Jekyll2024-01-30T14:22:32+00:00https://scoskey.org/feed.xmlSamuel CoskeyJump right in and discover...
MATH0046, Term 2 20232024-01-01T00:00:00+00:002024-01-01T00:00:00+00:00https://scoskey.org/course/2324s-0046<p>Calculus in several dimensions<!--more--></p>
<p><em>Catalog description</em>: Topics covered include optimisation with a constraint, complex numbers, differential equations, multiple integrals, eigenvalues and eigenvectors and quadratic forms.</p>Calculus in several dimensionsMATH0010, Term 1 20232023-08-01T00:00:00+00:002023-08-01T00:00:00+00:00https://scoskey.org/course/2324f-00010<p>Mathematical methods I<!--more--></p>
<p><em>Catalog description</em>: The aim of the course is to bring students from a background of diverse A-level syllabuses to a uniform level of confidence and competence in vectors, complex numbers, calculus and differential equations. The course covers vectors, complex numbers, standard functions of a real variable, methods of integration, ordinary differential equations and probability. Each topic is given a formal treatment and illustrated by examples of varying degrees of difficulty.</p>Mathematical methods IConjugacy, 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 mathematics