This book tries to show beginning biology majors
how mathematics, computer science and biology can
be usefully and pleasurably intertwined.
After the necessary start up costs to develop... More > some
essential calculus tools, we use a few select models to illustrate how these three fields influence each other in interesting and useful ways. Indeed, we believe that the three must be considered as part of a larger whole and that the use of these ideas is perhaps best described as an emergent phenomena! And we must always be careful to make sure our use of mathematics gives us insight. This fourth edition again adds a bit more biology and polishes the mathematical and numerical discussions. In addition,more exercises have been added and additional typographical errors have been found and corrected.< Less
This book introduces a beginning graduate student in Mathematics to the essentials of measure theory. This theory extends the notion of the length of an interval to more general notions of the size... More > of a set. These ideas are then used to build abstract versions of integration theory. We discuss how to build many such measures, Lebesgue and Lebesgue-Stieljes Integration and include a lengthy treatment of classical Riemann and Riemann-Stieljes integration tools
as these are covered very incompletely these days.< Less
This book is a primer on how information is processed in a typical mammalian brain. To talk about these ideas intelligently, the reader needs to use ideas from mathematics, computer science and many... More > areas of science. Intertwining these normally separate areas into a coherent whole provides an introduction to modern interdisciplinary work. In the book, we develop carefully how an excitable neuron collects information from many sources and then outputs a single voltage pulse which carries a variety of signaling information. Our modeling efforts are based on the use of MatLab (although octave is just fine) so it should be easy to do experiments yourself. We cover the usual basics of axonal pulse propagation including Hodgkin-Huxley models, dendritic cable models, first and second messenger signalling system abstractions and so forth. This book provides a good foundation towards building models of cognition which may be used for models of depression and other forms of dysfunction.< Less
In this book, we continue to discuss how to blend mathematics, computational tools and science into a cohesive point of view. Hence, this text is a follow up to our book on mathematics for... More > biologists, Calculus for Biologists. We now add new mathematics such as the ideas of partial differentiation and approximation of functions of more than one variable and a more complete study of nonlinear differential equation models using these new tools. We also discuss more fully how to develop code with MatLab/ Octave to solve our problems numerically. We study a model of the excitable neuron which leads to the cable equation which is a standard equation in biological information processing. We use the cable equation to develop an input side model of an excitable neuron -- the dendrite -- and then build a model of the excitable neuron itself. This consists of a dendrite, a cell body or soma and the axon along which generates the action potential.< Less
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