Wrocław, Poland

Bachelor's

Field of studies: Mathematics

Language: Polish

Subject area: mathematics and statistics

Kind of studies: full-time studies

University website: uni.wroc.pl/en/

Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.

Data ( DAY-tə, DAT-ə, DAH-tə) is a set of values of qualitative or quantitative variables.

Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains.

Government, in the last analysis, is organized opinion. Where there is little or no public opinion, there is likely to be bad government, which sooner or later becomes autocratic government.

William Lyon Mackenzie King, Message of the Carillon (1927)

My work in the future must be devoted entirely to pure mathematics in its abstract meaning. I shall apply all my strength to bring more light into the tremendous obscurity which one unquestionably finds in analysis. It lacks so completely all plan and system that it is peculiar that so many can have studied it. The worst of it is, it has never been treated stringently. There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general, and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes. It is really interesting to seek the cause.

Niels Henrik Abel, Letter to Professor Christoffer Hansteen (1826) Oeuvres Complètes de N. H. Abel, mathematician, Nouvelle edition (1881) ed., Peter Ludwig Mejdell Sylow & Sophus Lie, Vol. 2, pp. 263-265, as quoted by Øystein Ore, Niels Henrik Abel: Mathematician Extraordinary (1957) p. 113.

Now analysis is of two kinds, the one directed to searching for the truth and called theoretical, the other directed to finding what we are told to find and called problematical. (1) In the theoretical kind we assume what is sought as if it were existent and true, after which we pass through its successive consequences, as if they too were true and established by virtue of our hypothesis, to something admitted: then (a), if that something admitted is true, that which is sought will also be true and the proof will correspond in the reverse order to the analysis, but (b), if we come upon something admittedly false, that which is sought will also be false. (2) In the problematical kind we assume that which is propounded as if it were known, after which we pass through its successive consequences, taking them as true, up to something admitted: if then (a) what is admitted is possible and obtainable, that is, what mathematicians call given, what was originally proposed will also be possible, and the proof will again correspond in reverse order to the analysis, but if (b) we come upon something admittedly impossible, the problem will also be impossible.

Pappus, (c. 330 AD) as quoted by Thomas Little Heath, The Thirteen Books of Euclid's Elements (1908) Vol. 1, Ch. IX. §6.

50-137 Wrocław

pl. Uniwersytecki 1

tel. +48 71 375 22 15

tel. +48 71 375 20 11

pl. Uniwersytecki 1

tel. +48 71 375 22 15

tel. +48 71 375 20 11