chaseharmon/MIT_Course_Catalog · Datasets at Hugging Face

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17.878	Qualitative Methods and Fieldwork	Prepares students to conduct independent qualitative research, focusing on practical skills acquisition. Topics include methodological controversies, debates about transparency, human subjects protocols and research ethics, interviewing techniques, ethnography, focus groups, comparative historical case studies/archival research, and write-up of qualitative information collected from the field.	false	Spring	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
17.C08[J]	Causal Inference	Provides an accessible overview of modern quantitative methods for causal inference: testing whether an action causes an outcome to occur. Makes heavy use of applied, real-data examples using Python or R and drawn from the participating domains (economics, political science, business, public policy, etc.). Covers topics including potential outcomes, causal graphs, randomized controlled trials, observational studies, instrumental variable estimation, and a contrast with machine learning techniques. Seeks to provide an intuitive understanding of the core concepts and techniques to help students produce and consume evidence of causal claims.	true	Spring	Undergraduate	4-0-8	6.3800, 6.3900, 6.C01, 14.32, 17.803, 18.05, 18.650, or permission of instructor	15.C08[J]	false	false	false	False	False	False
17.UR	Undergraduate Research	Research opportunities in Political Science in theoretical and applied research. For further information, contact the Departmental Coordinator.	true	Fall, IAP, Spring, Summer	Undergraduate	rranged [P/D/F]	null	null	false	false	false	False	False	False
17.URG	Undergraduate Research	Research opportunities in political science in theoretical and applied research. For further information, contact the departmental coordinator.	true	Fall, IAP, Spring, Summer, Fall, Spring	Undergraduate	rranged	null	null	false	false	false	False	False	False
17.90	Politics, Policy, and Political Science: What Does It All Mean? (New)	Explores the scope of political science, policy, and politics through conversations with faculty who research across the field. Topics include misinformation and democracy, dictatorships, nuclear war and AI, and why governments make the policy decisions they do. Gives a broad overview of the role of methods and data in political science. This class counts towards the 6-unit discovery-focused credit limit for first-year students.	true	Fall	Undergraduate	2-0-1 [P/D/F]	null	null	false	false	false	False	False	False
17.902	Political Science Internship and Research	For students participating in off-campus internships relevant to the field of political science. Before registering, students must submit a 1-2 page application statement which describes the internship, the nature of the work, the time commitment (hours per week and number of weeks) and the connection to the field of political science. Students must also submit a formal offer letter from a host employer/organization which provides details of the internship. Subject to departmental approval. Consult departmental undergraduate office.	true	Fall, Spring	Undergraduate	rranged [P/D/F]	null	null	false	false	false	False	False	False
17.905-17.911	Reading Seminar in Social Science	Reading and discussion of special topics in the fields of social science. Open to advanced undergraduates by arrangement with individual staff members. 17.909 is taught P/D/F.	true	Fall, IAP, Spring, Summer	Undergraduate	rranged	null	null	false	false	false	False	False	False
17.922	Martin Luther King, Jr. Design Seminar	Facilitates design and construction of installations and other community projects in conjunction with and beyond MIT's celebration of Dr. King. Students discuss the ideas and goals of Dr. King and other human rights leaders in the US and the world. The first half of the class develops in-depth understanding of the history of US racial issues as well as past and present domestic and international political struggles. Addresses issues of justice, equality and racism through videos, readings and writings, and class discussions. In the second half, students work as a group complete the installation and projects which serve as models for connecting academics with real life problems and struggle.	true	IAP	Undergraduate	3-0-3 [P/D/F]	null	null	false	false	false	False	False	False
17.925	Fundamentals of Science and Technology Public Policy Making: Science and Technology Policy Boot Camp	Examines the public policy behind, and the government's role in, the science and technology-based innovation system. Focuses on the US, but also discusses international examples. Prepares students planning careers in and around science and technology with the basic background for involvement in science policy making. Limited to 35. Application required.	true	IAP	Undergraduate	2-0-1	null	null	false	false	false	False	False	False
17.959	Preparation for General Exams	Selected readings for Political Science doctoral students in preparation for qualifying exams.	true	Fall, Summer	Graduate	rranged [P/D/F]	Permission of instructor	null	false	false	false	False	False	False
17.954-17.958,	17.960 Reading Seminar in Social Science	Reading and discussion of special topics in the fields of social science. Open to advanced graduate students by arrangement with individual staff members. 17.954 and 17.959 are taught P/D/F.	true	Fall, Spring, Summer	Graduate	rranged	Permission of instructor	null	false	false	false	False	False	False
17.962	Second Year Paper Workshop	Workshop for research and writing of major research paper as part of pre-dissertation requirements. Restricted to doctoral students.	true	Spring	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
17.THG	Graduate Political Science Thesis	Program of research and writing of thesis; to be arranged by the student with supervising committee.	true	Fall, IAP, Spring, Summer	Graduate	rranged	Permission of instructor	null	false	false	false	False	False	False
17.THT	Thesis Research Design Seminar	Students writing a thesis in Political Science develop their research topics, review relevant research and scholarship, frame their research questions and arguments, choose an appropriate methodology for analysis, and draft the introductory and methodology sections of their theses.	true	Fall	Undergraduate	3-0-9	17.803 or permission of instructor	null	false	false	false	False	False	False
17.THU	Undergraduate Political Science Thesis	Program of research leading to the writing of an SB thesis. To be arranged by the student under approved supervision.	true	Fall, IAP, Spring, Summer	Undergraduate	rranged	null	null	false	false	false	False	False	False
17.S912	Special Undergraduate Subject in Political Science	Reading and discussion of topics in the field of social science not covered in the regular curriculum.	true	Fall, Spring	Undergraduate	rranged [P/D/F]	null	null	false	false	false	False	False	False
17.S914	Special Undergraduate Subject in Political Science	Reading and discussion of topics in the field of social science not covered in the regular curriculum.	true	Spring	Undergraduate	rranged	null	null	false	false	false	False	False	False
17.S916	Special Undergraduate Subject in Political Science	Reading and discussion of topics in the field of social science not covered in the regular curriculum.	true	Fall	Undergraduate	rranged [P/D/F]	null	null	false	false	false	False	False	False
17.S917	Special Undergraduate Subject in Political Science	Reading and discussion of topics in the field of social science not covered in the regular curriculum.	true	Spring	Undergraduate	rranged	null	null	false	false	false	False	False	False
17.S918	Special Undergraduate Subject in Political Science	Reading and discussion of topics in the field of social science not covered in the regular curriculum.	true	Spring	Undergraduate	rranged	null	null	false	false	false	False	False	False
17.S919	Special Undergraduate Subject in Political Science	Reading and discussion of topics in the field of social science not covered in the regular curriculum.	true	Fall	Undergraduate	rranged	null	null	false	false	false	False	False	False
17.S950	Special Graduate Subject in Political Science	Open to qualified graduate students who would like to pursue special studies or projects. Please consult graduate administration prior to registration.	false	Spring	Graduate	rranged	Permission of instructor	null	false	false	false	False	False	False
17.S951	Special Graduate Subject in Political Science	Open to qualified graduate students who would like to pursue special subjects or projects. Please consult graduate administration prior to registration.	true	Spring	Graduate	rranged	Permission of instructor	null	false	false	false	False	False	False
17.S952	Special Graduate Subject in Political Science	Open to qualified graduate students who would like to pursue special subjects or projects. Please consult graduate administration prior to registration.	true	Fall	Graduate	rranged	Permission of instructor	null	false	false	false	False	False	False
17.S953	Special Graduate Subject in Political Science	Open to qualified graduate students who would like to pursue special subjects or projects. Please consult graduate administration prior to registration.	true	Fall	Graduate	rranged	Permission of instructor	null	false	false	false	False	False	False
18.01	Calculus	Differentiation and integration of functions of one variable, with applications. Informal treatment of limits and continuity. Differentiation: definition, rules, application to graphing, rates, approximations, and extremum problems. Indefinite integration; separable first-order differential equations. Definite integral; fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Polar coordinates. L'Hopital's rule. Improper integrals. Infinite series: geometric, p-harmonic, simple comparison tests, power series for some elementary functions.	true	Fall, Spring	Undergraduate	5-0-7	null	null	false	false	false	Calculus 1	False	False
18.01A	Calculus	Six-week review of one-variable calculus, emphasizing material not on the high-school AB syllabus: integration techniques and applications, improper integrals, infinite series, applications to other topics, such as probability and statistics, as time permits. Prerequisites: one year of high-school calculus or the equivalent, with a score of 5 on the AB Calculus test (or the AB portion of the BC test, or an equivalent score on a standard international exam), or equivalent college transfer credit, or a passing grade on the first half of the 18.01 advanced standing exam.	true	Fall	Undergraduate	5-0-7	Knowledge of differentiation and elementary integration	null	false	false	false	Calculus 1	False	False
18.02	Calculus	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.	true	Fall, Spring	Undergraduate	5-0-7	Calculus I (GIR)	null	false	false	false	Calculus 2	False	False
18.02A	Calculus	First half is taught during the last six weeks of the Fall term; covers material in the first half of 18.02 (through double integrals). Second half of 18.02A can be taken either during IAP (daily lectures) or during the second half of the Spring term; it covers the remaining material in 18.02.	true	Fall, IAP, Spring	Undergraduate	5-0-7	Calculus I (GIR)	null	false	false	false	Calculus 2	False	False
18.022	Calculus	Calculus of several variables. Topics as in 18.02 but with more focus on mathematical concepts. Vector algebra, dot product, matrices, determinant. Functions of several variables, continuity, differentiability, derivative. Parametrized curves, arc length, curvature, torsion. Vector fields, gradient, curl, divergence. Multiple integrals, change of variables, line integrals, surface integrals. Stokes' theorem in one, two, and three dimensions.	true	Fall	Undergraduate	5-0-7	Calculus I (GIR)	null	false	false	false	Calculus 2	False	False
18.03	Differential Equations	Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.	true	Fall, Spring	Undergraduate	5-0-7	None. Coreq: Calculus II (GIR)	null	false	false	true	False	False	False
18.031	System Functions and the Laplace Transform	Studies basic continuous control theory as well as representation of functions in the complex frequency domain. Covers generalized functions, unit impulse response, and convolution; and Laplace transform, system (or transfer) function, and the pole diagram. Includes examples from mechanical and electrical engineering.	true	IAP	Undergraduate	1-0-2 [P/D/F]	None. Coreq: 18.03	null	false	false	false	False	False	False
18.032	Differential Equations	Covers much of the same material as 18.03 with more emphasis on theory. The point of view is rigorous and results are proven. Local existence and uniqueness of solutions.	true	Spring	Undergraduate	5-0-7	None. Coreq: Calculus II (GIR)	null	false	false	true	False	False	False
18.04	Complex Variables with Applications	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, Laplace transforms, and partial differential equations.	true	Fall	Undergraduate	4-0-8	Calculus II (GIR) and (18.03 or 18.032)	null	false	false	false	False	False	False
18.05	Introduction to Probability and Statistics	A unified introduction to probability, Bayesian inference, and frequentist statistics. Topics include: combinatorics, random variables, (joint) distributions, covariance, central limit theorem; Bayesian updating, odds, posterior prediction; significance tests, confidence intervals, bootstrapping, regression. Students also develop computational skills and statistical thinking by using R to simulate, analyze, and visualize data; and by exploring privacy, fairness, and causality in contemporary media and research. Flipped subject taught in a Technology Enabled Active Learning (TEAL) classroom to facilitate discussion, group problem solving, and coding studios with ample mentorship.	true	Spring	Undergraduate	4-0-8	Calculus II (GIR)	null	false	false	true	False	False	False
18.06	Linear Algebra	Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, singular value decomposition, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses linear algebra software. Compared with 18.700, more emphasis on matrix algorithms and many applications.	true	Fall, Spring	Undergraduate	4-0-8	Calculus II (GIR)	null	false	false	true	False	False	False
18.C06[J]	Linear Algebra and Optimization	Introductory course in linear algebra and optimization, assuming no prior exposure to linear algebra and starting from the basics, including vectors, matrices, eigenvalues, singular values, and least squares. Covers the basics in optimization including convex optimization, linear/quadratic programming, gradient descent, and regularization, building on insights from linear algebra. Explores a variety of applications in science and engineering, where the tools developed give powerful ways to understand complex systems and also extract structure from data.	true	Fall	Undergraduate	5-0-7	Calculus II (GIR)	6.C06[J]	false	false	true	False	False	False
18.062[J]	Mathematics for Computer Science	Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.	true	Fall, Spring	Undergraduate	5-0-7	Calculus I (GIR)	6.1200[J]	false	false	true	False	False	False
18.063	Matrix Calculus for Machine Learning and Beyond (New)	Covers a coherent approach to matrix calculus, showing techniques that allow the student to think of a matrix holistically, rather than as an array of scalars; generalize and compute derivatives of important matrix factorizations and other complicated-looking operations; and understand how differentiation formulas must be reimagined in large-scale computing. Discusses "adjoint" or "reverse-mode" differentiation, custom vector-Jacobian products, and how modern automatic differentiation is more computer science than calculus.	true	IAP	Undergraduate	1-0-2 [P/D/F]	Calculus II (GIR) and 18.06	null	false	false	false	False	False	False
18.065	Matrix Methods in Data Analysis, Signal Processing, and Machine Learning	Reviews linear algebra with applications to life sciences, finance, engineering, and big data. Covers singular value decomposition, weighted least squares, signal and image processing, principal component analysis, covariance and correlation matrices, directed and undirected graphs, matrix factorizations, neural nets, machine learning, and computations with large matrices.	true	Spring	Undergraduate	3-0-9	18.06	null	false	false	false	False	False	False
18.0651	Matrix Methods in Data Analysis, Signal Processing, and Machine Learning	Reviews linear algebra with applications to life sciences, finance, engineering, and big data. Covers singular value decomposition, weighted least squares, signal and image processing, principal component analysis, covariance and correlation matrices, directed and undirected graphs, matrix factorizations, neural nets, machine learning, and computations with large matrices. Students in Course 18 must register for the undergraduate version, 18.065.	true	Spring	Graduate	3-0-9	18.06	null	false	false	false	False	False	False
18.075	Methods for Scientists and Engineers	Covers functions of a complex variable; calculus of residues. Includes ordinary differential equations; Bessel and Legendre functions; Sturm-Liouville theory; partial differential equations; heat equation; and wave equations.	true	Spring	Undergraduate	3-0-9	Calculus II (GIR) and 18.03	null	false	false	false	False	False	False
18.0751	Methods for Scientists and Engineers	Covers functions of a complex variable; calculus of residues. Includes ordinary differential equations; Bessel and Legendre functions; Sturm-Liouville theory; partial differential equations; heat equation; and wave equations. Students in Courses 6, 8, 12, 18, and 22 must register for undergraduate version, 18.075.	true	Spring	Graduate	3-0-9	Calculus II (GIR) and 18.03	null	false	false	false	False	False	False
18.085	Computational Science and Engineering I	Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution. Frequent use of MATLAB in a wide range of scientific and engineering applications.	true	Fall, Spring, Summer	Undergraduate	3-0-9	Calculus II (GIR) and (18.03 or 18.032)	null	false	false	false	False	False	False
18.0851	Computational Science and Engineering I	Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution. Frequent use of MATLAB in a wide range of scientific and engineering applications. Students in Course 18 must register for the undergraduate version, 18.085.	true	Fall, Spring, Summer	Graduate	3-0-9	Calculus II (GIR) and (18.03 or 18.032)	null	false	false	false	False	False	False
18.086	Computational Science and Engineering II	Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes. Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients. Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods.	true	Spring	Undergraduate	3-0-9	Calculus II (GIR) and (18.03 or 18.032)	null	false	false	false	False	False	False
18.0861	Computational Science and Engineering II	Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes. Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients. Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods. Students in Course 18 must register for the undergraduate version, 18.086.	true	Spring	Graduate	3-0-9	Calculus II (GIR) and (18.03 or 18.032)	null	false	false	false	False	False	False
18.089	Review of Mathematics	One-week review of one-variable calculus (18.01), followed by concentrated study covering multivariable calculus (18.02), two hours per day for five weeks. Primarily for graduate students in Course 2N. Degree credit allowed only in special circumstances.	true	Summer	Graduate	5-0-7	Permission of instructor	null	false	false	false	False	False	False
18.090	Introduction to Mathematical Reasoning	Focuses on understanding and constructing mathematical arguments. Discusses foundational topics (such as infinite sets, quantifiers, and methods of proof) as well as selected concepts from algebra (permutations, vector spaces, fields) and analysis (sequences of real numbers). Particularly suitable for students desiring additional experience with proofs before going on to more advanced mathematics subjects or subjects in related areas with significant mathematical content.	true	Spring	Undergraduate	3-0-9	None. Coreq: Calculus II (GIR)	null	false	false	true	False	False	False
18.091	Introduction to Metric Spaces (New)	Covers metrics, open and closed sets, continuous functions (from a topological perspective), function spaces, completeness, and compactness. Aims to provide more complex concepts and proofs for students who have taken 18.100A as their real analysis subject.	true	IAP	Undergraduate	1-0-2 [P/D/F]	18.100A	null	false	false	false	False	False	False
18.094[J]	Teaching College-Level Science and Engineering	Participatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include theories of adult learning; course development; promoting active learning, problemsolving, 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. Appropriate for both novices and those with teaching experience.	true	Fall	Graduate	2-0-2 [P/D/F]	null	1.95[J], 5.95[J], 7.59[J], 8.395[J]	false	false	false	False	False	False
18.095	Mathematics Lecture Series	Ten lectures by mathematics faculty members on interesting topics from both classical and modern mathematics. All lectures accessible to students with calculus background and an interest in mathematics. At each lecture, reading and exercises are assigned. Students prepare these for discussion in a weekly problem session.	true	IAP	Undergraduate	2-0-4 [P/D/F]	Calculus I (GIR)	null	false	false	false	False	False	False
18.098	Internship in Mathematics	Provides academic credit for students pursuing internships to gain practical experience in the applications of mathematical concepts and methods.	true	Fall, IAP, Spring, Summer	Undergraduate	rranged [P/D/F]	Permission of instructor	null	false	false	false	False	False	False
18.099	Independent Study	Studies (during IAP) or special individual reading (during regular terms). Arranged in consultation with individual faculty members and subject to departmental approval. May not be used to satisfy Mathematics major requirements.	true	Fall, IAP, Spring, Summer	Undergraduate	rranged	Permission of instructor	null	false	false	false	False	False	False
18.1001	Real Analysis	Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. Proofs and definitions are less abstract than in 18.100B. Gives applications where possible. Concerned primarily with the real line. Students in Course 18 must register for undergraduate version 18.100A.	true	Fall, Spring	Graduate	3-0-9	Calculus II (GIR)	null	false	false	false	False	False	False
18.1002	Real Analysis	Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space. Students in Course 18 must register for undergraduate version 18.100B.	true	Fall, Spring	Graduate	3-0-9	Calculus II (GIR)	null	false	false	false	False	False	False
18.100A	Real Analysis	Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. Proofs and definitions are less abstract than in 18.100B. Gives applications where possible. Concerned primarily with the real line.	true	Fall, Spring	Undergraduate	3-0-9	Calculus II (GIR)	null	false	false	false	False	False	False
18.100B	Real Analysis	Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space.	true	Fall, Spring	Undergraduate	3-0-9	Calculus II (GIR)	null	false	false	false	False	False	False
18.100P	Real Analysis	Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. Proofs and definitions are less abstract than in 18.100B. Gives applications where possible. Concerned primarily with the real line. Includes instruction and practice in written communication. Enrollment limited.	true	Spring	Undergraduate	4-0-11	Calculus II (GIR)	null	false	false	false	False	False	False
18.100Q	Real Analysis	Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space. Includes instruction and practice in written communication. Enrollment limited.	true	Fall	Undergraduate	4-0-11	Calculus II (GIR)	null	false	false	false	False	False	False
18.101	Analysis and Manifolds	Introduction to the theory of manifolds: vector fields and densities on manifolds, integral calculus in the manifold setting and the manifold version of the divergence theorem. 18.901 helpful but not required.	true	Fall	Undergraduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.1011	Analysis and Manifolds	Introduction to the theory of manifolds: vector fields and densities on manifolds, integral calculus in the manifold setting and the manifold version of the divergence theorem. 18.9011 helpful but not required. Students in Course 18 must register for the undergraduate version, 18.101.	true	Fall	Graduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.102	Introduction to Functional Analysis	Normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators. Lebesgue measure, measurable functions, integrability, completeness of L-p spaces. Hilbert space. Compact, Hilbert-Schmidt and trace class operators. Spectral theorem.	true	Spring	Undergraduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.1021	Introduction to Functional Analysis	Normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators. Lebesgue measure, measurable functions, integrability, completeness of L-p spaces. Hilbert space. Compact, Hilbert-Schmidt and trace class operators. Spectral theorem. Students in Course 18 must register for the undergraduate version, 18.102.	true	Spring	Graduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.103	Fourier Analysis: Theory and Applications	Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.	true	Spring	Undergraduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.1031	Fourier Analysis: Theory and Applications	Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals. Students in Course 18 must register for the undergraduate version, 18.103.	true	Spring	Graduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.104	Seminar in Analysis	Students present and discuss material from books or journals. Topics vary from year to year. Instruction and practice in written and oral communication provided. Enrollment limited.	true	Fall, Spring	Undergraduate	3-0-9	18.100A, 18.100B, 18.100P, or 18.100Q	null	false	false	false	False	False	False
18.112	Functions of a Complex Variable	Studies the basic properties of analytic functions of one complex variable. Conformal mappings and the Poincare model of non-Euclidean geometry. Cauchy-Goursat theorem and Cauchy integral formula. Taylor and Laurent decompositions. Singularities, residues and computation of integrals. Harmonic functions and Dirichlet's problem for the Laplace equation. The partial fractions decomposition. Infinite series and infinite product expansions. The Gamma function. The Riemann mapping theorem. Elliptic functions.	true	Fall	Undergraduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.1121	Functions of a Complex Variable	Studies the basic properties of analytic functions of one complex variable. Conformal mappings and the Poincare model of non-Euclidean geometry. Cauchy-Goursat theorem and Cauchy integral formula. Taylor and Laurent decompositions. Singularities, residues and computation of integrals. Harmonic functions and Dirichlet's problem for the Laplace equation. The partial fractions decomposition. Infinite series and infinite product expansions. The Gamma function. The Riemann mapping theorem. Elliptic functions. Students in Course 18 must register for the undergraduate version, 18.112.	true	Fall	Graduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.116	Riemann Surfaces	Riemann surfaces, uniformization, Riemann-Roch Theorem. Theory of elliptic functions and modular forms. Some applications, such as to number theory.	true	Fall	Graduate	3-0-9	18.112	null	false	false	false	False	False	False
18.117	Topics in Several Complex Variables	Harmonic theory on complex manifolds, Hodge decomposition theorem, Hard Lefschetz theorem. Vanishing theorems. Theory of Stein manifolds. As time permits students also study holomorphic vector bundles on Kahler manifolds.	true	Spring	Graduate	3-0-9	18.112 and 18.965	null	false	false	false	False	False	False
18.118	Topics in Analysis	Topics vary from year to year.	true	Spring	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
18.125	Measure Theory and Analysis	Provides a rigorous introduction to Lebesgue's theory of measure and integration. Covers material that is essential in analysis, probability theory, and differential geometry.	true	Spring	Graduate	3-0-9	18.100A, 18.100B, 18.100P, or 18.100Q	null	false	false	false	False	False	False
18.137	Topics in Geometric Partial Differential Equations	Topics vary from year to year.	false	Fall	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
18.152	Introduction to Partial Differential Equations	Introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. Includes mathematical tools, real-world examples and applications, such as the Black-Scholes equation, the European options problem, water waves, scalar conservation laws, first order equations and traffic problems.	true	Fall	Undergraduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.1521	Introduction to Partial Differential Equations	Introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. Includes mathematical tools, real-world examples and applications, such as the Black-Scholes equation, the European options problem, water waves, scalar conservation laws, first order equations and traffic problems. Students in Course 18 must register for the undergraduate version, 18.152.	true	Spring	Graduate	3-0-9	(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)	null	false	false	false	False	False	False
18.155	Differential Analysis I	First part of a two-subject sequence. Review of Lebesgue integration. Lp spaces. Distributions. Fourier transform. Sobolev spaces. Spectral theorem, discrete and continuous spectrum. Homogeneous distributions. Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Recommended prerequisite: 18.112.	true	Fall	Graduate	3-0-9	18.102 or 18.103	null	false	false	false	False	False	False
18.156	Differential Analysis II	Second part of a two-subject sequence. Covers variable coefficient elliptic, parabolic and hyperbolic partial differential equations.	true	Spring	Graduate	3-0-9	18.155	null	false	false	false	False	False	False
18.157	Introduction to Microlocal Analysis	The semi-classical theory of partial differential equations. Discussion of Pseudodifferential operators, Fourier integral operators, asymptotic solutions of partial differential equations, and the spectral theory of Schroedinger operators from the semi-classical perspective. Heavy emphasis placed on the symplectic geometric underpinnings of this subject.	true	Spring	Graduate	3-0-9	18.155	null	false	false	false	False	False	False
18.158	Topics in Differential Equations	Topics vary from year to year.	false	Spring	Graduate	3-0-9	18.157	null	false	false	false	False	False	False
18.199	Graduate Analysis Seminar	Studies original papers in differential analysis and differential equations. Intended for first- and second-year graduate students. Permission must be secured in advance.	true	Spring	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
18.200	Principles of Discrete Applied Mathematics	Study of illustrative topics in discrete applied mathematics, including probability theory, information theory, coding theory, secret codes, generating functions, and linear programming. Instruction and practice in written communication provided. Enrollment limited.	true	Spring	Undergraduate	4-0-11	None. Coreq: 18.06	null	false	false	false	False	False	False
18.200A	Principles of Discrete Applied Mathematics	Study of illustrative topics in discrete applied mathematics, including probability theory, information theory, coding theory, secret codes, generating functions, and linear programming.	true	Fall	Undergraduate	3-0-9	None. Coreq: 18.06	null	false	false	false	False	False	False
18.204	Undergraduate Seminar in Discrete Mathematics	Seminar in combinatorics, graph theory, and discrete mathematics in general. Participants read and present papers from recent mathematics literature. Instruction and practice in written and oral communication provided. Enrollment limited.	true	Fall, Spring	Undergraduate	3-0-9	((6.1200 or 18.200) and (18.06, 18.700, or 18.701)) or permission of instructor	null	false	false	false	False	False	False
18.211	Combinatorial Analysis	Combinatorial problems and methods for their solution. Enumeration, generating functions, recurrence relations, construction of bijections. Introduction to graph theory. Prior experience with abstraction and proofs is helpful.	true	Fall	Undergraduate	3-0-9	Calculus II (GIR) and (18.06, 18.700, or 18.701)	null	false	false	false	False	False	False
18.212	Algebraic Combinatorics	Applications of algebra to combinatorics. Topics include walks in graphs, the Radon transform, groups acting on posets, Young tableaux, electrical networks.	true	Spring	Undergraduate	3-0-9	18.701 or 18.703	null	false	false	false	False	False	False
18.217	Combinatorial Theory	Content varies from year to year.	true	Fall	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
18.218	Topics in Combinatorics	Topics vary from year to year.	true	Spring	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
18.219	Seminar in Combinatorics	Content varies from year to year. Readings from current research papers in combinatorics. Topics to be chosen and presented by the class.	true	Fall	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
18.225	Graph Theory and Additive Combinatorics	Introduction to extremal graph theory and additive combinatorics. Highlights common themes, such as the dichotomy between structure versus pseudorandomness. Topics include Turan-type problems, Szemeredi's regularity lemma and applications, pseudorandom graphs, spectral graph theory, graph limits, arithmetic progressions (Roth, Szemeredi, Green-Tao), discrete Fourier analysis, Freiman's theorem on sumsets and structure. Discusses current research topics and open problems.	true	Fall	Graduate	3-0-9	((18.701 or 18.703) and (18.100A, 18.100B, 18.100P, or 18.100Q)) or permission of instructor	null	false	false	false	False	False	False
18.226	Probabilistic Methods in Combinatorics	Introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. Focuses on methodology as well as combinatorial applications. Suitable for students with strong interest and background in mathematical problem solving. Topics include linearity of expectations, alteration, second moment, Lovasz local lemma, correlation inequalities, Janson inequalities, concentration inequalities, entropy method.	false	Fall	Graduate	3-0-9	(18.211, 18.600, and (18.100A, 18.100B, 18.100P, or 18.100Q)) or permission of instructor	null	false	false	false	False	False	False
18.300	Principles of Continuum Applied Mathematics	Covers fundamental concepts in continuous applied mathematics. Applications from traffic flow, fluids, elasticity, granular flows, etc. Also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion and group velocity. Uses MATLAB computing environment.	true	Spring	Undergraduate	3-0-9	Calculus II (GIR) and (18.03 or 18.032)	null	false	false	false	False	False	False
18.303	Linear Partial Differential Equations: Analysis and Numerics	Provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science and engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Studies operator adjoints and eigenproblems, series solutions, Green's functions, and separation of variables. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems, including stability and convergence analysis and implicit/explicit timestepping. Some programming required for homework and final project.	true	Fall	Undergraduate	3-0-9	18.06 or 18.700	null	false	false	false	False	False	False
18.305	Advanced Analytic Methods in Science and Engineering	Covers expansion around singular points: the WKB method on ordinary and partial differential equations; the method of stationary phase and the saddle point method; the two-scale method and the method of renormalized perturbation; singular perturbation and boundary-layer techniques; WKB method on partial differential equations.	true	Fall	Graduate	3-0-9	18.04, 18.075, or 18.112	null	false	false	false	False	False	False
18.306	Advanced Partial Differential Equations with Applications	Concepts and techniques for partial differential equations, especially nonlinear. Diffusion, dispersion and other phenomena. Initial and boundary value problems. Normal mode analysis, Green's functions, and transforms. Conservation laws, kinematic waves, hyperbolic equations, characteristics shocks, simple waves. Geometrical optics, caustics. Free-boundary problems. Dimensional analysis. Singular perturbation, boundary layers, homogenization. Variational methods. Solitons. Applications from fluid dynamics, materials science, optics, traffic flow, etc.	true	Spring	Graduate	3-0-9	(18.03 or 18.032) and (18.04, 18.075, or 18.112)	null	false	false	false	False	False	False
18.327	Topics in Applied Mathematics	Topics vary from year to year.	true	Fall	Graduate	3-0-9	Permission of instructor	null	false	false	false	False	False	False
18.330	Introduction to Numerical Analysis	Basic techniques for the efficient numerical solution of problems in science and engineering. Root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra. Knowledge of programming in a language such as MATLAB, Python, or Julia is helpful.	true	Spring	Undergraduate	3-0-9	Calculus II (GIR) and (18.03 or 18.032)	null	false	false	false	False	False	False
18.335[J]	Introduction to Numerical Methods	Advanced introduction to numerical analysis: accuracy and efficiency of numerical algorithms. In-depth coverage of sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems). Floating-point arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) may also be surveyed. Final project involves some programming.	false	Spring	Graduate	3-0-9	18.06, 18.700, or 18.701	6.7310[J]	false	false	false	False	False	False
18.336[J]	Fast Methods for Partial Differential and Integral Equations	Unified introduction to the theory and practice of modern, near linear-time, numerical methods for large-scale partial-differential and integral equations. Topics include preconditioned iterative methods; generalized Fast Fourier Transform and other butterfly-based methods; multiresolution approaches, such as multigrid algorithms and hierarchical low-rank matrix decompositions; and low and high frequency Fast Multipole Methods. Example applications include aircraft design, cardiovascular system modeling, electronic structure computation, and tomographic imaging.	true	Fall, Spring	Graduate	3-0-9	6.7300, 16.920, 18.085, 18.335, or permission of instructor	6.7340[J]	false	false	false	False	False	False
18.337[J]	Parallel Computing and Scientific Machine Learning	Introduction to scientific machine learning with an emphasis on developing scalable differentiable programs. Covers scientific computing topics (numerical differential equations, dense and sparse linear algebra, Fourier transformations, parallelization of large-scale scientific simulation) simultaneously with modern data science (machine learning, deep neural networks, automatic differentiation), focusing on the emerging techniques at the connection between these areas, such as neural differential equations and physics-informed deep learning. Provides direct experience with the modern realities of optimizing code performance for supercomputers, GPUs, and multicores in a high-level language.	true	Spring	Graduate	3-0-9	18.06, 18.700, or 18.701	6.7320[J]	false	false	false	False	False	False

17.878

Qualitative Methods and Fieldwork

Prepares students to conduct independent qualitative research, focusing on practical skills acquisition. Topics include methodological controversies, debates about transparency, human subjects protocols and research ethics, interviewing techniques, ethnography, focus groups, comparative historical case studies/archival research, and write-up of qualitative information collected from the field.

false

Spring

Graduate

3-0-9

Permission of instructor

null

false

False

17.C08[J]

Causal Inference

Provides an accessible overview of modern quantitative methods for causal inference: testing whether an action causes an outcome to occur. Makes heavy use of applied, real-data examples using Python or R and drawn from the participating domains (economics, political science, business, public policy, etc.). Covers topics including potential outcomes, causal graphs, randomized controlled trials, observational studies, instrumental variable estimation, and a contrast with machine learning techniques. Seeks to provide an intuitive understanding of the core concepts and techniques to help students produce and consume evidence of causal claims.

true

Spring

Undergraduate

4-0-8

6.3800, 6.3900, 6.C01, 14.32, 17.803, 18.05, 18.650, or permission of instructor

15.C08[J]

false

False

17.UR

Undergraduate Research

Research opportunities in Political Science in theoretical and applied research. For further information, contact the Departmental Coordinator.

true

Fall, IAP, Spring, Summer

Undergraduate

rranged [P/D/F]

null

false

False

17.URG

Undergraduate Research

Research opportunities in political science in theoretical and applied research. For further information, contact the departmental coordinator.

true

Fall, IAP, Spring, Summer, Fall, Spring

Undergraduate

rranged

null

false

False

17.90

Politics, Policy, and Political Science: What Does It All Mean? (New)

Explores the scope of political science, policy, and politics through conversations with faculty who research across the field. Topics include misinformation and democracy, dictatorships, nuclear war and AI, and why governments make the policy decisions they do. Gives a broad overview of the role of methods and data in political science. This class counts towards the 6-unit discovery-focused credit limit for first-year students.

true

Fall

Undergraduate

2-0-1 [P/D/F]

null

false

False

17.902

Political Science Internship and Research

For students participating in off-campus internships relevant to the field of political science. Before registering, students must submit a 1-2 page application statement which describes the internship, the nature of the work, the time commitment (hours per week and number of weeks) and the connection to the field of political science. Students must also submit a formal offer letter from a host employer/organization which provides details of the internship. Subject to departmental approval. Consult departmental undergraduate office.

true

Fall, Spring

Undergraduate

rranged [P/D/F]

null

false

False

17.905-17.911

Reading Seminar in Social Science

Reading and discussion of special topics in the fields of social science. Open to advanced undergraduates by arrangement with individual staff members. 17.909 is taught P/D/F.

true

Fall, IAP, Spring, Summer

Undergraduate

rranged

null

false

False

17.922

Martin Luther King, Jr. Design Seminar

Facilitates design and construction of installations and other community projects in conjunction with and beyond MIT's celebration of Dr. King. Students discuss the ideas and goals of Dr. King and other human rights leaders in the US and the world. The first half of the class develops in-depth understanding of the history of US racial issues as well as past and present domestic and international political struggles. Addresses issues of justice, equality and racism through videos, readings and writings, and class discussions. In the second half, students work as a group complete the installation and projects which serve as models for connecting academics with real life problems and struggle.

true

IAP

Undergraduate

3-0-3 [P/D/F]

null

false

False

17.925

Fundamentals of Science and Technology Public Policy Making: Science and Technology Policy Boot Camp

Examines the public policy behind, and the government's role in, the science and technology-based innovation system. Focuses on the US, but also discusses international examples. Prepares students planning careers in and around science and technology with the basic background for involvement in science policy making. Limited to 35. Application required.

true

IAP

Undergraduate

2-0-1

null

false

False

17.959

Preparation for General Exams

Selected readings for Political Science doctoral students in preparation for qualifying exams.

true

Fall, Summer

Graduate

rranged [P/D/F]

Permission of instructor

null

false

False

17.954-17.958,

17.960 Reading Seminar in Social Science

Reading and discussion of special topics in the fields of social science. Open to advanced graduate students by arrangement with individual staff members. 17.954 and 17.959 are taught P/D/F.

true

Fall, Spring, Summer

Graduate

rranged

Permission of instructor

null

false

False

17.962

Second Year Paper Workshop

Workshop for research and writing of major research paper as part of pre-dissertation requirements. Restricted to doctoral students.

true

Spring

Graduate

3-0-9

Permission of instructor

null

false

False

17.THG

Graduate Political Science Thesis

Program of research and writing of thesis; to be arranged by the student with supervising committee.

true

Fall, IAP, Spring, Summer

Graduate

rranged

Permission of instructor

null

false

False

17.THT

Thesis Research Design Seminar

Students writing a thesis in Political Science develop their research topics, review relevant research and scholarship, frame their research questions and arguments, choose an appropriate methodology for analysis, and draft the introductory and methodology sections of their theses.

true

Fall

Undergraduate

3-0-9

17.803 or permission of instructor

null

false

False

17.THU

Undergraduate Political Science Thesis

Program of research leading to the writing of an SB thesis. To be arranged by the student under approved supervision.

true

Fall, IAP, Spring, Summer

Undergraduate

rranged

null

false

False

17.S912

Special Undergraduate Subject in Political Science

Reading and discussion of topics in the field of social science not covered in the regular curriculum.

true

Fall, Spring

Undergraduate

rranged [P/D/F]

null

false

False

17.S914

Special Undergraduate Subject in Political Science

Reading and discussion of topics in the field of social science not covered in the regular curriculum.

true

Spring

Undergraduate

rranged

null

false

False

17.S916

Special Undergraduate Subject in Political Science

Reading and discussion of topics in the field of social science not covered in the regular curriculum.

true

Fall

Undergraduate

rranged [P/D/F]

null

false

False

17.S917

Special Undergraduate Subject in Political Science

Reading and discussion of topics in the field of social science not covered in the regular curriculum.

true

Spring

Undergraduate

rranged

null

false

False

17.S918

Special Undergraduate Subject in Political Science

Reading and discussion of topics in the field of social science not covered in the regular curriculum.

true

Spring

Undergraduate

rranged

null

false

False

17.S919

Special Undergraduate Subject in Political Science

Reading and discussion of topics in the field of social science not covered in the regular curriculum.

true

Fall

Undergraduate

rranged

null

false

False

17.S950

Special Graduate Subject in Political Science

Open to qualified graduate students who would like to pursue special studies or projects. Please consult graduate administration prior to registration.

false

Spring

Graduate

rranged

Permission of instructor

null

false

False

17.S951

Special Graduate Subject in Political Science

Open to qualified graduate students who would like to pursue special subjects or projects. Please consult graduate administration prior to registration.

true

Spring

Graduate

rranged

Permission of instructor

null

false

False

17.S952

Special Graduate Subject in Political Science

Open to qualified graduate students who would like to pursue special subjects or projects. Please consult graduate administration prior to registration.

true

Fall

Graduate

rranged

Permission of instructor

null

false

False

17.S953

Special Graduate Subject in Political Science

Open to qualified graduate students who would like to pursue special subjects or projects. Please consult graduate administration prior to registration.

true

Fall

Graduate

rranged

Permission of instructor

null

false

False

18.01

Calculus

Differentiation and integration of functions of one variable, with applications. Informal treatment of limits and continuity. Differentiation: definition, rules, application to graphing, rates, approximations, and extremum problems. Indefinite integration; separable first-order differential equations. Definite integral; fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Polar coordinates. L'Hopital's rule. Improper integrals. Infinite series: geometric, p-harmonic, simple comparison tests, power series for some elementary functions.

true

Fall, Spring

Undergraduate

5-0-7

null

false

Calculus 1

False

18.01A

Calculus

Six-week review of one-variable calculus, emphasizing material not on the high-school AB syllabus: integration techniques and applications, improper integrals, infinite series, applications to other topics, such as probability and statistics, as time permits. Prerequisites: one year of high-school calculus or the equivalent, with a score of 5 on the AB Calculus test (or the AB portion of the BC test, or an equivalent score on a standard international exam), or equivalent college transfer credit, or a passing grade on the first half of the 18.01 advanced standing exam.

true

Fall

Undergraduate

5-0-7

Knowledge of differentiation and elementary integration

null

false

Calculus 1

False

18.02

Calculus

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.

true

Fall, Spring

Undergraduate

5-0-7

Calculus I (GIR)

null

false

Calculus 2

False

18.02A

Calculus

First half is taught during the last six weeks of the Fall term; covers material in the first half of 18.02 (through double integrals). Second half of 18.02A can be taken either during IAP (daily lectures) or during the second half of the Spring term; it covers the remaining material in 18.02.

true

Fall, IAP, Spring

Undergraduate

5-0-7

Calculus I (GIR)

null

false

Calculus 2

False

18.022

Calculus

Calculus of several variables. Topics as in 18.02 but with more focus on mathematical concepts. Vector algebra, dot product, matrices, determinant. Functions of several variables, continuity, differentiability, derivative. Parametrized curves, arc length, curvature, torsion. Vector fields, gradient, curl, divergence. Multiple integrals, change of variables, line integrals, surface integrals. Stokes' theorem in one, two, and three dimensions.

true

Fall

Undergraduate

5-0-7

Calculus I (GIR)

null

false

Calculus 2

False

18.03

Differential Equations

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

true

Fall, Spring

Undergraduate

5-0-7

None. Coreq: Calculus II (GIR)

null

false

true

False

18.031

System Functions and the Laplace Transform

Studies basic continuous control theory as well as representation of functions in the complex frequency domain. Covers generalized functions, unit impulse response, and convolution; and Laplace transform, system (or transfer) function, and the pole diagram. Includes examples from mechanical and electrical engineering.

true

IAP

Undergraduate

1-0-2 [P/D/F]

None. Coreq: 18.03

null

false

False

18.032

Differential Equations

Covers much of the same material as 18.03 with more emphasis on theory. The point of view is rigorous and results are proven. Local existence and uniqueness of solutions.

true

Spring

Undergraduate

5-0-7

None. Coreq: Calculus II (GIR)

null

false

true

False

18.04

Complex Variables with Applications

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, Laplace transforms, and partial differential equations.

true

Fall

Undergraduate

4-0-8

Calculus II (GIR) and (18.03 or 18.032)

null

false

False

18.05

Introduction to Probability and Statistics

A unified introduction to probability, Bayesian inference, and frequentist statistics. Topics include: combinatorics, random variables, (joint) distributions, covariance, central limit theorem; Bayesian updating, odds, posterior prediction; significance tests, confidence intervals, bootstrapping, regression. Students also develop computational skills and statistical thinking by using R to simulate, analyze, and visualize data; and by exploring privacy, fairness, and causality in contemporary media and research. Flipped subject taught in a Technology Enabled Active Learning (TEAL) classroom to facilitate discussion, group problem solving, and coding studios with ample mentorship.

true

Spring

Undergraduate

4-0-8

Calculus II (GIR)

null

false

true

False

18.06

Linear Algebra

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, singular value decomposition, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses linear algebra software. Compared with 18.700, more emphasis on matrix algorithms and many applications.

true

Fall, Spring

Undergraduate

4-0-8

Calculus II (GIR)

null

false

true

False

18.C06[J]

Linear Algebra and Optimization

Introductory course in linear algebra and optimization, assuming no prior exposure to linear algebra and starting from the basics, including vectors, matrices, eigenvalues, singular values, and least squares. Covers the basics in optimization including convex optimization, linear/quadratic programming, gradient descent, and regularization, building on insights from linear algebra. Explores a variety of applications in science and engineering, where the tools developed give powerful ways to understand complex systems and also extract structure from data.

true

Fall

Undergraduate

5-0-7

Calculus II (GIR)

6.C06[J]

false

true

False

18.062[J]

Mathematics for Computer Science

Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

true

Fall, Spring

Undergraduate

5-0-7

Calculus I (GIR)

6.1200[J]

false

true

False

18.063

Matrix Calculus for Machine Learning and Beyond (New)

Covers a coherent approach to matrix calculus, showing techniques that allow the student to think of a matrix holistically, rather than as an array of scalars; generalize and compute derivatives of important matrix factorizations and other complicated-looking operations; and understand how differentiation formulas must be reimagined in large-scale computing. Discusses "adjoint" or "reverse-mode" differentiation, custom vector-Jacobian products, and how modern automatic differentiation is more computer science than calculus.

true

IAP

Undergraduate

1-0-2 [P/D/F]

Calculus II (GIR) and 18.06

null

false

False

18.065

Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

Reviews linear algebra with applications to life sciences, finance, engineering, and big data. Covers singular value decomposition, weighted least squares, signal and image processing, principal component analysis, covariance and correlation matrices, directed and undirected graphs, matrix factorizations, neural nets, machine learning, and computations with large matrices.

true

Spring

Undergraduate

3-0-9

18.06

null

false

False

18.0651

Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

Reviews linear algebra with applications to life sciences, finance, engineering, and big data. Covers singular value decomposition, weighted least squares, signal and image processing, principal component analysis, covariance and correlation matrices, directed and undirected graphs, matrix factorizations, neural nets, machine learning, and computations with large matrices. Students in Course 18 must register for the undergraduate version, 18.065.

true

Spring

Graduate

3-0-9

18.06

null

false

False

18.075

Methods for Scientists and Engineers

Covers functions of a complex variable; calculus of residues. Includes ordinary differential equations; Bessel and Legendre functions; Sturm-Liouville theory; partial differential equations; heat equation; and wave equations.

true

Spring

Undergraduate

3-0-9

Calculus II (GIR) and 18.03

null

false

False

18.0751

Methods for Scientists and Engineers

Covers functions of a complex variable; calculus of residues. Includes ordinary differential equations; Bessel and Legendre functions; Sturm-Liouville theory; partial differential equations; heat equation; and wave equations. Students in Courses 6, 8, 12, 18, and 22 must register for undergraduate version, 18.075.

true

Spring

Graduate

3-0-9

Calculus II (GIR) and 18.03

null

false

False

18.085

Computational Science and Engineering I

Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution. Frequent use of MATLAB in a wide range of scientific and engineering applications.

true

Fall, Spring, Summer

Undergraduate

3-0-9

Calculus II (GIR) and (18.03 or 18.032)

null

false

False

18.0851

Computational Science and Engineering I

Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution. Frequent use of MATLAB in a wide range of scientific and engineering applications. Students in Course 18 must register for the undergraduate version, 18.085.

true

Fall, Spring, Summer

Graduate

3-0-9

Calculus II (GIR) and (18.03 or 18.032)

null

false

False

18.086

Computational Science and Engineering II

Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes. Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients. Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods.

true

Spring

Undergraduate

3-0-9

Calculus II (GIR) and (18.03 or 18.032)

null

false

False

18.0861

Computational Science and Engineering II

Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes. Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients. Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods. Students in Course 18 must register for the undergraduate version, 18.086.

true

Spring

Graduate

3-0-9

Calculus II (GIR) and (18.03 or 18.032)

null

false

False

18.089

Review of Mathematics

One-week review of one-variable calculus (18.01), followed by concentrated study covering multivariable calculus (18.02), two hours per day for five weeks. Primarily for graduate students in Course 2N. Degree credit allowed only in special circumstances.

true

Summer

Graduate

5-0-7

Permission of instructor

null

false

False

18.090

Introduction to Mathematical Reasoning

Focuses on understanding and constructing mathematical arguments. Discusses foundational topics (such as infinite sets, quantifiers, and methods of proof) as well as selected concepts from algebra (permutations, vector spaces, fields) and analysis (sequences of real numbers). Particularly suitable for students desiring additional experience with proofs before going on to more advanced mathematics subjects or subjects in related areas with significant mathematical content.

true

Spring

Undergraduate

3-0-9

None. Coreq: Calculus II (GIR)

null

false

true

False

18.091

Introduction to Metric Spaces (New)

Covers metrics, open and closed sets, continuous functions (from a topological perspective), function spaces, completeness, and compactness. Aims to provide more complex concepts and proofs for students who have taken 18.100A as their real analysis subject.

true

IAP

Undergraduate

1-0-2 [P/D/F]

18.100A

null

false

False

18.094[J]

Teaching College-Level Science and Engineering

Participatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include theories of adult learning; course development; promoting active learning, problemsolving, 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. Appropriate for both novices and those with teaching experience.

true

Fall

Graduate

2-0-2 [P/D/F]

null

1.95[J], 5.95[J], 7.59[J], 8.395[J]

false

False

18.095

Mathematics Lecture Series

Ten lectures by mathematics faculty members on interesting topics from both classical and modern mathematics. All lectures accessible to students with calculus background and an interest in mathematics. At each lecture, reading and exercises are assigned. Students prepare these for discussion in a weekly problem session.

true

IAP

Undergraduate

2-0-4 [P/D/F]

Calculus I (GIR)

null

false

False

18.098

Internship in Mathematics

Provides academic credit for students pursuing internships to gain practical experience in the applications of mathematical concepts and methods.

true

Fall, IAP, Spring, Summer

Undergraduate

rranged [P/D/F]

Permission of instructor

null

false

False

18.099

Independent Study

Studies (during IAP) or special individual reading (during regular terms). Arranged in consultation with individual faculty members and subject to departmental approval. May not be used to satisfy Mathematics major requirements.

true

Fall, IAP, Spring, Summer

Undergraduate

rranged

Permission of instructor

null

false

False

18.1001

Real Analysis

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. Proofs and definitions are less abstract than in 18.100B. Gives applications where possible. Concerned primarily with the real line. Students in Course 18 must register for undergraduate version 18.100A.

true

Fall, Spring

Graduate

3-0-9

Calculus II (GIR)

null

false

False

18.1002

Real Analysis

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space. Students in Course 18 must register for undergraduate version 18.100B.

true

Fall, Spring

Graduate

3-0-9

Calculus II (GIR)

null

false

False

18.100A

Real Analysis

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. Proofs and definitions are less abstract than in 18.100B. Gives applications where possible. Concerned primarily with the real line.

true

Fall, Spring

Undergraduate

3-0-9

Calculus II (GIR)

null

false

False

18.100B

Real Analysis

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space.

true

Fall, Spring

Undergraduate

3-0-9

Calculus II (GIR)

null

false

False

18.100P

Real Analysis

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. Proofs and definitions are less abstract than in 18.100B. Gives applications where possible. Concerned primarily with the real line. Includes instruction and practice in written communication. Enrollment limited.

true

Spring

Undergraduate

4-0-11

Calculus II (GIR)

null

false

False

18.100Q

Real Analysis

Covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Shows the utility of abstract concepts and teaches understanding and construction of proofs. More demanding than 18.100A, for students with more mathematical maturity. Places more emphasis on point-set topology and n-space. Includes instruction and practice in written communication. Enrollment limited.

true

Fall

Undergraduate

4-0-11

Calculus II (GIR)

null

false

False

18.101

Analysis and Manifolds

Introduction to the theory of manifolds: vector fields and densities on manifolds, integral calculus in the manifold setting and the manifold version of the divergence theorem. 18.901 helpful but not required.

true

Fall

Undergraduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.1011

Analysis and Manifolds

Introduction to the theory of manifolds: vector fields and densities on manifolds, integral calculus in the manifold setting and the manifold version of the divergence theorem. 18.9011 helpful but not required. Students in Course 18 must register for the undergraduate version, 18.101.

true

Fall

Graduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.102

Introduction to Functional Analysis

Normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators. Lebesgue measure, measurable functions, integrability, completeness of L-p spaces. Hilbert space. Compact, Hilbert-Schmidt and trace class operators. Spectral theorem.

true

Spring

Undergraduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.1021

Introduction to Functional Analysis

Normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators. Lebesgue measure, measurable functions, integrability, completeness of L-p spaces. Hilbert space. Compact, Hilbert-Schmidt and trace class operators. Spectral theorem. Students in Course 18 must register for the undergraduate version, 18.102.

true

Spring

Graduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.103

Fourier Analysis: Theory and Applications

Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.

true

Spring

Undergraduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.1031

Fourier Analysis: Theory and Applications

Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals. Students in Course 18 must register for the undergraduate version, 18.103.

true

Spring

Graduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.104

Seminar in Analysis

Students present and discuss material from books or journals. Topics vary from year to year. Instruction and practice in written and oral communication provided. Enrollment limited.

true

Fall, Spring

Undergraduate

3-0-9

18.100A, 18.100B, 18.100P, or 18.100Q

null

false

False

18.112

Functions of a Complex Variable

Studies the basic properties of analytic functions of one complex variable. Conformal mappings and the Poincare model of non-Euclidean geometry. Cauchy-Goursat theorem and Cauchy integral formula. Taylor and Laurent decompositions. Singularities, residues and computation of integrals. Harmonic functions and Dirichlet's problem for the Laplace equation. The partial fractions decomposition. Infinite series and infinite product expansions. The Gamma function. The Riemann mapping theorem. Elliptic functions.

true

Fall

Undergraduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.1121

Functions of a Complex Variable

Studies the basic properties of analytic functions of one complex variable. Conformal mappings and the Poincare model of non-Euclidean geometry. Cauchy-Goursat theorem and Cauchy integral formula. Taylor and Laurent decompositions. Singularities, residues and computation of integrals. Harmonic functions and Dirichlet's problem for the Laplace equation. The partial fractions decomposition. Infinite series and infinite product expansions. The Gamma function. The Riemann mapping theorem. Elliptic functions. Students in Course 18 must register for the undergraduate version, 18.112.

true

Fall

Graduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.116

Riemann Surfaces

Riemann surfaces, uniformization, Riemann-Roch Theorem. Theory of elliptic functions and modular forms. Some applications, such as to number theory.

true

Fall

Graduate

3-0-9

18.112

null

false

False

18.117

Topics in Several Complex Variables

Harmonic theory on complex manifolds, Hodge decomposition theorem, Hard Lefschetz theorem. Vanishing theorems. Theory of Stein manifolds. As time permits students also study holomorphic vector bundles on Kahler manifolds.

true

Spring

Graduate

3-0-9

18.112 and 18.965

null

false

False

18.118

Topics in Analysis

Topics vary from year to year.

true

Spring

Graduate

3-0-9

Permission of instructor

null

false

False

18.125

Measure Theory and Analysis

Provides a rigorous introduction to Lebesgue's theory of measure and integration. Covers material that is essential in analysis, probability theory, and differential geometry.

true

Spring

Graduate

3-0-9

18.100A, 18.100B, 18.100P, or 18.100Q

null

false

False

18.137

Topics in Geometric Partial Differential Equations

Topics vary from year to year.

false

Fall

Graduate

3-0-9

Permission of instructor

null

false

False

18.152

Introduction to Partial Differential Equations

Introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. Includes mathematical tools, real-world examples and applications, such as the Black-Scholes equation, the European options problem, water waves, scalar conservation laws, first order equations and traffic problems.

true

Fall

Undergraduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.1521

Introduction to Partial Differential Equations

Introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. Includes mathematical tools, real-world examples and applications, such as the Black-Scholes equation, the European options problem, water waves, scalar conservation laws, first order equations and traffic problems. Students in Course 18 must register for the undergraduate version, 18.152.

true

Spring

Graduate

3-0-9

(18.06, 18.700, or 18.701) and (18.100A, 18.100B, 18.100P, or 18.100Q)

null

false

False

18.155

Differential Analysis I

First part of a two-subject sequence. Review of Lebesgue integration. Lp spaces. Distributions. Fourier transform. Sobolev spaces. Spectral theorem, discrete and continuous spectrum. Homogeneous distributions. Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Recommended prerequisite: 18.112.

true

Fall

Graduate

3-0-9

18.102 or 18.103

null

false

False

18.156

Differential Analysis II

Second part of a two-subject sequence. Covers variable coefficient elliptic, parabolic and hyperbolic partial differential equations.

true

Spring

Graduate

3-0-9

18.155

null

false

False

18.157

Introduction to Microlocal Analysis

The semi-classical theory of partial differential equations. Discussion of Pseudodifferential operators, Fourier integral operators, asymptotic solutions of partial differential equations, and the spectral theory of Schroedinger operators from the semi-classical perspective. Heavy emphasis placed on the symplectic geometric underpinnings of this subject.

true

Spring

Graduate

3-0-9

18.155

null

false

False

18.158

Topics in Differential Equations

Topics vary from year to year.

false

Spring

Graduate

3-0-9

18.157

null

false

False

18.199

Graduate Analysis Seminar

Studies original papers in differential analysis and differential equations. Intended for first- and second-year graduate students. Permission must be secured in advance.

true

Spring

Graduate

3-0-9

Permission of instructor

null

false

False

18.200

Principles of Discrete Applied Mathematics

Study of illustrative topics in discrete applied mathematics, including probability theory, information theory, coding theory, secret codes, generating functions, and linear programming. Instruction and practice in written communication provided. Enrollment limited.

true

Spring

Undergraduate

4-0-11

None. Coreq: 18.06

null

false

False

18.200A

Principles of Discrete Applied Mathematics

Study of illustrative topics in discrete applied mathematics, including probability theory, information theory, coding theory, secret codes, generating functions, and linear programming.

true

Fall

Undergraduate

3-0-9

None. Coreq: 18.06

null

false

False

18.204

Undergraduate Seminar in Discrete Mathematics

Seminar in combinatorics, graph theory, and discrete mathematics in general. Participants read and present papers from recent mathematics literature. Instruction and practice in written and oral communication provided. Enrollment limited.

true

Fall, Spring

Undergraduate

3-0-9

((6.1200 or 18.200) and (18.06, 18.700, or 18.701)) or permission of instructor

null

false

False

18.211

Combinatorial Analysis

Combinatorial problems and methods for their solution. Enumeration, generating functions, recurrence relations, construction of bijections. Introduction to graph theory. Prior experience with abstraction and proofs is helpful.

true

Fall

Undergraduate

3-0-9

Calculus II (GIR) and (18.06, 18.700, or 18.701)

null

false

False

18.212

Algebraic Combinatorics

Applications of algebra to combinatorics. Topics include walks in graphs, the Radon transform, groups acting on posets, Young tableaux, electrical networks.

true

Spring

Undergraduate

3-0-9

18.701 or 18.703

null

false

False

18.217

Combinatorial Theory

Content varies from year to year.

true

Fall

Graduate

3-0-9

Permission of instructor

null

false

False

18.218

Topics in Combinatorics

Topics vary from year to year.

true

Spring

Graduate

3-0-9

Permission of instructor

null

false

False

18.219

Seminar in Combinatorics

Content varies from year to year. Readings from current research papers in combinatorics. Topics to be chosen and presented by the class.

true

Fall

Graduate

3-0-9

Permission of instructor

null

false

False

18.225

Graph Theory and Additive Combinatorics

Introduction to extremal graph theory and additive combinatorics. Highlights common themes, such as the dichotomy between structure versus pseudorandomness. Topics include Turan-type problems, Szemeredi's regularity lemma and applications, pseudorandom graphs, spectral graph theory, graph limits, arithmetic progressions (Roth, Szemeredi, Green-Tao), discrete Fourier analysis, Freiman's theorem on sumsets and structure. Discusses current research topics and open problems.

true

Fall

Graduate

3-0-9

((18.701 or 18.703) and (18.100A, 18.100B, 18.100P, or 18.100Q)) or permission of instructor

null

false

False

18.226

Probabilistic Methods in Combinatorics

Introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. Focuses on methodology as well as combinatorial applications. Suitable for students with strong interest and background in mathematical problem solving. Topics include linearity of expectations, alteration, second moment, Lovasz local lemma, correlation inequalities, Janson inequalities, concentration inequalities, entropy method.

false

Fall

Graduate

3-0-9

(18.211, 18.600, and (18.100A, 18.100B, 18.100P, or 18.100Q)) or permission of instructor

null

false

False

18.300

Principles of Continuum Applied Mathematics

Covers fundamental concepts in continuous applied mathematics. Applications from traffic flow, fluids, elasticity, granular flows, etc. Also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion and group velocity. Uses MATLAB computing environment.

true

Spring

Undergraduate

3-0-9

Calculus II (GIR) and (18.03 or 18.032)

null

false

False

18.303

Linear Partial Differential Equations: Analysis and Numerics

Provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science and engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Studies operator adjoints and eigenproblems, series solutions, Green's functions, and separation of variables. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems, including stability and convergence analysis and implicit/explicit timestepping. Some programming required for homework and final project.

true

Fall

Undergraduate

3-0-9

18.06 or 18.700

null

false

False

18.305

Advanced Analytic Methods in Science and Engineering

Covers expansion around singular points: the WKB method on ordinary and partial differential equations; the method of stationary phase and the saddle point method; the two-scale method and the method of renormalized perturbation; singular perturbation and boundary-layer techniques; WKB method on partial differential equations.

true

Fall

Graduate

3-0-9

18.04, 18.075, or 18.112

null

false

False

18.306

Advanced Partial Differential Equations with Applications

Concepts and techniques for partial differential equations, especially nonlinear. Diffusion, dispersion and other phenomena. Initial and boundary value problems. Normal mode analysis, Green's functions, and transforms. Conservation laws, kinematic waves, hyperbolic equations, characteristics shocks, simple waves. Geometrical optics, caustics. Free-boundary problems. Dimensional analysis. Singular perturbation, boundary layers, homogenization. Variational methods. Solitons. Applications from fluid dynamics, materials science, optics, traffic flow, etc.

true

Spring

Graduate

3-0-9

(18.03 or 18.032) and (18.04, 18.075, or 18.112)

null

false

False

18.327

Topics in Applied Mathematics

Topics vary from year to year.

true

Fall

Graduate

3-0-9

Permission of instructor

null

false

False

18.330

Introduction to Numerical Analysis

Basic techniques for the efficient numerical solution of problems in science and engineering. Root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra. Knowledge of programming in a language such as MATLAB, Python, or Julia is helpful.

true

Spring

Undergraduate

3-0-9

Calculus II (GIR) and (18.03 or 18.032)

null

false

False

18.335[J]

Introduction to Numerical Methods

Advanced introduction to numerical analysis: accuracy and efficiency of numerical algorithms. In-depth coverage of sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems). Floating-point arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) may also be surveyed. Final project involves some programming.

false

Spring

Graduate

3-0-9

18.06, 18.700, or 18.701

6.7310[J]

false

False

18.336[J]

Fast Methods for Partial Differential and Integral Equations

Unified introduction to the theory and practice of modern, near linear-time, numerical methods for large-scale partial-differential and integral equations. Topics include preconditioned iterative methods; generalized Fast Fourier Transform and other butterfly-based methods; multiresolution approaches, such as multigrid algorithms and hierarchical low-rank matrix decompositions; and low and high frequency Fast Multipole Methods. Example applications include aircraft design, cardiovascular system modeling, electronic structure computation, and tomographic imaging.

true

Fall, Spring

Graduate

3-0-9

6.7300, 16.920, 18.085, 18.335, or permission of instructor

6.7340[J]

false

False

18.337[J]

Parallel Computing and Scientific Machine Learning

Introduction to scientific machine learning with an emphasis on developing scalable differentiable programs. Covers scientific computing topics (numerical differential equations, dense and sparse linear algebra, Fourier transformations, parallelization of large-scale scientific simulation) simultaneously with modern data science (machine learning, deep neural networks, automatic differentiation), focusing on the emerging techniques at the connection between these areas, such as neural differential equations and physics-informed deep learning. Provides direct experience with the modern realities of optimizing code performance for supercomputers, GPUs, and multicores in a high-level language.

true

Spring

Graduate

3-0-9

18.06, 18.700, or 18.701

6.7320[J]

false

False