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The series aims to support graduate students and researchers with limited backgrounds in mathematics or biology in mathematical modeling of biological processes. This volume focuses on Mathematical Neuroscience, outlining connections from neuron dynamics to models such as Hodgkin-Huxley, dynamical systems, bifurcations, coupled neural oscillations, Parkinson’s disease, and auditory system modeling.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/tutorials-in-mathematical-biosciences-i-mathematical-neuroscience-preface/327011/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/tutorials-in-mathematical-biosciences-i-mathematical-neuroscience-preface/327011.png","ImageObject",300,407,{"name":92,"@type":93},"Evangeline","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-05","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the purpose of the series “Tutorials in Mathematical Biosciences” described in the preface?","Question",{"text":112,"@type":113},"The series aims to introduce graduate students and researchers, even with limited background in mathematics or biology, to mathematical modeling of biological processes.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which topic does this first volume focus on?",{"text":117,"@type":113},"The first volume is devoted to Mathematical Neuroscience, linked to the MBI program in 2002–2003.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the preface structure the volume’s chapters?",{"text":121,"@type":113},"It presents a brief neuron introduction for later chapters, then highlights a dynamical-systems and bifurcation focus for neuronal dynamics, followed by coupled neural oscillations, and finally specialization to the auditory system.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},327011,1790122161,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},13056703019662,"https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188","Lecture Notes in Mathematics 1860  \nEditors:  \nJ.--M. Morel, Cachan  \nF. Takens, Groningen  \nB. Teissier, Paris  \nAlla Borisyuk Avner Friedman Bard Ermentrout David Terman  \nTutorials in  \nMathematical BiosciencesI  \nMathematical Neuroscience  \n1 3  \nAuthors  \nAlla Borisyuk  \nMathematical Biosciences Institute The Ohio State University  \n231 West 18th Ave.  \nColumbus, OH 43210-1174, USA [e-mail: borisyuk@mbi.osu.edu](e-mail: borisyuk@mbi.osu.edu)  \nBard Ermentrout  \nDepartment of Mathematics University of Pittsburgh  \n502 Thackeray Hall Pittsburgh, PA 15260, USA [e-mail: bard@pitt.edu](e-mail: bard@pitt.edu)  \nAvner Friedman  \nMathematical Biosciences Institute The Ohio State University  \n231 West 18th Ave.  \nColumbus, OH 43210-1174, USA [e-mail: afriedman@mbi.osu.edu](e-mail: afriedman@mbi.osu.edu)[ ](e-mail: afriedman@mbi.osu.edu)David Terman  \nDepartment of Mathematics The Ohio State University  \n231 West 18th Ave.  \nColumbus, OH 43210-1174, USA e-mail: [terman@math.ohio-state.edu](terman@math.ohio-state.edu)  \nCover Figure: Cortical neurons (nerve cells), 􀀁c Dennis Kunkel Microscopy, Inc.  \nLibrary of Congress Control Number: 2004117383  \nMathematics Subject Classification (2000): 34C10, 34C15, 34C23, 34C25, 34C37, 34C55, 35K57, 35Q80, 37N25, 92C20, 92C37  \nISSN 0075-8434  \nISBN 3-540-23858-1 Springer-Verlag Berlin Heidelberg New York DOI 10. 1007/b102786  \nThis work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereofis permitted only under the provisions ofthe German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law.  \nSpringer is part of Springer Science+Business Media [springeronline.com](springeronline.com)  \n􀀁c Springer-Verlag Berlin Heidelberg 2005 Printed in Germany  \nThe use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.  \nTypesetting: Camera-ready TEX output by the authors  \nSPIN: 11348290 41/3142-543210-Printed on acid-free paper  \nPreface  \nThis is the first volume in the series “Tutorials in Mathematical Biosciences”.  \nThese lectures are based on material which was presented in tutorials or developed by visitors and postdoctoral fellows of the Mathematical Biosciences Institute (MBI), at The Ohio State University. The aim of this series is to introduce graduate students and researchers with just a little background in either mathematics or biology to mathematical modeling of biological processes. The first volume is devoted to Mathematical Neuroscience, which was the focus of the MBI program in 2002-2003; documentation of this year’s activities, including streaming videos of the workshops, can be found on the website [http://mbi.osu.edu](http://mbi.osu.edu).  \nThe use of mathematics in studying the brain has had great impact on the field of neuroscience and, simultaneously, motivated important research in mathematics. The Hodgkin-Huxley model, which originated in the early 1950s, has been fundamental in our understanding of the propagation of electrical impulses along a nerve axon. Reciprocally, the analysis of these equations has resulted in the development of sophisticated mathematical techniques in the fields of partial differential equations and dynamical systems. Interaction among neurons by means of their synaptic terminals has led to a study of coupled systems of ordinary differential and integro-differential equations, and the field of computational neurosciences can now be considered a mat","cbCaivebj2zmPM8i","https://ap.wps.com/l/cbCaivebj2zmPM8i","pdf",3069989,178,"English","# Preface\n# Contents\n## Introduction to Neurons\n## The Structure of Cells\n## Nerve Cells\n## Electrical Circuits and the Hodgkin-Huxley Model\n## The Cable Equation","[{\"question\":\"What is the purpose of the series “Tutorials in Mathematical Biosciences” described in the preface?\",\"answer\":\"The series aims to introduce graduate students and researchers, even with limited background in mathematics or biology, to mathematical modeling of biological processes.\"},{\"question\":\"Which topic does this first volume focus on?\",\"answer\":\"The first volume is devoted to Mathematical Neuroscience, linked to the MBI program in 2002–2003.\"},{\"question\":\"How does the preface structure the volume’s chapters?\",\"answer\":\"It presents a brief neuron introduction for later chapters, then highlights a dynamical-systems and bifurcation focus for neuronal dynamics, followed by coupled neural oscillations, and finally specialization to the auditory system.\"}]","Tutorials in Mathematical Biosciences I - Mathematical Neuroscience - Preface | PDF",1789975955,449]