From the 1 of 10 linked papers with an AI index.
10 papers
Elementary Real Analysis
Martin Klazar
A preliminary textbook covering the fundamentals of univariate real analysis, including numeric domains, limits, series, functions, continuity, differentiation, and various integra…
The transcendence of via formal power series
Martin Klazar
We review Hilbert's classical analytical proof of the transcendence of the number . Then, we show how this result can be obtained algebraically by means of formal power…
Extending the symbolic method in enumerative combinatorics. I
M. Klazar, R. Horský
We use our extension of the symbolic method in enumerative combinatorics (we extend finite sums defining coefficients in generating functions to infinite series) to generalize Pól…
Thomassen's proof and Filippov's proof of the Weak Jordan Theorem
Martin Klazar
We present, in detail and with a modern rigor, the two title proofs. The Weak Jordan Theorem (WJT) states that the complement of any topological circuit in the plane is disconnecte…
Cardinalities in proofreading
Martin Klazar
In 1975, G. Pólya suggested that if two proofreaders found and errors in a text, of which errors were found by both of them, then a reasonable approximation of the unk…
Catalan's conjecture is MihÄilescu's theorem
Martin Klazar
This text evolves from the lecture notes for my course on Catalan's conjecture in winter term 2025/26. The ultimate goal is to give full details of MihÄilescu's proof. Current cha…