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Full-Text Articles in Mathematics
Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova
Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova
Journal of Humanistic Mathematics
This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!
The Nature Of Numbers: Real Computing, Bradley J. Lucier
The Nature Of Numbers: Real Computing, Bradley J. Lucier
Journal of Humanistic Mathematics
While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both β¦
Games For One, Games For Two: Computationally Complex Fun For Polynomial-Hierarchical Families, Kye Shi
Games For One, Games For Two: Computationally Complex Fun For Polynomial-Hierarchical Families, Kye Shi
HMC Senior Theses
In the first half of this thesis, we explore the polynomial-time hierarchy, emphasizing an intuitive perspective that associates decision problems in the polynomial hierarchy to combinatorial games with fixed numbers of turns. Specifically, problems in π are thought of as 0-turn games, ππ as 1-turn βpuzzleβ games, and in general πΊβπ as π-turn games, in which decision problems answer the binary question, βcan the starting player guarantee a win?β We introduce the formalisms of the polynomial hierarchy through this perspective, alongside definitions of π-turn CIRCUIT SATISFIABILITY games, whose πΊβπ-completeness is assumed from prior work (we briefly justify this assumption β¦