Related papers: Mathematical Software: Past, Present, and Future
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
Quantum computing systems depend on the principles of quantum mechanics to perform multiple challenging tasks more efficiently than their classical counterparts. In classical software engineering, the software life cycle is used to document…
Over the past six decades, the computing systems field has experienced significant transformations, profoundly impacting society with transformational developments, such as the Internet and the commodification of computing. Underpinned by…
The software is changing rapidly with the invention of advanced technologies and methodologies. The ability to rapidly and successfully upgrade software in response to changing business requirements is more vital than ever. For the…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
Based on a variety of philosophical approaches and my own work for decades in pure and applied mathematics teaching and research, I explain my view upon the basic difficulties of acquiring the Mathematical Experience (in the sense of P.J.…
Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…
Computing in the life sciences has undergone a transformative evolution, from early computational models in the 1950s to the applications of artificial intelligence (AI) and machine learning (ML) seen today. This paper highlights key…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
The software engineering is a relatively new discipline compared to other sciences, since the origins of the term itself dates back to the years 1968 and 1969. At present, the market and the software industry have a significant relevance in…
As quantum computers advance, the complexity of the software they can execute increases as well. To ensure this software is efficient, maintainable, reusable, and cost-effective -key qualities of any industry-grade software-mature software…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Tensors (also commonly seen as multi-linear operators or as multi-dimensional arrays) are ubiquitous in scientific computing and in data science, and so are the software efforts for tensor operations. Particularly in recent years, we have…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…
In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and…
Software engineering research benefited for decades from openly available tools, accessible systems, and problems that could be studied at modest scale. Today, many of the most relevant software systems are large, proprietary, and embedded…
Most if not all of today's revolutionary technologies have a common foundation, namely the intelligent use of information. It is clear that computers play a central role: but the contribution of mathematics, though less visible, is no less…