structural design, failure, and longevity. Students will learn about the energy principles in structural analysis and their applications to statically-indeterminate structures and solid continua. Additionally, the course will examine matrix and finite-element methods of structured analysis including bars, beams, and two-dimensional plane stress elements. Structural materials and their properties will be considered, as will metals and composites. Other topics include modes of structural failure, criteria for yielding and fracture, crack formation and fracture mechanics, and fatigue and design for longevity. Students are expected to apply these concepts to their own structural design projSubjects

Expository writing | Expository writing | analyzing | analyzing | mass | mass | media | media | voice | voice | academic | academic | writing | writing | self-discovery | self-discovery | critical thinking | critical thinking | communicating | communicating | audience | audience | drafting | drafting | revising | revising | essays | essays | analysis techniques | analysis techniques | complex structures | complex structures | material properties | material properties | structural design | structural design | failure | failure | longevity | longevity | Energy principles | Energy principles | structural analysis | structural analysis | statically-indeterminate structures | statically-indeterminate structures | solid continua | solid continua | Crack formation | Crack formation | fracture mechanics | fracture mechanics | failure modes | failure modesLicense

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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. 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.Subjects

Air transportation | Air transportation | air transport | air transport | air transportation systems | air transportation systems | product definition | product definition | air transportation industry | air transportation industry | system case study | system case study | very large transport aircraft | very large transport aircraft | supersonic business jet | supersonic business jet | next generation cargo system | next generation cargo system | business plan | business plan | system specifications document | system specifications documentLicense

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See all metadata16.13 Aerodynamics of Viscous Fluids (MIT) 16.13 Aerodynamics of Viscous Fluids (MIT)

Description

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. 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.Subjects

aerodynamics | aerodynamics | viscous fluids | viscous fluids | viscosity | viscosity | fundamental theorem of kinematics | fundamental theorem of kinematics | convection | convection | vorticity | vorticity | strain | strain | Eulerian description | Eulerian description | Lagrangian description | Lagrangian description | conservation of mass | conservation of mass | continuity | continuity | conservation of momentum | conservation of momentum | stress tensor | stress tensor | newtonian fluid | newtonian fluid | circulation | circulation | Navier-Stokes | Navier-Stokes | similarity | similarity | dimensional analysis | dimensional analysis | thin shear later approximation | thin shear later approximation | TSL coordinates | TSL coordinates | boundary conditions | boundary conditions | shear later categories | shear later categories | local scaling | local scaling | Falkner-Skan flows | Falkner-Skan flows | solution techniques | solution techniques | finite difference methods | finite difference methods | Newton-Raphson | Newton-Raphson | integral momentum equation | integral momentum equation | Thwaites method | Thwaites method | integral kinetic energy equation | integral kinetic energy equation | dissipation | dissipation | asymptotic perturbation | asymptotic perturbation | displacement body | displacement body | transpiration | transpiration | form drag | form drag | stall | stall | interacting boundary layer theory | interacting boundary layer theory | stability | stability | transition | transition | small-perturbation | small-perturbation | Orr-Somemerfeld | Orr-Somemerfeld | temporal amplification | temporal amplification | spatial amplification | spatial amplification | Reynolds | Reynolds | Prandtl | Prandtl | turbulent boundary layer | turbulent boundary layer | wake | wake | wall layers | wall layers | inner variables | inner variables | outer variables | outer variables | roughness | roughness | Clauser | Clauser | Dissipation formula | Dissipation formula | integral closer | integral closer | turbulence modeling | turbulence modeling | transport models | transport models | turbulent shear layers | turbulent shear layers | compressible then shear layers | compressible then shear layers | compressibility | compressibility | temperature profile | temperature profile | heat flux | heat flux | 3D boundary layers | 3D boundary layers | crossflow | crossflow | lateral dilation | lateral dilation | 3D separation | 3D separation | constant-crossflow | constant-crossflow | 3D transition | 3D transition | compressible thin shear layers | compressible thin shear layersLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course covers a collection of geometric techniques that apply broadly in modern algorithm design. This course covers a collection of geometric techniques that apply broadly in modern algorithm design.Subjects

Spectral graph theory | Spectral graph theory | Iterative methods for linear algebra | Iterative methods for linear algebra | Convex geometry | Convex geometry | Lattices and basis reduction | Lattices and basis reduction | LPs and SDPs for approximating NP-hard problems | LPs and SDPs for approximating NP-hard problems | Graph Laplacians | Graph Laplacians | Cheeger inequalities | Cheeger inequalities | Fritz John?s theorem | Fritz John?s theoremLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc. This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc.Subjects

monoidal functors | monoidal functors | tensor | tensor | pivotal | pivotal | spherical | spherical | MacLane's | MacLane's | Grthendieck | Grthendieck | module categories | module categories | braided tensor | braided tensor | Muger centralizer | Muger centralizer | symmetric categories | symmetric categories | deligne's theorem | deligne's theorem | radford formula | radford formula | squared norms | squared norms | global dimensions | global dimensions | cohomology | cohomology | oceanu ridigity | oceanu ridigity | robenius-perron | robenius-perron | lifting theory | lifting theoryLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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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. 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.Subjects

partial differential equations (pde) | partial differential equations (pde) | nonlinear pde. Diffusion | nonlinear pde. Diffusion | dispersion | dispersion | Initial and boundary value problems | Initial and boundary value problems | Characteristics and shocks | Characteristics and shocks | Separation of variables | Separation of variables | transform methods | transform methods | Green's functions | Green's functions | Asymptotics | Asymptotics | geometrical theory | geometrical theory | Dimensional analysis | Dimensional analysis | self-similarity | self-similarity | traveling waves | traveling waves | Singular perturbation and boundary layers | Singular perturbation and boundary layers | Solitons | Solitons | Variational methods | Variational methods | Free-boundary problems | Free-boundary problemsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.705 Commutative Algebra (MIT) 18.705 Commutative Algebra (MIT)

Description

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory. In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.Subjects

rings | rings | ideals | ideals | modules | modules | chain conditions | chain conditions | integral | integral | localization | localization | decomposition | decomposition | dedekind domain | dedekind domain | tensor | tensor | dimension theory | dimension theory | Zorn's lemma | Zorn's lemma | hilbert theorem | hilbert theorem | DVR | DVR | normalization | normalization | artin ring | artin ring | nakayama's lemma | nakayama's lemma | zerodivisors | zerodivisors | noether | noether | nullsetellensatz | nullsetellensatzLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.112 Functions of a Complex Variable (MIT) 18.112 Functions of a Complex Variable (MIT)

Description

This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted. This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions. This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted. This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions.Subjects

functions of one complex variable | functions of one complex variable | Cauchy's theorem | Cauchy's theorem | holomorphic functions | holomorphic functions | meromorphic functions | meromorphic functions | residues | residues | contour integrals | contour integrals | conformal mapping | conformal mapping | Infinite series and products | Infinite series and products | the gamma function | the gamma function | the Mittag-Leffler theorem | the Mittag-Leffler theorem | Harmonic functions | Harmonic functions | Dirichlet's problem | Dirichlet's problem | The Riemann mapping theorem | The Riemann mapping theorem | The Riemann Zeta function | The Riemann Zeta functionLicense

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See all metadata18.310C Principles of Applied Mathematics (MIT) 18.310C Principles of Applied Mathematics (MIT)

Description

Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, game theory. There is an emphasis on topics that have direct application in the real world. This course was recently revised to meet the MIT Undergraduate Communication Requirement (CR). It covers the same content as 18.310, but assignments are structured with an additional focus on writing. Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, game theory. There is an emphasis on topics that have direct application in the real world. This course was recently revised to meet the MIT Undergraduate Communication Requirement (CR). It covers the same content as 18.310, but assignments are structured with an additional focus on writing.Subjects

sorting algorithms | sorting algorithms | information theory | information theory | coding theory | coding theory | secret codes | secret codes | generating functions | generating functions | linear programming | linear programming | game theory | game theoryLicense

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See all metadata18.098 Street-Fighting Mathematics (MIT) 18.098 Street-Fighting Mathematics (MIT)

Description

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) 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. This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) 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.Subjects

extreme-cases reasoning | extreme-cases reasoning | dimensional analysis | dimensional analysis | discretization | discretization | drag | drag | fluid mechanics | fluid mechanics | pendulum | pendulum | pictorial proofs | pictorial proofs | analogy | analogy | operators | operators | summation | summation | square roots | square roots | logarithms | logarithms | musical intervals | musical intervals | taking out the big part | taking out the big part | integration | integration | differentiation | differentiationLicense

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18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory. 18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory.Subjects

Infinitude of the primes | Infinitude of the primes | Summing powers of integers | Summing powers of integers | Bernoulli polynomials | Bernoulli polynomials | sine product formula | sine product formula | $\zeta(2n)$ | $\zeta(2n)$ | Fermat's Little Theorem | Fermat's Little Theorem | Fermat's Great Theorem | Fermat's Great Theorem | Averages of arithmetic functions | Averages of arithmetic functions | arithmetic-geometric mean | arithmetic-geometric mean | Gauss' theorem | Gauss' theorem | Wallis's formula | Wallis's formula | Stirling's formula | Stirling's formula | prime number theorem | prime number theorem | Riemann's hypothesis | Riemann's hypothesis | Euler's proof of infinitude of primes | Euler's proof of infinitude of primes | Density of prime numbers | Density of prime numbers | Euclidean algorithm | Euclidean algorithm | Golden Ratio | Golden RatioLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics. This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics.Subjects

basic computational methods cell on a molecular level | basic computational methods cell on a molecular level | sequence alignment algorithms | sequence alignment algorithms | dynamic programming | dynamic programming | hashing | hashing | suffix trees | suffix trees | Gibbs sampling | Gibbs sampling | genetic and physical mapping | genetic and physical mapping | genome sequencing | genome sequencing | assembly | assembly | and annotation | and annotation | RNA expression and secondary structure | RNA expression and secondary structure | protein structure and folding | protein structure and folding | and molecular interactions and dynamics | and molecular interactions and dynamics | annotation | annotation | molecular interactions and dynamics | molecular interactions and dynamicsLicense

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See all metadata18.409 Behavior of Algorithms (MIT) 18.409 Behavior of Algorithms (MIT)

Description

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. 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.Subjects

Condition number | Condition number | largest singluar value of a matrix | largest singluar value of a matrix | Smoothed analysis | Smoothed analysis | Gaussian elimination | Gaussian elimination | Growth factors of partial and complete pivoting | Growth factors of partial and complete pivoting | GE of graphs with low bandwidth or small separators | GE of graphs with low bandwidth or small separators | Spectral Partitioning of planar graphs | Spectral Partitioning of planar graphs | spectral paritioning of well-shaped meshes | spectral paritioning of well-shaped meshes | spectral paritioning of nearest neighbor graphs | spectral paritioning of nearest neighbor graphs | Turner's theorem | Turner's theorem | bandwidth of semi-random graphs. | bandwidth of semi-random graphs. | McSherry's spectral bisection algorithm | McSherry's spectral bisection algorithm | Linear Programming | Linear Programming | von Neumann's algorithm | von Neumann's algorithm | primal and dual simplex methods | and duality Strong duality theorem | primal and dual simplex methods | and duality Strong duality theorem | Renegar's condition numbers | Renegar's condition numbersLicense

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See all metadata18.S66 The Art of Counting (MIT) 18.S66 The Art of Counting (MIT)

Description

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment. The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.Subjects

enumerative combinatorics | enumerative combinatorics | finite set | finite set | sum of positive integers | sum of positive integers | bijective proofs | bijective proofs | bijection (one-to-one correspondence) | bijection (one-to-one correspondence) | permutations | permutations | partitions | partitions | Catalan numbers | Catalan numbers | Young tableaux | Young tableaux | lattice paths and tilings | lattice paths and tilingsLicense

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