Mathematical problems and games
type: Item
instance of: scholarly article
title: Mathematical problems and games
zbMATH Open document ID: 0642.00001
DOI: 10.1016/0196-8858(87)90026-1
author: R. Daniel Mauldin
author: Stanisław Ulam
published in: Advances in Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: S. M. Ulam was known for, among other things, the formulation of imaginative problems in a great variety of topics in mathematics and allied areas. His book ``A collection of mathematical problems'' was published in 1960 (see Zbl 0086.241). The problems continued to flow, often in discussions with Paul Erdős, R. L. Graham, R. D. Mauldin and others. Some years ago he invited Mauldin to help him develop, organize and present a new collection of problems, and the present paper is the result of that collaboration. Ulam died in 1984, and Mauldin completed the project, with some assistance from Françoise Ulam, Erdős, Graham, C. C. Rota and others. The material is divided into seven chapters with headings as follows: I. Logic, Set Theory. II. Combinatorics, Game Theory, Number Theory, Complexity. III. Algebra. IV. Topology. V. Real Variables, Functional Analysis, Measure Theory. VI. Metric Spaces, Geometry. VII. Physics and Biology. The chapters are further divided into a total of 79 sections. Along with the problems are comments on progress toward solutions, related known results, bounties offered and the like. A few samples: II.3. For a given subset E of [0,1] players and A and B give in turn a digit from \{0,1\(\}\). Player A wins if the number whose binary expansion results is in E. Consider the same game but with digits chosen from \{0,1,2\(\}\) and ternary expansion. Find a set E which is a winning set for the first player in the binary version but not in the ternary one. II.22.6 Show that for infinitely many n, g.c.d.\(({2n\choose n},105)=1\). III.5. Is there a group structure on a countable set such that the group of endomorphisms is maximal? IV.3. Let E and F be topological spaces and T a mapping from E to F such that if A,B\(\subset E\) are homeomorphic, then T(A) and T(B) are homeomorphic in F. Must T be a homeomorphism? V.3. Is there a measure m defined on all Borel subsets of the Hilbert cube such that if A and B are isometric, then \(m(A)=m(B)?\) V.8. What is…
Mathematics Subject Classification ID: 00A07
Mathematics Subject Classification ID: 00-02
zbMATH DE Number: 4045677
zbMATH Keywords: Logic
zbMATH Keywords: Set Theory
zbMATH Keywords: Combinatorics
zbMATH Keywords: Game Theory
zbMATH Keywords: Number Theory
zbMATH Keywords: Complexity
zbMATH Keywords: Algebra
zbMATH Keywords: Topology
zbMATH Keywords: Real Variables
zbMATH Keywords: Functional Analysis
zbMATH Keywords: Measure Theory
zbMATH Keywords: Metric Spaces
zbMATH Keywords: Geometry
zbMATH Keywords: Physics
zbMATH Keywords: Biology
reviewed by: Gerald A. Heuer
MaRDI profile type: Publication
full work available at URL: 0196-8858(87)90026-1
OpenAlex ID: W2160254234
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