Jekyll2023-11-17T23:01:31+00:00https://scoskey.org/feed.xmlSamuel CoskeyJump right in and discover...
Conjugacy, classification, and complexity2023-06-25T00:00:00+00:002023-06-25T00:00:00+00:00https://scoskey.org/presentation/conjugacy-classification-and-complexity<p>Two-Day Logic Meeting, Bristol, July 2023<!--more--></p>
<p><em>Abstract</em>: We investigate the classification of automorphisms of a countable structure up to conjugacy. We aim to identify the complexity of this classification for a variety of structures. To study the complexity, we use the Borel reducibility hierarchy of equivalence relations.</p>Two-Day Logic Meeting, Bristol, July 2023Introductory elliptic curves2023-05-01T00:00:00+00:002023-05-01T00:00:00+00:00https://scoskey.org/senior-thesis/an-introduction-to-elliptic-curves<p>A senior project by Miley House, Spring 2023<!--more--></p>
<p><em>Abstract</em>: We study several chapters on elliptic curves from A Friendly Introduction to Number Theory, by Silverman.</p>A senior project by Miley House, Spring 2023An overview of set theory2023-05-01T00:00:00+00:002023-05-01T00:00:00+00:00https://scoskey.org/senior-thesis/an-overview-of-set-theory<p>A senior presentation by Pangaea Finn, Spring 2023<!--more--></p>
<p><em>Abstract</em>: In this talk we will give an overview of the axioms of ZFC set theory.</p>A senior presentation by Pangaea Finn, Spring 2023Counting, anyone can do it2023-05-01T00:00:00+00:002023-05-01T00:00:00+00:00https://scoskey.org/senior-thesis/counting-anyone-can-do-it<p>A senior project by Joseph Knebel, Spring 2023<!--more--></p>
<p><em>Abstract</em>: We present a lesson plan introducing the multichoose counting technique.</p>A senior project by Joseph Knebel, Spring 2023Borel classification of conjugacy problems2023-03-21T00:00:00+00:002023-03-21T00:00:00+00:00https://scoskey.org/presentation/borel-classification-conjugacy-problems<p>Nankai Logic Colloquium, Nankai, March 2023<!--more--></p>
<p><em>Abstract</em>: We aim to study the complexity of conjugacy problems for automorphisms of countable graphs G. Since conjugacy is an equivalence relation on Aut(G), we will study complexity using the invariant descriptive set theory, that is, the Borel reducibility hierarchy. After introducing this background setup, we will give a series of examples of locally finite graphs G whose conjugacy problems have a variety of different complexities. We will see conjugacy problems which are smooth (completely classifiable), complete for hyperfinite relations (E0), complete for essentially countable Borel equivalence relations (E_infinity), and intermediate between E0 and E_infinity.</p>Nankai Logic Colloquium, Nankai, March 2023Five fabulous activities for your math circle2023-02-01T00:00:00+00:002023-02-01T00:00:00+00:00https://scoskey.org/5fab<p>With Paul Ellis and Japheth Wood. <em>Natural Math</em>, publisher.<!--more--></p>
<p><em>Abstract</em>: Math circle activities are often interactive, exploratory, flexible, open-ended, and social. This might sound like a really fun idea, but how does one make it happen? <em>Five fabulous activities for your math circle</em> will show you how. This book is a guide and a collection of recipes for anyone who wants to help others discover joyful and challenging math. Our book will help you guide mathematical learners of a wide variety of ages. We primarily target middle and high school students. We have also included activities and explanations intended for younger math friends. The underlying mathematics can be of interest even to adult learners, including ourselves!</p>With Paul Ellis and Japheth Wood. Natural Math, publisher.Tukey morphisms between finite relations2023-01-30T00:00:00+00:002023-01-30T00:00:00+00:00https://scoskey.org/tukeyfin<p>With Rhett Barton and Paul Ellis.<!--more--></p>
<p><em>Abstract</em>: We investigate Tukey morphisms between binary relations, establishing several fundamental lemmas. We then specialize to finite binary relations, using computational methods to classify all binary relations with at most $6$ points in the domain and codomain up to bimorphism. Finally we give a construction of finite binary relations with arbitrary dominating number and dual dominating number.</p>With Rhett Barton and Paul Ellis.Math 189, Spring 20232023-01-01T00:00:00+00:002023-01-01T00:00:00+00:00https://scoskey.org/course/2223s-189<p>Discrete mathematics<!--more--></p>
<p><em>Catalog description</em>: Content drawn from propositional and predicate logic; proof logic, induction and recursion, elementary set theory; functions and relations; combinatorial enumeration; graph theory and basic elementary number theory.</p>Discrete mathematicsMath 314, Spring 20232023-01-01T00:00:00+00:002023-01-01T00:00:00+00:00https://scoskey.org/course/2223s-314<p>Foundations of analysis<!--more--></p>
<p><em>Catalog description</em>: The real number system, completeness and compactness, sequences, continuity, foundations of the calculus.</p>Foundations of analysisDual spaces2022-12-01T00:00:00+00:002022-12-01T00:00:00+00:00https://scoskey.org/senior-thesis/dual-spaces<p>A senior presentation by Samuel Clark, Fall 2022<!--more--></p>
<p><em>Abstract</em>: Dual spaces are a fundamental piece of mathematics and are used for a variety of purposes. The ability to describe measurements in functions are an important aspect to be able to obtain and understand in all different fields of math. Functional analysis and many other disciplines are able to be further understood through the application of dual spaces. By seeing the connections between these different fields allows us to gain a better understanding of mathematics as a whole.</p>A senior presentation by Samuel Clark, Fall 2022