The Category of Matroids

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful; there is a functor to the category of geometric lattices, that is nearly full; there are various adjunctions and free constructions on subcategories, inducing a simplification monad; there are two orthogonal factorization systems; some, but not many, combinatorial constructions from matroid theory are functorial.Comment: 31 pages, 10 diagrams, 28 reference

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

A Historical Analysis of the Mathematics Major Requirements at Six Colleges in the United States from 1905 to 2005

This study attempts to document and explore the history of the undergraduate mathematics major at six United States colleges during the twentieth century. The six colleges were chosen based on their geographical diversity and their success in producing mathematics Ph.D. students. Three of the colleges are private, and three are public colleges. There are five key findings in this paper. Regarding specific courses, in 1955, courses in linear algebra, discrete mathematics, and computer science became widely available. This probably occurred due to the close relationship between discrete mathematics, linear algebra, and computing. Computer programming became easier and more popular during the 1950s, and computer science courses at most colleges migrated from the Mathematics Department to their own department. Yale was an exception; there were computer science courses available in the Mathematics Department at Yale until 2005. Advanced applied courses (Category 9) became more prevalent in some cases and disappeared in others. These courses may have migrated to other academic departments at the schools where they disappeared. This migration may have occurred at CCNY, Colorado College, Stanford University, and Yale. These findings are consistent with Garfunkel and Young's (1990) research on mathematics courses outside of mathematics departments. At the University of Texas, Austin, the advanced applied courses dramatically increased between 1945 and 2005. This is most likely due to the merger of the Pure Mathematics Department and Applied Mathematics Department between 1945 and 1955. Between 1975 and 1995, three of the four colleges from middle America and the west had many courses with unspecified content (Category 13). These courses included undergraduate colloquia, seminars, history of mathematics, problem-solving courses, tutorial courses, independent study, and experimental courses. Perhaps the schools outside the east coast experimented more with their upper division mathematics during this time. The three colleges that produced a significant number of undergraduates who eventually earned a doctoral degree in a STEM field between 1997 and 2006 did not credit general education mathematics courses (Category 2) during the entire study. Furthermore, these top future Ph.D.-producing colleges state that their undergraduates can take graduate courses 23 times in this study, whereas the other three colleges only mention it 9 times. Stanford University encouraged their undergraduates to take on graduate courses the most, then Yale and the University of California, Berkeley. After 1975, the percentage of mathematics courses needed to obtain the undergraduate degree converged at the colleges in this study to be in the range of 30% to 38%. The percentage never exceeded 40% at any of the schools in this study

Graduate School: Course Decriptions, 1972-73

Official publication of Cornell University V.64 1972/7

Progress in Commutative Algebra 2

This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and more