Faculty perceptions of grade 7-12 math and science teaching as a career: Evidence from a reduced-basis factor analysis of the PTAP.HE Instrument
- Award ID(s):
- 1821710
- PAR ID:
- 10338713
- Date Published:
- Journal Name:
- 2021 Physics Education Research Conference Proceedings
- Page Range / eLocation ID:
- 57 to 62
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In this paper we show that every set A⊂ℕ with positive density contains B+C for some pair B,C of infinite subsets of ℕ, settling a conjecture of Erd\H os. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups.more » « less
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