Gareth A. Jones - Böcker

Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics.

This book provides an elementary introduction to Information Theory and Coding Theory - two related aspects of the problem of how to transmit information efficiently and accurately. The first part of the book focuses on Information Theory, covering uniquely decodable and instantaneous codes, Huffman coding, entropy, information channels, and Shannon's Fundamental Theorem. In the second part, on Coding Theory, linear algebra is used to construct examples of such codes, such as the Hamming, Hadamard, Golay and Reed-Muller codes.The book emphasises carefully explained proofs and worked examples; exercises (with solutions) are integrated into the text as part of the learning process. Only some basic probability theory and linear algebra, together with a little calculus (as covered in most first-year university syllabuses), is assumed, making it suitable for second- and third-year undergraduates in mathematics, electronics and computer science.

This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications.   In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.

Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications.

This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. The first part of the book presents basic material, guiding the reader through the current field of research. A key point of the second part is the interplay between the automorphism groups of dessins and their Riemann surfaces, and the action of the absolute Galois group on dessins and their algebraic curves. It concludes by showing the links between the theory of dessins and other areas of arithmetic and geometry, such as the abc conjecture, complex multiplication and Beauville surfaces.Dessins d'Enfants on Riemann Surfaces will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic.

This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces.

Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back­ ground or maturity from the reader, and which can be read and understood with no extra assistance.

In 2006 a special semester on Gr. obner bases and related methods was or- nized by RICAM and RISC, directed by Bruno Buchberger and Heinz Engl. The main focus of the semester were the development of the formal theory of Gr. obner bases (brie?y GB), the e?cient implementation of all algorithms related to this theory, and the promotion of recent and new applications of GB. The workshop D1 "Gr. obner bases in cryptography, coding theory and - gebraic combinatorics", Linz, May 1-6, 2006 (chairmen M. Klin, L. Perret, M. Sala) was one of the main ingredients of the semester. The last two days of this workshop, devoted to combinatorics, made it possible to bring together experts in algorithmic problems related to coherent con?gurations and as- ciation schemes with a community of people working in the area of GB. Each side was interested in understanding the computational problems and current algorithmicpossibilitiesoftheother,withaparticularobjectiveofintroducing the practical use of GB in algebraic combinatorics. Materials (mainly slides of lectures and posters) available from the site http://www.ricam.oeaw.ac.at/specsem/srs/groeb/schedule D1.htmlprovidea helpful and vivid picture of the successful exchange of scienti?c information during the workshop D1. Asafollow-uptothespecialsemester,10volumesofproceedingsarebeing published by di?erent publishers. The current collection of papers re?ects diverse investigations in the area of algebraic combinatorics (with or without explicit use of GB), but with a de?nite emphasis on algorithmic approaches.