Tighter, Neater, Safer C and C++

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016Constructs are presented for alternative — tighter, neater and arguably less vulnerable — expression of frequently occurring patterns in C and C++ programming. We find them useful in several ways, both in teaching and in participating in programming competitions. Working programmers can also benefit from such or similar constructs.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski

Spiral Walk Exposed

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015Traversing a matrix along a spiral is a popular small programming problem, but one which is often solved incorrectly, or only partially, or in an ill-structured way. To benefit teaching and learning good programming style, we considered worthy to present the construction of several solutions to this problem in an expository manner. Some related combinatorial problems are also discussed. Hopefully, the text can be useful to high and higher school teachers and students, as well as to practicing programmers.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski

The Role of the Language in Teaching Introductory Programming

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, June, 2017Based on a present-day view of teaching programming, desirable features are formulated for a language suitable for teaching introductory programming. On the examples of programs solving several very simple problems, a comparative evaluation is done of the languages Java and Ruby in this respect. The significance of visualization in programming education is outlined, and a suitable solution for graphical visualization is pointed at.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski

Trees and Graphs: Simple, General, Abstract, and Efficient

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2019The representations of trees and graphs in general, as known from most textbooks on data structures and algorithms or similar sources, are in various ways deficient and outdated. We offer a straightforward approach, based on the notions of set and map, which is at once abstract, general, and efficient, and thus beneficial to the theory, practice, and teaching of programming.Association for the Development of the Information Societ

Език за композиционно програмиране: Обосновка и конструкция

Бойко Бл. Банчев - Представена е обосновка и описание на език за програмиране в композиционен стил за опитни и учебни цели. Под “композиционен” имаме предвид функционален стил на програмиране, при който пресмятането е йерархия от композиции и прилагания на функции. Един от данновите типове на езика е този на геометричните фигури, които могат да бъдат получавани чрез прости правила за съотнасяне и така също образуват йерархични композиции. Езикът е силно повлиян от GeomLab, но по редица свойства се различава от него значително. Статията разглежда основните черти на езика; подробното му описание и фигурноконструктивните му възможности ще бъдат представени в съпътстваща публикация.A rationale and description of a language for exploratory and educational programming in a compositional style is presented. By ‘compositional’ a functional programming style is meant where the computation is a hierarchy of function compositions and applications. One of the datatypes of the language is that of the geometrical figures that can be obtained by simple rules of spatial correlation, thus, too, forming hierarchical compositions. The language is strongly influenced by GeomLab, but differs from it substantially in many respects. The paper discusses the main features of the language; the detailed description along with the picture construction facilities will be presented in an accompanying publication. *2000 Mathematics Subject Classification: 68N15, 68N18

Речник на “пресмятането”, разбирано в широк смисъл

Бойко Банчев - Понятието пресмятане в широкия му смисъл и неговото присъствие в природата, науката, технологията и други области е свързано с редица неизяснени въпроси. Дори в по-тесните рамки на програмирането и използването на компютри то не е адекватно разбрано. Представяме тезата, че един начин за приближаване към такова разбиране е разкриването на дълбинните структури и отношения, свързани с пресмятането, и на тази основа построяване на речник на пресмятането.Important questions regarding what computing is and how it pervades nature, science, engineering and other fields remain unanswered. Even restricted to programming or using computer-based technology, computing lacks proper understanding. We argue that one way to bring this understanding closer is by discovering the most fundamental structures and relations in computing and, thus, building a dictionary of computing. *2000 Mathematics Subject Classification: 68Q01

Programming as Metacalculation

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013Elements of an approach to teaching programming in school are described, based on the functional paradigm and harmonically blending programming, calculation, and algebra. We believe that it ensures a smooth introduction to programming, free of contrived concepts and constructs, and also fosters the teaching of a wider and deeper mathematics in school.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Science

Compositional Geometry and Programming

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014Functional, or compositional, geometry is a method of constructing complex pictures from simpler ones, apllying binding operations. The method is naturally related to functional programming and can be used as a tool for education or self-education in programming. The paper introduces to compositional geometry, bringing attention to its several variants, more specifically the one implemented in the author's language U. Examples of simple, straightforward compositions are shown, as well as ones that can only be achieved through programming.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski

Нов поглед върху пространството на дробите

Бойко Бл. Банчев - Знае се, че рационалните числа образуват интересни и богати на изчислителни възможности структури като редици на Фарей (Феъри) и безкрайни дървета. Малко внимание се обръща на по-общо, систематично излагане на основните свойства на дробите като множество. Понятия биват въвеждани без обосноваване, някои доказателства са ненужно изкуствени, а почти винаги и едните, и другите като че биват отнесени към една или друга особена структура, вместо към множеството на дробите изобщо. Изненадващо е, че някои същностни твърдения изглежда дори не са формулирани в литературата по теория на числата. Тази статия има за цел да подобри състоянието на нещата в това отношение, като предлага общо, подходящо подредено изложение на понятия и свързани с тях твърдения. Като допълнение са представени бележки върху пораждането на множеството от всички дроби – откритие значително по-старо, отколкото е прието да се смята.Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set. Some concepts are being introduced without motivation, some proofs are unnecessarily artificial, and almost invariably both seem to be understood as related to specific structures rather than to the set of fractions in general. Surprisingly, there are essential propositions whose very statement seem to be missing in the number theory literature. This article aims at improving on the said state of affairs by proposing a general and properly ordered exposition of concepts and statements about them. In addition, historical remarks are made on generating the set of all fractions – a much older discovery than it is widely believed. *2000 Mathematics Subject Classification: 11B75, 01A99