By Dmitry A. Kondrashov
With Quantifying Life, Dmitry A. Kondrashov bargains an available advent to the breadth of mathematical modeling utilized in biology at the present time. Assuming just a beginning in highschool arithmetic, Quantifying Life takes an leading edge computational method of constructing mathematical abilities and instinct. via classes illustrated with copious examples, mathematical and programming routines, literature dialogue questions, and computational tasks of assorted levels of trouble, scholars construct and research types according to present learn papers and learn how to enforce them within the R programming language. This interaction of mathematical principles, systematically constructed programming talents, and a extensive choice of organic learn themes makes Quantifying Life a useful advisor for pro existence scientists and the subsequent new release of biologists alike.
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Additional info for Quantifying Life: A Symbiosis of Computation, Mathematics, and Biology
Example. The model for a population of bacteria that doubles every hour is described by the equation, where P0 is initial number of bacteria and P is the population after t hours: Let us define the quantity R = P/P0, so we can say that population increased by a factor of R after t hours. This ratio is a dimensionless quantity because P and P0 have the same dimension of bacterial population, which cancel out. The equation for R can be written as follows: According to dimensional analysis, both sides of the equation have to be dimensionless, so t must also be a dimensionless variable.
Html. net/tikz/. org/ for providing a repository for teaching resources and for connecting colleagues teaching at the interface of mathematics, computation, and biology. This book would not exist without the teachers whom I’ve been privileged to learn from, starting from middle school (School 2 in Pushchino, Russia), Memorial High School in Madison, Wisconsin, Simon’s Rock College of Bard, and the Graduate Program in Applied Mathematics at the University of Arizona. The teachers and mentors to whom I am most indebted are Yelena Gavrilovna Kuznetsova, Victor Levine, William Dunbar, Eileen Handelman, Joseph Watkins, Hermann Flaschka, Joceline Lega, and William Montfort.
Quantities with a dimension can be made dimensionless by dividing them by another quantity with the same dimension and “canceling” the dimensions. For instance, we can express the height of a person as a fraction of the mean height of the population; then the height of a tall person will become a number greater than 1, and the height of a short one will become less than 1. This new dimensionless height does not have units of length—the unit has been divided out by the mean height. This is known as rescaling the quantity by dividing it by a preferred scale.