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2016
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This graduate-level course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Computational complexity
- Resource Type:
- Courseware
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Courseware
Thermal conductivity, the Wiedemann-Franz law and the collision integral for electron-electron scattering. This course is about the electronic properties of materials and contains lectures about scattering, transport in metals, phonons and superconductivity.
- Subjects:
- Physics
- Keywords:
- Materials -- Electric properties Thermoelectricity Superconductivity
- Resource Type:
- Courseware
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Courseware
The aim of this class is to introduce the exciting and often under appreciated discoveries in RNA biology by exploring the diversity of RNAs—encompassing classical molecules such as ribosomal RNAs (rRNAs), transfer RNAs (tRNAs) and messenger RNAs (mRNAs) as well as newer species, such as microRNAs (miRNAs), long-noncoding RNAs (lncRNAs), and circular RNAs (circRNAs). For each new class of RNA, we will evaluate the evidence for its existence as well as for its proposed function. Students will develop both a deep understanding of the field of RNA biology and the ability to critically assess new papers in this fast-paced field. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching.
- Subjects:
- Biology
- Keywords:
- RNA
- Resource Type:
- Courseware
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Courseware
This course explores the relationship between ancient Greek philosophy and mathematics. We investigate how ideas of definition, reason, argument and proof, rationality / irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. The course examines how discovery of the incommensurability of magnitudes challenged the Greek presumption that the cosmos is fully understandable. Students explore the influence of mathematics on ancient Greek ethical theories. We read such authors as: Euclid, Plato, Aristotle, Nicomachus, Theon of Smyrna, Bacon, Descartes, Dedekind, and Newton.
- Subjects:
- Philosophy and Mathematics and Statistics
- Keywords:
- Philosophy Ancient Mathematics -- Philosophy
- Resource Type:
- Courseware
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Courseware
This course is an advanced treatment of biochemical mechanisms that underlie biological processes. Topics include macromolecular machines such as the ribosome, the proteasome, fatty acid synthases as a paradigm for polyketide synthases and non-ribosomal polypeptide synthases, and polymerases. Emphasis will be given to the experimental methods used to unravel how these processes fit into the cellular context as well as the coordinated regulation of these processes.
- Subjects:
- Biochemistry and Biology
- Keywords:
- Biochemistry
- Resource Type:
- Courseware
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Courseware
This first course in the physics curriculum introduces classical mechanics. Historically, a set of core concepts—space, time, mass, force, momentum, torque, and angular momentum—were introduced in classical mechanics in order to solve the most famous physics problem, the motion of the planets. The principles of mechanics successfully described many other phenomena encountered in the world. Conservation laws involving energy, momentum and angular momentum provided a second parallel approach to solving many of the same problems. In this course, we will investigate both approaches: Force and conservation laws. Our goal is to develop a conceptual understanding of the core concepts, a familiarity with the experimental verification of our theoretical laws, and an ability to apply the theoretical framework to describe and predict the motions of bodies.
- Subjects:
- Physics
- Keywords:
- Kinematics Torque Mass (Physics) Angular momentum Force energy Motion Mechanics
- Resource Type:
- Courseware
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Courseware
With the growing availability and lowering costs of genotyping and personal genome sequencing, the focus has shifted from the ability to obtain the sequence to the ability to make sense of the resulting information. This course is aimed at exploring the computational challenges associated with interpreting how sequence differences between individuals lead to phenotypic differences in gene expression, disease predisposition, or response to treatment.
- Subjects:
- Computing and Biology
- Keywords:
- Genomics Genomes
- Resource Type:
- Courseware
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Courseware
In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Fourier analysis Differential equations Partial
- Resource Type:
- Courseware
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Courseware
This course provides a rigorous treatment of non-cooperative solution concepts in game theory, including rationalizability and Nash, sequential, and stable equilibria. It covers topics such as epistemic foundations, higher order beliefs, bargaining, repeated games, reputation, supermodular games, and global games. It also introduces cooperative solution concepts—Nash bargaining solution, core, Shapley value—and develops corresponding non-cooperative foundations.
- Subjects:
- Economics and Mathematics and Statistics
- Keywords:
- Game theory
- Resource Type:
- Courseware
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Courseware
The Geology 1 course is composed of three parts dedicated to 1. general knowledge of the system Earth, 2. tools for the 3D geometric representation of geological objects and 3. methods and techniques for the recognition of fundamental minerals and rocks.
- Subjects:
- Environmental Sciences and Land Surveying and Geo-Informatics
- Keywords:
- Rock mechanics Minerals Earth sciences Geology
- Resource Type:
- Courseware
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