Jekyll2018-10-12T22:44:05+00:00http://scoskey.org/Samuel CoskeyDepartment of Mathematics, Boise State University, 1910 University Dr, Boise, ID 83725-1555.
On splitting families2018-10-12T00:00:00+00:002018-10-12T00:00:00+00:00http://scoskey.org/presentation/on-splitting-families<p>Boise Algebra, Geometry, and Combinatorics seminar, October 2018<!--more--></p>
<p><em>Abstract</em>: A set A splits an even-sized set B if A contains exactly half the elements of B. For a natural number k, a splitting family on k is a collection of sets that splits any even-sized subset of {1,…,k}. Variations on the concept of splitting families have appeared in applications of combinatorial search. We investigate the number of sets needed to make a splitting family on k. We give some examples and computational results, as well as theoretical partial results identifying the exact number under certain assumptions. This represents a portion of the work from the Summer 2018 REU CAD, with Bryce Frederickson, Sam Mathers, and Hao-Tong Yan.</p>Boise Algebra, Geometry, and Combinatorics seminar, October 2018Vertex-transitive graphs and linear orders2018-10-01T00:00:00+00:002018-10-01T00:00:00+00:00http://scoskey.org/presentation/vertex-transitive-graphs-and-linear-orders<p>Boise Set Theory Seminar, October 2018<!--more--></p>
<p><em>Abstract</em>: John Clemens proved that the classification of countable vertex-transitive graphs is Borel complete. Extending the terminology from graphs, let’s say that a structure A is vertex-transitive if Aut(A) acts transitively on A. In this talk we will discuss the classification of countable vertex-transitive directed graphs and linear orders. This is joint work with John Clemens and Stephanie Potter.</p>Boise Set Theory Seminar, October 2018Real and linear analysis2018-08-01T00:00:00+00:002018-08-01T00:00:00+00:00http://scoskey.org/course/1819f-515<p>Math 515, Fall 2018 (<a href="http://scoskey.org/m515">site</a>)<!--more--></p>
<p><em>Catalog description</em>: Lebesgue measure on the reals, construction of the Lebesgue integral and its basic properties. Advanced linear algebra and matrix analysis. Fourier analysis, introduction to functional analysis.</p>Math 515, Fall 2018 (site)Discrete and foundational mathematics2018-08-01T00:00:00+00:002018-08-01T00:00:00+00:00http://scoskey.org/course/1819f-187<p>Math 187, Fall 2018 (<a href="http://scoskey.org/m187">site</a>)<!--more--></p>
<p><em>Catalog description</em>: An introduction to the language and methods of reasoning used throughout mathematics. Topics include propositional and predicate logic, elementary set theory, proof techniques including mathematical induction,functions and relations, combinatorial enumeration, permutations and symmetry.</p>Math 187, Fall 2018 (site)Spherical trigonometry2018-05-15T00:00:00+00:002018-05-15T00:00:00+00:00http://scoskey.org/senior-thesis/spherical-trigonometry<p>A senior thesis by Phung Le, Spring 2018<!--more--></p>
<p><em>Abstract</em>: We explore spherical geometry and trigonometry. This poster consists of four parts: (1) Using classical trigonometry to figure out how large is the Earth and the distance to the Moon; (2) How to find the distance between two places in the Earth; (3) Napier’s Rule I and II and an application on the sea with a right-angle triangle; (4) Delambre’s first analogy and an example of an oblique triangle.</p>A senior thesis by Phung Le, Spring 2018Conjugacy for homogeneous ordered graphs2018-04-12T00:00:00+00:002018-04-12T00:00:00+00:00http://scoskey.org/ordered-graphs<p>With Paul Ellis. (<a href="http://arxiv.org/abs/1804.04609">arχiv</a> | <a href="https://dx.doi.org/10.1007/s00153-018-0645-0">journal</a>)<!--more--></p>
<p><em>Abstract</em>: We show that for any countable homogeneous ordered graph $G$, the conjugacy problem for automorphisms of $G$ is Borel complete. In fact we establish that each such $G$ satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of $G$ is Borel reducible to the conjugacy relation on automorphisms of $G$.</p>With Paul Ellis. (arχiv | journal)Classification of scattered linear orders2018-03-06T00:00:00+00:002018-03-06T00:00:00+00:00http://scoskey.org/presentation/classification-of-scattered-linear-orders<p>Boise Set Theory Seminar, March 2018<!--more--></p>
<p><em>Abstract</em>: A linear order is called scattered if the rational order doesn’t embed into it. Scattered linear orders admit a derivative operation and an ordinal rank. In this talk we introduce some machinery needed to study the complexity of the classification of scattered linear orders of a given countable rank.</p>Boise Set Theory Seminar, March 2018Hyperbinary numbers and fraction trees2018-02-06T00:00:00+00:002018-02-06T00:00:00+00:00http://scoskey.org/calkin-wilf<p>With Paul Ellis and Japheth Wood. (<a href="https://www.mathteacherscircle.org/news/mtc-magazine/s2018/touching-infinity/">article</a>)<!--more--></p>
<p><em>Abstract</em>: Questions about infinity are fascinating, and can lead into deep mathematical topics in set theory. The mathematics of infinite sets wasn’t clearly understood until Cantor defined cardinal numbers in the late 19th century, stating that two sets are the same size if there is a one-to-one correspondence between them. One surprising result from set theory, first proved by Cantor in 1873, is that there are precisely as many rational numbers (fractions) as there are counting numbers. Over one hundred years later, mathematicians Neil Calkin and Herbert S. Wilf published a more elegant proof of this fact.</p>
<p>This article is the result of our work to develop the ideas in the Calkin-Wilf proof, so that they would be accessible to the teachers in our three different Math Teachers’ Circles. We designed an investigation into the hyperbinary numbers (itself a 19th century topic that predates Cantor’s work on cardinality) and developed the Tree of Fractions, much in the style of Calkin and Wilf. We asked teachers to make observations, ask questions, and convince each other of the veracity of their claims.</p>With Paul Ellis and Japheth Wood. (article)Martin’s axiom and some applications2018-01-13T00:00:00+00:002018-01-13T00:00:00+00:00http://scoskey.org/presentation/martins-axiom-and-applications<p>Boise Set Theory Seminar, January 2018<!--more--></p>
<p><em>Abstract</em>: In this talk I presented the notation and machinery of forcing, the statement of Martin’s axiom, and some well-known applications in the area of Baire category and measure theory.</p>Boise Set Theory Seminar, January 2018Foundations of analysis2018-01-01T00:00:00+00:002018-01-01T00:00:00+00:00http://scoskey.org/course/1718s-314<p>Math 314, Spring 2018 (<a href="http://scoskey.org/m314">site</a>)<!--more--></p>
<p><em>Catalog description</em>: The real number system, completeness and compactness, sequences, continuity, foundations of the calculus.</p>Math 314, Spring 2018 (site)