by Leonard Soicher, Franco Vivaldi
Publisher: Queen Mary University of London 2004
Number of pages: 94
This text contains sufficient material for a one-semester course in mathematical algorithms, for second year mathematics students. The course requires some exposure to the basic concepts of discrete mathematics, but no computing experience. The aim of this course is twofold. Firstly, to introduce the basic algorithms for computing exactly with integers, polynomials and vector spaces. In doing so, the student is expected to learn how to think algorithmically and how to design and analyze algorithms. Secondly, to provide a constructive approach to abstract mathematics, algebra in particular. When introducing the elements of ring and field theory, algorithms offer concrete tools, constructive proofs, and a crisp environment where the benefits of rigour and abstraction become tangible. We shall write algorithms in a straightforward language, which incorporates freely standard mathematical notation. The specialized constructs are limited to the if-structure and the while-loop, which are universal.
Home page url
Download or read it online for free here:
The aim of this text is to develop an informal, light introduction to the world of fractal geometry and to inspire further research into the subject, whether your interest is of a pure, applied or even recreational nature.
by T. Nipkow, L.C. Paulson, M. Wenzel - Springer
This book is a self-contained introduction to interactive proof in higher-order logic, using the proof assistant Isabelle. It is a tutorial for potential users. The book has three parts: Elementary Techniques; Logic and Sets; Advanced Material.
by Jean Gallier - Morgan Kaufmann
This book offers both a theoretically unifying understanding of polynomial curves and surfaces and an effective approach to implementation that you can bring to bear on your own work -- whether you are a graduate student, scientist, or practitioner.
The purpose of this book is to show how the computer can draw technically perfect pictures of Julia and Mandelbrot sets. All the necessary theory is explained and some words are said about how to put the things into a computer program.