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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course offers an introduction to discrete and computational geometry. Emphasis is placed on teaching methods in combinatorial geometry. Many results presented are recent, and include open (as yet unsolved) problems.
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Tag(s):
 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course covers a collection of geometric techniques that apply broadly in modern algorithm design.
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Tag(s):
 mathematics
 spectral graph theory
 iterative methods for linear algebra
 convex geometry
 lattices and basis reduction
 lps and sdps for approximating nphard problems
 graph laplacians
 cheeger inequalities
 fritz john?s theorem
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.
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Tag(s):
 mathematics
 phase plane
 limit cycles
 poincarebendixson theory
 timedependent systems
 floquet theory
 poincare maps
 averaging
 stability of equilibria
 nearequilibrium dynamics
 center manifolds
 elementary bifurcations
 normal forms
 chaos
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted.
This course offers biweekly problem sets with sol
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Tag(s):
 mathematics
 functions of one complex variable
 cauchy's theorem
 holomorphic functions
 meromorphic functions
 residues
 contour integrals
 conformal mapping
 infinite series and products
 the gamma function
 the mittagleffler theorem
 harmonic functions
 dirichlet's problem
 the riemann mapping theorem
 the riemann zeta function
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and
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Tag(s):
 mathematics
 mirror symmetry
 deformation
 hodge theory
 pseudoholomorphic
 gromovwitten
 cohomology
 yukawa
 monodromy
 picardfuchs
 lagrangian floer theory
 homology
 syz conjecture
 submanifolds
 k3 surfaces
 matrices
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This is a graduatelevel course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.
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Tag(s):
 mathematics
 combinatorial theory
 hyperplane arrangements
 intersection poset
 matroids
 geometric lattices
 broken circuits
 modular elements
 supersolvability
 finite fields
 hyperplane
 arrangements
 intersection poset
 geometric lattices
 broken circuits
 modular elements
 supersolvability
 finite fields
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality
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Tag(s):
 mathematics
 probability spaces
 random variables
 distribution functions
 binomial
 geometric
 hypergeometric
 poisson distributions
 uniform
 exponential
 normal
 gamma and beta distributions
 conditional probability
 bayes theorem
 joint distributions
 chebyshev inequality
 law of large numbers
 and central limit theorem
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.
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Tag(s):
 mathematics
 computational algebra
 algebraic geometry
 geometry
 algebra
 algorithms
 groebner bases
 elimination theory
 algebrageometry dictionary
 polynomial functions
 rational functions
 geometric theorem proving
 invariant theory of finite groups
 projective algebraic geometry
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