Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory

Introduction.- A new look at the position operator in quantum theory.- Basic properties of de Sitter quantum theories.- Algebraic description of irreducible representations.- Two-body systems in discrete basis.- Why finite mathematics is the most general and finite quantum theory is more pertinent physical theory than standard one.- Semiclassical states in modular representations.- Basic properties of anti-de Sitter quantum theories.- Dirac singletons as the only true elementary particles.- A conjecture on the nature of time 11. Discussion and conclusion