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Course Criteria
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3.00 Credits
Current research topics in computational complexity theory. 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.
Prerequisite:
Prereq: 18.404
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3.00 Credits
Study of areas of current interest in theoretical computer science. Topics vary from term to term.
Prerequisite:
Prereq: Permission of instructor
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4.00 Credits
Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.
Prerequisite:
Prereq: 6.006
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5.00 Credits
First-year graduate subject in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Surveys a variety of computational models and the algorithms for them. Data structures, network flows, linear programming, computational geometry, approximation algorithms, online algorithms, parallel algorithms, external memory, streaming algorithms.
Prerequisite:
Prereq: 6.041, 6.042, or 18.440; 6.046
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5.00 Credits
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.
Prerequisite:
Prereq: 6.854J, 6.041 or 6.042J
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3.00 Credits
Introduces the basic computational methods used to model and predict the structure of biomolecules (proteins, DNA, RNA). Covers classical techniques in the field (molecular dynamics, Monte Carlo, dynamic programming) to more recent advances in analyzing and predicting RNA and protein structure, ranging from Hidden Markov Models and 3-D lattice models to attribute Grammars and tree Grammars.
Prerequisite:
Prereq: 6.01, 6.006, or permission of instructor
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3.00 Credits
Covers current research topics in computational molecular biology. Recent research papers presented from leading conferences such as the SIGACT International Conference on Computational Molecular Biology (RECOMB). Topics include original research (both theoretical and experimental) in comparative genomics, sequence and structure analysis, molecular evolution, proteomics, gene expression, transcriptional regulation, and biological networks. Recent research by course participants also covered. Participants will be expected to present either group or individual projects to the class.
Prerequisite:
Prereq: 18.417, 6.047, or permission of instructor
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3.00 Credits
Considers various topics in information theory, including data compression, Shannon's Theorems, and error-correcting codes. Students present and discuss the subject matter. Instruction and practice in written and oral communication provided. Enrollment limited.
Prerequisite:
Prereq: 18.05, 18.440, or 6.041; 18.06, 18.700, or 18.701
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3.00 Credits
A rigorous introduction to modern cryptography. Emphasis on the fundamental cryptographic primitives of public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements.
Prerequisite:
Prereq: 6.046J
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3.00 Credits
Recent results in cryptography, interactive proofs, and cryptographic game theory. Lectures by instructor, invited speakers, and students.
Prerequisite:
Prereq: 6.875
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