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21. Computational Cell Biology
22. An Introduction to Mathematical
23. Mathematical Methods in Biology
24. Mathematical Epidemiology of Infectious
25. Branching Processes in Biology
26. Applied Mathematical Demography
27. Population Biology: Concepts and
28. An Introduction to Systems Biology:
29. Optimal Control Applied to Biological
30. Tutorials in Mathematical Biosciences
31. A Biologist's Guide to Mathematical
32. Mechanics of Swimming and Flying
33. The Mathematical Theory of Selection,
34. Stochastic Modelling for Systems
35. Mathematical Aspects of Hodgkin-Huxley
36. Mathematical Models in Medical
37. Biological Kinetics (Cambridge
38. An Introduction to the Mathematics
39. Compositional Evolution: The Impact
40. Mathematical Foundations of Neuroscience

21. Computational Cell Biology
Hardcover: 488 Pages (2002-07-09)
list price: US$79.95 -- used & new: US$53.08
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Asin: 0387953698
Average Customer Review: 5.0 out of 5 stars
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This textbook provides an introduction to dynamic modeling in cell biology, emphasizing computational approaches based on realistic molecular mechanisms. It is designed to introduce cell biology and neuroscience students to computational modeling, and applied mathematics students, theoretical biologists, and engineers to many of the problems in dynamical cell biology. This volume was conceived of and begun by Professor Joel Keizer based on his many years of teaching and research together with his colleagues. The project was expanded and finished by his students and friends after his untimely death in 1999.

Carefully selected examples are used to motivate the concepts and techniques of computational cell biology, through a progression of increasingly more complex and demanding cases. Illustrative exercises are included with every chapter, and mathematical and computational appendices are provided for reference. This textbook will be useful for advanced undergraduate and graduate theoretical biologists, and for mathematics students and life scientists who wish to learn about modeling in cell biology.

Royalties from this book will be donated to the Joel E. Keizer memorial endowment for collaborative interdisciplinary research in the life sciences. ... Read more

Customer Reviews (1)

5-0 out of 5 stars An excellent overview
As a field of applied mathematics, computational biology has exploded in the last decade, and shows every sign of increasing in the next. This book overviews a few of the topics in the computational modeling of cells. I only read chapters 12 and 13 on molecular motors, and so my review will be confined to these.

Nanotechnology could be described as an up-and-coming field, but in the natural world one can find examples of this technology that surpass greatly what has been accomplished by human engineers. The authors begin their articles with a few examples of natural molecular machines, including the "rotary motors" DNA helicase and bacteriophage, and the "linear motor" kinesin, the latter they refer to as a "walking enzyme". Important in the modeling of all these is the theory of stochastic processes in the guise of Brownian motion, which the authors hold is the key to understanding the mechanics of proteins. In chapter 12 they give a detailed overview of the mathematical modeling of protein dynamics, followed in chapter 13 by an illustration of the mathematical formalism in the bacterial flagellar motor, a polymerization ratchet, and a motor governing ATP synthase.

To the authors a molecular motor is an entity that converts chemical energy into mechanical force. The production of mechanical force though may involve intermediate steps of energy transduction, all these involving the release of free energy during binding events. But due to their size, molecular motors are subjected to thermal fluctuations, and thus to model their motion accurately requires the theory of stochastic processes. Thus the authors begin a study of stochastic processes, restricting their attention to ones that satisfy the Markov property. Starting with a discrete model of protein motion as a simple random walk, the authors show that the variance of the motion grows linearly with time, which is a sign of diffusive motion. The partial differential equation satisfied by the probability distribution function, in the continuous limit where the space and time scales are large enough, is left to the reader to derive as an exercise.

The authors then consider polymer growth as another example of a stochastic process, a kind of hybrid one in that it involves both discrete and continuous random variables, the position of the polymer being continuous, while the number of monomers in the polymer is discrete. The authors derive an ordinary differential equation for the probability of there being exactly n polymers at a particular time. From this they show how to obtain sample paths for polymer growth and give a brief discussion on the statistics of polymer growth.

Attention is then turned to the modeling of molecular motions, with the first example being the Brownian motion of proteins in aqueous solutions. The (stochastic) Langevin equation is given for the motion of the protein, both with and without an external force acting on the protein. To find a numerical solution of this equation is straightforward, as the authors show. But they caution however that simulation of this solution on a computer is liable to introduce spurious results, and so they derive the Smoluchowski model, a somewhat different way of looking at random motion via the evolution of ensembles of paths. In this formulation the Brownian force is replaced by a diffusion term, and the external force is modeled by a drift term.

The authors then consider the modeling of chemical reactions, which supply the energy to the molecular motors. Because of the time scales involved in these reactions, a correct treatment of them would involve quantum mechanics, but the authors use the Smoluchowski model. The simple reaction model they consider involves a positive ion binding to negatively charged amino acid, and using as reaction coordinate the distance between the ion and the amino acid, study the free energy change as a function of the reaction coordinate.

The numerical simulation of the protein motion is then considered in much greater detail, using an algorithm that preserves detailed balance. This involves converting the problem to a Markov chain and a consideration of the boundary conditions, which the authors do for the case of periodic, reflecting, and absorbing. Euler's method is used to solve the resulting equations for the Markov chain, and after dealing with issues of stability and accuracy, the Crank-Nicolson method is used. The last few sections of the chapter are devoted to the physics of these solutions and the authors give some intuitive feel for the entropic factors and energy balance on a protein motor.

In the last chapter of the book, the considerations in chapter 12 are applied to concrete molecular motors. The first one examined is a model for switching in a bacterial flagellar motor, which involves the protein CheY as a signaling pathway. The binding of CheY to the motor is modeled as a two-state process, with the binding site being either empty or occupied. The resulting set of coupled differential equations for the probabilities is solved for when the concentration of CheY is constant. An expression for the change in free energy is obtained, and the authors give a discussion of the physics in the light of what was done in the last chapter. The switching rate is computed, along with the mean first passage time.

Some other examples of molecular motors are also discussed, including the flashing racket, the polymerization ratchet, and a simplified model of the ion-driven F0 motor of ATP synthase. This latter motor is fascinating, since it describes the electrochemical energy involved in mitochondria for the production of ATP. The authors do a nice job of showing how the techniques of chapter 12 are used to solve this model, and also give an analytical solution for a certain limiting case. ... Read more

22. An Introduction to Mathematical Biology
by Linda J.S. Allen
Paperback: 368 Pages (2006-07-29)
list price: US$84.00 -- used & new: US$32.50
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Asin: 0130352160
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KEY BENEFIT: This reference introduces a variety of mathematical models for biological systems, and presents the mathematical theory and techniques useful in analyzing those models. Material is organized according to the mathematical theory rather than the biological application. Contains applications of mathematical theory to biological examples in each chapter. Focuses on deterministic mathematical models with an emphasis on predicting the qualitative solution behavior over time. Discusses classical mathematical models from population , including the Leslie matrix model, the Nicholson-Bailey model, and the Lotka-Volterra predator-prey model. Also discusses more recent models, such as a model for the Human Immunodeficiency Virus - HIV and a model for flour beetles. KEY MARKET: Readers seeking a solid background in the mathematics behind modeling in biology and exposure to a wide variety of mathematical models in biology. ... Read more

23. Mathematical Methods in Biology (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)
by J. David Logan, William Wolesensky
Paperback: 417 Pages (2009-08-17)
list price: US$84.95 -- used & new: US$52.48
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Asin: 0470525878
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A one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciences

Highlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals the growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory.

The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic.

In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLAB®, but can also be replicated using other software packages, including R, Mathematica®, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study.

Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics. ... Read more

24. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (Wiley Series in Mathematical & Computational Biology)
by O. Diekmann, J. A. P. Heesterbeek
Paperback: 320 Pages (2000-05-25)
list price: US$130.00 -- used & new: US$102.76
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Asin: 0471492418
Average Customer Review: 3.0 out of 5 stars
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Provides systematic coverage of the mathematical theory of modelling epidemics in populations, with a clear and coherent discussion of the issues, concepts and phenomena. Mathematical modelling of epidemics is a vast and important area of study and this book helps the reader to translate, model, analyse and interpret, with numerous applications, examples and exercises to aid understanding. ... Read more

Customer Reviews (2)

1-0 out of 5 stars Very Advanced
Great book but unless you are a computational biologist with very advanced mathematical skills-don't bother.This was over my head as a basic epidemiology student.I was searching for a book to elucidate R-zero...this was not it.

5-0 out of 5 stars Great, but not as an intro to Infectious Disease Modeling
I purchased this book partially because one review proposed that this text would serve as a good, teach-yourself introduction to mathematical modeling of infectious disease (I.D.).I'm currently in a master's-level class on I.D. modeling which has no specific text requirement, and having only a so-so math background and little knowledge of model construction, I thought a self-teach book would be nice.

Simply said, this book is not for those who stumbled through calculus 1.In fact, unless you're quite well-to-do in the math department, you'll find much of this text either very challenging or impenetrable.The worked-out problems are a very nice touch--one that many authors would do well to note--but the high-level math is too much for this budding epidemiologist. ... Read more

25. Branching Processes in Biology (Interdisciplinary Applied Mathematics)
by Marek Kimmel, David E. Axelrod
Paperback: 230 Pages (2010-11-02)
list price: US$109.00 -- used & new: US$76.50
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Asin: 1441929584
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This book introduces biological examples of Branching Processes from molecular and cellular biology as well as from the fields of human evolution and medicine and discusses them in the context of the relevant mathematics. It provides a useful introduction to how the modeling can be done and for what types of problems branching processes can be used.

... Read more

26. Applied Mathematical Demography (Statistics for Biology and Health)
by N. Keyfitz, Hal Caswell
Paperback: 558 Pages (2010-11-02)
list price: US$115.00 -- used & new: US$91.73
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Asin: 1441919775
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The third edition of this classic text maintains its focus on applications of demographic models, while extending its scope to matrix models for stage-classified populations. The authors first introduce the life table to describe age-specific mortality, and then use it to develop theory for stable populations and the rate of population increase. This theory is then revisited in the context of matrix models, for stage-classified as well as age-classified populations. Reproductive value and the stable equivalent population are introduced in both contexts, and Markov chain methods are presented to describe the movement of individuals through the life cycle. Applications of mathematical demography to population projection and forecasting, kinship, microdemography, heterogeneity, and multi-state models are considered.

The new edition maintains and extends the book's focus on the consequences of changes in the vital rates. Methods are presented for calculating the sensitivity and elasticity of population growth rate, life expectancy, stable stage distribution, and reproductive value, and for applying those results in comparative studies.

Stage-classified models are important in both human demography and population ecology, and this edition features examples from both human and non-human populations. In short, this third edition enlarges considerably the scope and power of demography. It will be an essential resource for students and researchers in demography and in animal and plant population ecology.

Nathan Keyfitz is Professor Emeritus of Sociology at Harvard University. After holding positions at Canada's Dominion Bureau of Statistics, the University of Chicago, and the University of California at Berkeley, he became Andelot Professor of Sociology and Demography at Harvard in 1972. After retiring from Harvard, he became Director of the Population Program at the International Institute for Applied Systems Analysis (IIASA) in Vienna from 1983 to 1993. Keyfitz is a member of the U.S. National Academy of Sciences and the Royal Society of Canada, and a Fellow of the American Academy of Arts and Sciences. He has received the Mindel Sheps Award of the Population Association of America and the Lazarsfeld Award of the American Sociological Association, and was the 1997 Laureate of the International Union for the Scientific Study of Population. He has written 12 books, including Introduction to the Mathematics of Population (1968) and, with Fr. Wilhelm Flieger, SVD, World Population Growth and Aging: Demographic Trends in the Late Twentieth Century (1990).

Hal Caswell is a Senior Scientist in the Biology Department of the Woods Hole Oceanographic Institution, where he holds the Robert W. Morse Chair for Excellence in Oceanography. He is a Fellow of the American Academy of Arts and Sciences. He has held a Maclaurin Fellowship from the New Zealand Institute of Mathematics and its Applications and a John Simon Guggenheim Memorial Fellowship. His research focuses on mathematical population ecology with applications in conservation biology. He is the author of Matrix Population Models: Construction, Analysis, and Interpretation (2001).

... Read more

27. Population Biology: Concepts and Models (Volume 0)
by Alan Hastings
Paperback: 220 Pages (1996-12-13)
list price: US$47.95 -- used & new: US$13.94
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Asin: 0387948538
Average Customer Review: 4.0 out of 5 stars
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Population biology has been investigated quantitatively for many decades, resulting in a rich body of scientific literature. Ecologists often avoid this literature, put off by its apparently formidable mathematics. This textbook provides an introduction to the biology and ecology of populations by emphasizing the roles of simple mathematical models in explaining the growth and behavior of populations. The author only assumes acquaintance with elementary calculus, and provides tutorial explanations where needed to develop mathematical concepts. Examples, problems, extensive marginal notes and numerous graphs enhance the book's value to students in classes ranging from population biology and population ecology to mathematical biology and mathematical ecology. The book will also be useful as a supplement to introductory courses in ecology. ... Read more

Customer Reviews (4)

5-0 out of 5 stars Great book for beginners
Id say this is a great text for the biologist learning mathematical population biology for the first time. It is also a great text for an early math major (freshman, sophomore, or junior undergrad) to get started with mathematical ecology. The book is very readable, and only some familiarity with calculus is required (basically if you know what a derivative is, you are set to go). In addition I really appreciated the lean supplementary reading list at the end of each chapter. It highlights famous papers and books related to the lesson. Each of these papers are classics and all worth the read. Some books sight way to many papers at the end and you end up not knowing which ones are worth your while.

That being said, its probably not challenging enough for a graduate or advanced undergraduate student with a strong mathematical background. For this audience I would recommend Mark Kot's "Elements of Mathematical Ecology". For those who have done some modeling in Ecology, May's book may be more advanced from an ecological standpoint (rather than a mathematical one).

Basically this book hooked me into mathematical ecology. I stumbled upon it at the UC Davis library while looking for some applied math books. After reading the first few chapters, it inspired me not only to take Alan Hastings's class, but also apply to a math bio undergraduate research program. Now I am in a graduate program in Applied math, and while the book may appear too simple for me to continually use it, I keep on coming back to it, mainly for its excellent reading list, but also for when ever I get lost in a more advanced text or paper.

3-0 out of 5 stars GoodBookThatShouldBeEnlarged

4-0 out of 5 stars As clear and concise a population biology text can be!
At last a population biologist who can communicate ideas to the everyday student biologist.The biology and mathematics are completely integrated and well written.Minimal calculus is necessary to understand and use themathematics behind population biology. Thanks Al.

5-0 out of 5 stars a gentle but thorough introduction to a fascinating field
The field of mathematical biology has a long and storied history of examining relationships between species and scales since before Fisher's 1930 monograph "The Genetical Theory of Natural Selection."Although the excellent text by Edelstein-Keshet is still widely used, on the recommendation of a colleague I recently picked up a copy of the new (1997) text authored by Alan Hastings, out of UC Davis.A 220 page book published by Springer, its title is Population Biology: Concepts and Models.Available in paperback, the volume is divided into Single Species (with sections on density-independent and density-dependent population growth, population genetics, evolution of life histories) and Interacting Species (with sections on interactions, competition, predator-prey, host-parasitoid relationships and diseases).While detailing these concepts, the author includes bite-size reviews of matrix algebra, differential equations, stability computations, phase plane analysis and other topical quantitative techniques.I found the book eminently readable, which says a lot coming from someone who staggered through 18 semester hours of calculus and "Diff EQ" over 20 years ago.This book will be of great help to "ecologists ... [who] often avoid [population biology] literature, put off by its apparently formidable mathematics" (to quote from the back cover). ... Read more

28. An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall/CRC Mathematical & Computational Biology)
by Uri Alon
Paperback: 320 Pages (2006-07-07)
list price: US$58.95 -- used & new: US$53.06
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Asin: 1584886420
Average Customer Review: 4.5 out of 5 stars
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Thorough and accessible, this book presents the design principles of biological systems, and highlights the recurring circuit elements that make up biological networks. It provides a simple mathematical framework which can be used to understand and even design biological circuits. The textavoids specialist terms, focusing instead on several well-studied biological systems that concisely demonstrate key principles.

An Introduction to Systems Biology: Design Principles of Biological Circuits builds a solid foundation for the intuitive understanding of general principles. It encourages the reader to ask why a system is designed in a particular way and then proceeds to answer with simplified models. ... Read more

Customer Reviews (22)

5-0 out of 5 stars Beautiful book: concepts and the big picture
There are a number a books on systems biology out there and the majority seem hastily put together during the past couple of years just to ride the wave of the systems biology buzz of late (IMO: in reality biology has always been about systems, and using mathematical/computational models to study biological systems is nothing new, it has been going on for about 50 years or perhaps more). A significant fraction of the books I've seen are just a compilation or random subjects and application examples of dubious educational relevance, often ill explained, and rarely developed to the point of being useful as a guide. Strangely enough, I am often left with the odd feeling that the authors of these books actually forgot to talk about the "systems" aspect and the big picture.

Alon's book is different because it is about concepts; It is about how we can study the dialog between the different layers of complexity that constitute a biological system. A number of approaches are beautifully presented in simple terms. Most of the topics covered use very simple math, which often is not even essential to get the point. Alon approaches biology from a more engineering-oriented mindset, not a bad approach considering that organisms and their cells evolved to solve problems not all that different from what engineers deal with. The specifics ofnature's solutions are clearly different, but the underlying principles are often uncannily similar. This is a fact, that although not explicitly stated in the book,I think pervades Alon thinking here. One of the things that I liked the most about this book, is that Uri Alon not only focuses on the techniques themselves, but he also take a deep look into the kind of insight we can get out of them.

This is not a biology book, is a book about how to think about biological systems. The book is mostly focused on physiological systems (as opposed to population-level or ecological issues) and therefore the examples are heavily biased towards biophysical problems such as regulation of gene expression -very simplified-, intracellular signaling cascades, etc.

By force, the treatment is not complete (it's an introduction after all) and leaves out many important approaches currently used for analyzing biological systems that most would categorize under the umbrella of systems biology. But what it covers it covers well, the examples are well chosen, and the analysis insightful, and this is why in my opinion, this book is way above other book in the area.

I highly recommend this book to anyone who is planning on getting into gene-regulation and/or any area that involves signaling, regardless of their background. If you have never seen this material before, this book could be a wonderful eye-opener.

Note: I do not fully understand the reviewers that accuse the author's approach of being "too physical", claiming that no biologist thinks in these terms. On the one hand I see little or no physics in this book --perhaps some physical chemistry, or rather, some solutions from physical chemistry. As matter of fact the language used in this book is of common use among most of my bio-medical colleagues (I work in immune signaling) and in the conferences I attend. The thinking certainly is not foreign to my colleagues in pharmacology who, credit must be given, have been doing "systems thinking" of the kind described here well before the term became a catch-phrase (actually, even before computers!). If the comments refer to the use of chemical kinetics models (Michaelis-Menten or mass action for example) to represent processes operating inside living cells, then I think the reviewer didn't really get the point of the book, or at least some of it. Coarse grained models (lumping bunch of details into an equation for a conceptual entity often without a biochemical counterpart) could be sometimes enough to understand the fundamental principles underlying a biological process, principles that too much detailed data often obfuscate.Furthermore, I don't think Uri Alon, or anyone in their right mind for that matter, would take the model of chemotactic signaling for example as anything else than just a model that happens to capture the observations. The beauty is that such a simple model is enough to provide a sensible explanation of what's going on and be used to make predictions. That's what this book is about: using models and other tools to elucidate key principles with explanatory and predictive powers, in other words, understanding.

5-0 out of 5 stars Wow! This book elicits such a strong response!
I have never seen a book, especially a science one, with such a bimodal response. IMO, the people with one star were trained as biologists. They present a valid viewpoint--I'll get back to that later.

When I first read this book at the end of my undergrad days, I was simply amazed. I never realized biology could be so fun, if we asked questions about robustness, optimality, design principles, etc. Now that I'm in this field in my day job (as a grad student), I realize this book does have some issues.

First, the book does make some strong claims, ie. the idea of inherent design principles. This is what most of the one-star reviews here are angry about. Alon doesn't really discuss the philosophy behind systems biology, but jumps straight to the physicists' view that the system is understandable and our job is to understand it.

Also, the book pretty much only covers work done by people in Leibler's lab. The works presented in the book are considered hallmarks in the field of systems biology, but people familiar with the field might be sad to see some areas not presented here.

Finally, it should be noted that the book doesn't really teach you that much. It does a wonderful job telling the story of the papers that it does discuss, but it hides away the details. Thus, you don't learn the biology of what's going on nor will you learn common mathematical techniques used in this field (eg, bifurcation analysis).

Nonetheless, I give this book five stars enthusiastically. This is the most enjoyable book I have read, and I highly recommend it to everyone who has any interest in this field. The problems included in the chapters are not bad for use in a class, although I recommend Strogatz's Nonliner Dynamics for a class focused on the modeling.

5-0 out of 5 stars Great book for practical learning
I'm a professor in molecular biology and wanted to learn more about networks so I could begin to apply it in my research.This textbook is an excellent introduction for getting a professional in a related area up to speed to begin to apply and use these ideas in a technical capacity.Very easy to read and understand.The information plugs into a general knowledge of modern molecular biology.The math starts at the level we all were trained in, such as a Michaelis-Menten reaction. Excellent book and highly recommended.

5-0 out of 5 stars Great initiation into the field
This is a great and well written book, a milestone in the field.I use this book as part of the course material for my courses in "Systems Biology" and "Biological Networks" at Columbia University and I recommend this book to my students.
Systems Biology is a large and rapidly growing field, currently no two scientists agree on its complete scope.Rather than attempting to be an all encompassing shallow overview of the entire field, Uri Alon takes one topic and presents it in clarity and depth.This is the perfect introduction to the field because systems biology is not a pile of facts, but rather a scientific approach and way of thought.
This book takes the reader through the process of formulating an abstract simplification of very complex biology, using this simpler representation to discover recurring patterns (motifs)in the organization of biological networks. Then Alon rigorously demonstrates that this recurrence could not have occurred by chance, providing sound statistical arguments, and pedagogically highlighting statistical pitfalls. The majority of the book presents clear mathematical thought experiments to decipher what roles these "motifs" serve and why they are beneficial to the cell.Alon evaluates the type of environmental signals cells need to process and how the evolved network design provides the cell with robust and reliable signal processing.Importantly, the models proposed by Alon match observed empirical data.
Molecular biology is incredibly complex and Alon deductively presents a tour de force example on how one can use analytical tools to construct a simplified abstraction from which one can glean insight and understanding.A fine initiation into the field.

5-0 out of 5 stars An Introduction to Systems Biology: Design Principles of Biological Circuits
This is an excellent textbook for systems biology. I have used it two times. One is a short course of systems biology in the summer 2008 for some professors who are interested in systems biology from different departments and different universities in Hsinchu, with background in statistics, applied math, engineering and biology. They found this book very useful for their researches on systems biology. Another is as a textbook of computational biology for graduate course in EE department of National Tsing Hua University. My students and I have learned a bit more from this book. This book offers an entirely different perspective on biology, from gene circuits and network motifs to networks as well as from the robustness and demand rule for gene regulation to the optimal gene circuit design. They are all described with simple but precise mathematic equations. Further, the role of evolution in robustness design of different biological circuits and systems is also discussed with several famous biological examples. The language of the book is very clear and the math is very simple, with both the math and the biology beautifully written. Therefore, I strongly recommend this book to those interested in systems biology. ... Read more

29. Optimal Control Applied to Biological Models (Chapman & Hall/CRC Mathematical & Computational Biology)
by Suzanne Lenhart, John T. Workman
Hardcover: 280 Pages (2007-05-07)
list price: US$91.95 -- used & new: US$83.65
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Asin: 1584886404
Average Customer Review: 5.0 out of 5 stars
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From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models.

Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs).

Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based.

Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes. ... Read more

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5-0 out of 5 stars Excellent and Useful
This is an excellent introductory book on optimal control applied to biological models. It covers a variety of topics including optimal control on ODEs, PDEs and discrete system. The 14 Labs with Matlab codes with user-friendly interface provided on the web offer a good resource to manipulate and learn the materials. The last chapter about other approaches and extensions opens a new horizon. ... Read more

30. Tutorials in Mathematical Biosciences II: Mathematical Modeling of Calcium Dynamics and Signal Transduction (Lecture Notes in Mathematics / Mathematical Biosciences Subseries) (v. 2)
Paperback: 202 Pages (2005-08-11)
list price: US$59.95 -- used & new: US$48.31
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Asin: 3540254390
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This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models,  much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions.

It is intended primarily as a graduate text or a research reference.  It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.

... Read more

31. A Biologist's Guide to Mathematical Modeling in Ecology and Evolution
by Sarah P. Otto, Troy Day
Hardcover: 752 Pages (2007-02-20)
list price: US$78.50 -- used & new: US$57.79
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Asin: 0691123446
Average Customer Review: 5.0 out of 5 stars
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Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own.

The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction.

Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists.

A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available ... Read more

Customer Reviews (2)

5-0 out of 5 stars That's good book !!
This book is the best in Mathematical Modeling tha I read.
It's a good educational book.

5-0 out of 5 stars Very good on stability analysis
Although other books may have a better presentation of the models' use and context, this is the best presentation I have seen on stability analysis, plus it presents a good quantity of model examples. The presentation of the math used is ample and clear. I highly reccomend it. ... Read more

32. Mechanics of Swimming and Flying (Cambridge Studies in Mathematical Biology)
by Stephen Childress
Paperback: 168 Pages (1981-07-31)
list price: US$43.00 -- used & new: US$15.84
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Asin: 0521280710
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This book provides a clear and concise summary of the fluid dynamics of the locomotion of living organisms. The biological phenomena described in detail range from the swimming of bacteria and fish to the flying of insects and birds. The breadth of treatment requires the study of two basic fluid-dynamical regimes. In the first case, that of small organisms, the viscosity of the fluid is paramount in deciding the most effective swimming strategy. However, for larger insects, birds, and most fish, the viscosity of the air or water may be treated as if it were zero, and resulting mechanisms of propulsion are very different. Both these types are studied, with emphasis on the unsteady character of natural movements. Written for the advanced student, this volume assumes familiarity with basic fluid mechanics, although some elementary topics are included. It will be readily accessible to students of applied mathematics and biologists who have engineering or physics backgrounds. ... Read more

33. The Mathematical Theory of Selection, Recombination, and Mutation (Wiley Series in Mathematical & Computational Biology)
by R. Bürger
Hardcover: 422 Pages (2000-11-27)
list price: US$250.00 -- used & new: US$196.00
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Asin: 0471986534
Average Customer Review: 5.0 out of 5 stars
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"It is close to being a masterpiece...could well be the classic presentation of the area." Warren J. Ewens, University of Pennsylvania, USA
Population genetics is concerned with the study of the genetic, ecological, and evolutionary factors that influence and change the genetic composition of populations. The emphasis here is on models that have a direct bearing on evolutionary quantitative genetics. Applications concerning the maintenance of genetic variation in quantitative traits and their dynamics under selection are treated in detail.
* Provides a unified, self-contained and in-depth study of the theory of multilocus systems
* Introduces the basic population-genetic models
* Explores the dynamical and equilibrium properties of the distribution of quantitative traits under selection
* Summarizes important results from more demanding sections in a comprehensible way
* Employs a clear and logical presentation style
Following an introduction to elementary population genetics and discussion of the general theory of selection at two or more loci, the author considers a number of mutation-selection models, and derives the dynamical equations for polygenic traits under general selective regimes. The final chapters are concerned with the maintenance of quantitative-genetic variation, the response to directional selection, the evolutionary role of deleterious mutations, and other topics.
Graduate students and researchers in population genetics, evolutionary theory, and biomathematics will benefit from the in-depth coverage. This text will make an excellent reference volume for the fields of quantitative genetics, population and theoretical biology. ... Read more

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Well It is different than quantitative genetics, forget about the statistical work,forget the statistical rules. Now a new subject exists. Mathematical genetics (NOT QUANTITATIVE GENETICS). This book is a must for every one who is interested in genetics and who is planning a life for it. The book its self is not highly related with diagnosis genetics but IF YOU WANT TO UNDERSTAND THE THEORY OF GENETICS GET THIS BOOK WELL IT MAYBE EXPENSIVE BUT DO NOT FORGET THAT YOU WÝLL BUY ONCE NOT TWICE :) BUY IT DO NOT THINK MUCH AS I DID ... Read more

34. Stochastic Modelling for Systems Biology (Chapman & Hall/CRC Mathematical & Computational Biology)
by Darren J. Wilkinson
Hardcover: 280 Pages (2006-04-18)
list price: US$92.95 -- used & new: US$88.02
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Asin: 1584885408
Average Customer Review: 4.0 out of 5 stars
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Although stochastic kinetic models are increasingly accepted as the best way to represent and simulate genetic and biochemical networks, most researchers in the field have limited knowledge of stochastic process theory. The stochastic processes formalism provides a beautiful, elegant, and coherent foundation for chemical kinetics and there is a wealth of associated theory every bit as powerful and elegant as that for conventional continuous deterministic models. The time is right for an introductory text written from this perspective.

Stochastic Modelling for Systems Biology presents an accessible introduction to stochastic modellingusing examples that are familiar to systems biology researchers. Focusing on computer simulation, the author examines the use of stochastic processes for modelling biological systems. He provides a comprehensive understanding of stochastic kinetic modelling of biological networks in the systems biology context. The text covers the latest simulation techniques and research material, such as parameter inference, and includes many examples and figures as well as software code in R for various applications.

While emphasizing the necessary probabilistic and stochastic methods, the author takes a practical approach, rooting his theoretical development in discussions of the intended application. Written with self-study in mind, the book includes technical chapters that deal with the difficult problems of inference for stochastic kinetic models from experimental data. Providing enough background information to make the subject accessible to the non-specialist, the book integrates a fairly diverse literature into a single convenient and notationally consistent source. ... Read more

Customer Reviews (1)

4-0 out of 5 stars Correct title: Stochastic modeling of biological systems
This is one of several recent books with system biology in the title, but first book with emphasis on statistics and stochastic approach. The book discusses some simple math models for biological systems, mostly biochemical models. Main focus is on statistical issues in differentail modeling, those as discussed in the nice Bower and Bolouri (2000) book Computational Modeling of Genetic and Biochemical Networks (Computational Molecular Biology), and the strong point is the use of Bayesian Markov chain Monte Carlo method for stochastic modeling. Weakness is that, the systems considered are too low-dimensional, and there is a long way toward real system biology issues, which will likely be much more complex, and involve potentially many high-dimensional interactions. Overall, it is simply a very straightforward introductory book, lacks depth and breadth. However, it should serve as a good starting point for people who want to learn something about stat and probabilistic methods relevant to bios system modelling. ... Read more

35. Mathematical Aspects of Hodgkin-Huxley Neural Theory (Cambridge Studies in Mathematical Biology)
by Jane Cronin
Paperback: 276 Pages (2008-06-05)
list price: US$53.00 -- used & new: US$44.93
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Asin: 0521063884
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Professor Cronin offers, for the first time, a synthesis of the work of Hodgkin and Huxley on nerve conduction. This information has previously been scattered throughout various media and difficult to retrieve. In this book the author thoroughly describes and analyzes their mathematical models (nonlinear ordinary and partial differential equations) and later models. ... Read more

36. Mathematical Models in Medical and Health Science (Innovations in Applied Mathematics)
Hardcover: 496 Pages (1999-03-31)
list price: US$60.00 -- used & new: US$39.17
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Asin: 0826513107
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A unique assemblage of cutting-edge research on mathematical models in biology and medicine. This book is composed of refereed and carefully edited research articles derived from the Conference on Mathematical Models in Medical and Health Sciences, held at Vanderbilt University in conjunction with the thirteenth annual Shanks Lectures Series (May 1997). ... Read more

37. Biological Kinetics (Cambridge Studies in Mathematical Biology)
Paperback: 232 Pages (2008-06-05)
list price: US$50.00 -- used & new: US$40.14
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Asin: 0521064090
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The central purpose of this book is to illustrate the premise that examination of the kinetics of biological processes can give valuable information concerning the underlying mechanisms that are responsible for these processes. Topics covered range from cooperativity in protein binding, through receptor-infector coupling, to theories of biochemical oscillations in yeast and slime mold. In addition, an introduction to the explosively growing theoretical topic of chaos details attempts to apply this theory in physiology. The material in this book originally appeared as part of the volume Mathematical Models in Molecular and Cellular Biology (edited by Lee A. Segel and now out of print). Each article has been revised and updated. ... Read more

38. An Introduction to the Mathematics of Biology
by Edward K. Yeargers, James V. Herod, Ronald W. Shonkweiler
Hardcover: 432 Pages (1996-08-28)
list price: US$109.00 -- used & new: US$78.95
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Asin: 0817638091
Average Customer Review: 5.0 out of 5 stars
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The authors of this new textbook have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another but has a unity of its own. The biology and mathematics are equal; they are complete and flow smoothly into and out of one another. Student response to this approach has been exhilarating to watch as standard, unexciting applications give way to problems of contemporary interest- HIV, genetics and aging, for example.

The book has several important features that the authors have developed from their classroom experience. First and foremost, it is designed to be comprehensible to students of biology as well as to students of mathematics and related physical sciences. No prior study of biology is necessary and only a year of calculus is required. The mathematics proceeds from simple to more complex concepts, and the biology proceeds from the population level down to the molecular level. This arrangement makes the material accessible to most biology majors and to most mathematics students near the beginning of their mathematical studies.

A unique feature of the book is the use of a computer algebra system, Maple, in parts of every chapter. This hands-on approach to computation provides a rich source of information through the use of "what-if" scenarios and thus allows students to grasp important biological and mathematical concepts in a way that is not possible without such technology. For students who do not have access to a computer algebra system, each topic is complete without the use of either numerical or symbolic equations. Graphic visualizations are provided for all the mathematical results.

The text has extensive exercises, problems and examples, along with references for further study. It will be of interest to any mathematics department that teaches mathematical biology. It also lends itself to self-study for more advanced mathematicians and scientists who wish to explore further this most exciting frontier in the applications of mathematics and computers to the natural sciences.

This text has been adopted at:Georgia Institute of Technology, Carnegie Mellon University, University of California at Los Angeles, California State University, Northeastern Illinois University, and University of Colorado. ... Read more

Customer Reviews (1)

5-0 out of 5 stars An excellent book for a beginner interested in math and bio
I found this book useful as a beginner in biology with a background inmathematics.There is an emphasis on the biology aspect, but themathematics in fairly in depth. ... Read more

39. Compositional Evolution: The Impact of Sex, Symbiosis, and Modularity on the Gradualist Framework of Evolution (Vienna Series in Theoretical Biology)
by Richard A. Watson
Hardcover: 344 Pages (2006-02-17)
list price: US$50.00 -- used & new: US$4.97
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Asin: 026223243X
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No biological concept has had greater impact on the way we view ourselves and the world around us than the theory of evolution by natural selection. Darwin's masterful contribution was to provide an algorithmic model (a formal step-by-step procedure) of how adaptation may take place in biological systems. However, the simple process of linear incremental improvement that he described is only one algorithmic possibility, and certain biological phenomena provide the possibility of implementing alternative processes. In Compositional Evolution, Richard Watson uses the tools of computer science and computational biology to show that certain mechanisms of genetic variation (such as sex, gene transfer, and symbiosis) allowing the combination of preadapted genetic material enable an evolutionary process, compositional evolution, that is algorithmically distinct from the Darwinian gradualist framework.

After reviewing the gradualist framework of evolution and outlining the analogous principles at work in evolutionary computation, Watson describes the compositional mechanisms of evolutionary biology and provides computational models that illustrate his argument. He uses models such as the genetic algorithm as well as novel models to explore different evolutionary scenarios, comparing evolution based on spontaneous point mutation, sexual recombination, and symbiotic encapsulation. He shows that the models of sex and symbiosis are algorithmically distinct from simpler stochastic optimization methods based on gradual processes. Finally, Watson discusses the impact of compositional evolution on our understanding of natural evolution and, similarly, the utility of evolutionary computation methods for problem solving and design. ... Read more

40. Mathematical Foundations of Neuroscience (Interdisciplinary Applied Mathematics)
by G. Bard Ermentrout, David H. Terman
Hardcover: 422 Pages (2010-07-08)
list price: US$74.95 -- used & new: US$52.34
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Asin: 038787707X
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This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.

... Read more

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