Continues 18.100. Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.

This course covers French politics, culture, and society from Louis XIV to Napoleon Bonaparte. Attention is given to the growth of the central state, the beginnings of a modern consumer society, the Enlightenment, the French Revolution, including its origins, and the rise and fall of Napoleon.

The basic properties of functions of one complex variable. Cauchy's theorem, holomorphic and meromorphic functions, residues, contour integrals, conformal mapping. Infinite series and products, the gamma function, the Mittag-Leffler theorem. Harmonic functions, Dirichlet's problem. This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted. This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions.

This subject explores the legal history of the United States as a gendered system. It examines how women have shaped the meanings of American citizenship through pursuit of political rights such as suffrage, jury duty, and military service, how those political struggles have varied for across race, religion, and class, as well as how the legal system has shaped gender relations for both women and men through regulation of such issues as marriage, divorce, work, reproduction, and the family. The course readings will draw from primary and secondary materials in American history, as well as some court cases. However, the focus of the class is on the broader relationship between law and society, and no technical legal knowledge is required or assumed.

Introduction to discrete and computational geometry. Topics covered: planar graphs, geometric graphs, the theory of crossings, extremal graph theory, arrangements of curves and points in the plane (mainly pseudolines and pseudocircles), problems involving distances, Gallai-Sylvester-type problems, Davenport-Schinzel sequences. Emphasis on teaching methods in combinatorial geometry. Many results presented are recent, and include open problems.

This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.

A rigorous introduction designed for mathematicians into perturbative quantum field theory, using the language of functional integrals. Basics of classical field theory. Free quantum theories. Feynman diagrams. Renormalization theory. Local operators. Operator product expansion. Renormalization group equation. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and string theory.

This is a second-semester graduate course on the geometry of manifolds. The main emphasis is on the geometry of symplectic manifolds, but the material also includes long digressions into complex geometry and the geometry of 4-manifolds, with special emphasis on topological considerations.

This course focuses on an in-depth reading of Principia Mathematica Philosophiae Naturalis by Isaac Newton, as well as several related commentaries and historical philosophical texts.

This course examines the history of MIT through the lens of the broader history of science and technology, and vice versa. The course covers the founding of MIT in 1861 and goes through the present, including such topics as William Barton Rogers, educational philosophy, biographies of MIT students and professors, intellectual and organizational development, the role of science, changing laboratories and practices, and MIT's relationship with Boston, the federal government, and industry. Assignments include short papers, presentations, and final paper. A number of classes are concurrent with the MIT150 Symposia.

This course offers an introduction to the history and historiography of science from ancient Greece to the present. It is designed to serve as an introduction for those who have no prior background in the field and to deepen the knowledge of those who already do. We will consider how the history of science has responded to its encounters with philosophy, sociology, economics, and anthropology. Our readings and discussions will focus on determining what makes particular works effective, understanding major contemporary trends and debates in the history of science, and establishing resources for further research.

This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems.

This course is an introduction to data cleaning, analysis and visualization. We will teach the basics of data analysis through concrete examples. You will learn how to take raw data, extract meaningful information, use statistical tools, and make visualizations. This was offered as a non-credit course during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB in particular.

Analysis I in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

This course provides an overview of Asian American history and its relevance for contemporary issues. It covers the first wave of Asian immigration in the 19th century, the rise of anti-Asian movements, the experiences of Asian Americans during WWII, the emergence of the Asian American movement in the 1960s, and the new wave of post–1965 Asian immigration. The class examines the role these experiences played in the formation of Asian American ethnicity. The course addresses key societal issues such as racial stereotyping, media racism, affirmative action, the glass ceiling, the "model minority" syndrome, and anti-Asian harassment or violence. The course is taught in English.

This is a fast-paced introductory course to the C++ programming language. It is intended for those with little programming background, though prior programming experience will make it easier, and those with previous experience will still learn C++-specific constructs and concepts. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This is a undergraduate course. It will cover 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; as well as spectral theorem.

A general introduction to manifolds and Lie groups. The role of Lie groups in mathematics and physics. The exponential mapping. Correspondence with Lie algebras. Homogeneous spaces and transformation groups. Adjoint representation. Covering groups. Automorphism groups. Invariant differential forms and cohomology of Lie groups and homogeneous spaces. 18.101 recommended but not required. DThis course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.