Gyula Bereznai

Gyula Bereznai (around 1960)

Gyula Bereznai (born May 1, 1921 in Sátoraljaújhely ; † September 6, 1990 Nyíregyháza ) was a Hungarian mathematician and head of department at the Nyíregyháza teacher training college.

Life

His father was a hairdresser, his mother a housewife. He graduated from primary school in Tornyospálca , then secondary school in Kisvárda . His studies at the University of Debrecen were interrupted by the war . After six years in prison, he received a degree in mathematics from the Eötvös Loránd University in Budapest . After working at the Nyíregyháza vocational school and the Kölcsey grammar school, he was accepted into the mathematics department of the György Bessenyei teacher training college in 1962. From 1969 to 1983 he was head of department there. For more than two decades he taught the future generation of teachers the basics of mathematical analysis. His work was shaped by numerous specialist and method publications. He has written and edited several books and examples.

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He specialized in mathematical analysis .

Quote from the publication About a simple convergence criterion : The following applies: If the ratio of one series link to the following one is sufficient , ${\displaystyle a_{n}}$ ${\displaystyle a_{n+1}}$ ${\displaystyle {\frac {a_{n}}{a_{n+1}}}}$, of some value in the inequality ${\displaystyle n}$ ${\displaystyle \left({\frac {a_{n}}{a_{n+1}}}\right)^{n}\geq p>e}$, where does not depend on, the series with positive terms converges . However, it is reversed from a certain value onwards ${\displaystyle p}$ ${\displaystyle n}$ ${\displaystyle \sum _{}a_{n}}$ ${\displaystyle n}$ ${\displaystyle \left({\frac {a_{n}}{a_{n+1}}}\right)^{n}\leq e}$, so the given series diverges. (The theorem was generalized by József Sándor ..) It is known that the method of Gyula Bereznai is more effective than the so-called D'Alembert - quotient and the so-called Raabe - Duhamel - method , the most common to determine the convergence of numerical series with positive numbers is used. That is, the result of Gyula Bereznai offers, among other things, a useful tool for the study of a very intensely researched branch of mathematics , harmonic analysis . (Dr.Habil. György Gát)

The mathematics competition named after Gyula Bereznai has been held every year since 1991 under the name "Gyula Bereznai mathematics competition".

Awards and honors

• 1960 - Beke Manó Memorial Prize
• 1969 - Excellent education worker
• 1972 - Ministerial Praise
• 1979 - For excellent work
• 1983 - For socialist culture

Fonts

• Pythagorean theorem
• History of numbering
• Mathematics competitions of the teacher training colleges

Publications

• Curiosities about the parable ; Yearbook of Ferenc Kölcsey's high school for girls , Nyíregyháza, 1960.
• Indirect proof in mathematics education of secondary school ; Pedagogue of the Szabolcs-Szatmár County, Nyíregyháza
• Studies in the p-ed part under monotonically increasing or decreasing series ; Acta Academiae Paedagogicae Nyíregyháziensis ( AAPN ), 1965. ( ISSN = 0133-6037 )
• A simple proof of the inequality of the arithmetic mean and the geometric mean ; A Matematika Tanítása (Teaching Mathematics), 1968.
• Letter of reply to a high school teacher ; A Matematika Tanítása, 1968.
• Two properties of Stalley - function ; AAPN, 1968.
• A reduction of an ordinary linear differential equation with a constant coefficient ; AAPN, 1968.
• About a certain class of rational numbers ; AAPN, 1968.
• Teaching the quadratic equation on a particular aspect ; A Matematika Tanítása, 1969.
• Hint for a task in math class ; A Matematika Tanítása, 1969.
• Investigation of the monotony of elementary functions with elementary means ; A Matematika Tanítása, 1970.
• Simple proof of the irrationality of ${\displaystyle {\sqrt {2}}}$ ; A Matematika Tanítása, 1970.
• Theorem of Pythagoras Tankönyvkiadó, 1970 (textbook publisher)
• For solving irrational equations ; A Matematika Tanítása, 1971.
• Post a discussion A Matematika Tanítása, 1971.
• Bereznai Gyula - Gilányi Jánosné : A generalization of the concept of a convex function and mean inequalities ; AAPN, 1972.
• A common cause of Minkowski - inequality and Cauchy - Bunyakovskys - Black - inequality ; AAPN, 1972.
• Additive to the theory of curves of constant width ; AAPN, 1972.
• About an approximation to x-shaped real numbers ; AAPN, 1973.
• About the number ; Mathematics in School, 1973/1.
• About a reduction of partial differential equations ; AAPN, 1973.
• An approximation to real numbers of the form ${\displaystyle {\sqrt {2}}}$ ; AAPN, 1973.
• A simple convergence criterion ; AAPN, 1973. ( 1973. Matematika, 19-24. P. ISSN 0133-882X)
• Irrationality of the root sets ; A Matematika Tanítása, 1974/1.
• Footnote for the proof of an element in the operator calculation ; AAPN, 1974.
• To factorization of Mersenne - primes ; AAPN, 1974.
• Commentary on a proposition of number theory ; AAPN, 1974.
• The computer center of our university ; Yearbook of György Bessenyei Teacher Training College , 1974.
• Example of a curve that completely fills an n-dimensional unit cube ; AAPN, 1977.
• Another proof of the inequality between the arithmetic and geometric mean ; A Matematika Tanítása, 1977/3.
• Equivalence of equations ; Library for the advanced training of teachers, 1977.
• Mathematics competitions in teacher seminars I. 1952-1970. ; (with Dr Varecza Árpád ) Tankönyvkiadó, 1978.
• Bereznai Gyula - Dr Varecza Árpád - Dr Rozgonyi Tibor : National mathematics competitions at teachers' seminars ; Tankönyvkiadó, 1978.
• Division with faction ; A Matematika Tanítása, 1979.
• For the integration of complex and inverse functions ; AAPN, 1980.
• Note for a competition task A Matematika Tanítása, 1980.
• Mathematics competitions in teachers' seminars II. 1971-1979. ; (with Dr Varecza Árpád) Tankönyvkiadó, 1981.
• Bereznai Gyula - Dr.Varecza Árpád : About the background of a competition task ; AAPN, 1982.
• Bereznai Gyula - Dr Filep László : The story of writing the number Gondolat Verlag, Bp. 1982. ( Kelet-Magyarország newspaper )
• Modern teaching in modern mathematics ; Pedagogical workshop , 1983.
• The role of classification in the process of scientific knowledge ; Publication of the János Bolyai Mathematical Society , 1983.
• The scientist and peace fighter Pierre Curie was born 125 years ago ; Kelet-Magyarország , May 15, 1984.
• I found this: Why do we teach math logic ? ; Pedagógiai műhely (Pedagogical Workshop), 1984.
• A general divisibility rule ; AAPN, 1985.
• Bereznai Gyula - Dr Varecza Árpád: On the convergence of a certain sequence ; AAPN, 1985.
• To the criticism of our math classes ; Pedagógiai műhely, 1987.
• We saw it in math class ... ; Tanító  : methodological journal, 1987.
• Teaching the field of polygons in high school ; AAPN, 1988.
• Open Sentences and Their Role in Mathematics Classes in Elementary Schools ; Pedagógiai műhely, 1988.
• Mathematics competitions in teacher seminars III. 1980-1985. ; (with Dr Varecza Árpád) Tankönyvkiadó, 1981.
• Basic concepts of set theory in elementary school ; Pedagógiai műhely, 1990.
• Bereznai Gyula + - Dr.Rozgonyi Tibor: Notes on functional continuity ; AAPN, 1992.

Web links

• Gyula Bereznai
• Bereznai Gyula educational award

Individual evidence

1. ↑ Nyíregyháza College website
2. ↑ Bereznai Gyula: Egy egyszerű konvergenciakritérium . - In: Acta Academiae Paedagogicae Nyíregyháziensis, ISSN  0133-882X , 1973. Matematika, pp. 19-24.
3. ↑ A generalization of Bereznai's theorem on infinite series
4. ↑ Debreceni Egyetem Matematikai intézet
5. ↑ Bereznai Gyula matematikaverseny
6. ↑ Pitagorasz tétele NSZL LAP Publishing, 1970
7. ↑ Filep László - Bereznai Gyula: A számírás története, Gondolat Verlag, 1982, ISBN 963-281-070-8
8. ↑ Gyula Bereznai - Dr. Árpád Varecza - Dr Tibor Rozgonyi : Tanárképző főiskolák matematika versenyei (1952-1970: ISBN 978-963-17-3627-4 ; 1971-1979: ISBN 978-963-17-6159-7 ; 1980-1985: ISBN 978- 963-18-1606-8 )
   Tanárképző főiskolák országos matematika versenyei: ISBN 978-963-17-3626-7