Computer Science

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Touching the transcendentals: tractional motion from the birth of calculus to future perspectives

Submitted by IMAGINARY on

When the rigorous foundation of calculus was developed, it marked an epochal change in the approach of mathematicians to geometry. Tools from geometry had been one of the foundations of mathematics until the 17th century but today, mainstream conception relegates geometry to be merely a tool of visualization. In this snapshot, however, we consider geometric and constructive components of calculus.

Limits of graph sequences

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Graphs are simple mathematical structures used to model a wide variety of real-life objects. With the rise of computers, the size of the graphs used for these models has grown enormously. The need to efficiently represent and study properties of extremely large graphs led to the development of the theory of graph limits.

Diophantine equations and why they are hard

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Diophantine equations are polynomial equations whose solutions are required to be integer numbers. They have captured the attention of mathematicians during millennia and are at the center of much of contemporary research. Some Diophantine equations are easy, while some others are truly difficult. After some time spent with these equations, it might seem that no matter what powerful methods we learn or develop, there will always be a Diophantine equation immune to them, which requires a new trick, a better idea, or a refined technique. In this snapshot, we explain why.

Number theory in quantum computing

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Algorithms are mathematical procedures developed to solve a problem. When encoded on a computer, algorithms must be “translated” to a series of simple steps, each of which the computer knows how to do. This task is relatively easy to do on a classical computer and we witness the benefits of this success in our everyday life. Quantum mechanics, the physical theory of the very small, promises to enable completely novel architectures of our machines, which will provide specific tasks with higher comput- ing power. Translating and implementing algorithms on quantum computers is hard.

Science Spaces: An Open Workshop Concept to Create Science Exhibits

Submitted by Bianca Violet on

We introduce and outline a workshop concept called Science Spaces aimed at High School students, which combines mathematics and natural sciences with art to strengthen creativity, imagination, and perceptual abilities. The workshop guides the participants through the process of designing and implementing a public exhibition.

Mathematics plays a key role in scientific computing

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I attended a very interesting workshop at the research center MFO in Oberwolfach on “Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws”. The title sounds a bit technical, but in plain language we could say: The theme is to survey recent research concerning how mathematics is used to study numerical algorithms involving a special class of equations.

Prony’s method: an old trick for new problems

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In 1795, French mathematician Gaspard de Prony invented an ingenious trick to solve a recovery problem, aiming at reconstructing functions from their values at given points, which arose from a specific application in physical chemistry. His technique became later useful in many different areas, such as signal processing, and it relates to the concept of sparsity that gained a lot of well-deserved attention recently. Prony’s contribution, therefore, has developed into a very modern mathematical concept. 

Computational Optimal Transport

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Optimal transport is the mathematical discipline of matching supply to demand while minimizing shipping costs. This matching problem becomes extremely challenging as the quantity of supply and demand points increases; modern applications must cope with thousands or millions of these at a time. Here, we introduce the computational optimal transport problem and summarize recent ideas for achieving new heights in efficiency and scalability. 

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