This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called Chargaffs grammar of biology by providing the conceptual theoretical framework necessary to generalize Chargaffs rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.

Michel Eduardo Beleza Yamagishi is a senior researcher at Embrapa Informática Agropecuária, working at Embrapa Multiuser Bioinformatics Laboratory. He holds a PhD (2001) and a Masters in Applied Mathematics from the University of Campinas (Unicamp). His fields of research include bioinformatics, genomics and optimization problems.

Chapter 01- Introduction.- Chapter 02- Modeling Human Nucleotide Frequencies.- Chapter 03- Expanding the Grammar of Biology.- Chapter 04 - "In God We Trust; All Others, Bring Data."- References.