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Sturm oscillation and comparison theorems
 Proc. Sturm 200th Birthday Conference
, 2003
"... Abstract. This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author. 1. ..."
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Abstract. This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author. 1.
Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
Minimum Area Venn Diagrams Whose Curves are Polyominoes
"... While working at the Berlin Academy, the renowned Swiss mathematician Leonard Euler was asked ..."
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While working at the Berlin Academy, the renowned Swiss mathematician Leonard Euler was asked
Early Writings on Graph Theory: Topological Connections
"... The earliest origins of graph theory can be found in puzzles and game, including Euler’s Königsberg Bridge Problem and Hamilton’s Icosian Game. A second important branch of mathematics that grew out of these same humble beginnings was the study of position (“analysis situs”), known today as topology ..."
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The earliest origins of graph theory can be found in puzzles and game, including Euler’s Königsberg Bridge Problem and Hamilton’s Icosian Game. A second important branch of mathematics that grew out of these same humble beginnings was the study of position (“analysis situs”), known today as topology 1. In this project, we examine some important connections between algebra, topology
WDS'07 Proceedings of Contributed Papers, Part I, 251–256, 2007. ISBN 9788073780234 © MATFYZPRESS
"... Abstract. The present paper is dedicated to Felix Klein (1849–1925), one of the leading German mathematicians in the second half of the 19th century. It gives a brief account of his professional life. Some of his activities connected with the reform of mathematics teaching at German schools are ment ..."
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Abstract. The present paper is dedicated to Felix Klein (1849–1925), one of the leading German mathematicians in the second half of the 19th century. It gives a brief account of his professional life. Some of his activities connected with the reform of mathematics teaching at German schools are mentioned as well. In the following text, we describe fundamental ideas of his Erlanger Programm in more detail. References containing selected papers relevant to this theme are attached.
“Es steht schon bei Dedekind ” 1 Lecture at the DM/Algebra Seminar on 11/4/2005.
"... The content of this lecture is influenced very much by writings and translations by John Stillwell, and several books at the end of these notes which I highly recommend. The most important thing I wish to share is the realization of the similarity between several contributions by R. Dedekind to mode ..."
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The content of this lecture is influenced very much by writings and translations by John Stillwell, and several books at the end of these notes which I highly recommend. The most important thing I wish to share is the realization of the similarity between several contributions by R. Dedekind to modern mathematics: residue classes, the theory of real numbers and the theory of ideals. These notes are very rough and informal; I did not make any serious attempt to polish them. Some comments I made during the lecture may be missing: I forgot what exactly I said, and I do not believe that some of them were really important. On the other hand, several remarks that I planned to make at the lecture, and did not because of the shortage of time, are included in these notes. I do assume that most listeners had at least one course of abstract algebra or number theory, but it will be easier for those who had two. 1. When we think how we came to like mathematics, or how our tastes were formed, or which were the most memorable moments, we can make a relatively short list of these events. Thinking about this lecture I compounded about twenty five, with about five being major. To me, one of the most cherished events are those when mathematical facts which were disjoint in my mind, suddenly come together, and