{"product_id":"mathematical-tools-for-neuroscience-a-geometric-approach-9783030984977","title":"Mathematical Tools for Neuroscience: A Geometric Approach","description":"\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003eThe book explains how the brain is adept at processing biological objects by exploiting the geometric properties of such objects. It introduces the concept of a manifold, which extends the idea of a surface to many dimensions, and discusses how to use tangent spaces to investigate the local linear behavior of manifolds. Examples of the geometric approach to neuroscience include the analysis of color and spatial vision measurements and the control of eye and arm movements. The book is intended for a reader with an interest in neuroscience who may have been introduced to calculus in the past but is not aware of the many insights obtained by a geometric approach. \u003c\/blockquote\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 162 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 22 April 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer Nature Switzerland AG\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003eThis comprehensive book offers a concise yet accessible introduction to a diverse range of mathematical concepts that have proven invaluable in understanding the complexities of the brain and behavior. By meticulously recording the eye movements of individuals observing a riverside scene, one can observe a variety of focal points, including the river, the barge, the people on the bridge, and so on. However, when a duck takes flight, it captures the attention of everyone present. How is it that the brain possesses such remarkable capabilities in processing such biological objects? This book aims to shed light on this question by demonstrating that brains are particularly adept at leveraging the geometric properties inherent in these objects.\u003cbr\u003e\u003cbr\u003eCentral to the geometric approach is the concept of a manifold, which expands the notion of a surface to multiple dimensions. The manifold can be defined through collections of n-dimensional data points or by the trajectories of a system traversing state space. Similar to how tangent planes are employed to analyze the local linear behavior of points on a surface, the extension to tangent spaces enables the investigation of the local linear behavior of manifolds. The majority of the geometric techniques introduced in this book revolve around manipulating tangent spaces.\u003cbr\u003e\u003cbr\u003eBy employing the geometric approach, researchers in neuroscience have been able to analyze various aspects of vision, including color perception and spatial perception. For instance, they have studied the measurements of color and spatial vision and developed methods to control eye and arm movements. Furthermore, additional examples are provided to showcase the broader applications of this approach and demonstrate its potential to yield new techniques for exploring neural systems.\u003cbr\u003e\u003cbr\u003eOne of the significant advantages of adopting a geometric approach is its ability to facilitate visual illustration of the concepts. Each example is accompanied by comprehensive diagrams that provide clear explanations and enhance the reader's understanding. This book is designed for individuals with an interest in neuroscience who may have a foundational understanding of the field field. It serves as a valuable resource for those seeking to delve deeper into the complexities of the brain and behavior, offering a comprehensive and accessible guide to the realm of geometric neuroscience.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 273g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 235 x 155 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783030984977\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2022\u003c\/p\u003e","brand":"Richard A. Clement","offers":[{"title":"Paperback \/ softback","offer_id":44307615416570,"sku":"9783030984977","price":91.62,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_4045ba18-962e-4eae-9541-4c811c0a76a8.jpg?v=1688110459","url":"https:\/\/shulphink.com\/products\/mathematical-tools-for-neuroscience-a-geometric-approach-9783030984977","provider":"Shulph Ink","version":"1.0","type":"link"}