Mathematics for neuroscientists /:
This book provides 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 stude...
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| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam ; Boston :
Elsevier Academic Press,
2010.
|
| Ausgabe: | 1st ed. |
| Schriftenreihe: | Elsevier science & technology books.
|
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | This book provides 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. The book alternates between mathematical chapters, introducing important concepts and numerical methods, and neurobiological chapters, applying these concepts and methods to specific topics. It covers topics ranging from classical cellular biophysics and proceeding up to systems level neuroscience. Starting at an introductory mathematical level, presuming no more than calculus through elementary differential equations, the level will build up as increasingly complex techniques are introduced and combined with earlier ones. Each chapter includes a comprehensive series of exercises with solutions, taken from the set developed by the authors in their course lectures. MATLAB code is included for each computational figure, to allow the reader to reproduce them. Biographical notes referring the reader to more specialized literature and additional mathematical material that may be needed either to deepen the reader's understanding or to introduce basic concepts for less mathematically inclined readers completes each chapter. 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 Provides implementation examples in MATLAB code, also included for download on the accompanying support website (which will be updated with additional code and in line with major MATLAB releases) Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework. |
| Beschreibung: | 1 online resource (xi, 486 pages) : illustrations (some color) |
| Bibliographie: | Includes bibliographical references (pages 473-482) and index. |
| ISBN: | 9780080890494 0080890490 9780128019061 0128019069 |
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| 245 | 1 | 0 | |a Mathematics for neuroscientists / |c Fabrizio Gabbiani, Steven J. Cox. |
| 250 | |a 1st ed. | ||
| 260 | |a Amsterdam ; |a Boston : |b Elsevier Academic Press, |c 2010. | ||
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| 520 | |a This book provides 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. The book alternates between mathematical chapters, introducing important concepts and numerical methods, and neurobiological chapters, applying these concepts and methods to specific topics. It covers topics ranging from classical cellular biophysics and proceeding up to systems level neuroscience. Starting at an introductory mathematical level, presuming no more than calculus through elementary differential equations, the level will build up as increasingly complex techniques are introduced and combined with earlier ones. Each chapter includes a comprehensive series of exercises with solutions, taken from the set developed by the authors in their course lectures. MATLAB code is included for each computational figure, to allow the reader to reproduce them. Biographical notes referring the reader to more specialized literature and additional mathematical material that may be needed either to deepen the reader's understanding or to introduce basic concepts for less mathematically inclined readers completes each chapter. 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 Provides implementation examples in MATLAB code, also included for download on the accompanying support website (which will be updated with additional code and in line with major MATLAB releases) Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework. | ||
| 504 | |a Includes bibliographical references (pages 473-482) and index. | ||
| 505 | 0 | |a Passive isopotential cell -- Differential equations -- Active isopotential cell -- Quasi-active isopotential cell -- Passive cable -- Fourier series and transforms -- Passive dendritic tree -- Active dendritic tree -- Reduced single neuron models -- Probability and random variables -- Synaptic transmission and quantal release -- Neuronal calcium signaling -- Singular value decomposition and applications -- Quantification of spike train variability -- Stochastic processes -- Membrane noise -- Power and cross spectra -- Natural light signals and phototransduction -- Firing rate codes and early vision -- Models of simple and complex cells -- Stochastic estimation theory -- Reverse-correlation and spike train decoding -- Signal detection theory -- Relating neuronal responses and psychophysics -- Population codes -- Neuronal networks -- Solutions to selected exercises. | |
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Computational neuroscience. |0 http://id.loc.gov/authorities/subjects/sh97006370 | |
| 650 | 0 | |a Computational biology. |0 http://id.loc.gov/authorities/subjects/sh2003008355 | |
| 650 | 0 | |a Neurosciences. |0 http://id.loc.gov/authorities/subjects/sh91006099 | |
| 650 | 0 | |a Neural circuitry. |0 http://id.loc.gov/authorities/subjects/sh85091089 | |
| 650 | 0 | |a Neural transmission. |0 http://id.loc.gov/authorities/subjects/sh85091095 | |
| 650 | 1 | 2 | |a Computational Biology |x methods |
| 650 | 2 | 2 | |a Mathematical Concepts |
| 650 | 2 | 2 | |a Models, Neurological |
| 650 | 2 | 2 | |a Nerve Net |
| 650 | 2 | 2 | |a Neurons |x physiology |
| 650 | 2 | 2 | |a Neurosciences |x methods |
| 650 | 2 | 2 | |a Synaptic Transmission |
| 650 | 2 | |a Computational Biology |0 https://id.nlm.nih.gov/mesh/D019295 | |
| 650 | 2 | |a Neurosciences |0 https://id.nlm.nih.gov/mesh/D009488 | |
| 650 | 6 | |a Neurosciences informatiques. | |
| 650 | 6 | |a Bio-informatique. | |
| 650 | 6 | |a Neurosciences. | |
| 650 | 6 | |a Réseaux nerveux. | |
| 650 | 6 | |a Transmission nerveuse. | |
| 650 | 7 | |a MEDICAL |x Neuroscience. |2 bisacsh | |
| 650 | 7 | |a PSYCHOLOGY |x Neuropsychology. |2 bisacsh | |
| 650 | 7 | |a Neural transmission |2 fast | |
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| 650 | 7 | |a Computational neuroscience |2 fast | |
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| 650 | 7 | |a Neurosciences |x Modèles mathématiques. |2 ram | |
| 655 | 4 | |a Internet Resources. | |
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| 776 | 0 | 8 | |i Print version: |a Gabbiani, Fabrizio. |t Mathematics for neuroscientists. |b 1st ed. |d Amsterdam ; Boston : Elsevier Academic Press, 2010 |z 9780123748829 |w (OCoLC)441761565 |
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| adam_text | |
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| author | Gabbiani, Fabrizio |
| author2 | Cox, Steven J. (Steven James), 1960- |
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| author_GND | http://id.loc.gov/authorities/names/n2004016542 |
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| contents | Passive isopotential cell -- Differential equations -- Active isopotential cell -- Quasi-active isopotential cell -- Passive cable -- Fourier series and transforms -- Passive dendritic tree -- Active dendritic tree -- Reduced single neuron models -- Probability and random variables -- Synaptic transmission and quantal release -- Neuronal calcium signaling -- Singular value decomposition and applications -- Quantification of spike train variability -- Stochastic processes -- Membrane noise -- Power and cross spectra -- Natural light signals and phototransduction -- Firing rate codes and early vision -- Models of simple and complex cells -- Stochastic estimation theory -- Reverse-correlation and spike train decoding -- Signal detection theory -- Relating neuronal responses and psychophysics -- Population codes -- Neuronal networks -- Solutions to selected exercises. |
| ctrlnum | (OCoLC)668196264 |
| dewey-full | 612.8 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 612 - Human physiology |
| dewey-raw | 612.8 |
| dewey-search | 612.8 |
| dewey-sort | 3612.8 |
| dewey-tens | 610 - Medicine and health |
| discipline | Medizin |
| edition | 1st ed. |
| format | Electronic eBook |
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Cox.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1st ed.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Amsterdam ;</subfield><subfield code="a">Boston :</subfield><subfield code="b">Elsevier Academic Press,</subfield><subfield code="c">2010.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xi, 486 pages) :</subfield><subfield code="b">illustrations (some color)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Elsevier science & technology books</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides 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. 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| genre | Internet Resources. |
| genre_facet | Internet Resources. |
| id | ZDB-4-EBA-ocn668196264 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:33Z |
| institution | BVB |
| isbn | 9780080890494 0080890490 9780128019061 0128019069 |
| language | English |
| oclc_num | 668196264 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 486 pages) : illustrations (some color) |
| psigel | ZDB-4-EBA |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Elsevier Academic Press, |
| record_format | marc |
| series | Elsevier science & technology books. |
| series2 | Elsevier science & technology books |
| spelling | Gabbiani, Fabrizio. Mathematics for neuroscientists / Fabrizio Gabbiani, Steven J. Cox. 1st ed. Amsterdam ; Boston : Elsevier Academic Press, 2010. 1 online resource (xi, 486 pages) : illustrations (some color) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file Elsevier science & technology books This book provides 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. The book alternates between mathematical chapters, introducing important concepts and numerical methods, and neurobiological chapters, applying these concepts and methods to specific topics. It covers topics ranging from classical cellular biophysics and proceeding up to systems level neuroscience. Starting at an introductory mathematical level, presuming no more than calculus through elementary differential equations, the level will build up as increasingly complex techniques are introduced and combined with earlier ones. Each chapter includes a comprehensive series of exercises with solutions, taken from the set developed by the authors in their course lectures. MATLAB code is included for each computational figure, to allow the reader to reproduce them. Biographical notes referring the reader to more specialized literature and additional mathematical material that may be needed either to deepen the reader's understanding or to introduce basic concepts for less mathematically inclined readers completes each chapter. 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 Provides implementation examples in MATLAB code, also included for download on the accompanying support website (which will be updated with additional code and in line with major MATLAB releases) Allows the mathematical novice to analyze their results in more sophisticated ways, and consider them in a broader theoretical framework. Includes bibliographical references (pages 473-482) and index. Passive isopotential cell -- Differential equations -- Active isopotential cell -- Quasi-active isopotential cell -- Passive cable -- Fourier series and transforms -- Passive dendritic tree -- Active dendritic tree -- Reduced single neuron models -- Probability and random variables -- Synaptic transmission and quantal release -- Neuronal calcium signaling -- Singular value decomposition and applications -- Quantification of spike train variability -- Stochastic processes -- Membrane noise -- Power and cross spectra -- Natural light signals and phototransduction -- Firing rate codes and early vision -- Models of simple and complex cells -- Stochastic estimation theory -- Reverse-correlation and spike train decoding -- Signal detection theory -- Relating neuronal responses and psychophysics -- Population codes -- Neuronal networks -- Solutions to selected exercises. Print version record. Computational neuroscience. http://id.loc.gov/authorities/subjects/sh97006370 Computational biology. http://id.loc.gov/authorities/subjects/sh2003008355 Neurosciences. http://id.loc.gov/authorities/subjects/sh91006099 Neural circuitry. http://id.loc.gov/authorities/subjects/sh85091089 Neural transmission. http://id.loc.gov/authorities/subjects/sh85091095 Computational Biology methods Mathematical Concepts Models, Neurological Nerve Net Neurons physiology Neurosciences methods Synaptic Transmission Computational Biology https://id.nlm.nih.gov/mesh/D019295 Neurosciences https://id.nlm.nih.gov/mesh/D009488 Neurosciences informatiques. Bio-informatique. Neurosciences. Réseaux nerveux. Transmission nerveuse. MEDICAL Neuroscience. bisacsh PSYCHOLOGY Neuropsychology. bisacsh Neural transmission fast Neural circuitry fast Computational biology fast Computational neuroscience fast Neurosciences fast Neurosciences Informatique. ram Neurosciences Modèles mathématiques. ram Internet Resources. Cox, Steven J. (Steven James), 1960- http://id.loc.gov/authorities/names/n2004016542 Print version: Gabbiani, Fabrizio. Mathematics for neuroscientists. 1st ed. Amsterdam ; Boston : Elsevier Academic Press, 2010 9780123748829 (OCoLC)441761565 Elsevier science & technology books. FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/book/9780123748829 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=342483 Volltext |
| spellingShingle | Gabbiani, Fabrizio Mathematics for neuroscientists / Elsevier science & technology books. Passive isopotential cell -- Differential equations -- Active isopotential cell -- Quasi-active isopotential cell -- Passive cable -- Fourier series and transforms -- Passive dendritic tree -- Active dendritic tree -- Reduced single neuron models -- Probability and random variables -- Synaptic transmission and quantal release -- Neuronal calcium signaling -- Singular value decomposition and applications -- Quantification of spike train variability -- Stochastic processes -- Membrane noise -- Power and cross spectra -- Natural light signals and phototransduction -- Firing rate codes and early vision -- Models of simple and complex cells -- Stochastic estimation theory -- Reverse-correlation and spike train decoding -- Signal detection theory -- Relating neuronal responses and psychophysics -- Population codes -- Neuronal networks -- Solutions to selected exercises. Computational neuroscience. http://id.loc.gov/authorities/subjects/sh97006370 Computational biology. http://id.loc.gov/authorities/subjects/sh2003008355 Neurosciences. http://id.loc.gov/authorities/subjects/sh91006099 Neural circuitry. http://id.loc.gov/authorities/subjects/sh85091089 Neural transmission. http://id.loc.gov/authorities/subjects/sh85091095 Computational Biology methods Mathematical Concepts Models, Neurological Nerve Net Neurons physiology Neurosciences methods Synaptic Transmission Computational Biology https://id.nlm.nih.gov/mesh/D019295 Neurosciences https://id.nlm.nih.gov/mesh/D009488 Neurosciences informatiques. Bio-informatique. Neurosciences. Réseaux nerveux. Transmission nerveuse. MEDICAL Neuroscience. bisacsh PSYCHOLOGY Neuropsychology. bisacsh Neural transmission fast Neural circuitry fast Computational biology fast Computational neuroscience fast Neurosciences fast Neurosciences Informatique. ram Neurosciences Modèles mathématiques. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh97006370 http://id.loc.gov/authorities/subjects/sh2003008355 http://id.loc.gov/authorities/subjects/sh91006099 http://id.loc.gov/authorities/subjects/sh85091089 http://id.loc.gov/authorities/subjects/sh85091095 https://id.nlm.nih.gov/mesh/D019295 https://id.nlm.nih.gov/mesh/D009488 |
| title | Mathematics for neuroscientists / |
| title_auth | Mathematics for neuroscientists / |
| title_exact_search | Mathematics for neuroscientists / |
| title_full | Mathematics for neuroscientists / Fabrizio Gabbiani, Steven J. Cox. |
| title_fullStr | Mathematics for neuroscientists / Fabrizio Gabbiani, Steven J. Cox. |
| title_full_unstemmed | Mathematics for neuroscientists / Fabrizio Gabbiani, Steven J. Cox. |
| title_short | Mathematics for neuroscientists / |
| title_sort | mathematics for neuroscientists |
| topic | Computational neuroscience. http://id.loc.gov/authorities/subjects/sh97006370 Computational biology. http://id.loc.gov/authorities/subjects/sh2003008355 Neurosciences. http://id.loc.gov/authorities/subjects/sh91006099 Neural circuitry. http://id.loc.gov/authorities/subjects/sh85091089 Neural transmission. http://id.loc.gov/authorities/subjects/sh85091095 Computational Biology methods Mathematical Concepts Models, Neurological Nerve Net Neurons physiology Neurosciences methods Synaptic Transmission Computational Biology https://id.nlm.nih.gov/mesh/D019295 Neurosciences https://id.nlm.nih.gov/mesh/D009488 Neurosciences informatiques. Bio-informatique. Neurosciences. Réseaux nerveux. Transmission nerveuse. MEDICAL Neuroscience. bisacsh PSYCHOLOGY Neuropsychology. bisacsh Neural transmission fast Neural circuitry fast Computational biology fast Computational neuroscience fast Neurosciences fast Neurosciences Informatique. ram Neurosciences Modèles mathématiques. ram |
| topic_facet | Computational neuroscience. Computational biology. Neurosciences. Neural circuitry. Neural transmission. Computational Biology methods Mathematical Concepts Models, Neurological Nerve Net Neurons physiology Neurosciences methods Synaptic Transmission Computational Biology Neurosciences Neurosciences informatiques. Bio-informatique. Réseaux nerveux. Transmission nerveuse. MEDICAL Neuroscience. PSYCHOLOGY Neuropsychology. Neural transmission Neural circuitry Computational biology Computational neuroscience Neurosciences Informatique. Neurosciences Modèles mathématiques. Internet Resources. |
| url | https://www.sciencedirect.com/science/book/9780123748829 https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=342483 |
| work_keys_str_mv | AT gabbianifabrizio mathematicsforneuroscientists AT coxstevenj mathematicsforneuroscientists |