In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form understandable by undergraduate students of mathematics.

This paper examines six theoretical reasons for considering the application of quantum theory to human cognition. It also presents six empirical examples that –while puzzling from a classic probability framework –are coherently explained by a quantum approach. Quantum physics was created to explain puzzling …ndings that were impossible to understand using the older classical physical theory. In...

In cognitive load theory, the superiority of Example-Problem sequence over Problem-Example has become a classic paradigm. The comparative effectiveness these sequences, however,...

We introduce a method for obtaining provable polynomial time solutions of problems in nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and more efficient than earlier methods. After demonstrating its applicability to the major classic nonabelian protocols, we use this method to cryptanalyze the Triple Decomposition key exchange protocol, the only classic gro...

This chapter describes widespread methods of model-based fuzzy control systems. The subject of this chapter is a systematic framework for the stability and design of nonlinear fuzzy control systems. We are trying to build a bridge between conventional fuzzy control and classic control theory. By building this bridge, the strong well developed tools of classic control could be used in model-base...

We describe Richardson's functor from the Diophantine equations and Diophantine problems into elementary real-valued functions and problems. We then derive a general undecidability and incompleteness result for elementary functions within ZFC set theory, and apply it to some problems in Hamiltonian mechanics and dynamical systems theory. Our examples deal with the algorithmic impossibility of d...

This is a chapter for the forthcoming Handbook of Rational and Social Choice, Paul Anand, Prasanta Pattanaik, and Clemens Puppe, eds., Oxford University Press, 2008. We review classic normative expected utility theory. Our goal is to frame the subsequent chapters (which consider more modern extensions to and deviations from this classic theory) in a way that is accessible to the nonspecialist b...

The classic central limit theorem and α-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the random variables that are being summed. A generalization of the BG theory, usually referred to as nonextensive statistical mechanics and characterized by the index ...