8 results found in 4 ms.
Page 1 of 1
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
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.
Author(s):
Tag(s):
- mathematics
- discrete geometry
- computational geometry
- convex partitions
- binary space partitions
- art gallery problems
- planar graphs
- pseudo-triangulations
- encompassing graphs
- geometric graphs
- crossing numbers
- extremal graph theory
- gallai-sylvester problems
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
This course covers a collection of geometric techniques that apply broadly in modern algorithm design.
Author(s):
Tag(s):
- mathematics
- spectral graph theory
- iterative methods for linear algebra
- convex geometry
- lattices and basis reduction
- lps and sdps for approximating np-hard problems
- graph laplacians
- cheeger inequalities
- fritz john?s theorem
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
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.
Author(s):
Tag(s):
- mathematics
- phase plane
- limit cycles
- poincare-bendixson theory
- time-dependent systems
- floquet theory
- poincare maps
- averaging
- stability of equilibria
- near-equilibrium dynamics
- center manifolds
- elementary bifurcations
- normal forms
- chaos
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
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
Author(s):
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 mittag-leffler theorem
- harmonic functions
- dirichlet's problem
- the riemann mapping theorem
- the riemann zeta function
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
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
Author(s):
Tag(s):
- mathematics
- mirror symmetry
- deformation
- hodge theory
- pseudoholomorphic
- gromov-witten
- cohomology
- yukawa
- monodromy
- picard-fuchs
- lagrangian floer theory
- homology
- syz conjecture
- submanifolds
- k3 surfaces
- matrices
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
This is a graduate-level 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.
Author(s):
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
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
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
Author(s):
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
More OCW like this |
|
Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
Share in:
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.
Author(s):
Tag(s):
- mathematics
- computational algebra
- algebraic geometry
- geometry
- algebra
- algorithms
- groebner bases
- elimination theory
- algebra-geometry dictionary
- polynomial functions
- rational functions
- geometric theorem proving
- invariant theory of finite groups
- projective algebraic geometry
8 results found.
Page 1 of 1