Related papers: Computing with Equations
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
The main goal of this research is to develop the concepts of a revolutionary processor system called Functional Processor System. The fairly novel work carried out in this proposal concentrates on decoding of function pipelines and…
Disco is a pure, strict, statically typed functional programming language designed to be used in the setting of a discrete mathematics course. The goals of the language are to introduce students to functional programming concepts early, and…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts…
Computational thinking in physics has many different forms, definitions, and implementations depending on the level of physics, or the institution it is presented in. In order to better integrate computational thinking in introductory…
The quality of software produced by students is often poor. How to teach students to develop good quality software has long been a topic in computer science education and research. We must conclude that we still do not have a good answer to…
This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
Functional logic languages can solve equations over user-defined data and functions. Thus, the definition of an appropriate meaning of equality has a long history in these languages, ranging from reflexive equality in early equational logic…
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…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and…
Computational thinking is a new problem soling method named for its extensive use of computer science techniques. It synthesizes critical thinking and existing knowledge and applies them in solving complex technological problems. The term…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Current approaches to making programming languages and reasoning assistants more effective for people focus on leveraging feedback from users and on evaluating the success of particular techniques. These approaches, although helpful, may…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…