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APMA 2820T: Foundations in Statistical Inference in Molecular Biology
1.00 Credits
Brown University
In molecular biology, inferences in high dimensions with missing data are common. A conceptual framework for Bayesian and frequentist inferences in this setting including: sequence alignment. RNA secondary structure prediction, database search, and tiled arrays. Statistical topics: parameter estimation, hypothesis testing, recursions, and characterization of posterior spaces. Core course in proposed PhD program in computational molecular biology.
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APMA 2820T - Foundations in Statistical Inference in Molecular Biology
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APMA 2820U: Structure Theory of Control Systems
1.00 Credits
Brown University
The course deals with the following problems: given a family of control systems S and a family of control systems S', when does there exist an appropriate embedding of S into S' ? Most of the course will deal with the families of linear control systems. Knowledge of control theory and mathematical sophistication are required.
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APMA 2820U - Structure Theory of Control Systems
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APMA 2820V: Progress in the Theory of Shock Waves
1.00 Credits
Brown University
Course begins with self-contained introduction to theory of "hyperbolic conservation laws", that is quasilinear first order systems of partial differential equations whose solutions spontaneously develop singularities that propagate as shock waves. A number of recent developments will be discussed. Aim is to familiarize the students with current status of the theory as well as with the expanding areas of applications of the subject.
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APMA 2820V - Progress in the Theory of Shock Waves
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APMA 2820W: An Introduction to the Theory of Large Deviations
1.00 Credits
Brown University
The theory of large deviations attempts to estimate the probability of rare events and identify the most likely way they happen. The course will begin with a review of the general framework, standard techniques (change¿of¿measure, subadditivity, etc.), and elementary examples (e.g., Sanov's and Cramer's Theorems). We then will cover large deviations for diffusion processes and the Wentsel¿Freidlin theory. The last part of the course will be one or two related topics, possibly drawn from (but not limited to) risk¿sensitive control; weak convergence methods; Hamilton¿Jacobi¿Bellman equations; Monte Carlo methods. Prerequisites: AM 263 and 264.
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APMA 2820W - An Introduction to the Theory of Large Deviations
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APMA 2820X: Boundary Conditions for Hyperbolic Systems: Numerical and Far Field
1.00 Credits
Brown University
Course description unavailable
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APMA 2820X - Boundary Conditions for Hyperbolic Systems: Numerical and Far Field
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APMA 2820Y: Approaches to Problem Solving in Applied Mathematics
1.00 Credits
Brown University
TBA
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APMA 2820Y - Approaches to Problem Solving in Applied Mathematics
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APMA 2820Z: Topics in Discontinuous Galerkin Methods
1.00 Credits
Brown University
We will cover discontinuous Galerkin methods for time-dependent and steady state problems. Stability and error estimates of different discontinuous Galerkin methods will be discussed. In particular, we will discuss in depth the local discontinuous Galerkin method. Prerequisite: APMA 2550 or equivalent knowledge of numerical analysis.
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APMA 2820Z - Topics in Discontinuous Galerkin Methods
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APMA 2821A: Parallel Scientific Computing: Algorithms and Tools
1.00 Credits
Brown University
No description available.
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APMA 2821A - Parallel Scientific Computing: Algorithms and Tools
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APMA 2821B: To Be Determined
1.00 Credits
Brown University
Course description unavailable
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APMA 2821B - To Be Determined
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APMA 2821C: Topics in Partial Differential Equations
1.00 Credits
Brown University
The course will start by reviewing the theory of elliptic and parabolic equations in Holder spaces. Then we will discuss several topics in nonlinear elliptic and parabolic equations, for instance, the Navier-Stokes equation and Monge-Ampere type equations. This course is a sequel to APMA 2810V, but APMA 2810V is not a prerequisite.
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APMA 2821C - Topics in Partial Differential Equations
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