Related papers: Fundamentals of Computing
This paper proposes a specific conceptualization of intelligence as computation. This conceptualization is intended to provide a unified view for all disciplines of intelligence research. Already, it unifies several conceptualizations…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We present a brief introduction to analytic capacity, with an emphasis on its numerical computation. We also discuss several related open problems.
Quantum computers promise to surpass the most powerful classical supercomputers when it comes to solving many critically important practical problems, such as pharmaceutical and fertilizer design, supply chain and traffic optimization, or…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation
This article outlines our point of view regarding the applicability, state-of-the-art, and potential of quantum computing for problems in finance. We provide an introduction to quantum computing as well as a survey on problem classes in…
A recent normative turn in computer science has brought concerns about fairness, bias, and accountability to the core of the field. Yet recent scholarship has warned that much of this technical work treats problematic features of the status…
In this paper, we examine the state art of quantum computing and analyze its potential effects in scientific computing and cybersecurity. Additionally, a non-technical description of the mechanics of the listed form of computing is provided…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…