Mathematics (18) - Archived
https://hdl.handle.net/1721.1/33995
Mathematics (18)2024-09-13T14:16:57Z18.S096 Matrix Calculus for Machine Learning and Beyond, January IAP 2022
https://hdl.handle.net/1721.1/155680
18.S096 Matrix Calculus for Machine Learning and Beyond, January IAP 2022
Edelman, Alan; Johnson, Steven G.
We all know that calculus courses such as 18.01 Single Variable Calculus and 18.02 Multivariable Calculus cover univariate and vector calculus, respectively. Modern applications such as machine learning require the next big step, matrix calculus.
This class covers a coherent approach to matrix calculus showing techniques that allow you to think of a matrix holistically (not just as an array of scalars), compute derivatives of important matrix factorizations, and really understand forward and reverse modes of differentiation. We will discuss adjoint methods, custom Jacobian matrix vector products, and how modern automatic differentiation is more computer science than mathematics in that it is neither symbolic nor based on finite differences.
2022-01-01T00:00:00Z18.S097 Introduction to Metric Spaces, January IAP 2022
https://hdl.handle.net/1721.1/153933
18.S097 Introduction to Metric Spaces, January IAP 2022
Bright, Paige
This course provides a basic introduction to metric spaces. It covers metrics, open and closed sets, continuous functions (in the topological sense), function spaces, completeness, and compactness.
2022-01-01T00:00:00Z18.05 Introduction to Probability and Statistics, Spring 2014
https://hdl.handle.net/1721.1/153490
18.05 Introduction to Probability and Statistics, Spring 2014
Orloff, Jeremy; Bloom, Jonathan
This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression. The Spring 2014 version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT students with learning and assessment tools such as online problem sets, lecture videos, reading questions, pre-lecture questions, problem set assistance, tutorial videos, exam review content, and even online exams.
2014-06-01T00:00:00Z18.218 Probabilistic Method in Combinatorics, Spring 2019
https://hdl.handle.net/1721.1/151192
18.218 Probabilistic Method in Combinatorics, Spring 2019
Zhao, Yufei
This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with positive probability. The course focuses on methodology as well as combinatorial applications.
2019-06-01T00:00:00Z18.785 Number Theory I, Fall 2019
https://hdl.handle.net/1721.1/150787
18.785 Number Theory I, Fall 2019
Sutherland, Andrew
This is the first semester of a one-year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
2019-12-01T00:00:00Z18.783 Elliptic Curves, Spring 2019
https://hdl.handle.net/1721.1/148618
18.783 Elliptic Curves, Spring 2019
Sutherland, Andrew
This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
2019-06-01T00:00:00Z18.404J / 6.840J Theory of Computation, Fall 2006
https://hdl.handle.net/1721.1/137168
18.404J / 6.840J Theory of Computation, Fall 2006
Sipser, Michael
This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.
2006-12-01T00:00:00Z18.906 Algebraic Topology II, Spring 2006
https://hdl.handle.net/1721.1/126831
18.906 Algebraic Topology II, Spring 2006
Behrens, Mark
In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.
2006-06-01T00:00:00Z18.785 Number Theory I, Fall 2017
https://hdl.handle.net/1721.1/124987
18.785 Number Theory I, Fall 2017
Sutherland, Andrew
This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
2017-12-01T00:00:00Z18.312 Algebraic Combinatorics, Spring 2009
https://hdl.handle.net/1721.1/123321
18.312 Algebraic Combinatorics, Spring 2009
Musiker, Gregg
This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.
2009-06-01T00:00:00Z18.783 Elliptic Curves, Spring 2017
https://hdl.handle.net/1721.1/122962
18.783 Elliptic Curves, Spring 2017
Sutherland, Andrew
This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
2017-06-01T00:00:00Z18.04 Complex Variables with Applications, Fall 2003
https://hdl.handle.net/1721.1/122961
18.04 Complex Variables with Applications, Fall 2003
Toomre, Alar
This course explored topics such as complex algebra and functions, analyticity, contour integration, Cauchy's theorem, singularities, Taylor and Laurent series, residues, evaluation of integrals, multivalued functions, potential theory in two dimensions, Fourier analysis and Laplace transforms.
2003-12-01T00:00:00Z18.335J Introduction to Numerical Methods, Fall 2004
https://hdl.handle.net/1721.1/122013
18.335J Introduction to Numerical Methods, Fall 2004
Koev, Plamen
The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems.
2004-12-01T00:00:00Z18.335J / 6.337J Introduction to Numerical Methods, Fall 2010
https://hdl.handle.net/1721.1/122006
18.335J / 6.337J Introduction to Numerical Methods, Fall 2010
Johnson, Steven G.
This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.
2010-12-01T00:00:00Z18.S34 Problem Solving Seminar, Fall 2007
https://hdl.handle.net/1721.1/121169
18.S34 Problem Solving Seminar, Fall 2007
Rogers, Hartley; Kedlaya, Kiran; Stanley, Richard
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.
2007-12-01T00:00:00Z18.905 Algebraic Topology, Fall 2006
https://hdl.handle.net/1721.1/115074
18.905 Algebraic Topology, Fall 2006
Lawson, Tyler
This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the Lefschetz fixed point theorem.
2006-12-01T00:00:00Z18.785 Number Theory I, Fall 2016
https://hdl.handle.net/1721.1/114496
18.785 Number Theory I, Fall 2016
Sutherland, Andrew
This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
2016-12-01T00:00:00Z2.062J / 1.138J / 18.376J Wave Propagation, Fall 2006
https://hdl.handle.net/1721.1/111950
2.062J / 1.138J / 18.376J Wave Propagation, Fall 2006
Mei, Chiang; Rosales, Rodolfo; Akylas, Triantaphyllos
This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media.
2006-12-01T00:00:00Z18.783 Elliptic Curves, Spring 2015
https://hdl.handle.net/1721.1/111949
18.783 Elliptic Curves, Spring 2015
Sutherland, Andrew
This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
2015-06-01T00:00:00Z18.785 Number Theory I, Fall 2015
https://hdl.handle.net/1721.1/109488
18.785 Number Theory I, Fall 2015
Sutherland, Andrew
This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
2015-12-01T00:00:00Z18.06 Linear Algebra, Spring 2005
https://hdl.handle.net/1721.1/59010
18.06 Linear Algebra, Spring 2005
Strang, Gilbert
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
2005-06-01T00:00:00Z18.336 Numerical Methods of Applied Mathematics II, Spring 2005
https://hdl.handle.net/1721.1/56567
18.336 Numerical Methods of Applied Mathematics II, Spring 2005
Koev, Plamen S.
Advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities. From the course home page: Course Description This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.
2005-06-01T00:00:00Z18.311 Principles of Applied Mathematics, Spring 2006
https://hdl.handle.net/1721.1/55891
18.311 Principles of Applied Mathematics, Spring 2006
Bazant, Martin Z.
Introduction to fundamental concepts in "continuous" applied mathematics. Extensive use of demonstrational software. Discussion of computational and modelling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world. From the course home page: Course Description This course introduces fundamental concepts in "continuous'' applied mathematics, with an emphasis on nonlinear partial differential equations (PDEs). Topics include linear and nonlinear waves: kinematic waves, method of characteristics, expansion fans, wave breaking, shock dynamics, shock structure; linear and nonlinear diffusion: Green functions, Fourier transform, similarity solutions, boundary layers, Nernst-Planck equations. Applications include traffic flow, gas dynamics, and granular flow.
2006-06-01T00:00:00Z18.781 Theory of Numbers, Spring 2003
https://hdl.handle.net/1721.1/76771
18.781 Theory of Numbers, Spring 2003
Olsson, Martin
This course provides an elementary introduction to number theory with no algebraic prerequisites. Topics include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions and elliptic curves.
2003-06-01T00:00:00Z5.95J / 6.982J / 7.59J / 8.395J / 18.094J / 1.95J / 2.978J Teaching College-Level Science and Engineering, Fall 2012
https://hdl.handle.net/1721.1/107185
5.95J / 6.982J / 7.59J / 8.395J / 18.094J / 1.95J / 2.978J Teaching College-Level Science and Engineering, Fall 2012
Rankin, Janet
This participatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. This course is designed for graduate students interested in an academic career, and anyone else interested in teaching. Topics include theories of adult learning; course development; promoting active learning, problem-solving, and critical thinking in students; communicating with a diverse student body; using educational technology to further learning; lecturing; creating effective tests and assignments; and assessment and evaluation. Students research and present a relevant topic of particular interest. The subject is appropriate for both novices and those with teaching experience.
2012-12-01T00:00:00Z12.006J / 18.353J / 2.050J Nonlinear Dynamics I: Chaos, Fall 2006
https://hdl.handle.net/1721.1/84612
12.006J / 18.353J / 2.050J Nonlinear Dynamics I: Chaos, Fall 2006
Rothman, Daniel
This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.
2006-12-01T00:00:00Z22.00J / 1.021J / 2.030J / 3.021J / 10.333J / 18.361J / HST.558J Introduction to Modeling and Simulation, Spring 2006
https://hdl.handle.net/1721.1/50265
22.00J / 1.021J / 2.030J / 3.021J / 10.333J / 18.361J / HST.558J Introduction to Modeling and Simulation, Spring 2006
Yip, Sidney; Beers, Kenneth J.; Buehler, Markus J.; Hadjiconstantinou, Nicolas G (Nicholas George); Mirny, Leonid A.; Bazant, Martin Z.; Marzari, Nicola; Powell, Adam C.; Radovitzky, Raul A.; Rosales, Rodolfo; Ulm, F.-J. (Franz-Josef)
Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute.
2006-06-01T00:00:00Z18.312 Algebraic Combinatorics, Spring 2005
https://hdl.handle.net/1721.1/52320
18.312 Algebraic Combinatorics, Spring 2005
Postnikov, Alexander
Applications of algebra to combinatorics and conversely. Topics include enumeration methods, partially ordered sets and lattices, matching theory, partitions and tableaux, algebraic graph theory, and combinatorics of polytopes.
2005-06-01T00:00:00Z18.950 Differential Geometry, Spring 2005
https://hdl.handle.net/1721.1/49826
18.950 Differential Geometry, Spring 2005
Wickramasekera, Neshan Geethike
This course is an introduction to differential geometry. Metrics, Lie bracket, connections, geodesics, tensors, intrinsic and extrinsic curvature are studied on abstractly defined manifolds using coordinate charts. Curves and surfaces in three dimensions are studied as important special cases. Gauss-Bonnet theorem for surfaces and selected introductory topics in special and general relativity are also analyzed. From the course home page: Course Description This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied.
2005-06-01T00:00:00Z22.00J / 1.021J / 3.021J / 10.333J / 18.361J / 2.030J / HST.558 Introduction to Modeling and Simulation, Spring 2002
https://hdl.handle.net/1721.1/35256
22.00J / 1.021J / 3.021J / 10.333J / 18.361J / 2.030J / HST.558 Introduction to Modeling and Simulation, Spring 2002
Yip, Sidney; Powell, Adam C.; Bazant, Martin Z.; Carter, W. Craig; Marzari, Nicola; Rosales, Rodolfo; White, Jacob K.; Cao, Jianshu; Hadjiconstantinou, Nicolas G (Nicholas George); Mirny, Leonid A.; Trout, Bernhardt L.; Ulm, F.-J. (Franz-Josef)
Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute.
2002-06-01T00:00:00Z18.441 Statistical Inference, Spring 2002
https://hdl.handle.net/1721.1/45587
18.441 Statistical Inference, Spring 2002
Hardy, Michael
Reviews probability and introduces statistical inference. Point and interval estimation. The maximum likelihood method. Hypothesis testing. Likelihood-ratio tests and Bayesian methods. Nonparametric methods. Analysis of variance, regression analysis and correlation. Chi-square goodness of fit tests. More theoretical than 18.443 (Statistics for Applications) and more detailed in its treatment of statistics than 18.05 (Introduction to Probability and Statistics).
2002-06-01T00:00:00Z18.701 Algebra I, Fall 2003
https://hdl.handle.net/1721.1/45589
18.701 Algebra I, Fall 2003
Artin, Michael
The Algebra I class covers subjects such as Group Theory, Linear Algebra, and Geometry. In more detail groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups are discussed.
2003-12-01T00:00:00Z18.S34 Problem Solving Seminar, Fall 2004
https://hdl.handle.net/1721.1/45131
18.S34 Problem Solving Seminar, Fall 2004
Rogers, H. (Hartley), 1926-; Stanley, Richard P., 1944-
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.
2004-12-01T00:00:00Z18.306 Advanced Partial Differential Equations with Applications, Spring 2004
https://hdl.handle.net/1721.1/56302
18.306 Advanced Partial Differential Equations with Applications, Spring 2004
Margetis, Dionisios
A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform methods, eigenvalue and eigenfunction expansions, Green's functions. Theory of characteristics and shocks. Boundary layers and other singular perturbation phenomena. Elementary concepts for the numerical solution of pde's. Illustrative examples from fluid dynamics, nonlinear waves, geometrical optics, and other applications.
2004-06-01T00:00:00Z6.852J / 18.437J Distributed Algorithms, Fall 2005
https://hdl.handle.net/1721.1/60694
6.852J / 18.437J Distributed Algorithms, Fall 2005
Lynch, Nancy
This course intends to provide a rigorous introduction to the most important research results in the area of distributed algorithms, and prepare interested students to carry out independent research in distributed algorithms. Topics covered include: design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks, process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration is given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation are also discussed. Detailed information on the course textbook can be found here: Lynch, Nancy A. Distributed Algorithms. San Francisco, CA: Morgan Kaufmann, 1997. ISBN: 1558603484.
2005-12-01T00:00:00Z12.006J / 18.353J Nonlinear Dynamics I: Chaos, Fall 2005
https://hdl.handle.net/1721.1/38877
12.006J / 18.353J Nonlinear Dynamics I: Chaos, Fall 2005
Rothman, Daniel H.
Introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial conditions and strange attractors. Lorenz attractor. Period doubling, intermittency, and quasiperiodicity. Scaling and universality. Analysis of experimental data: Fourier transforms, Poincar, sections, fractal dimension, and Lyapunov exponents. Applications drawn from fluid dynamics, physics, geophysics, and chemistry. See 12.207J/18.354J for Nonlinear Dynamics II.
2005-12-01T00:00:00Z6.042J / 18.062J Mathematics for Computer Science, Spring 2005
https://hdl.handle.net/1721.1/104427
6.042J / 18.062J Mathematics for Computer Science, Spring 2005
Leiserson, Charles; Lehman, Eric; Devadas, Srinivas; Meyer, Albert R.
This course is offered to undergraduates and is an elementary discrete mathematics course oriented towards applications in computer science and engineering. Topics covered include: formal logic notation, induction, sets and relations, permutations and combinations, counting principles, and discrete probability.
2005-06-01T00:00:00Z18.311 Principles of Applied Mathematics, Spring 2003
https://hdl.handle.net/1721.1/34883
18.311 Principles of Applied Mathematics, Spring 2003
Rosales, Rodolfo
Introduction to fundamental concepts in "continuous" applied mathematics. Extensive use of demonstrational software. Discussion of computational and modelling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.
2003-06-01T00:00:00Z6.854J / 18.415J Advanced Algorithms, Fall 2001
https://hdl.handle.net/1721.1/49420
6.854J / 18.415J Advanced Algorithms, Fall 2001
Goemans, Michel
A first-year graduate course in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Data structures. Network flows. Linear programming. Computational geometry. Approximation algorithms. Alternate years. From the course home page: Course Description This is a graduate course on the design and analysis of algorithms, covering several advanced topics not studied in typical introductory courses on algorithms. It is especially designed for doctoral students interested in theoretical computer science.
2001-12-01T00:00:00Z18.465 Topics in Statistics: Statistical Learning Theory, Spring 2004
https://hdl.handle.net/1721.1/39660
18.465 Topics in Statistics: Statistical Learning Theory, Spring 2004
Panchenko, Dmitry A.
The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.
2004-06-01T00:00:00Z18.310C Principles of Applied Mathematics, Fall 2007
https://hdl.handle.net/1721.1/98262
18.310C Principles of Applied Mathematics, Fall 2007
Shor, Peter; Kleitman, Daniel
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.
2007-12-01T00:00:00Z21H.421 Introduction to Environmental History, Spring 2004
https://hdl.handle.net/1721.1/74615
21H.421 Introduction to Environmental History, Spring 2004
Ritvo, Harriet
This seminar provides a historical overview of the interactions between people and their environments. Focusing primarily on the experience of Europeans in the period after Columbus, the subject explores the influence of nature (climate, topography, plants, animals, and microorganisms) on human history and the reciprocal influence of people on nature. Topics include the biological consequences of the European encounter with the Americas, the environmental impact of technology, and the roots of the current environmental crisis.
2004-06-01T00:00:00ZSP.721 D-Lab: Development, Dialogue and Delivery, Fall 2004
https://hdl.handle.net/1721.1/74616
SP.721 D-Lab: Development, Dialogue and Delivery, Fall 2004
Smith, Amy J.; Kornbluth, Kurt
D-Lab is a year-long series of courses and field trips. The fall class provides a basic background in international development and appropriate technology through guest speakers, case studies and hands-on exercises. Students will also have the opportunity to participate in an IAP field trip to Haiti, India, Brazil, Honduras, Zambia, Samoa, or Lesotho and continue their work in a spring term design class. As part of the fall class, students will partner with community organizations in these countries and develop plans for the IAP site visit. In addition, students will learn about the culture, language, economics, politics and history of their host country.
2004-12-01T00:00:00Z18.303 Linear Partial Differential Equations: Analysis and Numerics, Fall 2010
https://hdl.handle.net/1721.1/97715
18.303 Linear Partial Differential Equations: Analysis and Numerics, Fall 2010
Johnson, Steven G.
This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.
2010-12-01T00:00:00Z18.701 Algebra I, Fall 2007
https://hdl.handle.net/1721.1/66918
18.701 Algebra I, Fall 2007
Artin, Michael
This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.
2007-12-01T00:00:00Z18.112 Functions of a Complex Variable, Fall 2006
https://hdl.handle.net/1721.1/49419
18.112 Functions of a Complex Variable, Fall 2006
Helgason, Sigurdur, 1927-
The basic properties of functions of one complex variable. Cauchy's theorem, holomorphic and meromorphic functions, residues, contour integrals, conformal mapping. Infinite series and products, the gamma function, the Mittag-Leffler theorem. Harmonic functions, Dirichlet's problem. From the course home page: Course 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.
2006-12-01T00:00:00Z18.712 Introduction to Representation Theory, Fall 2008
https://hdl.handle.net/1721.1/74129
18.712 Introduction to Representation Theory, Fall 2008
Etingof, Pavel
This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.
2008-12-01T00:00:00Z18.440 Probability and Random Variables, Fall 2005
https://hdl.handle.net/1721.1/49827
18.440 Probability and Random Variables, Fall 2005
Dudley, R. M. (Richard M.)
This course introduces students to probability and random variable. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.
2005-12-01T00:00:00Z6.852J / 18.437J Distributed Algorithms, Fall 2001
https://hdl.handle.net/1721.1/36405
6.852J / 18.437J Distributed Algorithms, Fall 2001
Lynch, Nancy A. (Nancy Ann), 1948-
Design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks. Process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation. Alternate years. From the course home page: Course Description 6.852J / 18.437J intends to: (1) provide a rigorous introduction to the most important research results in the area of distributed algorithms, and (2) prepare interested students to carry out independent research in distributed algorithms. Topics covered include: design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks, process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration is given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation are also discussed.
2001-12-01T00:00:00Z18.03 Differential Equations, Spring 2004
https://hdl.handle.net/1721.1/34888
18.03 Differential Equations, Spring 2004
Miller, Haynes R., 1948-; Mattuck, Arthur
Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms.
2004-06-01T00:00:00Z18.335J / 6.337J Numerical Methods of Applied Mathematics I, Fall 2001
https://hdl.handle.net/1721.1/37330
18.335J / 6.337J Numerical Methods of Applied Mathematics I, Fall 2001
Stefanica-Nica, Dan Octavian
IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-order reduction, fast Fourier transforms, multigrid, wavelets and other multiresolution methods, matrix sparsification. Nonlinear root finding (Newton's method). Numerical interpolation and extrapolation. Quadrature.
2001-12-01T00:00:00Z18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005
https://hdl.handle.net/1721.1/45575
18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005
Johnson, Steven G., 1973-
Topics vary from year to year. Topic for Fall: Eigenvalues of random matrices. How many are real? Why are the spacings so important? Subject covers the mathematics and applications in physics, engineering, computation, and computer science. From the course home page: Course Description This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.
2005-12-01T00:00:00Z18.085 Mathematical Methods for Engineers I, Fall 2005
https://hdl.handle.net/1721.1/45136
18.085 Mathematical Methods for Engineers I, Fall 2005
Strang, Gilbert
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
2005-12-01T00:00:00Z18.085 Mathematical Methods for Engineers I, Fall 2002
https://hdl.handle.net/1721.1/35746
18.085 Mathematical Methods for Engineers I, Fall 2002
Strang, Gilbert
Review of linear algebra, applications to networks, structures, and estimation, Lagrange multipliers, differential equations of equilibrium, Laplace's equation and potential flow, boundary-value problems, minimum principles and calculus of variations, Fourier series, discrete Fourier transform, convolution, applications.
2002-12-01T00:00:00Z18.702 Algebra II, Spring 2003
https://hdl.handle.net/1721.1/45579
18.702 Algebra II, Spring 2003
Artin, Michael
More extensive and theoretical than the 18.700-18.703 sequence. Experience with proofs helpful. First term: group theory, geometry, and linear algebra. Second term: group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, Galois theory. From the course home page: Course Description The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.
2003-06-01T00:00:00Z18.337J / 6.338J Applied Parallel Computing (SMA 5505), Spring 2003
https://hdl.handle.net/1721.1/35786
18.337J / 6.338J Applied Parallel Computing (SMA 5505), Spring 2003
Edelman, Alan
Advanced interdisciplinary introduction to modern scientific computing on parallel supercomputers. Numerical topics include dense and sparse linear algebra, N-body problems, and Fourier transforms. Geometrical topics include partitioning and mesh generation. Other topics include architectures and software systems with hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines.
2003-06-01T00:00:00Z6.172 Performance Engineering of Software Systems, Fall 2009
https://hdl.handle.net/1721.1/74613
6.172 Performance Engineering of Software Systems, Fall 2009
Leiserson, Charles; Amarasinghe, Saman
Modern computing platforms provide unprecedented amounts of raw computational power. But significant complexity comes along with this power, to the point that making useful computations exploit even a fraction of the potential of the computing platform is a substantial challenge. Indeed, obtaining good performance requires a comprehensive understanding of all layers of the underlying platform, deep insight into the computation at hand, and the ingenuity and creativity required to obtain an effective mapping of the computation onto the machine. The reward for mastering these sophisticated and challenging topics is the ability to make computations that can process large amount of data orders of magnitude more quickly and efficiently and to obtain results that are unavailable with standard practice. This course is a hands-on, project-based introduction to building scalable and high-performance software systems. Topics include: performance analysis, algorithmic techniques for high performance, instruction-level optimizations, cache and memory hierarchy optimization, parallel programming, and building scalable distributed systems. The course also includes code reviews with industry mentors, as described in this MIT News article.
2009-12-01T00:00:00Z18.022 Calculus, Fall 2005
https://hdl.handle.net/1721.1/74133
18.022 Calculus, Fall 2005
Rogers, Hartley
This is an undergraduate course on calculus of several variables. It covers all of the topics covered in Calculus II (18.02), but presents them in greater depth. These topics are vector algebra in 3-space, determinants, matrices, vector-valued functions of one variable, space motion, scalar functions of several variables, partial differentiation, gradient, optimization techniques, double integrals, line integrals in the plane, exact differentials, conservative fields, Green's theorem, triple integrals, line and surface integrals in space, the divergence theorem, and Stokes' theorem. Additional topics covered in 18.022 are geometry, vector fields, and linear algebra.
2005-12-01T00:00:00Z6.042J / 18.062J Mathematics for Computer Science (SMA 5512), Fall 2002
https://hdl.handle.net/1721.1/70477
6.042J / 18.062J Mathematics for Computer Science (SMA 5512), Fall 2002
Nagpal, Radhika; Meyer, Albert R.
This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental concepts of Mathematics: definitions, proofs, sets, functions, relations. Discrete structures: modular arithmetic, graphs, state machines, counting. Discrete probability theory. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science). Contributors Srinivas Devadas Lars Engebretsen David Karger Eric Lehman Thomson Leighton Charles Leiserson Nancy Lynch Santosh Vempala
2002-12-01T00:00:00Z18.303 Linear Partial Differential Equations, Fall 2005
https://hdl.handle.net/1721.1/37289
18.303 Linear Partial Differential Equations, Fall 2005
Hancock, Matthew James, 1975-
The classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. Methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized. 18.04 or 18.112 are useful, as well as previous acquaintance with the equations as they arise in scientific applications.
2005-12-01T00:00:00Z18.385 Nonlinear Dynamics and Chaos, Fall 2002
https://hdl.handle.net/1721.1/36890
18.385 Nonlinear Dynamics and Chaos, Fall 2002
Rosales, Rodolfo
Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.
2002-12-01T00:00:00Z18.175 Theory of Probability, Fall 2008
https://hdl.handle.net/1721.1/96865
18.175 Theory of Probability, Fall 2008
Panchenko, Dmitry
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.
2008-12-01T00:00:00Z6.854J / 18.415J Advanced Algorithms, Fall 1999
https://hdl.handle.net/1721.1/36897
6.854J / 18.415J Advanced Algorithms, Fall 1999
Karger, David
A first-year graduate course in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Data structures. Network flows. Linear programming. Computational geometry. Approximation algorithms. Alternate years.
1999-12-01T00:00:00Z18.783 Elliptic Curves, Spring 2013
https://hdl.handle.net/1721.1/97521
18.783 Elliptic Curves, Spring 2013
Sutherland, Andrew
This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
2013-06-01T00:00:00Z18.702 Algebra II, Spring 2008
https://hdl.handle.net/1721.1/66919
18.702 Algebra II, Spring 2008
Artin, Michael
This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.
2008-06-01T00:00:00Z18.466 Mathematical Statistics, Spring 2003
https://hdl.handle.net/1721.1/103814
18.466 Mathematical Statistics, Spring 2003
Dudley, Richard
This graduate level mathematics course covers decision theory, estimation, confidence intervals, and hypothesis testing. The course also introduces students to large sample theory. Other topics covered include asymptotic efficiency of estimates, exponential families, and sequential analysis.
2003-06-01T00:00:00Z18.100C Analysis I, Spring 2006
https://hdl.handle.net/1721.1/78574
18.100C Analysis I, Spring 2006
Ciubotaru, Dan
This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, and integration.
2006-06-01T00:00:00Z5.95J / 7.59J / 8.395J / 18.094J Teaching College-Level Science, Spring 2006
https://hdl.handle.net/1721.1/77248
5.95J / 7.59J / 8.395J / 18.094J Teaching College-Level Science, Spring 2006
Breslow, Lori
This seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include: using current research in student learning to improve teaching; developing courses; lecturing; promoting students' ability to think critically and solve problems; communicating with a diverse student body; using educational technology; creating effective assignments and tests; and utilizing feedback to improve instruction. Students research and teach a topic of particular interest. This subject is appropriate for both novices and those with teaching experience.
2006-06-01T00:00:00Z18.024 Calculus with Theory II, Spring 2003
https://hdl.handle.net/1721.1/74132
18.024 Calculus with Theory II, Spring 2003
Munkres, James; Lachowska, Anna
This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor and Alex Retakh for their help with this course web site.
2003-06-01T00:00:00Z18.100A Analysis I, Fall 2007
https://hdl.handle.net/1721.1/76713
18.100A Analysis I, Fall 2007
Mattuck, Arthur
Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 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 beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.
2007-12-01T00:00:00ZSP.718 Special Topics at Edgerton Center: D-Lab Health: Medical Technologies for the Developing World, Spring 2009
https://hdl.handle.net/1721.1/74614
SP.718 Special Topics at Edgerton Center: D-Lab Health: Medical Technologies for the Developing World, Spring 2009
Gomez-Marquez, Jose; Srivastava, Amit; Bardsley, Ryan Scott; Tracey, Brian
D-Lab Health provides multi-disciplinary approach to global health technology design via guest lectures and a major project based on fieldwork. We will explore the current state of global health challenges and learn how design medical technologies that address those problems. Students may travel to Nicaragua during spring break and work with health professionals, using medical technology design kits to gain field experience for their device challenge. As a final class deliverable, you will create a product design solution to address the challenges observed in the field. The resulting designs are prototyped in the summer for continued evaluation and testing.
2009-06-01T00:00:00Z18.440 Probability and Random Variables, Spring 2009
https://hdl.handle.net/1721.1/74130
18.440 Probability and Random Variables, Spring 2009
Dudley, Richard
This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.
2009-06-01T00:00:00Z18.100B Analysis I, Fall 2006
https://hdl.handle.net/1721.1/74139
18.100B Analysis I, Fall 2006
Lenzmann, Enno; Albin, Pierre
Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations.
2006-12-01T00:00:00Z3.021J / 1.021J / 10.333J / 18.361J / 22.00J Introduction to Modeling and Simulation, Spring 2011
https://hdl.handle.net/1721.1/85561
3.021J / 1.021J / 10.333J / 18.361J / 22.00J Introduction to Modeling and Simulation, Spring 2011
Buehler, Markus; Grossman, Jeffrey
This subject provides an introduction to modeling and simulation (IM/S), covering continuum methods, atomistic and molecular simulation (e.g. molecular dynamics) as well as quantum mechanics. These tools play an increasingly important role in modern engineering. You will get hands-on training in both the fundamentals and applications of these methods to key engineering problems. The lectures will provide an exposure to areas of application, based on the scientific exploitation of the power of computation. We will use web based applets for simulations and thus extensive programming skills are not required.
2011-06-01T00:00:00Z18.335J / 6.337J Introduction to Numerical Methods, Fall 2006
https://hdl.handle.net/1721.1/75282
18.335J / 6.337J Introduction to Numerical Methods, Fall 2006
Persson, Per-Olof
This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.
2006-12-01T00:00:00Z18.404J / 6.840J Theory of Computation, Fall 2002
https://hdl.handle.net/1721.1/39661
18.404J / 6.840J Theory of Computation, Fall 2002
Sipser, Michael
A more extensive and theoretical treatment of the material in 6.045J/18.400J, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.
2002-12-01T00:00:00Z18.034 Honors Differential Equations, Spring 2007
https://hdl.handle.net/1721.1/55903
18.034 Honors Differential Equations, Spring 2007
Mikyoung Hur, Vera
Covers the same material as 18.03 with more emphasis on theory. First order equations, separation, initial value problems. Systems, linear equations, independence of solutions, undetermined coefficients. Singular points and periodic orbits for planar systems. From the course home page: Course Description This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems.
2007-06-01T00:00:00Z18.310 Principles of Applied Mathematics, Fall 2002
https://hdl.handle.net/1721.1/36375
18.310 Principles of Applied Mathematics, Fall 2002
Kleitman, Daniel J.
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.
2002-12-01T00:00:00Z18.103 Fourier Analysis - Theory and Applications, Spring 2004
https://hdl.handle.net/1721.1/101676
18.103 Fourier Analysis - Theory and Applications, Spring 2004
Melrose, Richard
18.103 picks up where 18.100B (Analysis I) left off. Topics covered include the theory of the Lebesgue integral with applications to probability, Fourier series, and Fourier integrals.
2004-06-01T00:00:00Z6.045J / 18.400J Automata, Computability, and Complexity, Spring 2005
https://hdl.handle.net/1721.1/68649
6.045J / 18.400J Automata, Computability, and Complexity, Spring 2005
Lynch, Nancy
This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.
2005-06-01T00:00:00Z18.405J / 6.841J Advanced Complexity Theory, Fall 2001
https://hdl.handle.net/1721.1/106671
18.405J / 6.841J Advanced Complexity Theory, Fall 2001
Spielman, Daniel
The topics for this course cover various aspects of complexity theory, such as  the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved.
2001-12-01T00:00:00Z18.S34 Problem Solving Seminar, Fall 2002
https://hdl.handle.net/1721.1/35896
18.S34 Problem Solving Seminar, Fall 2002
Stanley, Richard P., 1944-; Rogers, H. (Hartley), 1926-
This course 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.
2002-12-01T00:00:00Z18.013A Calculus with Applications, Fall 2001
https://hdl.handle.net/1721.1/35712
18.013A Calculus with Applications, Fall 2001
Kleitman, Daniel J.
Differential calculus in one and several dimensions. Java applets and spreadsheet assignments. Vector algebra in 3D, vector- valued functions, gradient, divergence and curl, Taylor series, numerical methods and applications. Given in the first half of the first term. However, those wishing credit for 18.013A only, must attend the entire semester. Prerequisites: a year of high school calculus or the equivalent, with a score of 4 or 5 on the AB, or the AB portion of the BC, Calculus test, or an equivalent score on a standard international exam, or a passing grade on the first half of the 18.01 Advanced Standing exam.
2001-12-01T00:00:00Z1.138J / 2.062J / 18.376J Wave Propagation, Fall 2004
https://hdl.handle.net/1721.1/41865
1.138J / 2.062J / 18.376J Wave Propagation, Fall 2004
Akylas, Triantaphyllos R.; Li, Guangda; Mei, Chiang C.; Rosales, Rodolfo
This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media, etc.
2004-12-01T00:00:00Z18.311 Principles of Applied Mathematics, Spring 2009
https://hdl.handle.net/1721.1/97754
18.311 Principles of Applied Mathematics, Spring 2009
Kasimov, Aslan
This course is about mathematical analysis of continuum models of various natural phenomena. Such models are generally described by partial differential equations (PDE) and for this reason much of the course is devoted to the analysis of PDE. Examples of applications come from physics, chemistry, biology, complex systems: traffic flows, shock waves, hydraulic jumps, bio-fluid flows, chemical reactions, diffusion, heat transfer, population dynamics, and pattern formation.
2009-06-01T00:00:00Z18.05 Introduction to Probability and Statistics, Spring 2005
https://hdl.handle.net/1721.1/96772
18.05 Introduction to Probability and Statistics, Spring 2005
Panchenko, Dmitry
This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression.
2005-06-01T00:00:00Z18.785 Analytic Number Theory, Spring 2007
https://hdl.handle.net/1721.1/101679
18.785 Analytic Number Theory, Spring 2007
Kedlaya, Kiran
This course is an introduction to analytic number theory, including the use of zeta functions and L-functions to prove distribution results concerning prime numbers (e.g., the prime number theorem in arithmetic progressions).
2007-06-01T00:00:00Z18.904 Seminar in Topology, Fall 2005
https://hdl.handle.net/1721.1/76253
18.904 Seminar in Topology, Fall 2005
Behrens, Mark
In this course, students present and discuss the subject matter with faculty guidance. Topics presented by the students include the fundamental group and covering spaces. Instruction and practice in written and oral communication are provided to the students.
2005-12-01T00:00:00Z18.336 Numerical Methods of Applied Mathematics II, Spring 2004
https://hdl.handle.net/1721.1/36900
18.336 Numerical Methods of Applied Mathematics II, Spring 2004
Koev, Plamen S.
Advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities.
2004-06-01T00:00:00Z18.175 Theory of Probability, Spring 2005
https://hdl.handle.net/1721.1/37302
18.175 Theory of Probability, Spring 2005
Panchenko, Dmitry A.
Laws of large numbers and central limit theorems for sums of independent random variables, conditioning and martingales, Brownian motion and elements of diffusion theory.
2005-06-01T00:00:00Z18.155 Differential Analysis, Fall 2002
https://hdl.handle.net/1721.1/35774
18.155 Differential Analysis, Fall 2002
Melrose, Richard B.
Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Method of characteristics. Review of Lebesgue integration. Distributions. Fourier transform. Homogeneous distributions. Asymptotic methods.
2002-12-01T00:00:00Z18.303 Linear Partial Differential Equations, Fall 2004
https://hdl.handle.net/1721.1/36869
18.303 Linear Partial Differential Equations, Fall 2004
Hancock, Matthew James, 1975-
The classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. Methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized. 18.04 or 18.112 are useful, as well as previous acquaintance with the equations as they arise in scientific applications.
2004-12-01T00:00:00Z18.06 Linear Algebra, Fall 2002
https://hdl.handle.net/1721.1/35861
18.06 Linear Algebra, Fall 2002
Strang, Gilbert
Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB. Compared with 18.700, more emphasis on matrix algorithms and many applications.
2002-12-01T00:00:00Z6.045J / 18.400J Automata, Computability, and Complexity, Spring 2002
https://hdl.handle.net/1721.1/36867
6.045J / 18.400J Automata, Computability, and Complexity, Spring 2002
Rivest, Ronald L.
Slower paced than 6.840J/18.404J. Introduces basic mathematical models of computation and the finite representation of infinite objects. Finite automata and regular languages. Context-free languages. Turing machines. Partial recursive functions. Church's Thesis. Undecidability. Reducibility and completeness. Time complexity and NP-completeness. Probabilistic computation. Interactive proof systems.
2002-06-01T00:00:00Z15.067 Competitive Decision-Making and Negotiation, Spring 2003
https://hdl.handle.net/1721.1/84613
15.067 Competitive Decision-Making and Negotiation, Spring 2003
Kaufman, Gordon
This course is centered on twelve negotiation exercises that simulate competitive business situations. Specific topics covered include distributive bargaining (split the pie!), mixed motive bargaining (several issues at stake) with two and with more than two parties, auctions and fair division. Ethical dilemmas in negotiation are discussed at various times throughout the course. There are two principal objectives for this course. The first is to provide you with negotiation tools that enable you to achieve your negotiation objectives in a fair and responsible fashion. The second is to "learn by doing." That is, we provide a forum in which you actively apply these tools to a wide variety of business oriented negotiation settings.
2003-06-01T00:00:00Z18.03 Differential Equations, Spring 2006
https://hdl.handle.net/1721.1/70961
18.03 Differential Equations, Spring 2006
Miller, Haynes; Mattuck, Arthur
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.
2006-06-01T00:00:00Z18.152 Introduction to Partial Differential Equations, Fall 2004
https://hdl.handle.net/1721.1/75812
18.152 Introduction to Partial Differential Equations, Fall 2004
Staffilani, Gigliola; Vasy, Andras
This course analyzes initial and boundary value problems for ordinary differential equations and the wave and heat equation in one space dimension. It also covers the Sturm-Liouville theory and eigenfunction expansions, as well as the Dirichlet problem for Laplace's operator and potential theory.
2004-12-01T00:00:00Z18.101 Analysis II, Fall 2004
https://hdl.handle.net/1721.1/36871
18.101 Analysis II, Fall 2004
Guillemin, V., 1937-
Continues 18.100, in the direction of manifolds and global analysis. Differentiable maps, inverse and implicit function theorems, n-dimensional Riemann integral, change of variables in multiple integrals, manifolds, differential forms, n-dimensional version of Stokes' theorem. 18.901 helpful but not required.
2004-12-01T00:00:00Z18.01 Single Variable Calculus, Fall 2003
https://hdl.handle.net/1721.1/34901
18.01 Single Variable Calculus, Fall 2003
Starr, Jason M.
DIFFERENTIATION AND INTEGRATION OF FUNCTIONS OF ONE VARIABLE, WITH APPLICATIONS. CONCEPTS OF FUNCTION, LIMITS, AND CONTINUITY. DIFFERENTIATION RULES, APPLICATION TO GRAPHING, RATES, APPROXIMATIONS, AND EXTREMUM PROBLEMS. DEFINITE AND INDEFINITE INTEGRATION. FUNDAMENTAL THEOREM OF CALCULUS. APPLICATIONS OF INTEGRATION TO GEOMETRY AND SCIENCE. ELEMENTARY FUNCTIONS. TECHNIQUES OF INTEGRATION. APPROXIMATION OF DEFINITE INTEGRALS, IMPROPER INTEGRALS, AND L'HÔPITAL'S RULE.
2003-12-01T00:00:00Z18.700 Linear Algebra, Fall 2005
https://hdl.handle.net/1721.1/91562
18.700 Linear Algebra, Fall 2005
Ciubotaru, Dan
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.
2005-12-01T00:00:00Z18.014 Calculus with Theory I, Fall 2002
https://hdl.handle.net/1721.1/74131
18.014 Calculus with Theory I, Fall 2002
Munkres, James; Lachowska, Anna
18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, and Alex Retakh for their help with this course web site.
2002-12-01T00:00:00Z18.440 Probability and Random Variables, Spring 2011
https://hdl.handle.net/1721.1/97467
18.440 Probability and Random Variables, Spring 2011
Sheffield, Scott
This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.
2011-06-01T00:00:00Z18.366 Random Walks and Diffusion, Spring 2003
https://hdl.handle.net/1721.1/35916
18.366 Random Walks and Diffusion, Spring 2003
Bazant, Martin Z.
Discrete and continuum modeling of diffusion processes in physics, chemistry, and economics. Topics include central limit theorems, continuous-time random walks, Levy flights, correlations, extreme events, mixing, renormalization, and percolation.
2003-06-01T00:00:00Z18.112 Functions of a Complex Variable, Fall 2005
https://hdl.handle.net/1721.1/37301
18.112 Functions of a Complex Variable, Fall 2005
Helgason, Sigurdur, 1927-
The basic properties of functions of one complex variable. Cauchy's theorem, holomorphic and meromorphic functions, residues, contour integrals, conformal mapping. Infinite series and products, the gamma function, the Mittag-Leffler theorem. Harmonic functions, Dirichlet's problem.
2005-12-01T00:00:00Z18.366 Random Walks and Diffusion, Spring 2005
https://hdl.handle.net/1721.1/39664
18.366 Random Walks and Diffusion, Spring 2005
Bazant, Martin Z.
Discrete and continuum modeling of diffusion processes in physics, chemistry, and economics. Topics include central limit theorems, continuous-time random walks, Levy flights, correlations, extreme events, mixing, renormalization, and percolation. From the course home page: Course Description This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.
2005-06-01T00:00:00Z18.086 Mathematical Methods for Engineers II, Spring 2005
https://hdl.handle.net/1721.1/35273
18.086 Mathematical Methods for Engineers II, Spring 2005
Strang, Gilbert
Scientific computing: Fast Fourier Transform, finite differences, finite elements, spectral method, numerical linear algebra. Complex variables and applications. Initial-value problems: stability or chaos in ordinary differential equations, wave equation versus heat equation, conservation laws and shocks, dissipation and dispersion. Optimization: network flows, linear programming. Includes one computational project.
2005-06-01T00:00:00Z6.868J / MAS.731J The Society of Mind, Spring 2007
https://hdl.handle.net/1721.1/85562
6.868J / MAS.731J The Society of Mind, Spring 2007
Minsky, Marvin
This course is an introduction to a theory that tries to explain how minds are made from collections of simpler processes. The subject treats such aspects of thinking as vision, language, learning, reasoning, memory, consciousness, ideals, emotions, and personality. Ideas incorporate psychology, artificial intelligence, and computer science to resolve theoretical issues such as whole vs. parts, structural vs. functional descriptions, declarative vs. procedural representations, symbolic vs. connectionist models, and logical vs. common-sense theories of learning.
2007-06-01T00:00:00Z15.082J / 6.855J Network Optimization, Spring 2003
https://hdl.handle.net/1721.1/74617
15.082J / 6.855J Network Optimization, Spring 2003
Orlin, James
15.082J/6.855J is an H-level graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, finance as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem.
2003-06-01T00:00:00Z3.021J / 1.021J / 10.333J / 18.361J / 22.00J Introduction to Modeling and Simulation, Spring 2008
https://hdl.handle.net/1721.1/74612
3.021J / 1.021J / 10.333J / 18.361J / 22.00J Introduction to Modeling and Simulation, Spring 2008
Buehler, Markus; Thonhauser, Timo; Radovitzky, Raúl
This course explores the basic concepts of computer modeling and simulation in science and engineering. We'll use techniques and software for simulation, data analysis and visualization. Continuum, mesoscale, atomistic and quantum methods are used to study fundamental and applied problems in physics, chemistry, materials science, mechanics, engineering, and biology. Examples drawn from the disciplines above are used to understand or characterize complex structures and materials, and complement experimental observations.
2008-06-01T00:00:00Z18.304 Undergraduate Seminar in Discrete Mathematics, Spring 2006
https://hdl.handle.net/1721.1/100853
18.304 Undergraduate Seminar in Discrete Mathematics, Spring 2006
Kleitman, Daniel
This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.
2006-06-01T00:00:00Z18.443 Statistics for Applications, Spring 2009
https://hdl.handle.net/1721.1/100851
18.443 Statistics for Applications, Spring 2009
Dudley, Richard
This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics. Note: Please see the syllabus for a description of the different versions of 18.443 taught at MIT.
2009-06-01T00:00:00Z18.310 Principles of Applied Mathematics, Fall 2004
https://hdl.handle.net/1721.1/45132
18.310 Principles of Applied Mathematics, Fall 2004
Kleitman, Daniel J.
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.
2004-12-01T00:00:00Z18.175 Theory of Probability, Spring 2007
https://hdl.handle.net/1721.1/49508
18.175 Theory of Probability, Spring 2007
Panchenko, Dmitry A.
Laws of large numbers and central limit theorems for sums of independent random variables, conditioning and martingales, Brownian motion and elements of diffusion theory.
2007-06-01T00:00:00Z18.085 Computational Science and Engineering I, Fall 2007
https://hdl.handle.net/1721.1/46740
18.085 Computational Science and Engineering I, Fall 2007
Strang, Gilbert
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. Note: This course was previously called "Mathematical Methods for Engineers I".
2007-12-01T00:00:00Z18.314 Combinatorial Analysis, Fall 2005
https://hdl.handle.net/1721.1/96864
18.314 Combinatorial Analysis, Fall 2005
Postnikov, Alexander
This course analyzes combinatorial problems and methods for their solution. Prior experience with abstraction and proofs is helpful. Topics include: Enumeration, generating functions, recurrence relations, construction of bijections, introduction to graph theory, network algorithms and, extremal combinatorics.
2005-12-01T00:00:00Z18.337J / 6.338J Applied Parallel Computing (SMA 5505), Spring 2005
https://hdl.handle.net/1721.1/77902
18.337J / 6.338J Applied Parallel Computing (SMA 5505), Spring 2005
Edelman, Alan
Applied Parallel Computing is an advanced interdisciplinary introduction to applied parallel computing on modern supercomputers.
2005-06-01T00:00:00Z18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit, Fall 2007
https://hdl.handle.net/1721.1/55908
18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit, Fall 2007
LinkKelner, Jonathan, 1980-
Study of an area of current interest in theoretical computer science. Topic varies from term to term.
2007-12-01T00:00:00Z6.046J / 18.410J Introduction to Algorithms, Fall 2001
https://hdl.handle.net/1721.1/36847
6.046J / 18.410J Introduction to Algorithms, Fall 2001
Demaine, Erik D.; Leiserson, Charles Eric; Lee, Wee Sun
Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing. Enrollment may be limited.
2001-12-01T00:00:00Z18.100B Analysis I, Fall 2002
https://hdl.handle.net/1721.1/37329
18.100B Analysis I, Fall 2002
Melrose, Richard B.
Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. <I>Option A</I> chooses less abstract definitions and proofs, and gives applications where possible. <I>Option B</I> is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology.
2002-12-01T00:00:00Z6.042J / 18.062J Mathematics for Computer Science, Spring 2010
https://hdl.handle.net/1721.1/104426
6.042J / 18.062J Mathematics for Computer Science, Spring 2010
Meyer, Albert R.
This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. The subject coverage divides roughly into thirds: Fundamental concepts of mathematics: definitions, proofs, sets, functions, relations. Discrete structures: graphs, state machines, modular arithmetic, counting. Discrete probability theory. On completion of 6.042, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in Computer Science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.
2010-06-01T00:00:00Z