Ingo Althöfer - Böcker

This collection of articles is published in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, "Numbers and Combinations", "Information Theory" (channels and networks, combinatorial and algebraic coding, cryptology, with the related fields data compression, entropy theory, symbolic dynamics, probability and statistics), and "Complexity". Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to natural sciences are discussed.

Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, 'Numbers and Combinations', 'Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and 'Complexity'. Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on Combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to Natural Sciences are discussed.

The fifth volume of Rudolf Ahlswede’s lectures on Information Theory focuses on several problems that were at the heart of a lot of his research. After a short Part II on continuous data compression, Part III, the longest part of the book, is devoted to distributed information.

The sixth volume of Rudolf Ahlswede's lectures on Information Theory is focused on Identification Theory. The theory of identification has now developed into a sophisticated mathematical discipline with many branches and facets, forming part of the Post Shannon theory in which Ahlswede was one of the leading experts.

Cai’s passion for science inspired his collaborators across the fields of classical and quantum information theory, combinatorics, computation, post-Shannon theory, and coding theory, and the contributions in this volume reflect his success as a researcher and mentor.

The volume “Storing and Transmitting Data” is based on Rudolf Ahlswede's introductory course on "Information Theory I" and presents an introduction to Shannon Theory. This is the first of several volumes that will serve as a collected research documentation of Rudolf Ahlswede’s lectures on information theory.

The calculation of channel capacities was one of Rudolf Ahlswede's specialties and is the main topic of this second volume of his Lectures on Information Theory. Here we find a detailed account of some very classical material from the early days of Information Theory, including developments from the USA, Russia, Hungary and (which Ahlswede was probably in a unique position to describe) the German school centered around his supervisor Konrad Jacobs. These lectures made an approach to a rigorous justification of the foundations of Information Theory. This is the second of several volumes documenting Rudolf Ahlswede's lectures on Information Theory. Each volume includes comments from an invited well-known expert. In the supplement to the present volume, Gerhard Kramer contributes his insights. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

Devoted to information security, this volume begins with a short course on cryptography, mainly basedon lectures given by Rudolf Ahlswede at the University of Bielefeld in the mid1990s. It was the second of his cycle of lectures on information theory whichopened with an introductory course on basic coding theorems, as covered inVolume 1 of this series. In this third volume, Shannon’s historical work onsecrecy systems is detailed, followed by an introduction to aninformation-theoretic model of wiretap channels, and such important concepts ashomophonic coding and authentication. Once the theoretical arguments have beenpresented, comprehensive technical details of AES are given. Furthermore, ashort introduction to the history of public-key cryptology, RSA and El Gamalcryptosystems is provided, followed by a look at the basic theory of ellipticcurves, and algorithms for efficient addition in elliptic curves. Lastly, theimportant topic of “oblivious transfer” is discussed, which is stronglyconnected to the privacy problem in communication. Today, the importance ofthis problem is rapidly increasing, and further research and practical realizationsare greatly anticipated.This is the third of several volumes serving as thecollected documentation of Rudolf Ahlswede’s lectures on information theory.Each volume includes comments from an invited well-known expert. In thesupplement to the present volume, Rüdiger Reischuk contributes his insights.Classicalinformation processing concerns the main tasks of gaining knowledge and thestorage, transmission and hiding of data. The first task is the prime goal ofStatistics. For transmission and hiding data, Shannon developed an impressivemathematical theory called Information Theory, which he based on probabilisticmodels. The theory largely involves the concept of codes with small errorprobabilities in spite of noise in the transmission, which is modeled bychannels. The lectures presentedin this work are suitable for graduatestudents in Mathematics, and also for those working in Theoretical ComputerScience, Physics, and Electrical Engineering with a background in basicMathematics. The lectures can be used as the basis for courses or to supplementcourses in many ways. Ph.D. students will also find research problems, oftenwith conjectures, that offer potential subjects for a thesis. More advancedresearchers may find questions which form the basis of entire researchprograms.

The volume “Storing and Transmitting Data” is based on Rudolf Ahlswede's introductory course on "Information Theory I" and presents an introduction to Shannon Theory. Readers, familiar or unfamiliar with the technical intricacies of Information Theory, will benefit considerably from working through the book; especially Chapter VI with its lively comments and uncensored insider views from the world of science and research offers informative and revealing insights. This is the first of several volumes that will serve as a collected research documentation of Rudolf Ahlswede’s lectures on information theory. Each volume includes comments from an invited well-known expert. Holger Boche contributed his insights in the supplement of the present volume.Classical information processing concerns the main tasks of gaining knowledge, storage, transmitting and hiding data. The first task is the prime goal of Statistics. For the two next, Shannon presented an impressive mathematical theorycalled Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also in Theoretical Computer Science, Physics, and Electrical Engineering with background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find the basis of entire research programs.

The calculation of channel capacities was one of Rudolf Ahlswede's specialties and is the main topic of this second volume of his Lectures on Information Theory. Here we find a detailed account of some very classical material from the early days of Information Theory, including developments from the USA, Russia, Hungary and (which Ahlswede was probably in a unique position to describe) the German school centered around his supervisor Konrad Jacobs. These lectures made an approach to a rigorous justification of the foundations of Information Theory. This is the second of several volumes documenting Rudolf Ahlswede's lectures on Information Theory. Each volume includes comments from an invited well-known expert. In the supplement to the present volume, Gerhard Kramer contributes his insights. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

The fourth volume of Rudolf Ahlswede’s lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon’s zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem.A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring and covering techniques and their applications are introduced in this book. Furthermore, codes produced by permutations and one of Ahlswede’s favourite research fields -- extremal problems in Combinatorics -- are presented.   Whereas the first part of the book concentrateson combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory. Here the code concept already relies on a rather combinatorial structure, as in several concrete models of multiple access channels or more refined distortions. An analytical tool coming into play, especially during the analysis of perfect codes, is the use of orthogonal polynomials.Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presentedin this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.

Devoted to information security, this volume begins with a short course on cryptography, mainly basedon lectures given by Rudolf Ahlswede at the University of Bielefeld in the mid1990s.

Whereas the first part of the book concentrateson combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory.

Auf breiter fachlicher Ebene werden in dem Lehrbuch einfache elementare zahlentheoretische Inhalte besprochen, aber auch Stoffkomplexe aus der analytischen und algebraischen Zahlentheorie dargestellt. Das Buch bietet so auf überschaubaren mathematischen Niveau einen Einstieg in ausgewählte Themen der Zahlentheorie. Sämtliche Kapitel enthalten umfassend Beispiele, Übungsaufgaben mit Lösungen, Abbildungen und ausführlich durchgerechnete Beweise, so dass es sich sehr gut zur Prüfungsvorbereitung eignet.

Wie kann man das Mühle-Spiel vor dem Remis-Tod retten? Wie werden heutzutage neue Spiele erfunden? Welche Varianten des Sudokus lohnen einen näheren Blick?Die Autoren berichten Ihnen Spannendes und Amüsantes, Anregendes und Herausforderndes aus den folgenden vier großen Bereichen:Sie lernen fünf moderne 2-Personen-Spiele und ihre Geschichten kennen: Lasker-Mühle, Havannah, Clobber, EinStein würfelt nicht, Yavalath.Ausgehend von dem Sudoku, dem bekanntesten Vertreter, werden Sie in die Welt logischer Rätsel eingeführt. Dabei werden sowohl konkrete Rätselarten vorgestellt als auch allgemeine mathematische Hintergründe diskutiert.Erzählt und diskutiert wird die Computerisierung des Leistungs-Schachs, mit dem 3-Hirn-Ansatz als einem Schwerpunkt und eDoping als einem anderen.Aus der Wunderwelt der Zahlen werden zwei Experimente in Text und Bild vorgestellt: Transport-Optimierung in Ritterspordanien und Tanzfigurenin der komplexen Zahlen-Ebene.Ingo Althöfer ist angewandter Mathematiker an der Universität Jena. Spielen und Spiele sind seine Leidenschaft. Roland Voigt ist Diplom-Mathematiker aus Leipzig und beschäftigt sich seit vielen Jahren mit logischen Rätseln.