UCLA ADE Qualifying Exam Solutions Spring 2007 – Spring 2015

Notes on Numerical Analysis

This set of notes covers topics that most commonly show up on the Numerical Analysis qualifying exam in the Mathematics department at UCLA. Each section covers a specific area of numerical analysis. At the end of each section, we provide a list of key theorems. If the proof of the theorem is directly relevant to the qualifying exam, it will be included in this document. Otherwise, we simply inc...

UCLA ALGEBRA QUALIFYING EXAM Solutions

Proof. Let L/F be an algebraic extension. Let f : L −→ L be a homomorphism fixing F . Recall that field homomorphisms are always injective, it remains to show that it is surjective. Let a ∈ L. As L/F is algebraic, there exists a1, . . . , ad ∈ F such that a satisfy p(x) = x + a1xd−1 + . . .+ ad. Let S = {s ∈ L : p(s) = 0}. As f is a homomorphism fixing the coefficients of the polynomial p(x), i...

Review Notes for the Basic Qualifying Exam

Purpose: This document is a compilation of notes generated to prepare for the Basic Qualifying Exam. I have documented some of my solutions so that I may not forget and repeat the frustrations of failing this cursed exam again. Best of luck to anyone using these notes to prepare. Also see Brent Woodhouse's study guide. I do not guarantee accuracy of all the presented solutions. This document is...

219B — Final Exam — Spring 2014

COMPARATIVE POLITICS QUALIFYING EXAMINATION Department of International Studies Spring 2008 DO NOT PUT YOUR NAME OR STUDENT NUMBER ON YOUR EXAM

1. Leading scholars have conceptualized the field of Comparative Politics in terms of a contrast or a choice of theories and methods between a “disciplined center” and a “messy center.” While the former is driven by the search for a single, predominant theoretical and dominant methodological approach, the latter is characterized by a caseor problem-driven empirical research agenda with a multip...