The study of differential algebraic geometry and model theory occupies a pivotal position at the interface of algebra, geometry, and logic. Differential algebraic geometry investigates solution sets ...

Recent advances in computing make it practical to use complex hierarchical models. However, the complexity makes it difficult to see how features of the data determine the fitted model. This paper ...

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 ...

Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of polynomials.

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

Geometric objects take on different properties depending on the space in which you visualize them. Using techniques from an upstart field called tropical geometry — which analyzes complicated shapes ...

For decades, generations of Americans took the same basic high school math track. Algebra. Geometry. Algebra 2. Now, school districts across the country are overhauling their approach, combining ...

Next year, Nashville public schools will begin the transition from teaching Algebra I, Geometry, and Algebra II to teaching integrated math courses, which weave together concepts from each discipline.

Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction. The ...