Mathematics Degrees

...No prior knowledge of combinatorics is expected, but I will assume a familiarity with linear algebra and finite groups. We will cover a number of topics...

...spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion... Learn about: GCSE Mathematics...

...Prior experience with abstraction and proofs is helpful. Topics include: Bona, Miklos. A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory...

...though familiarity with combinatorics is assumed. Students should already be familiar with Catalan numbers, Ramsey Theorem, generating functions...

...representation theory, and commutative algebra. Those with insufficient backgrounds in these topics should still be able to follow most of the course...

...about once every two weeks. A paper of 6-12 pages related to algebraic combinatorics is due on the last class. A tentative description of the first...

...linear algebra and least squares, as well as some basic physics. A knowledge of basic computer programming is also needed. This class covers the mathematics... Learn about: GCSE Mathematics...

...graduate students of all fields who are interested in numerical methods for partial differential equations, with focus on a rigorous mathematical basis... Learn about: GCSE Mathematics, Fluid Dynamics...

...helps, but is not required. The assignments will involve basic computer programming in the language of your choice (Matlab® recommended; this class encourages...

...transforms, complex variables, asymptotic analysis, and computer programming would be helpful, but an ambitious student could take the class to learn some of these topics...

...Continuum Systems; 18.355 Fluid Mechanics; and 12.800 Fluid Dynamics of the Atmosphere and Ocean, or 2.25 Fluid Mechanics. This graduate-level course covers... Learn about: Fluid Mechanics...

...mathematics of nanophotonics - electromagnetic waves in media structured on the scale of the wavelength. In this regime, which is the basis for everything... Learn about: GCSE Mathematics, GCSE Physics...

...of Algorithms or equivalent and 6.041SC Probabilistic Systems Analysis and Applied Probability or 18.440 Probability and Random Variables or equivalent...

...isoperimetric and Cheeger inequalities, expanders, and random graphs. Applications to include graph cutting, clustering, approximate counting...

...then be applied to the decoding of Turbo, LDPC, and Serially-Concatenated codes. The technical portion of the course will conclude with a study of tools...

...we will discuss rigorous approaches to explaining the typical performance of algorithms. In particular, we examine alternatives to the traditional worst-case...

...Flow & Matching Theory, Randomization, and Approximation. We will tackle a variety of optimization problems by applying these techniques to find efficient algorithms...

...1 hour / session 18.02SC Multivariable Calculus This course introduces students to probability and random variables. Topics include distribution functions... Learn about: IT Law...

...Lectures: 2 sessions / week, 1.5 hours / session Structure and Interpretation of Computer Programs (6.001) or Introduction to Algorithms (18.410J/6.046J)... Learn about: Molecular Biology...

...(ideal but not required): Theory of Probability (18.175) and either Statistical Learning Theory and Applications (9.520) or Machine Learning (6...