Petar Kenderov | Bulgarian Academy of Sciences (original) (raw)

Papers by Petar Kenderov

A mathematics competition for primary school students was held in Bucharest, Romania, as early as... more A mathematics competition for primary school students was held in Bucharest, Romania, as early as 1885. There were 70 participants and eleven prizes, awarded to two girls and nine boys. One cannot completely rule out the possibility that similar competitions were held elsewhere even before 1885. Nevertheless, the Eötvös competition in Hungary (held in 1894) is widely credited as the forerunner of contemporary mathematics (and physics) competitions for secondary school students. The competitors were given four hours to solve three problems (no interaction with other students or teachers was allowed). The problems in the Eötvös competition were designed to check creativity and mathematical thinking, not just acquired technical skills. In particular, the students were asked to provide a proof of a statement. The Eötvös competition model is now widely spread and still dominates a large portion of competition scene.

Report published in the Proceedings of the National Conference on "Education and Research in... more Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015The paper deals with the experience of the authors in promoting the Inquiry Based Learning (IBL) in mathematics and science education within international and national projects. The emphasis is on in-service teacher education. Various types of activities and resources in support of all levels of IBL are considered, e.g. professional development courses, seminars, workshop, and performances; implementation of resources stimulating students to behave like working mathematicians. The first visible positive effects and potential problems in the implementation of IBL in the Bulgarian schools are discussed.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski

The problems of practical importance which are considered in school today necessarily have to lea... more The problems of practical importance which are considered in school today necessarily have to lead to a mathematical model that can be solved by school mathematics knowledge. This includes systems of equations of at most second degree, some simple trigonometry and/or some basic geometry. This restricts severely the class of such problems and conveys the impression that mathematics is not applicable enough. We provide examples of problems related to practice which are difficult to solve by means of traditional school mathematics but are amenable for solving (at least with a certain precision) with the use of software systems dealing with mathematical problems. We also present the results of an experiment with such problems that were given to school students participating in the second round of the competition “VIVA Mathematics with Computer”. ACM Computing Classification System (1998): K.3.1.

Mathematics and Informatics, 2021

The characteristic features of the online competition “VIVA Mathematics with Computer”, organized... more The characteristic features of the online competition “VIVA Mathematics with Computer”, organized by the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, the Union of Mathematicians in Bulgaria and the telecommunications company VIVACOM are described. The tasks are classified according to the type of their answers. The GeoGebra help-files accompanying some of the tasks are discussed as tools for simultaneous development of students‘ digital and mathematical competence. An analysis of the results of the competition, held on April 25, 2020, is presented.

In many countries the standard education in mathematics is mainly oriented to serve the average a... more In many countries the standard education in mathematics is mainly oriented to serve the average ability students. This is natural because such students form a majority in schools. Special care is usually assigned to lower ability students so that they could cover the educational standards. Less attention is paid however to students with higher than average abilities in mathematics. The standard curriculum and syllabus requirements are no challenge for these students. As a result, a lot of mathematical abilities (and even mathematical talents) remain undiscovered and undeveloped. On the other hand, the higher ability individuals provide a critical resource for the development of the society, if they are properly educated, motivated to work and supported. With this in mind a project named MATHEU was started aimed at developing tools for identification, motivation and support of students with higher ability (and perhaps talent) in mathematics. The project has been carried out with the ...

Set-Valued and Variational Analysis

Let X be a completely regular topological space and f a real-valued bounded from above lower semi... more Let X be a completely regular topological space and f a real-valued bounded from above lower semicontinuous function in it. Let C(X) be the space of all bounded continuous real-valued functions in X endowed with the usual sup-norm. We show that the following two properties are equivalent: X is α-favourable (in the sense of the Banach-Mazur game); The set of functions h in C(X) for which f + h attains its supremum in X contains a dense and Gδ-subset of the space C(X). In particular, property (b) has place if X is a compact space or, more generally, if X is homeomorphic to a dense Gδ subset of a compact space.We show also the equivalence of the following stronger properties: X contains some dense completely metrizable subset; the set of functions h in C(X) for which f + h has strong maximum in X contains a dense and Gδ-subset of the space C(X). If X is a complete metric space and f is bounded, then the set of functions h from C(X) for which f + h has both strong maximum and strong min...

MATHEMATICA SCANDINAVICA, 1984

Proc Amer Math Soc, 2005

In this paper we prove a theorem more general than the following. Suppose that X is Lindelöf and ... more In this paper we prove a theorem more general than the following. Suppose that X is Lindelöf and α-favourable and Y is Lindelöf andČech-complete. Then for each separately continuous function f : X × Y → R there exists a residual set R in X such that f is jointly continuous at each point of R × Y .

Siam J Math Anal, 1983

Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metri... more Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections. [SIAM Journal on Mathematical Analysis 14, 185 (1983)]. Frank Deutsch, Petar Kenderov. Abstract. Two new ...

Pacific Journal of Mathematics, 1996

We study a class of Banach spaces which have the property that every continuous convex function o... more We study a class of Banach spaces which have the property that every continuous convex function on an open convex subset of the dual possessing a weak * continuous subgradient at points of a dense G § subset of its domain, is Frechet differentiate on a dense G$ subset of its domain. A smaller more amenable class consists of Banach spaces where every minimal weak * cusco from a complete metric space into subsets of the second dual which intersect the embedding from a residual subset of the domain is single-valued and norm upper semi-continuous at the points of a residual subset of the domain. It is known that all Banach spaces with the Radon-Nikodym property belong to these classes as do all with equivalent locally uniformly rotund norm. We show that all with an equivalent weakly locally uniformly rotund norm belong to these classes. The condition closest to a characterisation is that the Banach space have its weak topology fragmentable by a metric whose topology on bounded sets is stronger than the weak topology. We show that the space ^oo(Γ), where Γ is uncountable, does not belong to our special classes.

Topology and its Applications, 2006

Let T be the class of Banach spaces E for which every weakly continuous mapping from an α-favorab... more Let T be the class of Banach spaces E for which every weakly continuous mapping from an α-favorable space to E is norm continuous at the points of a dense subset. We show that:

Proceedings of the American Mathematical Society, 2005

International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, 1984

ABSTRACT

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006, 2007

Mathematics competitions, together with the people and organizations engaged with them, form an i... more Mathematics competitions, together with the people and organizations engaged with them, form an immense and vibrant global network today. This network has many roles. Competitions help identify students with higher abilities in mathematics. They motivate these students to develop their talents and to seek professional realization in science. Competitions have positive impact on education and on educational institutions. Last but not least, a significant part of the classical mathematical heritage known as "Elementary Mathematics" is preserved, kept alive and developed through the network of competitions and competition-related activities. Nevertheless, competitions need to evolve in order to meet the demands of the new century.