The Beginning of a Partnership in the Process of Studying Mathematics

In this paper we present the beginning of a partnership between the students in the upper classes and those in the beginner classes in 21st Secondary School “Hristo Botev”, Sofia. We examine deeply two of the used types of cooperative activity. The work shows the main steps in the organization of the project. We have included the motives for work both of the teachers and the students. The present work shows the concrete advantages for the different age groups and the reflection on the parents, as well.

A Prototype of an Extension to the UDDI Registry Allowing Pubilcation and Search Based on Subjective Evaluations

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko and Lubomir Tschakalo , So a, July, 2006.

Generalized Nets Model of an E-Learning System Software Architecture

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko ff and Lubomir Tschakaloff , Sofi a, July, 2006.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

Financial Education Through Mathematics and IT Curricula: Pocket Money Management

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Financial Decisions via Methods of Guaranteed Control Theory

AMS subject classification: 93C95, 90A09.

Recent Developments in Digital Mathematics Libraries

The paper presents recent developments in the domain of digital mathematics libraries towards the envisioned 21st Century Global Library for Mathematics. The Bulgarian Digital Mathematical Library BulDML and the Czech Digital Mathematical Library DML-CZ are founding partners of the EuDML Initiative and through it contribute to the sustainable development of the European Digital Mathematics Library EuDML and to the global advancements in this area.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

Structure of the Unit Group of FD10

2000 Mathematics Subject Classification: 16U60, 20C05.

On Distributed Oblivious Transfer

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at INDOCRYPT 2002

On Proactive Verifiable Secret Sharing Schemes

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at the 11th Workshop on Selected Areas in Cryptography (SAC) 2004

When does a Bounded Domain Cover a Projective Manifold? (Survey)

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and Technology

Mathematica Balkanica New Series Book Volume 24 2010

Muharem Avdispahic 1 Coordinator of the TEMPUS Project SEE Doctoral Studies in Mathematical Sciences (144703-TEMPUS-2008-BA-TEMPUS-JPCR) The main goals of the TEMPUS Project ”SEE Doctoral Studies in Math- ematical Sciences”, funded by European Commission under the TEMPUS IV first call, consist of the development of a model of structured doctoral studies in Mathematical Sciences involving the network of Western Balkans universi- ties, the curricula design based on the existing strenghts and tendencies in the areas of Pure Mathematics, Applied Mathematics and Theoretical Computer Science and the first phase of implementation of the agreed model during the SEE Doctoral Year in Mathematical Sciences 2011. A decisive step in this direction was ”SEE Young Researchers Workshop” held in Ohrid, FYR Macedonia, September 16-20, 2009, as a part of the Math- ematical Society of South-Eastern Europe (MASSEE) International Congress on Mathematics - MICOM 2009. MICOM 2009 continued the tradition of two previous highly successful MASSEE congresses that took place in Bulgaria in 2003 and in Cyprus in 2006. This volume of the journal Mathematika Balkanica contains the talks de- livered at Ohrid Workshop by South-Eastern European PhD students in various stage of their research towards a doctoral degree in mathematics or informat- ics. Facilitating publication efforts of young researchers from the universities of Sarajevo, Tuzla, Belgrade, Skopje, Stip, Graz, and Sofia fully coincides with MASSEE goals to promote, organize and support scientific, research and edu- cational activities in South-Eastern Europe. The consent of the Editorial Board of Mathematica Balkanica to publish ”SEE Young Researchers Workshop” contributions aptly meets intentions of European reform processes aimed at creating the European Higher Education Area and European Research Area. It is an encouragement to these young researchers in the first place and at the same time an encouragement to their institutions in overcoming fragmentation and enhancing their capacities through fostering reciprocal development of human resources.

Percent in a Nutshell …

Ironically, the “learning of percent” is one of the most problematic aspects of school mathematics. In our view, these difficulties are not associated with the arithmetic aspects of the “percent problems”, but mostly with two methodological issues: firstly, providing students with a simple and accurate understanding of the rationale behind the use of percent, and secondly - overcoming the psychological complexities of the fluent and comprehensive understanding by the students of the sometimes specific wordings of “percent problems”. Before we talk about percent, it is necessary to acquaint students with a much more fundamental and important (regrettably, not covered by the school syllabus) classical concepts of quantitative and qualitative comparison of values, to give students the opportunity to learn the relevant standard terminology and become accustomed to conventional turns of speech. Further, it makes sense to briefly touch on the issue (important in its own right) of different representations of numbers. Percent is just one of the technical, but common forms of data representation: p% = p × % = p × 0.01 = p × 1/100 = p/100 = p × 10-2 "Percent problems” are involved in just two cases: I. The ratio of a variation m to the standard M II. The relative deviation of a variation m from the standard M The hardest and most essential in each specific "percent problem” is not the routine arithmetic actions involved, but the ability to figure out, to clearly understand which of the variables involved in the problem instructions is the standard and which is the variation. And in the first place, this is what teachers need to patiently and persistently teach their students. As a matter of fact, most primary school pupils are not yet quite ready for the lexical specificity of “percent problems”. ....Math teachers should closely, hand in hand with their students, carry out a linguistic analysis of the wording of each problem ... Schoolchildren must firmly understand that a comparison of objects is only meaningful when we speak about properties which can be objectively expressed in terms of actual numerical characteristics. In our opinion, an adequate acquisition of the teaching unit on percent cannot be achieved in primary school due to objective psychological specificities related to this age and because of the level of general training of students. Yet, if we want to make this topic truly accessible and practically useful, it should be taught in high school. A final question to the reader (quickly, please): What is greater: % of e or e% of Pi