Algebraic structures and state theory represent a confluence of abstract algebra and logic, where the former provides a rigorous framework for describing systems such as BL-algebras, residuated ...

Let $Z/n$ denote the integers $\operatorname{mod} n$ and let $\mathscr{F}_n$ denote the finite Fourier transform on $L^2(Z/n)$. We let $\bigoplus\Sigma \mathscr{F}_n ...

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape. We are fond of saying things are symmetric, but what does ...

PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, commentaries, perspectives, reviews, colloquium papers, and actions of the Academy. In ...

The purpose of all of the developmental mathematics courses is to support student success academically and beyond by advancing critical thinking and reasoning skills. Specifically in Algebra II, as a ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...