Technical Transactions iss. 20. Fundamental Sciences iss. 2-NP

Technical Transactions iss. 20. Fundamental Sciences iss. 2-NP

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Collection items (21)


Philosophy of exact sciences (logic and mathematics) in Poland in 1918–1939

Woleński, Jan
Article
2015
This paper describes the philosophy of logic and mathematics in Poland in the years 1918‒1939. The special attention is attributed to the views developed in the Polish Mathematical School and the Warsaw School of Logic. The paper indicates various differences between mathematical circles in Warszawa, Lvov and Kraków.

Kaczmarz algorithm revisited

Sznajder, Roman
Article
2015
In 1937, Stefan Kaczmarz proposed a simple method, called the Kaczmarz algorithm, to solve iteratively systems of linear equations Ax = b in Euclidean spaces. This procedure employs cyclic orthogonal projections onto the hyperplanes associated with such a system. In the case of a nonsingular matrix A, Kaczmarz showed that his method guarantees convergence to the solution of Ax = b. The Kaczmarz algorithm was rediscovered in 1948 and became an important tool in medical engineering. We briefly discuss generalizations of this method and its ramifications, including applications in computer tomography, image processing and contemporary harmonic analysis.

Some remarks of Jan Śleszyński regarding foundations of mathematics of Stanisław Leśniewski

Obojska, Lidia
Article
2015
Jan Śleszyński, a great mathematician, is considered a pioneer of Polish logic; however, he was not connected with the famous Warsaw School of Logic (WSL). He believed that his mission was a critical evaluation of work of other logicians in the field of foundations of mathematics and proof theory. Among his writings we find several notes regarding the work of Stanisław Leśniewski (the co-founder of the WSL) and his collective set theory. These remarks are the subject of investigation of the presented paper.

A few facts concerning the outstanding Polish mathematician Franciszek Leja

Kosek, Marta
Article
2015
We present a collection of facts given by the outstanding Polish mathematician Franciszek Leja (1885‒1979) in his unpublished memoirs, add some other information about him and list some institutions bearing his name.

Stanisław Zaremba (1863‒1942) and his results in the field of differential equations

Koroński, Jan
Article
2015
The subject of the paper is presentation of the publications of Stanisław Zaremba in the field of partial differential equations. We present selected results in detail. Zaremba published about 120 works. Among them more than 60 were devoted to partial differential equations.

Stanisław Kępiński (1867‒1908) and his papers in the field of differential equations

Koroński, Jan
Article
2015
The subject of this paper is an analysis of the publications of Stanisław Kępiński in the field of ordinary and partial differential equations. In particular we present part I and part II of the monograph (textbook) of Stanisław Kępiński on the ordinary and partial differential equations.

A note on the mathematical publications in the Dissertations and Reports of Meetings of the Academy of Arts and Sciences in Cracow in the years 1874‒1951

Koroński, Jan
Article
2015
This paper contains some information on the Academy of Arts and Sciences in Cracow. It gives a detailed list of mathematical publications in the Dissertations and Reports of Meetings of the Academy of Arts and Sciences in Cracow in the years 1874‒1951.

Teaching thinking in terms of functions – fulfilling the fundamental idea of the Merano Programme at Torun Classical Grammar School in the early twentieth century

Karpińska, Karolina
Article
2015
In this article, one of the main postulates of the Merano Programme for teaching mathematics will be analysed, namely: teaching thinking in terms of functions. This postulate will be discussed in the context of its implementation at Torun Classical Grammar School. Through the detailed analysis of mathematics curricula implemented in the Torun lassical Grammar School at the beginning of the twentieth century, the mathematical textbooks then used and school-leaving examinations problems from the years 1905‒1911, the degree of fulfillment of the said postulate of the Merano Programme at the Torun school will be assessed.

Ludwik Silberstein and the operator calculus

Flin, Piotr, Bajan, Katarzyna, Godłowski, Włodzimierz
Article
2015
In the article we outline the life of Ludwik Silberstein (1872‒1948). We present his approach to the matrix calculus and its application to the operator form of relativity. We also give the list of books on the subject written by him as well as translated by him.

The emergence of national mathematical research communities in Central-Eastern Europe

Duda, Roman
Article
2015
Since medieval times mathematics was being developed mainly in Central and Western Europe but in the 19th century it greatly expanded both to the United States and to some countries of Central-Eastern Europe. This expansion, accompanied by the rapid growth of mathematics as a whole, has recently become an object of interest and investigation. The interest, however, reflects the Western viewpoint, cf. [17], with the bibliography covering Germany, Spain, Italy, France, Moscow. The aim of this paper is to outline the history of emerging national mathematical research communities in Russia, Poland, Bohemia, Lithuania and some other countries of Central-Eastern Europe.