Section I: Symmetrical Analysis Techniques and Symbolic Matrices of Matrix Genetics

Chapter I: Genetic Code: Emergence of Symmetrical Pattern, Beginnings of Matrix Genetics

Introduction and background
Significance of symmetrical patterns for biology, molecular genetics and bioinformatics
Information science, noise immunity and the matrix approach to the genetic code
The basic structures of the genetic code
The binary sub-alphabets of the genetic alphabet for numbering the multiplets in genetic matrices
The natural system of numbering the genetic multiplets
The matrix numbering the genetic multiplets and matrices of diadic shifts
Future trends and conclusion

Chapter II: Symmetries of Degeneracy of The Vertebrate Mitochondrial Code in The Matrix Form

Introduction and background
Peculiarities of degeneracy of the genetic code
Symmetrical properties of genetic matrices of triplets under permutations of positions inside triplets
Genomatrices with the property of the tetra-self-reproducing
Symmetrical properties of genetic matrices under alphabetic permutations in the set of 64 triplets
Future trends and conclusion

Chapter III: Biological Evolution of Dialects of The Genetic Code

Introduction and background
Phenomenological rules of evolution of known dialects of genetic codes
The chronocyclic conception and the degeneracy in the dialects of the genetic code
Why 20 amino-acids?
Future trends and conclusion

Section II: Symmetrical Analysis Techniques and Numeric Matrices of The Genetic Code

Chapter IV: Numeric Genomatrices of Hydrogen Bonds, The Golden Section, Musical Harmony and Aesthetic Feelings

Introduction and background
Numeric genomatrices of hydrogen bonds
The numeric genomatrices and the golden section
The genomatrices, musical harmony and Pythagorean musical scale
A scale of the golden wurf, music and Fibonacci numbers
On harmony of a scale of protons in the set of amino-acids
Future trends and conclusion

Chapter V: Genetic Code and Stochastic Matrices

Introduction and background
Genetic code, Hamming distance, and stochastic matrices
Genetic code, attributive mapping, and stochastic matrices
Genetic code, power of matrices, and stochastic matrices
Future trends and conclusion

Chapter VI: The Genetic Code, Hadamard Matrices, Noise Immunity and Quantum Computers

Introduction and background
The genetic code and Hadamard matrices
About importance of amino-groups NH2
Genetic informatics, Hadamard matrices and quantum computers
Why does the genetic alphabet consist of four letters?
Cyclic shifts, cyclic codes and the principle of molecular economy in genetic informatics
Future trends and conclusion

Section III: Algebras of Genetic Codes

Chapter VII: Genomatrices and the Genetic Octet Yin-Yang-Algebras

Introduction and background
The genetic octet matrix as the matrix form of presentation of the octet algebra
The alphabetic algorithm of the Yin-Yang-digitization of 64 triplets
The genomatrix YY8 as the element of the octet Yin-Yang-algebra
The structural analogies between the genomatrix [C A; G U](3) and the matrix YY8
The six kinds of the genetic octet Yin-Yang-algebras connected with permutations of positions in triplets
The genetic Yin-Yang octets as “double genoquaternions”
The comparison between the classical vector calculation and the genovector calculation
The parametric reduction of the genetic octet Yin-Yang-algebra to the 4-dimensional algebra of tetrions
About genetic mechanics and the idea by Pythagoras
What is life from the viewpoint of algebra? The problem of algebraization of bioinformatics and biology
Solutions and recommendations
Future trends and conclusion

Chapter VIII: The Evolution of the Genetic Code From The Viewpoint of The Genetic 8-Dimensional Yin-Yang-Algebra

Introduction and background
The comparison analysis and phenomenological rules of dialects of the genetic code
The molecular-sexual approach in molecular genetics
The example of the pairs of histones
Whether an unknown quantum mechanical factor of a “sexual attraction” among genetic molecules exists?
The analysis of the insulin structure as the simplest example
Some applications of results of matrix genetics in bioinformatics and algebraic biology
Solutions and recommendations
Future trends and conclusion

Chapter IX: Multidimensional Numbers and the Genomatrices of Hydrogen Bonds

Introduction and background
The hyperbolic matrions as a special kind of hypercomplex numbers
The circular matrions
The rules of eigenvalues of matrices of circular matrions
Circular matrions and the series of natural numbers
Solutions and recommendations
Future trends and conclusion

Section IV: Connections of Matrix Genetics With Other Fields of Science and Culture

Chapter X: Genetic System, Fibonacci Numbers and Phyllotaxis Laws

Introduction and background
Fibonacci’s matrices and biological laws of phyllotaxis
Additional facts about the golden section and matrices
Hadamard matrices, projective geometry and the golden wurf
Future trends and conclusion

Chapter XI: Physiological Cycles and Their Algebraic Models in Matrix Genetics

Introduction and background
Revealing new genetic algebras as a result of cyclic permutations of genetic elements
The oppositional category of genetic Yin-Yang-matrices
Generative and suppressive properties of yin-yang-matrices of the two categories
Joining of the idea by Pythagoras and the idea of cyclic changes: about cellular automata, neurocomputers and a notion of biological time
Solutions and recommendations
Future trends and conclusion

Chapter XII: Matrix Genetics and Culture

Introduction and background
Genetic code and linguistics
The genetic code, a color perception and a color communication
Parallels between patterns of the genetic code and patterns of "I Ching"
Musical harmony in the matrices of the genetic code and of “I Ching”
Future trends and conclusion