Biology and Mathematics History and Challenges 1st Edition by Roger Buis 1119663515 9781119663515

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ISBN-10 :  1119663515 

ISBN-13 : 9781119663515

Author:  Roger Buis 

To formalize the dynamics of living things is to search for invariants in a system that contains an irreducible aspect of “fuzziness”, because biological processes are characterized by their large statistical variability, and strong dependence on temporal and environmental factors. What is essential is the identification of what remains stable in a “living being” that is highly fluctuating. The use of mathematics is not limited to the use of calculating tools to simulate and predict results. It also allows us to adopt a way of thinking that is founded on concepts and hypotheses, leading to their discussion and validation. Instruments of mathematical intelligibility and coherence have gradually “fashioned” the view we now have of biological systems. Teaching and research, fundamental or applied, are now dependent on this new order known as Integrative Biology or Systems Biology.

Biology and Mathematics History and Challenges 1st Table of contents:

1 On the Status of Biology: On the Definition of Life
1.1. Causality in biology
1.2. Variability in biology
2 On the Nature of the Contribution Made by Mathematics to Biology
2.1. On the affinity of mathematics with biology
2.2. Mathematics, an instrument of work and thought on biology
3 Some Historical Reference Points: Biology Fashioned by Mathematics
3.1. The first remarkable steps in biomathematics
3.2. Some pertinent contributions from mathematics in the modern era
3.3. Introduction of the notion of a probabilistic model in biology
3.4. The physiology of C. Bernard (1813–1878): the call to mathematics
3.5. The principle of optimality in biology
3.6. Introduction of the formalism of dynamic systems in biology
3.7. Morphogenesis: the need for mathematics in the study of biological forms
3.8. The theory of automatons and cybernetics in biology
3.9. Molecular biology
3.10. Information and communication, important notions in biology
3.11. The property of self-organization in biology
3.12. Systemic biology
3.13. Game theory in biology
3.14. Artificial life
3.15. Bioinformatics
4 Laws and Models in Biology
4.1. Biological laws in literary language
4.2. Biological laws in mathematical language
4.3. Theoretical laws
5 Mathematical Tools and Concepts in Biology
5.1. An old biomathematical subject: describing and/or explaining phyllotaxis
5.2. The notion of invariant and its substrate: time and space
5.3. Continuous formalism
5.4. Discreet formalism
5.5. Spatialized models
5.6. Random processes in biology
5.7. Logic kinetics of regulation

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