Mathematics for Neuroscientists

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 neuroscience Provides introductions to linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processes Introduces numerical methods used to implement algorithms related to each mathematical concept Illustrates 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 neurons Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework

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  • Author : Fabrizio Gabbiani
  • Publisher : Academic Press
  • Pages : 498 pages
  • ISBN : 9780080890494
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKMathematics for Neuroscientists

Mathematics for Neuroscientists

Mathematics for Neuroscientists
  • Author : Fabrizio Gabbiani,Steven James Cox
  • Publisher : Academic Press
  • Release : 16 September 2010
GET THIS BOOKMathematics for Neuroscientists

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.

Mathematical Foundations of Neuroscience

Mathematical Foundations of Neuroscience
  • Author : G. Bard Ermentrout,David H. Terman
  • Publisher : Springer Science & Business Media
  • Release : 01 July 2010
GET THIS BOOKMathematical Foundations of Neuroscience

This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve

Mathematical Neuroscience

Mathematical Neuroscience
  • Author : Stanislaw Brzychczy,Roman R. Poznanski
  • Publisher : Academic Press
  • Release : 16 August 2013
GET THIS BOOKMathematical Neuroscience

Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally

Music, Math, and Mind

Music, Math, and Mind
  • Author : David Sulzer
  • Publisher : Columbia University Press
  • Release : 27 April 2021
GET THIS BOOKMusic, Math, and Mind

Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas? This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. David Sulzer, also known in

MATLAB for Neuroscientists

MATLAB for Neuroscientists
  • Author : Pascal Wallisch,Michael E. Lusignan,Marc D. Benayoun,Tanya I. Baker,Adam Seth Dickey,Nicholas G. Hatsopoulos
  • Publisher : Academic Press
  • Release : 09 January 2014
GET THIS BOOKMATLAB for Neuroscientists

MATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that a wide variety of computational problems can be addressed in a single programming environment. This updated edition features additional

The Oxford Handbook of Numerical Cognition

The Oxford Handbook of Numerical Cognition
  • Author : Roi Kadosh,Ann Dowker
  • Publisher : OUP Oxford
  • Release : 30 July 2015
GET THIS BOOKThe Oxford Handbook of Numerical Cognition

How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using

Signal Processing for Neuroscientists

Signal Processing for Neuroscientists
  • Author : Wim van Drongelen
  • Publisher : Elsevier
  • Release : 18 December 2006
GET THIS BOOKSignal Processing for Neuroscientists

Signal Processing for Neuroscientists introduces analysis techniques primarily aimed at neuroscientists and biomedical engineering students with a reasonable but modest background in mathematics, physics, and computer programming. The focus of this text is on what can be considered the ‘golden trio’ in the signal processing field: averaging, Fourier analysis, and filtering. Techniques such as convolution, correlation, coherence, and wavelet analysis are considered in the context of time and frequency domain analysis. The whole spectrum of signal analysis is covered, ranging

Proceedings of the 13th International Congress on Mathematical Education

Proceedings of the 13th International Congress on Mathematical Education
  • Author : Gabriele Kaiser
  • Publisher : Springer
  • Release : 31 October 2017
GET THIS BOOKProceedings of the 13th International Congress on Mathematical Education

This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices

Understanding Emotions in Mathematical Thinking and Learning

Understanding Emotions in Mathematical Thinking and Learning
  • Author : Ulises Xolocotzin
  • Publisher : Academic Press
  • Release : 12 May 2017
GET THIS BOOKUnderstanding Emotions in Mathematical Thinking and Learning

Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally,

Mathematical and Theoretical Neuroscience

Mathematical and Theoretical Neuroscience
  • Author : Giovanni Naldi,Thierry Nieus
  • Publisher : Springer
  • Release : 20 March 2018
GET THIS BOOKMathematical and Theoretical Neuroscience

This volume gathers contributions from theoretical, experimental and computational researchers who are working on various topics in theoretical/computational/mathematical neuroscience. The focus is on mathematical modeling, analytical and numerical topics, and statistical analysis in neuroscience with applications. The following subjects are considered: mathematical modelling in Neuroscience, analytical and numerical topics; statistical analysis in Neuroscience; Neural Networks; Theoretical Neuroscience. The book is addressed to researchers involved in mathematical models applied to neuroscience.

Brain Signals

Brain Signals
  • Author : Risto J. Ilmoniemi,Jukka Sarvas
  • Publisher : MIT Press
  • Release : 28 May 2019
GET THIS BOOKBrain Signals

A unified treatment of the generation and analysis of brain-generated electromagnetic fields. In Brain Signals, Risto Ilmoniemi and Jukka Sarvas present the basic physical and mathematical principles of magnetoencephalography (MEG) and electroencephalography (EEG), describing what kind of information is available in the neuroelectromagnetic field and how the measured MEG and EEG signals can be analyzed. Unlike most previous works on these topics, which have been collections of writings by different authors using different conventions, this book presents the material in

An Introductory Course in Computational Neuroscience

An Introductory Course in Computational Neuroscience
  • Author : Paul Miller
  • Publisher : MIT Press
  • Release : 02 October 2018
GET THIS BOOKAn Introductory Course in Computational Neuroscience

A textbook for students with limited background in mathematics and computer coding, emphasizing computer tutorials that guide readers in producing models of neural behavior. This introductory text teaches students to understand, simulate, and analyze the complex behaviors of individual neurons and brain circuits. It is built around computer tutorials that guide students in producing models of neural behavior, with the associated Matlab code freely available online. From these models students learn how individual neurons function and how, when connected, neurons

Conversations on Mind, Matter, and Mathematics

Conversations on Mind, Matter, and Mathematics
  • Author : Jean-Pierre Changeux,Alain Connes
  • Publisher : Princeton University Press
  • Release : 27 December 1998
GET THIS BOOKConversations on Mind, Matter, and Mathematics

Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them? Does the physical world actually obey mathematical laws, or does it seem to conform to them simply because physicists have increasingly been able to make mathematical sense of it? Does mathematics constitute a universal language that in principle

Fundamentals of Computational Neuroscience

Fundamentals of Computational Neuroscience
  • Author : Thomas Trappenberg
  • Publisher : Oxford University Press
  • Release : 13 April 2021
GET THIS BOOKFundamentals of Computational Neuroscience

The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the first edition. It introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain. The book covers the introduction and motivation of simplified models of neurons that are suitable for exploring information processing in large brain-like networks. Additionally, it introduces several fundamental networkarchitectures and discusses their relevance for information processing in the brain, giving some examples of

Stochastic Processes in the Neurosciences

Stochastic Processes in the Neurosciences
  • Author : Henry C. Tuckwell
  • Publisher : SIAM
  • Release : 01 January 1989
GET THIS BOOKStochastic Processes in the Neurosciences

This monograph is centered on quantitative analysis of nerve-cell behavior. The work is foundational, with many higher order problems still remaining, especially in connection with neural networks. Thoroughly addressed topics include stochastic problems in neurobiology, and the treatment of the theory of related Markov processes.