Physical Sciences and Mathematics Commons^™

Discovering Properties Of Complex Numbers By Starting With Known Properties Of Real Numbers, Esther D. Hatch

Honors College

No abstract provided.

Deductive Mathematics: An Introduction To Proof And Discovery For Mathematics Education, Andrew Wohlgemuth

Mathematics and Statistics Faculty Scholarship

Mathematics has two fundamental aspects: (1) discovery/logical deduction and (2) description/ computation. Discovery/deductive mathematics asks the questions:

1. What is true about this thing being studied?

2. How do we know it is true?

On the other hand, descriptive/computational mathematics asks questions of the type:

3. What is the particular number, function, and so on, that satisfies ... ?

4. How can we find the number, function, and so on?

In descriptive/computational mathematics, some pictorial, physical, or business situation is described mathematically, and then computational techniques are applied to the mathematical description, in order to find values of interest. The …

A Mathematical Model For Simplifying Representations Of Objects In A Geographic Information System, Gabriel Perrow

Electronic Theses and Dissertations

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that …

The Distribution Of The Irreducibles In An Algebraic Number Field, Rebecca Rozario

Electronic Theses and Dissertations

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

Extracting Movement Patterns Using Fuzzy And Neuro-Fuzzy Approaches, Haci Mustafa Palancioglu

Electronic Theses and Dissertations

Several applications generate large volumes of data on movements including vehicle navigation, fleet management, wildlife tracking and in the near future cell phone tracking. Such applications require support to manage the growing volumes of movement data. Understanding how an object moves in space and time is fundamental to the development of an appropriate movement model of the object. Many objects are dynamic and their positions change with time. The ability to reason about the changing positions of moving objects over time thus becomes crucial. Explanations on movements of an object require descriptions of the patterns they exhibit over space and …