Comprehensive Oral Exam

Comprehensive Exam

Oral Comprehensive Exam Study Plan: Simulating Processes with Spatial Variability

Ecological processes play a critical role in shaping the world in which we live and guiding our interactions with it. As humans we are consistently attempting to predict, understand and sometimes control the behaviour of the natural world. Whether we are trying to forecast the upcoming seasonal rains, recreating a forest fire to understand why it burned in a particular manner, or making land ma...

Solver Schemes for Linear Systems Oral Comprehensive Exam Position Paper

This report presents different approaches to solving sparse linear systems—direct and iterative solvers—and compares a number of methods in each category. I also consider the two techniques of using solvers for linear systems: single method solver schemes and multi-method solver schemes. I also present some of the popular systems that use these techniques. This involves surveying the relevant l...

Statistics Oral Exam Notes 2008

(a) complete statistic: T (X) is complete w.r.t. a family P if ∀g : R → R measurable, E[g(T )] = 0 ∀P ∈ P ⇒ g = 0 a.s. w.r.t. P. (b) sufficient statistic:: We define a sub σ-field Σ ⊆ Bn to be sufficient for P (or equivalently, Θ) if ∀A ∈ Bn, ∃fA Σ-measurable s.t. ∀P ∈ P, fA(x) = EP [1A|Σ] a.s. wrt P (i.e. the conditional expectations given Σ is independent of the law of X, P ∈ P).We say T (X) ...

Algebra Oral Qualifying Exam Syllabus

algebra is the study of fundamental algebraic structures that occur throughout mathematics: groups, rings, modules, categories, and fields—as well as maps between them. A solid grasp of algebra can be useful to students of all mathematical stripes, and accordingly the suggested syllabus is a “strong core plus more” model: a student preparing for an oral qualifying exam in algebra should (1) fee...