Дискретная математика
Математика
  • формат djvu
  • размер 2.91 МБ
  • добавлен 01 ноября 2011 г.
Fritsch R., Fritsch G. The Four-Color Theorem. History, Topological Foundations, and Idea of Proof
Издательство Springer, 1998, -138 pp.

During the university reform of the 1970s, the classical Faculty of Science of the venerable Ludwig-Maximilians-Universit?t in Munich was divided into five smaller faculties. One was for mathematics, the others for physics, chemistry and pharmaceutics, biology, and the earth sciences. Nevertheless, in order to maintain an exchange of ideas between the various disciplines and so as not to permit the complete undermining of the original notion of "universitas" the Carl-Friedrich-yon-Siemens Foundation periodically invites the pro- lessors from the former Faculty of Science to a luncheon gathering. These are working luncheons during which recent developments in the various disciplines are presented by means of short talks. The motivation for such talks does not come, in the majority of cases, from the respective subject itself, but from another discipline that is loosely affiliated with it.
In this way, the controversy over the mode methods used in the proof of the Four-Color Theorem had also spread to disciplines outside of mathematics. I, as a trained algebraic topologist, was asked to comment on this. Naturally, I was acquainted with the Four-Color Problem but, up to that point, had never intensively studied it. As an outsider, z I dove into the material, not so much to achieve any scientific progress with it but to make this already achieved objective more understandable.
My talk on this subject was given in the winter semester of 1987/88, and it generated interest among my colleagues. This brought to mind my primary jurisdiction-the Professorship for Mathematical Education at the University of Munich. I then began to think about how one could make the mathematical workings of the Four-Color Problem more accessible to student and professor alike-many of whom were already fascinated by this famous problem.
This led to a lecture at the 80th gathering of the Deutscher Verein zur F?rderung des mathonatischen und naturwissenschaftlichen Unterrichts (German Association for the Advancement of Teaching in Mathematics and the Sciences), which was held in 1989 in Darmstadt [Fritsch 1990]. The director of B.I. Wissenschaftsverlag, who attended that meeting, approached me about formulating more precisely my thoughts on this matter-from the point of view of an outsider to other interested outsiders. In other words, I was to put them into book form.
Therefore, this book has been written to explain the Four-Color Theorem to a lay readership. It is for this reason that a chapter on the historical development and the people involved in it has also been included. When my efforts conceing the historical side of things bogged down, I managed to persuade my wife to take on this task. She dedicated herself to it wholeheartedly, for which I am truly grateful.

History
(Topological) Maps
The Four-Color Theorem (Topological Version)
Topology to Combinatorics
The Four-Color Theorem (Combinatorial Version)
Reducibility
The Quest for Unavoidable Sets
Похожие разделы
Смотрите также

Erd?s P. Old and New Problems and Results in Combinatorial Number Theory

  • формат djvu
  • размер 1.79 МБ
  • добавлен 04 октября 2011 г.
L'Enseignement Mathematique. University de Geneve, 1980, -128 pp. In the present work we will discuss various problems in elementary number theory, most of which have a combinatorial flavor. In general, we will avoid classical problems, just mentioning references for the interested reader. We will almost never give proofs but on the other hand we will try to give as exact references as we can. We will restrict ourselves mostly to problems on whi...

Fragouli C., Soljanin E. Network Coding Fundamentals

  • формат pdf
  • размер 958.71 КБ
  • добавлен 31 января 2012 г.
Из серии Foundations and Trends in Networking издательства NOWPress, 2007, -149 pp. Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new technique: how network coding works and what are its benefits, how netwo...

Gessel I., Rota G.-C. (eds.) Classic Papers in Combinatorics

  • формат pdf
  • размер 9.82 МБ
  • добавлен 06 января 2012 г.
Издательство Birkh?user, 2009, -501 pp. This volume surveys the development of combinatorics since 1930 by presenting in chronological order the fundamental results of the subject proved in the orginal papers. We begin with the celebrated theorem of Ramsey [1930], originally developed to settle a special case of the decision problem for the predicate calculus with equality. It remains to this day the fundamental generalization of the classical p...

Givant S., Halmos P. Introduction to Boolean Algebras

  • формат pdf
  • размер 3.54 МБ
  • добавлен 24 октября 2011 г.
Издательство Springer, 2009, -588 pp. Серия Undergraduate Texts in Mathematics The theory of Boolean algebras was created in 1847 by the English mathematician George Boole. He conceived it as a calculus (or arithmetic) suitable for a mathematical analysis of logic. The form of his calculus was rather different from the modern version, which came into being during the period 1864–1895 through the contributions of William Stanley Jevons, Augustus...

Kaski P., ?sterg?rd P.R.J. Classification Algorithms for Codes and Designs

  • формат pdf
  • размер 1.99 МБ
  • добавлен 05 декабря 2011 г.
Издательство Springer, 2006, -413 pp. The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classification results. Almost a century earlier, in 1782, Euler [180] published some results on...

Lov?sz L. Combinatorial Problems and Exercises

  • формат djvu
  • размер 3.82 МБ
  • добавлен 04 октября 2011 г.
Издательство North-Holland, 1993, -630 pp. When the publishers of this book asked me to revise and update my problem book for a second edition, I had to decide how much to change, taking into consideration the fast development of the field (but also that the first edition was out of print). Combinatorics has grown a lot in the last decade, especially in those fields interacting with other branches of mathematics, like polyhedral combinatorics,...

Luccio F., Pagli L., Steel G. Mathematical and Algorithmic Foundations of the Internet

  • формат pdf
  • размер 1.68 МБ
  • добавлен 17 августа 2011 г.
Chapman & Hall/CRC, 2011. - 221 pages. To truly understand how the Internet and Web are organized and function requires knowledge of mathematics and computation theory. Mathematical and Algorithmic Foundations of the Internet introduces the concepts and methods upon which computer networks rely and explores their applications to the Internet and Web. The book offers a unique approach to mathematical and algorithmic concepts, demonstrating t...

Ore O. The Four Color Problem

  • формат pdf
  • размер 8.97 МБ
  • добавлен 01 января 2012 г.
N. Y. ; L. : Academic Press, 1967.— xvi, 260 p. Puzzling problems permeate mathematics, and this is probably the strongest reason for the burgeoning growth of this queen of the sciences. The object of this book is to discuss the methods in graph theory that have been developed in the last century for attacking the four-color problem. It may be said without exaggeration concerning the writers on graph theory in this period, that however practical...

Troelstra A.S., Schwichtenberg H. Basic Proof Theory

  • формат djvu
  • размер 4.79 МБ
  • добавлен 31 января 2012 г.
Издательство Cambridge University Press, 1996, -353 pp. The discovery of the set-theoretic paradoxes around the turn of the century, and the resulting uncertainties and doubts concerning the use of high-level abstractions among mathematicians, led D. HUbert to the formulation of his programme: to prove the consistency of axiomatizations of the essential parts of mathematics by methods which might be considered as evident and reliable because of...

Wilson R.J. Introduction to Graph Theory, 4th Edition

  • формат pdf
  • размер 13.09 МБ
  • добавлен 31 января 2011 г.
Addison Wesley – 1996, 184 pages, ISBN: 0582249937. Provides a basic foundation on trees, algorithms, Eulerian and Hamilton graphs, planar graphs and coloring, with special reference to four color theorem. Discusses directed graphs and transversal theory and related these areas to Markov chains and network flows.