by René Schott (IECN and LORIA, Université Henri Poincaré, Nancy, France) & G Stacey Staples (Southern Illinois University Edwardsville, USA)

Table of Contents (260k)
Preface (134k)
Chapter 1: Introduction (337k)

This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.

Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

• Combinatorial Algebras and Their Properties:
  • Introduction
  • Combinatorial Algebra
  • Norm Inequalities on Clifford Algebras
• Combinatorics and Graph Theory:
  • Specialized Adjacency Matrices
  • Random Graphs
  • Graph Theory and Quantum Probability
  • Geometric Graph Processes
• Probability on Algebraic Structures:
  • Time-Homogeneous Random Walks
  • Dynamic Walks in Clifford Algebras
  • Iterated Stochastic Integrals
  • Partition-Dependent Stochastic Measures
• Operator Calculus:
  • Appell Systems in Clifford Algebras
  • Operator Homology and Cohomology
• Symbolic Computations:
  • Multivector-Level Complexity
  • Blade-Level Complexity
  • Operator Calculus Approach to Minimal Path Problems
  • Symbolic Computations with Mathematica