Related papers: WZ Theory, Chapter II
In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…
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…
Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and…
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special…
We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and theoretical physics in 2017, we summarize how this emerging field has…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. On grounds…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From…
We discuss the process of deterioration of quality of mathematical conferences caused by computer presentations.
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a…
The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are…
Computer models and information systems have been used for urban planning and design since the 1950s. Their capacity for analysis and problem-solving has increased substantially since then with hardware and software being able to manage…
In recent years there has been interest in the theory of local computation over probabilistic Bayesian graphical models. In this paper, local computation over Bayes linear belief networks is shown to be amenable to a similar approach.…
This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the…
We address the problems of estimating the computer efficiency and the computer capacity. We define the computer efficiency and capacity and suggest a method for their estimation, based on the analysis of processor instructions and kinds of…
Present day mathematics is a human construct, where computers are used more and more but do not play a creative role. This situation may change however: computers may become creative, and since they function very differently from the human…
The Internet and computer commercialization have transformed the computing systems area over the past sixty years, affecting society. Computer systems have evolved to meet diverse social needs thanks to technological advances. The Internet…
Various models of the information society have been developed so far and they are so different from country to country that it would be rather unwise to look for a single, allencompassing definition. In our time a number of profound…