"Fibonacci Arithmetic, Coding and Computers"
For the students who learn the computer theory and design the course "Fibonacci Arithmetic, Coding and Computers" is rather useful and interesting.
Program of the course:
 Number systems. Basic concepts and definitions. Positional and nonpositional notations. A little of a history. Radix of notation. Requirements to notations. Canonical positional notations. Binary notations and binary arithmetic. Special binary notations. Conversion algorithms of numbers from one notation in other. Optimal radix for notations. Symmetrical notations. Ternary symmetrical notation and ternary arithmetic. Negapositional notations and arithmetics. Notations with the complex radix. Factorial notation. Notation in residual classes.
 Golden Section and Fibonacci Numbers. Golden Section problem. Algebraic and geometric properties of the golden section. Fibonacci and Lucas numbers. Generalized Fionacci numbers. Generalized golden sections. Fibonacci Qmatrix. Generalized Fibonacci matrices.
 Algorithmic measurement theory. Fibonacci's "weighing problem". Asymmetry principle of measurement. Classical measurement algorithms. "Binary" measurement algorithm and its generalization. Measurement algorithms based on Pascal Triangle. Fibonacci measurement algorithms.
 Fibonacci codes and arithmetic. Fibonacci representation. Zeckendorf representation. Redundancy of Fibonacci codes. Fibonacci addition and subtraction. Fibonacci multiplication and division. Basic micro operations. Noisetolerant Fibonacci arithmetic. Concept of Fibonacci computer. Fibonacci selfsynchronization codes.
 Bergman's notation. Mathematical properties of the "Tausystem". Multiplicity of number representation. Zproperty of natural numbers. F è Lcodes. "Golden" arithmetic. Notations based on generalized golden proportions. New definition of a number.
 Ternary mirrorsymmetrical notation. Number conversion from the "Tausystem to the ternary "golden" representation. Ternary F and Lcodes. Property of "mirror symmetry". Representation of negative numbers. Range of number representation. Redundancy of the ternary mirrorsymmetrical representation. Ternary mirrorsymmetrical addition and subtraction. "Swing"phenomenon. Ternary mirrorsymmetrical multiplication and division. Mirrorsymmetrical representation with the floating point. Ternary flipflapflop. Ternary mirrorsymmetrical adder.
 "Golden" analogtodigit and digittoanalog converters. Resistive divisor for the "Tausystem". Resistive divisor for the ternary mirrorsymmetrical number system. Digittoanalog converters for number systems with irrational radices. Selfcorrecting analogtodigit converters.
 Coding theory based on Fibonacci matrices. Coding based on the Qmatrix. Error detection. Basic check correlation for Fibonacci coding. Error correction. Fibonacci coding based on the generalized Fibonacci matrices. Application to cryptography.
