Marcia Jean Groszek is an American mathematician whose research concerns mathematical logic, set theory, forcing, and recursion theory. She is a professor of mathematics at Dartmouth College.[1]
Education
editAs a high school student, Groszek felt isolated for her interest in mathematics, but she found a sense of community through her participation in the Hampshire College Summer Mathematics Program,[2] and she went on to earn her bachelor's degree at Hampshire College.[1] She completed her Ph.D. in 1981 at Harvard University. Her dissertation, Iterated Perfect Set Forcing and Degrees of Constructibility, was supervised by Akihiro Kanamori.[3]
Research
editWith Theodore Slaman, Groszek showed that (if they exist at all) non-constructible real numbers must be widespread, in the sense that every perfect set contains one of them, and they asked analogous questions of the non-computable real numbers.[4][C] With Slaman, she has also shown that the existence of a maximally independent set of Turing degrees, of cardinality less than the cardinality of the continuum, is independent of ZFC.[A]
In the theory of ordinal definable sets, an unordered pair of sets is said to be a Groszek–Laver pair if the pair is ordinal definable but neither of its two elements is; this concept is named for Groszek and Richard Laver, who observed the existence of such pairs in certain models of set theory.[5][B]
Service and outreach
editGroszek was program chair of the 2014 North American annual meeting of the Association for Symbolic Logic.[6] Her interest in logic extends to education as well as to research; she has participated in the Association for Symbolic Logic Committee on Logic Education,[7] and in 2011 she was co-organizer of an Association for Symbolic Logic special session on "Logic in the Undergraduate Mathematics Curriculum".[8] With mathematics colleague Dorothy Wallace and performance artist Josh Kornbluth, Groszek has also helped write and produce a sequence of educational videos about mathematics.[9]
Selected publications
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| B. |
| C. | Groszek, Marcia J.; Slaman, Theodore A. (1998), "A basis theorem for perfect sets", The Bulletin of Symbolic Logic, 4 (2): 204–209, CiteSeerX 10.1.1.32.5166, doi:10.2307/421023, JSTOR 421023, MR 1632148, S2CID 26705447
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References
edit- ^ a b "Marcia J. Groszek", Faculty directory, Dartmouth College, retrieved 2019-08-18
- ^ Henrion, Claudia (1997), Women in Mathematics: The Addition of Difference, Indiana University Press, pp. xiii, 10, 16–17, 76, 81, 274, ISBN 9780253114990
- ^ Marcia Groszek at the Mathematics Genealogy Project
- ^ Lewis, Andrew E. M. (2008), "On a question of Slaman and Groszek", Proceedings of the American Mathematical Society, 136 (10): 3663–3668, doi:10.1090/S0002-9939-08-09345-3, MR 2415052
- ^ Golshani, Mohammad; Kanovei, Vladimir; Lyubetsky, Vassily (2017), "A Groszek–Laver pair of undistinguishable -classes", Mathematical Logic Quarterly, 63 (1–2): 19–31, arXiv:1601.03477, doi:10.1002/malq.201500020, MR 3647830, S2CID 27302694
- ^ "ASL Meetings" (PDF), ASL Newsletter, Association for Symbolic Logic, pp. 3–5, November 2013, retrieved 2019-08-30
- ^ "Marcia Groszek" (PDF), Faculty Highlights, Math is Power: the newsletter of the Dartmouth College Department of Mathematics, p. 4, September 2012
- ^ Logic in the Undergraduate Mathematics Curriculum, ASL Committee on Logic Education, retrieved 2019-08-18
- ^ Thrall, Erica (September 23, 1997), "Videos highlight math series", The Dartmouth, retrieved 2019-08-18