John Baylis

Bio: John Baylis is an academic researcher from University of Nottingham. The author has contributed to research in topics: Real number & Infinite set. The author has an hindex of 5, co-authored 30 publications receiving 110 citations.

Representations and characters of groups (2nd edn) , by Gordon James and Martin Liebeck. Pp. 458. £24.95. 2001. ISBN 0 521 00392 X (Cambridge University Press).

Abstract: The chapter on paths and networks introduces graph theory and covers the travelling salesman problem, the greedy algorithm and Prim's algorithm. Tilings and polyhedra are the subject of the next chapter, whilst the final chapter is devoted to game theory and an introduction to linear programming. The penultimate chapter is entitled Number Theory and begins with primes, divisors (but only mentions Euclid's algorithm for GCD as an extension item), modular arithmetic and divisibility tests. It then covers check digits (including bar codes and ISBN) and tournament scheduling, before embarking upon a brief introduction to cryptology.

Cyclic and negacyclic codes over finite chain rings

Abstract: The structures of cyclic and negacyclic codes of length n and their duals over a finite chain ring R are established when n is not divisible by the characteristic of the residue field R~. Some cases where n is divisible by the characteristic of the residue field R~ are also considered. Namely, the structure of negacyclic codes of length 2/sup t/ over /spl Zopf//sub 2//sup m/ and that of their duals are derived.

A first course in coding theory, by Raymond Hill. Pp 251. £12·50. 1986. ISBN 0-19-853803-0 (Oxford University Press)

Abstract: Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

An Onto-Semiotic Analysis of Combinatorial Problems and the Solving Processes by University Students

Abstract: In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of combinatorial reasoning. We finally analyze the implications of the theoretical model and type of analysis presented for mathematics education research and practice.

Ramanujan sums as supercharacters

Abstract: The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, is used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality.

On the maneuvering of vehicles

Abstract: Equations are derived to govern the motion of vehicles which move on rolling wheels. A relation between the centers of curvature of the trajectories of the wheels and the center of rotation of the vehicle is established. From this relation the general kinematic laws of motion are derived. Applications to questions of offtracking (the difference between the trajectories of the front and back wheels of the vehicle) and optimal steering (how to steer around a tight corner) are considered.