Discrete and continuum modeling of diffusion processes in physics, chemistry, and economics. Topics include central limit theorems, continuous-time random walks, Levy flights, correlations, extreme events, mixing, renormalization, and percolation.

Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and minimum cuts. Geometric algorithms: convex hulls, linear programming in fixed or arbitrary dimension. Approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

The scope of this video lesson consists in studying the sets of Rational and Irrational numbers. It is best suited for an advanced math course: Algebra 2 or higher.

This course explores the form, content, and historical context of various works of fiction specifically through the thematic lens of "dysfunctional families." We will focus primarily on questions pertaining to the structure, language, story, and characters of these fictional works.

""Reading Poetry" has several aims: primarily, to increase the ways you can become more engaged and curious readers of poetry; to increase your confidence as writers thinking about literary texts; and to provide you with the language for literary description. The course is not designed as a historical survey course but rather as an introductory approach to poetry from various directions -- as public or private utterances; as arranged imaginative shapes; and as psychological worlds, for example. One perspective offered is that poetry offers intellectual, moral and linguistic pleasures as well as difficulties to our private lives as readers and to our public lives as writers. Expect to hear and read poems aloud and to memorize lines; the class format will be group discussion, occasional lecture."

How do you read a poem? Intuition is not the only answer. In this class, we will investigate some of the formal tools poets use—meter, sound, syntax, word-choice, and other properties of language—as well as exploring a range of approaches to reading poetry, from the old (memorization and reading out loud) to the new (digitally enabled visualization and annotation). We will use readings available online via the generosity of the Poetry Foundation and the Academy of American Poets. We will also think collectively about how to approach difficult poems.

Aims to develop a teaching knowledge of the field through extensive reading and discussion of major works. The reading covers a broad range of topics -- political, economic, social, and cultural -- and represents a variety of historical methods. Students make frequent oral presentations and prepare a 20-page review essay.

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

This half-semester course introduces and surveys the major public capital market real estate vehicles, REITs and MBS (with primary emphasis on CMBS). Some background is also included in basic modern portfolio theory and equilibrium asset pricing. This course is primarily designed to provide MSRED students with a basic introduction to the public capital market sources of financial capital for real estate, and how those markets value such capital investments.

" This course, offered by the MIT Center for Real Estate, focuses on developing an understanding of the macroeconomic factors that shape and influence markets for real property. We will develop the theory of land markets and locational choice. The material covered includes studies of changing economic activities, demographic trends, transportation and local government behavior as they affect real estate."

This course is an introduction to the most fundamental concepts, principles, analytical methods and tools useful for making investment and finance decisions regarding commercial real estate assets. As the first of a two-course sequence, this course will focus on the basic building blocks and the "micro" level, which pertains to individual properties and deals.

To provide instruction and dialog on practical ethical issues relating to the responsible conduct of human and animal research in the brain and cognitive sciences. Specific emphasis will be placed on topics relevant to young researchers including data handling, animal and human subjects, misconduct, mentoring, intellectual property, and publication.

"2010 marks the 400th anniversary of Galileo's astonishing sightings of features on the moon, stars, and moons around Jupiter that no one had seen before. Recreate these new ways of seeing and exploring from the materials and techniques Galileo had on hand, while you reflect on the times and works of Galileo. What was it like to improvise new ways of seeing and exploring from the materials and techniques on hand? What do we notice? What surprises us? How can we relate to past experience and ideas? What are we curious to research? How does our experimenting grow into our learning? Let your own curiosity drive your explorations."

Small group study of advanced subjects under staff supervision. For graduate students wishing to pursue further study in advanced areas of urban studies and city and regional planning not covered in regular subjects of instruction. The course is an introduction to the approach of Reflective Practice developed by Donald SchĚŚn. It is an approach that enables professionals to understand how they use their knowledge in practical situations and how they can combine practice and learning in a more effective way. Through greater awareness of how they deploy their knowledge in practical situations, professionals can increase their capacities of learning in a more timely way. Understanding how they frame situations and ideas helps professionals to achieve greater flexibility and increase their capacity of conceptual innovation. The objective of the course is to introduce students to the approach and methods of reflective practice by raising their awareness about their own cognitive resources and how they use them in their practice. The course will introduce theories of learning, knowledge generation, framing and reframing, theories of action, reflection-in-practice, and conceptual innovation, and provide students with opportunities to experiment with these theories in real life through practical exercises in which they reflect on real situations that they have faced in their past professional experience. Through these practical exercises, students will have the opportunity to reflect on their thinking capacities in the context of their practice.

For the last century, precepts of scientific management and administrative rationality have concentrated power in the hands of technical specialists, which in recent decades has contributed to widespread disenfranchisement and discontent among stakeholders in natural resources cases. In this seminar we examine the limitations of scientific management as a model both for governance and for gathering and using information, and describe alternative methods for informing and organizing decision-making processes. We feature cases involving large carnivores in the West (mountain lions and grizzly bears), Northeast coastal fisheries, and adaptive management of the Colorado River. There will be nightly readings and a short written assignment.

This subject is on regional energy-environmental modeling rather than on general energy-environmental policies, but the models should have some policy relevance. We will start with some discussion of green accounting issues; then, we will cover a variety of theoretical and empirical topics related to spatial energy demand and supply, energy forecasts, national and regional energy prices, and environmental implications of regional energy consumption and production. Where feasible, the topics will have a spatial dimension. This is a new seminar, so we expect students to contribute material to the set of readings and topics covered during the semester.

" The seminar is designed to provide advanced graduate students with a thorough understanding of selected regional economic theories and techniques and with experience in using alternative socioeconomic impact assessment models and related regional techniques on microcomputers. Discussions will be held on particular theoretical modeling and economic issues; linkages among theories, accounts, and policies; relationships between national and regional economic structures; and methods of adjusting and estimating regional input-output accounts and tables. Examples from the Boston area and other U.S. cities/regions will be used to illustrate points throughout the seminar. We will also examine how such models are used in other countries. New material on analyzing regional development issues will be covered."

This course examines the issues, principles, and challenges toward building relational machines through a combination of studio-style design and critique along with lecture, lively discussion of course readings, and assignments. Insights from social psychology, human-computer interaction, and design will be examined, as well as how these ideas are manifest in a broad range of applications for software agents and robots.

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material.

A three-semester subject sequence on quantum field theory stressing the relativistic quantum field theories relevant to the physics of the Standard Model. 8.323 is a one-semester self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics and condensed matter physics. Includes the basic tools of field theory required for phenomenological studies. Topics: Functional integral formulation of quantum mechanics and many-particle systems. Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Renormalization and renormalization group. Spinors and the Dirac equation. Quantization of Dirac fields. Supersymmetry. Quantization of abelian gauge fields. Calculations in quantum electrodynamics. Classical Yang-Mills fields. The Higgs phenomenon and a description of the Standard Model. 8.324 is the second term of the quantum field theory sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: Quantization of nonabelian gauge theories. BRST symmetry. Perturbation theory anomalies. Renormalization and symmetry breaking. The renormalization group. Critical exponents and scalar field theory. Conformal field theory. 8.325 is the third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physic