This course is a first-year graduate course in algorithms. Emphasis is placed on fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Techniques to be covered include amortization, randomization, fingerprinting, word-level parallelism, bit scaling, dynamic programming, network flow, linear programming, fixed-parameter algorithms, and approximation algorithms. Domains include string algorithms, network optimization, parallel algorithms, computational geometry, online algorithms, external memory, cache, and streaming algorithms, and data structures.

The design of algorithms is studied, according to methodology and application. Methodologies include: divide and conquer, dynamic programming, and greedy strategies. Applications involve: sorting, ordering and searching, graph algorithms, geometric algorithms, mathematical (number theory, algebra and linear algebra) algorithms, and string matching algorithms. Analysis of algorithms is studied - worst case, average case, and amortized - with an emphasis on the close connection between the time complexity of an algorithm and the underlying data structures. NP-Completeness theory is examined along with methods of coping with intractability, such as approximation and probabilistic algorithms.

This course covers concepts of computation used in analysis of engineering systems. It includes the following topics: data structures, relational database representations of engineering data, algorithms for the solution and optimization of engineering system designs (greedy, dynamic programming, branch and bound, graph algorithms, nonlinear optimization), and introduction to complexity analysis. Object-oriented, efficient implementations of algorithms are emphasized.

Introduction to the theory and application of large-scale dynamic programming. Markov decision processes. Dynamic programming algorithms. Simulation-based algorithms. Theory and algorithms for value function approximation. Policy search methods. Games. Applications in areas such as dynamic resource allocation, finance and queueing networks, among others.

Sequential decision-making via dynamic programming. Unified approach to optimal control of stochastic dynamic systems and Markovian decision problems. Applications in linear-quadratic control, inventory control, and resource allocation models. Optimal decision making under perfect and imperfect state information. Certainty equivalent and open loop-feedback control, and self-tuning controllers. Infinite horizon problems, successive approximation, and policy iteration. Discounted problems, stochastic shortest path problems, and average cost problems. Optimal stopping, scheduling, and control of queues. Approximations and neurodynamic programming.

Introduction to computational biology including the fundamentals of protein and nucleic acid sequence analysis, phylogenetic analysis, motif finding, hidden Markov models, and 3D structure prediction and modeling. An overview of emerging fields including expression profiling, quantitative image analysis and the modeling of cellular signal transduction networks are also included. Subject designed for advanced undergraduates and graduate students with strong backgrounds in either molecular biology or computer science but not necessarily both. Two self-study tracks are offered, introducing either basic statistical methods and programming (to biologists) or the fundamentals of molecular biology (to computer scientists). Lectures combine both perspectives to illustrate how computation is having a significant impact on modern biology. Serving as an introduction to computational biology, this course emphasizes the fundamentals of nucleic acid and protein sequence analysis, structural analysis, and the analysis of complex biological systems. The principles and methods used for sequence alignment, motif finding, structural modeling, structure prediction, and network modeling are covered. Students are also exposed to currently emerging research areas in the fields of computational and systems biology.

Survey of modern macroeconomics at a fairly advanced level. Topics include neoclassical and new growth theory, consumption and saving behavior, investment, and unemployment. Use of the dynamic programming techniques. Assignments include problem sets and written discussions of macroeconomic events. Recommended for students planning to apply to graduate school in economics. Credit not given for both 14.05 and 14.06.

Survey of modern macroeconomics at a fairly advanced level. Topics include neoclassical and new growth theory, consumption and saving behavior, investment, and unemployment. Use of the dynamic programming techniques. Assignments include problem sets and written discussions of macroeconomic events. Recommended for students planning to apply to graduate school in economics. Credit not given for both 14.05 and 14.06.

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.

This course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems.

Introduces the basic computational methods used to understand the cell on a molecular level. Covers sequence alignment algorithms: dynamic programming, hashing, suffix trees, Gibbs sampling. Focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics.

Models of economic growth, old and new. Half-term subject. Introduction to the theories of economic growth. Topics will include basic facts of economic growth and long-run economic development; brief overview of optimal control theory and dynamic programming; basic neoclassical growth model under a variety of market structures; human capital and economic growth; endogenous growth models; models with endogenous technology; models of directed technical change; competition, market structure and growth; financial and economic development; international trade and economic growth; institutions and economic development.

This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information technology, and graduate (16.413) students.

This course surveys a variety of reasoning, optimization and decision making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their application, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, and machine learning. Optimization paradigms include linear programming, integer programming, and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes.