Browsing Pure Mathematics by Subject "Mathematics"
Now showing items 1-13 of 13
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Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Field and R)
(University of Waterloo, 1998)This thesis is concerned with the classification of 7-dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension <i>n</i> given those ... -
Counting points of bounded height on del Pezzo surfaces
(University of Waterloo, 2006)del Pezzo surfaces are isomorphic to either P<sup>1</sup> x P<sup>1</sup> or P<sup>2</sup> blown up <i>a</i> times, where <i>a</i> ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P<sup>2</sup> ... -
Gröbner Bases Theory and The Diamond Lemma
(University of Waterloo, 2006)Commutative Gröbner bases theory is well known and widely used. In this thesis, we will discuss thoroughly its generalization to noncommutative polynomial ring <em>k</em><<em>X</em>> which is also an associative free ... -
Infinite Sets of D-integral Points on Projective Algebrain Varieties
(University of Waterloo, 2005)Let <em>X</em>(<em>K</em>) ⊂ <strong>P</strong><sup><em>n</em></sup> (<em>K</em>) be a projective algebraic variety over <em>K</em>, and let <em>D</em> be a subset of <strong>P</strong><sup><em>n</em></sup><sub><em>O ... -
Intervals with few Prime Numbers
(University of Waterloo, 2004)In this thesis we discuss some of the tools used in the study of the number of primes in short intervals. In particular, we discuss a large sieve density estimate due to Gallagher and two classical delay equations. ... -
Lower order terms of moments of L-functions
(University of Waterloo, 2011-06-17)<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the k-th moments of the central values of quadratic Dirichlet L-functions. The conjectured formula ... -
The Model Theory of Algebraically Closed Fields
(University of Waterloo, 2000)Model theory can express properties of algebraic subsets of complex n-space. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of ... -
Multiplicities of Linear Recurrence Sequences
(University of Waterloo, 2006)In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and ... -
Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces
(University of Waterloo, 2006)<html> <head> <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"> </head> Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, ... -
On the Similarity of Operator Algebras to C*-Algebras
(University of Waterloo, 2006)This is an expository thesis which addresses the requirements for an operator algebra to be similar to a <em>C</em>*-algebra. It has been conjectured that this similarity condition is equivalent to either amenability ... -
Reductions and Triangularizations of Sets of Matrices
(University of Waterloo, 2006)Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in ... -
Some Functional Equations Connected with the Utility of Gains and Losses
(University of Waterloo, 2002)The behavioral properties shown by people when they make selections between different choices will be studied. Based on empirical and logical data a mathematical axiomatic model is built. D. Luce is a major ... -
A survey of Roth's Theorem on progressions of length three
(University of Waterloo, 2011-12-19)For any finite set B and a subset A⊆B, we define the density of A in B to be the value α=|A|/|B|. Roth's famous theorem, proven in 1953, states that there is a constant C>0, such that if A⊆{1,...,N} for a positive integer ...