Mathematics for Neuroscientists 1st Edition by Fabrizio Gabbiani (PDF)

Description

Virtually all scientific problems in neuroscience require mathematical analysis, and all neuroscientists are increasingly required to have a significant understanding of mathematical methods. There is currently no comprehensive, integrated introductory book on the use of mathematics in neuroscience; existing books either concentrate solely on theoretical modeling or discuss mathematical concepts for the treatment of very specific problems. This book fills this need by systematically introducing mathematical and computational tools in precisely the contexts that first established their importance for neuroscience. All mathematical concepts will be introduced from the simple to complex using the most widely used computing environment, Matlab. This book will provide a grounded introduction to the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a springboard to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students.A very didactic and systematic introduction to mathematical concepts of importance for the analysis of data and the formulation of concepts based on experimental data in neuroscienceProvides introductions to linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processesIntroduces numerical methods used to implement algorithms related to each mathematical conceptIllustrates numerical methods by applying them to specific topics in neuroscience, including Hodgkin-Huxley equations, probabilities to describe stochastic release, stochastic processes to describe noise in neurons, Fourier transforms to describe the receptive fields of visual neuronsAllows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book was what I was looking for, but there are a few weaknesses with the book. One of the obvious difficulties for some individuals would be that there are specific steps in the derivation of equations that the authors skipped a number of steps which would be confusing to someone lacking a certain level of math skills. However with the appropriate level of math skill the discussions are quite good and methodical. Personally, I found the book to contain the material I was look for discussed at an appropriate level for me with an engineering degree. Overall, the book seems a little too much for a biologist and for a mathematician or physicist the book is a little lacking except in the biology. I do agree with another reviewer that the title is not adequate, but I would suggest the title as “Mathematics for Neuroscience” or “Application of Mathematics in Neuroscience”.

⭐Life saver for the electrophysiologist trying to understand more of the math behind our science. You will get the best use out of this text with access to MathLab.

⭐I have mixed feelings about this book, which is why I gave it 3.5/5 stars. (Unfortunately, Amazon forces you to round to an integer value, and I felt 3 was more appropriate than 4.)On one hand, it is one of the few sources that cover all of the math you will need to do research in computational neuroscience. (In fact, it pretty much covers all the math anyone would ever need to do research in computational neuroscience – you don’t necessarily need to go this deep into mathematical methods to do comp. neurosci. research.) On the other hand, I feel that the title is somewhat misleading – a better title might be “Neuroscience for Mathematicians and Physicists”. I suspect that it would be hard to actually learn the mathematics covered in this book from this book. Rather, this seems more appropriate for researchers who already have a solid understanding of the relevant mathematical methods and who want to learn how to apply them to problems in neuroscience. That isn’t a bad thing, (indeed, this probably has the most encyclopedic coverage of mathematical methods for neuroscience), but I doubt I would recommend this to graduate students coming into computational neuroscience from the neuroscience/biology side of the field.Readers who would prefer an approach that assumes an understanding of the biological systems, rather than an understanding of the math, would appreciate Sterratt et al.’s “Principles of Computational Modelling in Neuroscience” and Izhikevich’s “Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting”. The latter, in particular, does a superb job of developing readers’ understanding of the math without assuming a particularly strong math background.

⭐this is a first class mathematics book both for neurosciences but students studying advanced mathematics.it is well set out with good examples

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