Working in mathematical oncology is a slow and difficult process, requiring the acquisition of a special mindset that goes well beyond the usual applications of mathematics and physics. "Mathematical Oncology 2013" presents the most significant recent results in the field of mathematical oncology, highlighting the work of world-class research teams. This innovative volume emphasizes the way different researchers see and approach problems, not just technical results. It covers many of the most important topics related to the mathematical modeling of tumors, including: Free boundaries. Tumors are growing entities, as such their spatial mean field description involves free boundary problems.Constitutive equations. Tumors should be described as nontrivial porous media.Stochastic dynamics. At the end of anti-cancer therapy, a small number of cells remain, whose dynamics is thus inherently stochastic.Noise-induced state transitions. The growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. This may induce phenomena that are mathematically equivalent to phase transitions.Stochastic and fractal geometry. Tumor vascular growth is self-similar.

The intended audience consists of graduate students and researchers in the fields biomathematics, computational and theoretical biology, biophysics and bioengineering, where the phenomenon tumor is acquiring the same relevance as in modern molecular biology."

The future of oncology seems to lie in Molecular Medicine (MM). MM is a new science based on three pillars. Two of them are evident in its very name and are well known: medical science and molecular biology. However, there is a general unawareness that MM is firmly based on a third, and equally important, pillar: Systems Biomedicine. Currently, this term denotes multilevel, hierarchical models integrating key factors at the molecular, cellular, tissue, through phenotype levels, analyzed to reveal the global behavior of the biological process under consideration. It becomes increasingly evident that the tools to construct such complex models include, not only bioinformatics and modern applied statistics, as is unanimously agreed, but also other interdisciplinary fields of science, notably, Mathematical Oncology, Systems Biology and Theoretical Biophysics.

The future of oncology seems to lie in Molecular Medicine (MM). MM is a new science based on three pillars. Two of them are evident in its very name and are well known: medical science and molecular biology. However, there is a general unawareness that MM is firmly based on a third, and equally important, pillar: Systems Biomedicine. Currently, this term denotes multilevel, hierarchical models integrating key factors at the molecular, cellular, tissue, through phenotype levels, analyzed to reveal the global behavior of the biological process under consideration. It becomes increasingly evident that the tools to construct such complex models include, not only bioinformatics and modern applied statistics, as is unanimously agreed, but also other interdisciplinary fields of science, notably, Mathematical Oncology, Systems Biology and Theoretical Biophysics.