" This course covers concepts and techniques for the design and implementation …
" This course covers concepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers, computer-algebra systems, deductive systems, and some artificial intelligence applications. Topics include combinators, generic operations, pattern matching, pattern-directed invocation, rule systems, backtracking, dependencies, indeterminacy, memoization, constraint propagation, and incremental refinement. Substantial weekly programming Assignments and Labs are an integral part of the subject. There will be extensive programming Assignments and Labs, using MIT/GNU Scheme. Students should have significant programming experience in Scheme, Common Lisp, Haskell, CAML or some other "functional" language."
" We will study the fundamental principles of classical mechanics, with a …
" We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and PoincarĚŠ integral invariants; PoincarĚŠ-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overlap and transition to chaos; properties of chaotic motion. Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis."
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