Algorithmic Mathematics
by Leonard Soicher, Franco Vivaldi
Publisher: Queen Mary University of London 2004
Number of pages: 94
Description:
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.
Download or read it online for free here:
Download link
(0.5MB, PDF)
Similar books
by Joseph O'Rourke - Oxford University Press
Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas.
(20907 views)
by Allen B. Downey - Green Tea Press
Think Stats is an introduction to Probability and Statistics for Python programmers. This new book emphasizes simple techniques you can use to explore real data sets and answer interesting statistical questions. Basic skills in Python are assumed.
(23188 views)
by Thomas Hales - arXiv
Computers have rapidly become so pervasive in mathematics that future generations may look back to this day as a golden dawn. The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
(16568 views)
by Jonathan M. Borwein - DocServer
The desire to understand Pi, the challenge, and originally the need, to calculate ever more accurate values of Pi, has challenged mathematicians for many many centuries, and Pi has provided compelling examples of computational mathematics.
(20625 views)