Mathematics for Neuroscientists (Hardcover)

Fabrizio Gabbiani, Steven James Cox

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商品描述

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

商品描述(中文翻譯)

幾乎所有神經科學中的科學問題都需要數學分析,而所有神經科學家都越來越需要對數學方法有深入的理解。目前還沒有一本全面且整合性的介紹數學在神經科學中應用的入門書籍;現有的書籍要麼只專注於理論建模,要麼只討論用於處理特定問題的數學概念。本書通過在首次確立其在神經科學中重要性的情境中系統地介紹數學和計算工具,填補了這一需求。所有數學概念將從簡單到複雜地介紹,並使用最廣泛使用的計算環境Matlab。

本書將提供對數學、神經科學及其結合使用的基本概念的扎實介紹,從而為讀者提供一個跳板,進入尖端研究主題,並促進數學和神經科學在未來一代學生中更緊密地融合。

- 提供了對數據分析和基於實驗數據制定概念的重要數學概念的教學性和系統性介紹
- 介紹了線性代數、常微分方程和偏微分方程、傅立葉變換、概率和隨機過程
- 介紹了用於實現與每個數學概念相關的算法的數值方法
- 通過將數值方法應用於神經科學中的特定主題,包括霍奇金-赫胥黎方程、概率描述隨機釋放、隨機過程描述神經元中的噪聲、傅立葉變換描述視覺神經元的感受野,來說明數值方法
- 讓數學新手能夠以更複雜的方式分析其結果,並在更廣泛的理論框架中考慮這些結果。