CORRECTION: Some scientists and philosophers have tried to draw a line between "hard" sciences (e.g., chemistry and physics) and "soft" ones (e.g., psychology and sociology). The thinking was that hard science used more rigorous, quantitative methods than soft science did and so were more trustworthy. In fact, the rigor of a scientific study has much more to do with the investigator's approach than with the discipline. Many psychology studies, for example, are carefully controlled, rely on large sample sizes, and are highly quantitative. To learn more about how rigorous and fair tests are designed, regardless of discipline, check out our side trip .
Basic probabilistic problems and methods in operations research and management science. Methods of problem formulation and solution. Markov chains, birth-death processes, stochastic service and queueing systems, the theory of sequential decisions under uncertainty, dynamic programming. Applications. Prerequisite: APMA 1650 or MATH 1610, or equivalent.
So, their first action is toattack the standard theory in an attempt to show that it is in reality so flawed,and so failing when compared to observation, that it must be abandoned and replacedby some "better" theory.
Standard theories are standard for a reason, and it's not prejudice or bias, as thesupporters of much alternative "science" would have you believe.
The criticismsthat claim to reaveal weaknesses in standard theory are in fact so full of mistakes,misinterpretations and misrepresentations that they can hardly be taken seriously.
Aspects of the theory on nonlinear evolution equations, which includes kinetic theory, nonlinear wave equations, variational problems, and dynamical stability.
Nonlinear instabilities as well as boundary effects in a collisionless plasmas; Stable galaxy configurations; A nonlinear energy method in the Boltzmann theory will also be introduced. Self-contained solutions to specific concrete problems. Focus on ideas but not on technical aspects. Open problems and possible future research directions will then be discussed so that students can gain a broader perspective. Prerequisite: One semester of PDE (graduate level) is required.
What Scott is talking about here is helioseismology, and theone paper he cites (wrongly, as we shall see) dates from the early days of helioseismology.
Develops the ideas of algebraic geometry in the context of control theory. The first semester examines scalar linear systems and affine algebraic geometry while the second semester addresses multivariable linear systems and projective algebraic geometry.
There are two key issues with this story. First and foremost there is no documented evidence to verify it. Considering the discovery of 's name on the lifeboat(s) allegedly occurred at least twice, on different continents, and no doubt seen by at least several people, why there are no written accounts, sketches or photographs of at the very least the boat, let alone the discovery, should ring alarm bells in the mind of any serious researcher. Secondly, and rather importantly, the names were not engraved on the lifeboats. They were metal plates which were screwed on. They were also not on the gunwhales but on the sides of the lifeboat.
But theresearch represented here clearly shows that Scott's admonition that standardtheory is "incapable" of explaining the coronal temperature is itself unexplainable.
APMA 2810O. Stochastic Differential Equations
This course develops the theory and some applications of stochastic differential equations. Topics include: stochastic integral with respect to Brownian motion, existence and uniqueness for solutions of SDEs, Markov property of solutions, sample path properties, Girsanov's Theorem, weak existence and uniqueness, and connections with partial differential equations. Possible additional topics include stochastic stability, reflected diffusions, numerical approximation, and stochastic control. Prerequisite: APMA 2630, 2640
APMA 2810A. Computational Biology
Provides an up-to-date presentation of the main problems and algorithms in bioinformatics. Emphasis is given to statistical/probabilistic methods for various molecular biology tasks, including, comparison of genomes of different species, finding genes and motifs, understanding transcription control mechanisms, analyzing microarray data for gene clustering, and predicting RNA structure.
APMA 2720. Information Theory
Information theory and its relationship with probability, statistics, and data compression. Entropy. The Shannon-McMillan-Breiman theorem. Shannon's source coding theorems. Statistical inference; hypothesis testing; model selection; the minimum description length principle. Information-theoretic proofs of limit theorems in probability: Law of large numbers, central limit theorem, large deviations, Markov chain convergence, Poisson approximation, Hewitt-Savage 0-1 law. Prerequisites: APMA 2630; APMA 1710.
APMA 2810. Seminars in Applied Mathematics Topics Courses