Related papers: Computing with Equations
This paper investigates how high school students in an introductory computer science course approach computing in the Logic Programming (LP) paradigm. This qualitative study shows how novice students operate within the LP paradigm while…
This paper analyses the security contribution of typical functional-language features by examining them in the light of accepted information security principles. Imperative and functional code are compared to illustrate various cases. In…
In this paper we discuss how semantic annotations can be used to introduce mathematical algorithmic information of the underlying imperative code to enable compilers to produce code transformations that will enable better performance. By…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
In upper-division undergraduate physics courses, it is desirable to give numerical problem-solving exercises integrated naturally into weekly problem sets. I explain a method for doing this that makes use of the built-in class structure of…
The purpose of this note is to raise two different questions, which are rarely if ever considered, and to which, it seems, we lack convincing, systematic answers. These questions can be posed as: - Why do we compute? - What do we compute?…
This paper investigates how high school students approach computing through an introductory computer science course situated in the Logic Programming (LP) paradigm. This study shows how novice students operate within the LP paradigm while…
Computer programs are part of our daily life, we use them, we provide them with data, they support our decisions, they help us remember, they control machines, etc. Programs are made by people, but in most cases we are not their authors, so…
Introducing inner-city high school students to program design presents unique challenges. The typical assumptions of an introductory programming course, like students understand what variables and functions are, may not be safe. Therefore,…
These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that…
Philosophical thinking has a side effect: by aiming to find the essence of a diverse set of phenomena, it often makes it difficult to see the differences between them. This can be the case with Mathematics, Programming, Writing and…
A visual programming language uses pictorial tools such as diagrams to represent its structural units and control stream. It is useful for enhancing understanding, maintenance, verification, testing, and parallelism. This paper proposes a…
Computation holds great potential for introducing new opportunities for creativity and exploration into the physics curriculum. At the University of Oslo we have begun development of a new class of assignment called computational essays to…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
Partial functions are common abstractions in formal specification notations such as Z, B and Alloy. Conversely, executable programming languages usually provide little or no support for them. In this paper we propose to add partial…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
This essay contains three parts. The first part of essay focuses on the hypothesis of the functional semantic constructions (FSC-Hypothesis). This hypothesis explains that a language, a number, a money are the functional semantic…