Mathematics Symposium: "Mathematics Awareness Month at UNO"
"Zeno's Paradoxes, Philosophical Discussions, Mathematics, and More."
The talk will consider such classical paradoxes as "The Dichotomy", "Achilles and the tortoise", etc. We will comment on both their mathematical and philosophical aspects.
"Prime Gaps & Clusters"
This talk concerns "Paterns among the Primes", a rich source of number theoretic inquiry throughout history. In keeping with the theme, Math Spans All Dimensions, we will consider this topic for the primes among the natural numbers (the dimesion 1 case), and then for the primes among the Gaussian numbers (a dimension 2 case).
"Exploring Geometry Through Paper Circle Folding"
This presentation illustrates the wide variety of two and three dimensional geometry concepts illustrated through a simple folding activity using paper circles. More than 50 geometric terms are used within the context of the activity and the related discussions with the audience.
"Using the Elliptic-Range Theorem to Span All Dimensions"
The talk will report on the classical "Elliptic-Range Theorem" describing the shape of numerical ranges of two by two matrices, and the way it can be used in order to view and calculate numerical ranges of matrices of superior size, infinite matrices included.
"The Origins of Counting"
This presentation is an introduction to multicultural and historical perspectives of counting. Topics will include counting in different cultures, the origins of place value based number systems, and the elementary number theory of mathematical operations in different bases.
"Use of Artificial Neural Networks to Classify Nonlinearly Separable Input Paterns"
Initial studies of neurons yielded a mathematical model of neuron function called the perceptron, or artificial neuron. The perceptron has the impressive ability to classify even complicated input patterns provided the patterns are linearly separable. However, nonlinearly separable patterns are of common occurence in nature. The subsequent development of the artificial neural network, a model involving layers of interconnected artificial neurons, solved the problem of classifying nonlinearly separable patterns. The mathematical basis and potential applications of artificial neural networks will be discussed as well as the remarkable ability of these networks to "learn".
"True, False, or ..."
In the talk we will discuss the meaning of "true" and "false" in mathematics. We will present (in)completeness theorems and we will finish with examples of statements that cannot be decided from the standard axioms (ZFC).
"Euler was on to something!"
We will explore how the Konigsberg bridge problem went from a simple curiosity into a powerful problem solving tool through the branch of mathematics called Graph Theory. Participants will be introduced to some terminology and shown some ways to integrate Graph Theory into their existing curriculum.
Lydia Thompson and Richard Longman,
"Continuity Versus Differentiability and Weierstrass's "Monster""
The talk will revisit an old, famous problem, namely "How smooth needs a continuous function be?". Remarcable examples originating in Karl Weierstrass's work will be considered and graphed using MAPLE.