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**Adress:** College of Nyíregyháza

Department of Mathematics

4400 Nyíregyháza, Sóstói út 31/b

Hungary

**Tel:** (42) 599-460

**Fax:** (42) 402-485

**Head of Department:** Dr. Zoltán Kovács

**Members of the Department**

Please visit our electronic mathematical journal Acta Mathematica Nyíregyháziensis, the journal of College of Nyíregyháza, (Hungary) publishes a papers in any parts of mathematics and informatics. The papers will be refered in the traditional manner, with one anonymus referee. The journal appears in one volume per annum only in electronic form.

IJMTL, International Journal for Mathematics Teaching and Learning was founded by the Centre for Innovation in Mathematics Teaching, CIMT ) and the Institute of Mathematics and Informatics of College of Nyíregyháza in 2000.

The journal published only in electronic form aims to enhance mathematics teaching for all ages, through relevant articles, reviews and information from around the word.

**Research in Mathematics:**

Algebraic investigations focus on modular group algebras, representations of finite dimension algebras, embedding problems, as well as on solvability and Engel length of group algebras and of associated Lie algebras. Besides, researches on fuzzy groups and relations are also carried out. In geometry we study the field of Finsler spaces,namely their geodetic and homology theory. In combinatorics there are researches concerning optimal ordering algorithms. In analysis our main research topic is dyadic harmonic analysis.Further,there are investigations on linear recursive series.In pedagogy and methodology we wrote textbook series for general schools (upper four classes),worked out methods for their usage.We compiled "local" and "frame" curricula for these schools,too. There are researches in the history of mathematics, mainly in the history of Hungarian mathematics in XXth century.

- In *algebra* the close link between group commutators and associated Lie algebras was discovered.In certain cases the Engel length and nilpotent class of group algebras and its associated Lie algebras were determined.We characterised those modular group algebras in which symmetric units form a subgroup.We dealt with the representations of algebras of finite dimension.We managed to give a perfect answer to the question:when can the coronary product of two P-order groups be embedded into the unit group of the group algebra.In certain cases we determined the order of the unitary subgroup and gave its generators.

- In *geometry* we reached results in differential geometry.Chern-Weil-type homomorphism was constructed on a manifold with l-form.We extended Masumoto investigations on Finsler spaces with conic section geodetic to the ones with ellipse geodetic.

- In *analysis: *1. * *some important problems of the theory of 2-adic integers were solved: Proof of Fejér-Lebesgue theorem on their characters solve a 25 year old problem. 2. The fundamental theorem of dyadic derivate in two-variable case was studed in the Walsh (1995) and bounded Vilenkin case. 3. Verification of double Walsh-Fejér means in spaces wider than L log L. The problem is from 1938. 4. Proof of Fejér-Lebesgue theorem on unbounded Vilenkin groups answering one of the most sought-after question of dyadic analysis. 5. Nowadays we investigate questions related to the Marcinkiewicz means (with respect to Vilenkin and Walsh-Kaczmarz systems) and logarithmic means (with respect to Vilenkin and Vilenkin like systems). Research goes on the character systems of noncommutative groups too. For more details see the homepage of Dyadic Harmonic Analysis Group.

- As for *methodology,* a textbook series of Muszaki Publisher House was completed that are now used in 95% of general schools. To these books helping materials were prepared including evaluation tests that make possible a nation-wide unified measurement of pupils' mathematical performance. Some members of our department are co-authors in this series. "Local" and "frame" curricula were also compiled. Since 1994 we have been involved in the Kassel/Exeter and the IPMA international projects

and we also help the MEP mathematics teaching experiment with teacher support and pupil's material in the U.K.

- By *historical research* we explored the life and work of some emigrated XXth century Hungarian mathematicians who were unknown in Hungary.We managed to solve some important problems of antique Greek mathematics concerning incommensurability.