“Our goal was to build a clear mathematical bridge between abstract algebra and the experience of listening to music,” said study co-author Olga Ibragimova. “When we think of melodies as shapes we can ...

Why do some melodies feel instantly right, balanced, memorable and satisfying, even if you have never heard them before? New research from the University of Waterloo suggests that more than creativity ...

Why do some melodies feel instantly right, balanced, memorable and satisfying, even if you have never heard them before? New research from the ...

My students know all too well that if they need help in math, I’m the last teacher to ask. Math was extremely hard for me in school. Numbers moved around ...

Functorial Semantics of Algebraic Theories Original unpublished; Ph.D. thesis, Columbia University, 1963. See extended TAC reprint 2004 1963 Functorial Semantics of Algebraic Theories (short notice) ...

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ABSTRACT: This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The ...