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15.062 Data Mining (MIT) 15.062 Data Mining (MIT)

Description

Data that has relevance for managerial decisions is accumulating at an incredible rate due to a host of technological advances. Electronic data capture has become inexpensive and ubiquitous as a by-product of innovations such as the internet, e-commerce, electronic banking, point-of-sale devices, bar-code readers, and intelligent machines. Such data is often stored in data warehouses and data marts specifically intended for management decision support. Data mining is a rapidly growing field that is concerned with developing techniques to assist managers to make intelligent use of these repositories. A number of successful applications have been reported in areas such as credit rating, fraud detection, database marketing, customer relationship management, and stock market investments. The f Data that has relevance for managerial decisions is accumulating at an incredible rate due to a host of technological advances. Electronic data capture has become inexpensive and ubiquitous as a by-product of innovations such as the internet, e-commerce, electronic banking, point-of-sale devices, bar-code readers, and intelligent machines. Such data is often stored in data warehouses and data marts specifically intended for management decision support. Data mining is a rapidly growing field that is concerned with developing techniques to assist managers to make intelligent use of these repositories. A number of successful applications have been reported in areas such as credit rating, fraud detection, database marketing, customer relationship management, and stock market investments. The f

Subjects

data warehouses | data warehouses | internet | internet | e-commerce | e-commerce | electronic banking | electronic banking | point-of-sale devices | point-of-sale devices | bar-code readers | bar-code readers | intelligent machines | intelligent machines

License

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15.515 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 company

License

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15.974 Leadership Lab (MIT) 15.974 Leadership Lab (MIT)

Description

This five-day interactive and experiential workshop focuses on how leaders lead innovations that both promote social responsibility and produce business success. The workshop is organized around three main parts: observation, sense-making, and creating. During the observation phase, students spend a full day inside the Boston office of the design company IDEO and visit some of the most interesting proven innovators in corporate social responsibility such as Ben & Jerry’s, KLD, MBDC, Plug Power (fuel cell technology), PwC, Schlumberger, or core team members of the UN Global Compact. After returning from their company visits, students describe to one another what they saw and learned. In the final part of the Lab, students conceive and implement innovation projects that serve This five-day interactive and experiential workshop focuses on how leaders lead innovations that both promote social responsibility and produce business success. The workshop is organized around three main parts: observation, sense-making, and creating. During the observation phase, students spend a full day inside the Boston office of the design company IDEO and visit some of the most interesting proven innovators in corporate social responsibility such as Ben & Jerry’s, KLD, MBDC, Plug Power (fuel cell technology), PwC, Schlumberger, or core team members of the UN Global Compact. After returning from their company visits, students describe to one another what they saw and learned. In the final part of the Lab, students conceive and implement innovation projects that serve

Subjects

leadership | leadership | ethics | ethics | corporate | corporate | responsibility | responsibility | social innovation | social innovation | organizational change | organizational change | business | business | rapid prototyping | rapid prototyping | collaboration | collaboration | corporate responsibility | corporate responsibility

License

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15.351 Managing the Innovation Process (MIT) 15.351 Managing the Innovation Process (MIT)

Description

This course approaches "managing the innovation process" through five levels of analysis: individual, team, network, organizational, and industrial. At each level of analysis, particular attention is given to the conditions under which innovation processes succeed and fail. The weekly readings consist of a mixture of book chapters, journal articles, and cases, and an online forum will be used for further discussion of the required readings outside of class. Tuesday classes will begin with a reflection exercise that entails critical thinking about the topic for the week, followed by an activity and lecture introducing material found both within and outside of the readings. Thursday classes will begin with a case analysis completed in small groups, followed by a discussion based on the iss This course approaches "managing the innovation process" through five levels of analysis: individual, team, network, organizational, and industrial. At each level of analysis, particular attention is given to the conditions under which innovation processes succeed and fail. The weekly readings consist of a mixture of book chapters, journal articles, and cases, and an online forum will be used for further discussion of the required readings outside of class. Tuesday classes will begin with a reflection exercise that entails critical thinking about the topic for the week, followed by an activity and lecture introducing material found both within and outside of the readings. Thursday classes will begin with a case analysis completed in small groups, followed by a discussion based on the iss

Subjects

Innovation | Innovation | Technology | Technology | strategy | strategy | Product development | Product development | New venture | New venture | open source | open source

License

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16.660J Introduction to Lean Six Sigma Methods (MIT) 16.660J Introduction to Lean Six Sigma Methods (MIT)

Description

Includes audio/video content: AV lectures. This course covers the fundamental principles, practices and tools of Lean Six Sigma methods that underlay modern organizational productivity approaches applied in aerospace, automotive, health care, and other sectors. It includes lectures, active learning exercises, a plant tour, talks by industry practitioners, and videos. One third of the course is devoted to a physical simulation of an aircraft manufacturing enterprise or a clinic to illustrate the power of Lean Six Sigma methods. The 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. Includes audio/video content: AV lectures. This course covers the fundamental principles, practices and tools of Lean Six Sigma methods that underlay modern organizational productivity approaches applied in aerospace, automotive, health care, and other sectors. It includes lectures, active learning exercises, a plant tour, talks by industry practitioners, and videos. One third of the course is devoted to a physical simulation of an aircraft manufacturing enterprise or a clinic to illustrate the power of Lean Six Sigma methods. The 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

16.660 | 16.660 | ESD.62 | ESD.62 | lean | lean | six sigma | six sigma | lean aerospace initiative | lean aerospace initiative | enterprise leaders | enterprise leaders | value stream mapping | value stream mapping | healthcare | healthcare | medicine | medicine | simulation | simulation | supply chain | supply chain | lean engineering | lean engineering | value stream analysis | value stream analysis | variability | variability | southwest airlines | southwest airlines | boeing | boeing | rockwell collins | rockwell collins | lockheed martin | lockheed martin

License

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16.430J Sensory-Neural Systems: Spatial Orientation from End Organs to Behavior and Adaptation (MIT) 16.430J Sensory-Neural Systems: Spatial Orientation from End Organs to Behavior and Adaptation (MIT)

Description

This course introduces sensory systems and multi-sensory fusion using the vestibular and spatial orientation systems as a model. Topics range from end organ dynamics to neural responses, to sensory integration, to behavior, and adaptation, with particular application to balance, posture and locomotion under normal gravity and space conditions. Depending upon the background and interests of the students, advanced term project topics might include motion sickness, astronaut adaptation, artificial gravity, lunar surface locomotion, vestibulo-cardiovascular responses, vestibular neural prostheses, or other topics of interest. This course introduces sensory systems and multi-sensory fusion using the vestibular and spatial orientation systems as a model. Topics range from end organ dynamics to neural responses, to sensory integration, to behavior, and adaptation, with particular application to balance, posture and locomotion under normal gravity and space conditions. Depending upon the background and interests of the students, advanced term project topics might include motion sickness, astronaut adaptation, artificial gravity, lunar surface locomotion, vestibulo-cardiovascular responses, vestibular neural prostheses, or other topics of interest.

Subjects

16.430 | 16.430 | HST.514 | HST.514 | sensory systems | sensory systems | neural processing | neural processing | sensorimotor processing | sensorimotor processing | vestibular system | vestibular system | spatial orientation system | spatial orientation system | sensory integration | sensory integration | balance | balance | astronaut adaptation | astronaut adaptation | motion sickness | motion sickness | spatial disorientation | spatial disorientation

License

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16.682 Prototyping Avionics (MIT) 16.682 Prototyping Avionics (MIT)

Description

In the past building prototypes of electronic components for new projects/products was limited to using protoboards and wirewrap. Manufacturing a printed-circuit-board was limited to final production, where mistakes in the implementation meant physically cutting traces on the board and adding wire jumpers - the final products would have these fixes on them! Today that is no longer the case, while you will still cut traces and use jumpers when debugging a board, manufacturing a new final version without the errors is a simple and relatively inexpensive task. For that matter, manufacturing a prototype printed circuit board which you know is likely to have errors but which will get the design substantially closer to the final product than a protoboard setup is not only possible, but desirable In the past building prototypes of electronic components for new projects/products was limited to using protoboards and wirewrap. Manufacturing a printed-circuit-board was limited to final production, where mistakes in the implementation meant physically cutting traces on the board and adding wire jumpers - the final products would have these fixes on them! Today that is no longer the case, while you will still cut traces and use jumpers when debugging a board, manufacturing a new final version without the errors is a simple and relatively inexpensive task. For that matter, manufacturing a prototype printed circuit board which you know is likely to have errors but which will get the design substantially closer to the final product than a protoboard setup is not only possible, but desirable

Subjects

engineering design | engineering design | rapid prototyping | rapid prototyping | manufacturing | manufacturing | testing | testing | system components | system components | complex structural parts | complex structural parts | hand sketching | hand sketching | CAD | CAD | CAD modeling | CAD modeling | CAE | CAE | CAE analysis | CAE analysis | CAM programming | CAM programming | CNC | CNC | CNC machining | CNC machining | computer aided design | computer aided design | computer aided | computer aided | structual testing | structual testing | multiobjective design | multiobjective design | optimization | optimization | computational methods | computational methods | tools | tools | design process | design process | design competition | design competition | active learning | active learning | hands-on | hands-on | human creativity | human creativity | holistic | holistic | solidworks | solidworks | finite element | finite element | FEM | FEM | FEM analysis | FEM analysis | COSMOS | COSMOS | omax | omax | presentation | presentation | CDIO | CDIO

License

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16.100 Aerodynamics (MIT) 16.100 Aerodynamics (MIT)

Description

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. 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.

Subjects

aerodynamics | aerodynamics | airflow | airflow | air | air | body | body | aircraft | aircraft | aerodynamic modes | aerodynamic modes | aero | aero | forces | forces | flow | flow | computational | computational | CFD | CFD | aerodynamic analysis | aerodynamic analysis | lift | lift | drag | drag | potential flows | potential flows | imcompressible | imcompressible | supersonic | supersonic | subsonic | subsonic | panel method | panel method | vortex lattice method | vortex lattice method | boudary layer | boudary layer | transition | transition | turbulence | turbulence | inviscid | inviscid | viscous | viscous | euler | euler | navier-stokes | navier-stokes | wind tunnel | wind tunnel | flow similarity | flow similarity | non-dimensional | non-dimensional | mach number | mach number | reynolds number | reynolds number | integral momentum | integral momentum | airfoil | airfoil | wing | wing | stall | stall | friction drag | friction drag | induced drag | induced drag | wave drag | wave drag | pressure drag | pressure drag | fluid element | fluid element | shear strain | shear strain | normal strain | normal strain | vorticity | vorticity | divergence | divergence | substantial derivative | substantial derivative | laminar | laminar | displacement thickness | displacement thickness | momentum thickness | momentum thickness | skin friction | skin friction | separation | separation | velocity profile | velocity profile | 2-d panel | 2-d panel | 3-d vortex | 3-d vortex | thin airfoil | thin airfoil | lifting line | lifting line | aspect ratio | aspect ratio | twist | twist | camber | camber | wing loading | wing loading | roll moments | roll moments | finite volume approximation | finite volume approximation | shocks | shocks | expansion fans | expansion fans | shock-expansion theory | shock-expansion theory | transonic | transonic | critical mach number | critical mach number | wing sweep | wing sweep | Kutta condition | Kutta condition | team project | team project | blended-wing-body | blended-wing-body | computational fluid dynamics | computational fluid dynamics

License

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16.322 Stochastic Estimation and Control (MIT) 16.322 Stochastic Estimation and Control (MIT)

Description

The major themes of this course are estimation and control of dynamic systems. Preliminary topics begin with reviews of probability and random variables. Next, classical and state-space descriptions of random processes and their propagation through linear systems are introduced, followed by frequency domain design of filters and compensators. From there, the Kalman filter is employed to estimate the states of dynamic systems. Concluding topics include conditions for stability of the filter equations. The major themes of this course are estimation and control of dynamic systems. Preliminary topics begin with reviews of probability and random variables. Next, classical and state-space descriptions of random processes and their propagation through linear systems are introduced, followed by frequency domain design of filters and compensators. From there, the Kalman filter is employed to estimate the states of dynamic systems. Concluding topics include conditions for stability of the filter equations.

Subjects

probability | probability | stochastic estimation | stochastic estimation | estimation | estimation | random variables | random variables | random processes | random processes | state space | state space | Wiener filter | Wiener filter | control system design | control system design | Kalman filter | Kalman filter

License

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16.225 Computational Mechanics of Materials (MIT) 16.225 Computational Mechanics of Materials (MIT)

Description

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course includes: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms include: variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There is a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science is 16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course includes: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms include: variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There is a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science is

Subjects

Computational Mechanics | Computational Mechanics | Computation | Computation | Mechanics | Mechanics | Materials | Materials | Numerical Methods | Numerical Methods | Numerical | Numerical | Nonlinear Continuum Response | Nonlinear Continuum Response | Continuum | Continuum | Deformation | Deformation | Elasticity | Elasticity | Inelasticity | Inelasticity | Dynamics | Dynamics | Variational Formulation | Variational Formulation | Variational Constitutive Updates | Variational Constitutive Updates | Finite Element | Finite Element | Discretization | Discretization | Error Estimation | Error Estimation | Constrained Problems | Constrained Problems | Time Integration | Time Integration | Convergence Analysis | Convergence Analysis | Programming | Programming | Continuum Response | Continuum Response | Computational | Computational | state-of-the-art | state-of-the-art | methods | methods | modeling | modeling | simulation | simulation | mechanical | mechanical | response | response | engineering | engineering | aerospace | aerospace | civil | civil | material | material | science | science | biomechanics | biomechanics | behavior | behavior | finite | finite | deformation | deformation | elasticity | elasticity | inelasticity | inelasticity | contact | contact | friction | friction | coupled | coupled | numerical | numerical | formulation | formulation | algorithms | algorithms | Variational | Variational | constitutive | constitutive | updates | updates | element | element | discretization | discretization | mesh | mesh | generation | generation | error | error | estimation | estimation | constrained | constrained | problems | problems | time | time | convergence | convergence | analysis | analysis | parallel | parallel | computer | computer | implementation | implementation | programming | programming | assembly | assembly | equation-solving | equation-solving | formulating | formulating | implementing | implementing | complex | complex | approximations | approximations | equations | equations | motion | motion | dynamic | dynamic | deformations | deformations | continua | continua | plasticity | plasticity | rate-dependency | rate-dependency | integration | integration

License

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18.S996 Category Theory for Scientists (MIT) 18.S996 Category Theory for Scientists (MIT)

Description

The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields. The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.

Subjects

Sets | Sets | functions | functions | commutative diagrams | commutative diagrams | products | products | coproducts | coproducts | finite limits | finite limits | monoids | monoids | groups | groups | graphs | graphs | orders | orders | schemas | schemas | instances | instances | databases | databases | categories | categories | functors | functors | mathematics | mathematics | natural transformations | natural transformations | limits | limits | colimits | colimits | adjoint functors | adjoint functors | monads | monads | operads | operads | isomorphism | isomorphism | molecular dynamics | molecular dynamics | olog | olog

License

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18.100C Real Analysis (MIT) 18.100C Real Analysis (MIT)

Description

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.   The three options for 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginni This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.   The three options for 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginni

Subjects

mathematical analysis | mathematical analysis | Archimedean principle | Archimedean principle | decimal expansion | decimal expansion | Cauchy-Schwarz | Cauchy-Schwarz | metric spaces | metric spaces | open subsets | open subsets | Euclidean space | Euclidean space | convergent sequences | convergent sequences | subsequential limits | subsequential limits | inverse functions | inverse functions | Stone-Weierstrass theorem | Stone-Weierstrass theorem | theory of integration | theory of integration | Riemann-Stjeltjes integral | Riemann-Stjeltjes integral | Fourier series | Fourier series

License

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18.337J Parallel Computing (MIT) 18.337J Parallel Computing (MIT)

Description

This is an advanced interdisciplinary introduction to applied parallel computing on modern supercomputers. It has a hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines. We will make prominent use of the Julia Language, a free, open-source, high-performance dynamic programming language for technical computing. This is an advanced interdisciplinary introduction to applied parallel computing on modern supercomputers. It has a hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines. We will make prominent use of the Julia Language, a free, open-source, high-performance dynamic programming language for technical computing.

Subjects

cloud computing | cloud computing | dense linear algebra | dense linear algebra | sparse linear algebra | sparse linear algebra | N-body problems | N-body problems | multigrid | multigrid | fast-multipole | fast-multipole | wavelets | wavelets | Fourier transforms | Fourier transforms | partitioning | partitioning | mesh generation | mesh generation | applications oriented architecture | applications oriented architecture | parallel programming paradigms | parallel programming paradigms | MPI | MPI | data parallel systems | data parallel systems | Star-P | Star-P | parallel Python | parallel Python | parallel Matlab | parallel Matlab | graphics processors | graphics processors | virtualization | virtualization | caches | caches | vector processors | vector processors | VHLLs | VHLLs | Very High Level Languages | Very High Level Languages | Julia programming language | Julia programming language | distributed parallel execution | distributed parallel execution

License

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18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics (MIT) 18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics (MIT)

Description

Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems. Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.

Subjects

dunkl operators | dunkl operators | cherednik | cherednik | affine algebra | affine algebra | representation theory | representation theory | hecke | hecke | knizknik-zamoldchikov | knizknik-zamoldchikov | orbifolds | orbifolds | calogero-moser space | calogero-moser space | hilbert scheme | hilbert scheme | algebra | algebra | macdonald-mehta integral | macdonald-mehta integral | integrable system | integrable system

License

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18.705 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 | nullsetellensatz

License

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18.175 Theory of Probability (MIT)

Description

This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory.

Subjects

Earth | Solar System | Geophysics | Gravitational Field | Magnetic Field | Seismology | Geodynamics | Laws of large numbers | central limit theorems for sums of independent random variables | conditioning and martingales | Brownian motion and elements of diffusion theory | functional limit theorems

License

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

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18.969 Topics in Geometry: Dirac Geometry (MIT) 18.969 Topics in Geometry: Dirac Geometry (MIT)

Description

This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry. This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.

Subjects

generalized geometry | generalized geometry | Dirac geometry | Dirac geometry | Gerbes | Gerbes | B-fields | B-fields | Courant algebroids | Courant algebroids | sigma models | sigma models | baby String theory | baby String theory | linear algebra | linear algebra | pure spinors | pure spinors | Riemannian structures | Riemannian structures | Hodge star | Hodge star | integrability | integrability | Dirac structures | Dirac structures | Lie algebroids and bialgebroids | Lie algebroids and bialgebroids | holomorphic bundles | holomorphic bundles | Picard group | Picard group | Kodaira-Spencer-Kuranishi deformation theory | Kodaira-Spencer-Kuranishi deformation theory | Kahler geometry | Kahler geometry | Hermitian geometry | Hermitian geometry | Calabi-Yau structures | Calabi-Yau structures | D-branes | D-branes

License

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18.700 Linear Algebra (MIT)

Description

This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with Linear Algebra (18.06), more emphasis is placed on theory and proofs.

Subjects

linear algebra | vector space | system of linear equations | bases | linear independence | matrices | matrix | determinant | eigenvalue | inner product | quadratic form | canonical form

License

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18.319 Geometric Combinatorics (MIT) 18.319 Geometric Combinatorics (MIT)

Description

This course offers an introduction to discrete and computational geometry. Emphasis is placed on teaching methods in combinatorial geometry. Many results presented are recent, and include open (as yet unsolved) problems. This course offers an introduction to discrete and computational geometry. Emphasis is placed on teaching methods in combinatorial geometry. Many results presented are recent, and include open (as yet unsolved) problems.

Subjects

discrete geometry | discrete geometry | computational geometry | computational geometry | convex partitions | convex partitions | binary space partitions | binary space partitions | art gallery problems | art gallery problems | Planar graphs | Planar graphs | pseudo-triangulations | pseudo-triangulations | encompassing graphs | encompassing graphs | geometric graphs | geometric graphs | crossing numbers | crossing numbers | extremal graph theory | extremal graph theory | Gallai-Sylvester problems | Gallai-Sylvester problems

License

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18.385J Nonlinear Dynamics and Chaos (MIT) 18.385J Nonlinear Dynamics and Chaos (MIT)

Description

This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software. This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.

Subjects

Phase plane | Phase plane | limit cycles | limit cycles | Poincare-Bendixson theory | Poincare-Bendixson theory | Time-dependent systems | Time-dependent systems | Floquet theory | Floquet theory | Poincare maps | Poincare maps | averaging | averaging | Stability of equilibria | Stability of equilibria | near-equilibrium dynamics | near-equilibrium dynamics | Center manifolds | Center manifolds | elementary bifurcations | elementary bifurcations | normal forms | normal forms | chaos | chaos | 18.385 | 18.385 | 2.036 | 2.036

License

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20.453J Biomedical Information Technology (MIT) 20.453J Biomedical Information Technology (MIT)

Description

This course teaches the design of contemporary information systems for biological and medical data. Examples are chosen from biology and medicine to illustrate complete life cycle information systems, beginning with data acquisition, following to data storage and finally to retrieval and analysis. Design of appropriate databases, client-server strategies, data interchange protocols, and computational modeling architectures. Students are expected to have some familiarity with scientific application software and a basic understanding of at least one contemporary programming language (e.g. C, C++, Java, Lisp, Perl, Python). A major term project is required of all students. This subject is open to motivated seniors having a strong interest in biomedical engineering and information system desig This course teaches the design of contemporary information systems for biological and medical data. Examples are chosen from biology and medicine to illustrate complete life cycle information systems, beginning with data acquisition, following to data storage and finally to retrieval and analysis. Design of appropriate databases, client-server strategies, data interchange protocols, and computational modeling architectures. Students are expected to have some familiarity with scientific application software and a basic understanding of at least one contemporary programming language (e.g. C, C++, Java, Lisp, Perl, Python). A major term project is required of all students. This subject is open to motivated seniors having a strong interest in biomedical engineering and information system desig

Subjects

20.453 | 20.453 | 2.771 | 2.771 | HST.958 | HST.958 | imaging | imaging | medical imaging | medical imaging | metadata | metadata | molecular biology | molecular biology | medical records | medical records | DICOM | DICOM | RDF | RDF | OWL | OWL | SPARQL | SPARQL | SBML | SBML | CellML | CellML | semantic web | semantic web | BioHaystack | BioHaystack | database | database | schema | schema | ExperiBase | ExperiBase | genomics | genomics | proteomics | proteomics | bioinformatics | bioinformatics | computational biology | computational biology | clinical decision support | clinical decision support | clinical trial | clinical trial | microarray | microarray | gel electrophoresis | gel electrophoresis | diagnosis | diagnosis | pathway modeling | pathway modeling | XML | XML | SQL | SQL | relational database | relational database | biological data | biological data | ontologies | ontologies | drug development | drug development | drug discovery | drug discovery | drug target | drug target | pharmaceutical | pharmaceutical | gene sequencing | gene sequencing

License

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20.181 Computation for Biological Engineers (MIT) 20.181 Computation for Biological Engineers (MIT)

Description

This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition. An official course Web site and Wiki is maintained on OpenWetWare: 20.181 Computation for Biological Engineers. This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition. An official course Web site and Wiki is maintained on OpenWetWare: 20.181 Computation for Biological Engineers.

Subjects

Phylogenetic Inference | Phylogenetic Inference | Molecular Modeling | Molecular Modeling | Protein Design | Protein Design | Discrete Reaction Event Network Modeling | Discrete Reaction Event Network Modeling | Python | Python | genetics | genetics | DNA sequence | DNA sequence | genomics | genomics | gene sequencing | gene sequencing | UPGMA | UPGMA | Newick notation | Newick notation | parsimony | parsimony | downpass | downpass | uppass | uppass | jukes-cantor | jukes-cantor | invertase | invertase | genetic memory | genetic memory

License

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21A.801J Cross-Cultural Investigations: Technology and Development (MIT) 21A.801J Cross-Cultural Investigations: Technology and Development (MIT)

Description

This course enhances cross-cultural understanding through the discussion of practical, ethical, and epistemological issues in conducting social science and applied research in foreign countries or unfamiliar communities. It includes a research practicum to help students develop interviewing, participant-observation, and other qualitative research skills, as well as critical discussion of case studies. The course is open to all interested students, but intended particularly for those planning to undertake exploratory research or applied work abroad. Students taking the graduate version complete additional assignments. This course enhances cross-cultural understanding through the discussion of practical, ethical, and epistemological issues in conducting social science and applied research in foreign countries or unfamiliar communities. It includes a research practicum to help students develop interviewing, participant-observation, and other qualitative research skills, as well as critical discussion of case studies. The course is open to all interested students, but intended particularly for those planning to undertake exploratory research or applied work abroad. Students taking the graduate version complete additional assignments.

Subjects

21A.801 | 21A.801 | EC.702 | EC.702 | STS.071 | STS.071 | EC.792 | EC.792 | 21A.839 | 21A.839 | STS.481 | STS.481 | ethnography | ethnography | cultural anthropology | cultural anthropology | genealogy | genealogy | interviews | interviews | fieldwork | fieldwork | observation | observation | technology | technology | technology transfer | technology transfer | development | development | globalization | globalization | research | research | culture | culture | health | health | gender | gender | women | women | economics | economics | international | international | global | global | D-lab | D-lab

License

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21A.235 American Dream: Exploring Class in the U.S. (MIT) 21A.235 American Dream: Exploring Class in the U.S. (MIT)

Description

Americans have historically preferred to think of the United States in classless terms, as a land of economic opportunity equally open to all. Yet, social class remains a central fault line in the U.S. Subject explores the experiences and understandings of class among Americans positioned at different points along the U.S. social spectrum. Considers a variety of classic frameworks for analyzing social class and uses memoirs, novels and ethnographies to gain a sense of how class is experienced in daily life and how it intersects with other forms of social difference such as race and gender. Americans have historically preferred to think of the United States in classless terms, as a land of economic opportunity equally open to all. Yet, social class remains a central fault line in the U.S. Subject explores the experiences and understandings of class among Americans positioned at different points along the U.S. social spectrum. Considers a variety of classic frameworks for analyzing social class and uses memoirs, novels and ethnographies to gain a sense of how class is experienced in daily life and how it intersects with other forms of social difference such as race and gender.

Subjects

Class | Class | inequality | inequality | anthropology | anthropology | narrative | narrative | ethnography | ethnography | marx | marx | weber | weber | bourdieu | bourdieu | post-structuralism | post-structuralism | habitus | habitus | race | race | gender | gender | upward mobility | upward mobility | downward mobility | downward mobility | deindustrialization | deindustrialization | assembly line | assembly line | rich | rich | post war | post war | underclass | underclass

License

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