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The preface highlights growing connections between mathematics and biology, ranging from population and disease modeling to genomics driven by DNA sequence data. 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The material is also presented in an engaging style intended to broaden interest across disciplines.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},327004,1790375465,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},962075114101,"https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165","MATHEMATICAL MODELS IN BIOLOGY AN INTRODUCTION  \nTo J., R., and K., may reality live up to the model  \nMATHEMATICAL MODELS IN BIOLOGY AN INTRODUCTION  \nELIZABETH S . ALLMAN  \nDepartment of Mathematics and Statistics,  \nUniversity of Southern Maine  \nJOHN A . RHODES  \nDepartment of Mathematics,  \nBates College  \n􀀁􀀂􀀃􀀄􀀅􀀆􀀇􀀈􀀉 􀀋􀀌􀀆􀀍􀀉􀀅􀀎􀀆􀀏􀀐 􀀑􀀅􀀉􀀎􀀎  \nCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo  \nCambridge University Press  \nThe Edinburgh Building, Cambridge 􀀁􀀄􀀒 􀀒􀀅􀀋, United Kingdom  \nPublished in the United States of America by Cambridge University Press, New York [www.cambridge.org](www.cambridge.org)  \nInformation on this [title: www.cambridge.org/9780521819800](title: www.cambridge.org/9780521819800)  \n© Elizabeth S. Allman and John A. Rhodes 2004  \nThis book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.  \nFirst published in print format 2003  \n􀀆􀀎􀀄􀀌-􀀔􀀕 􀀖􀀗􀀘-􀀙-􀀚􀀔􀀔-􀀙􀀗􀀘􀀜􀀛-􀀙 eBook (NetLibrary)  \n􀀆􀀎􀀄􀀌-􀀔􀀙 􀀙-􀀚􀀔􀀔-􀀙􀀗􀀘􀀜􀀛-􀀕 eBook (NetLibrary)  \n􀀆􀀎􀀄􀀌-􀀔􀀕 􀀖􀀗􀀘-􀀙-􀀚􀀒􀀔-􀀘􀀔􀀖􀀘􀀙-􀀙 hardback 􀀆􀀎􀀄􀀌-􀀔􀀙 􀀙-􀀚􀀒􀀔-􀀘􀀔􀀖􀀘􀀙-􀀛 hardback  \n􀀆􀀎􀀄􀀌-􀀔􀀕 􀀖􀀗􀀘-􀀙-􀀚􀀒􀀔-􀀚􀀒􀀚􀀘􀀛-􀀒 paperback 􀀆􀀎􀀄􀀌-􀀔􀀙 􀀙-􀀚􀀒􀀔-􀀚􀀒􀀚􀀘􀀛-􀀔 paperback  \nCambridge University Press has no responsibility for the persistence or accuracy of 􀀋􀀅􀀝s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.  \nContents  \nPreface page vii  \nNote on MATLAB xi  \n1. Dynamic Modeling with Difference Equations 1  \n1.1. The Malthusian Model 2  \n1.2. Nonlinear Models 11  \n1.3. Analyzing Nonlinear Models 20  \n1.4. Variations on the Logistic Model 33  \n1.5. Comments on Discrete and Continuous Models 39  \n2. Linear Models of Structured Populations 41  \n2.1. Linear Models and Matrix Algebra 41  \n2.2. Projection Matrices for Structured Models 53  \n2.3. Eigenvectors and Eigenvalues 65  \n2.4. Computing Eigenvectors and Eigenvalues 78  \n3. Nonlinear Models of Interactions 85  \n3.1. A Simple Predator–Prey Model 86  \n3.2. Equilibria of Multipopulation Models 94  \n3.3. Linearization and Stability 99  \n3.4. Positive and Negative Interactions 105  \n4. Modeling Molecular Evolution 113  \n4.1. Background on DNA 114  \n4.2. An Introduction to Probability 116  \n4.3. Conditional Probabilities 130  \n4.4. Matrix Models of Base Substitution 138  \n4.5. Phylogenetic Distances 155  \n5. Constructing Phylogenetic Trees 171  \n5.1. Phylogenetic Trees 172  \n5.2. Tree Construction: Distance Methods – Basics 180  \n5.3. Tree Construction: Distance Methods – Neighbor Joining 191  \nvi Contents  \n5.4. Tree Construction: Maximum Parsimony 198  \n5.5. Other Methods 206  \n5.6. Applications and Further Reading 208  \n6. Genetics 215  \n6.1. Mendelian Genetics 215  \n6.2. Probability Distributions in Genetics 228  \n6.3. Linkage 244  \n6.4. Gene Frequency in Populations 261  \n7. Infectious Disease Modeling 279  \n7.1. Elementary Epidemic Models 280  \n7.2. Threshold Values and Critical Parameters 286  \n7.3. Variations on a Theme 296  \n7.4. Multiple Populations and Differentiated Infectivity 307  \n8. Curve Fitting and Biological Modeling 315  \n8.1. Fitting Curves to Data 316  \n8.2. The Method of Least Squares 325  \n8.3. Polynomial Curve Fitting 335  \nA. Basic Analysis of Numerical Data 345  \nA.1 . The Meaning of a Measurement 345  \nA.2 . Understanding Variable Data – Histograms and  \nDistributions 348  \nA.3 . Mean, Median, and Mode 352  \nA.4 . The Spread of Data 355  \nA.5 . Populations and Samples 359  \nA.6 . Practice 360  \nB. For Further Reading 362  \nReferences 365  \nIndex 367  \nPreface  \nInteractions between the mathematical and biological sciences have been increasing rapidly in recent years. Both traditional topics, such as population and disease modeling, and new ones, such as those in genomics arising from the accumulation of DNA sequence data, have made biomathematics an","cbCaibRXlpAIAt5C","https://ap.wps.com/l/cbCaibRXlpAIAt5C","pdf",1341232,385,"English","# Contents\n## Preface\n## Note on MATLAB\n## 1. Dynamic Modeling with Difference Equations\n## 2. Linear Models of Structured Populations\n## 3. Nonlinear Models of Interactions\n## 4. Modeling Molecular Evolution\n## 5. Constructing Phylogenetic Trees\n## 6. Genetics\n## 7. Infectious Disease Modeling\n## 8. Curve Fitting and Biological Modeling\n## A. Basic Analysis of Numerical Data\n## B. For Further Reading\n# References\n# Index","[{\"question\":\"What level of mathematical background does the book assume?\",\"answer\":\"The text targets students with a mathematical background sufficient to study calculus, without assuming prior training in calculus beyond that level. It keeps prerequisites minimal by emphasizing modeling through difference equations.\"},{\"question\":\"What modeling approach is emphasized in the book?\",\"answer\":\"Modeling is primarily developed through difference equations, which helps introduce mathematical tools as needed for constructing and analyzing models rather than relying on extensive prerequisite courses.\"},{\"question\":\"How does the book support students with different backgrounds?\",\"answer\":\"Although the core organization minimizes prerequisites, the authors include comments and clearly marked problems for students who have taken additional mathematics. The material is also presented in an engaging style intended to broaden interest across disciplines.\"}]","MATHEMATICAL MODELS IN BIOLOGY - An Introduction | PDF",1789975938,970]