Book Description
This volume teaches calculus in the biology context without compromising the level of regular calculus. The material is organized in the standard way and explains how the different concepts are logically related. Each new concept is typically introduced with a biological example; the concept is then developed without the biological context and then the concept is tied into additional biological examples. This allows readers to first see why a certain concept is important, then lets them focus on how to use the concepts without getting distracted by applications, and then, once readers feel more comfortable with the concepts, it revisits the biological applications to make sure that they can apply the concepts. The book features exceptionally detailed, step-by-step, worked-out examples and a variety of problems, including an unusually large number of word problems.
The volume begins with a preview and review and moves into discrete time models, sequences, and difference equations, limits and continuity, differentiation, applications of differentiation, integration techniques and computational methods, differential equations, linear algebra and analytic geometry, multivariable calculus, systems of differential equations and probability and statistics.
For faculty and postdocs in biology departments.
Customer Reviews:
This book sucks.......2007-03-25
I've taken calculus in the past and have had much better books. I currently own this book because my current class requires it, but it is terrible.
Why so bad?
1) A lot of wrong answers in back of book
2) Not enough examples
3) Examples given are very brief and unhelpful
4) Uses mathematical terms that are not the standard for professors and the mathematics world. Making it difficult to transition from pre-calc
5) Teacher hates it too but got stuck with it from prior professors
Just avoid it all together and get a substitute.
Average customer rating:
- Lacking in going from abstract to application
- Finite Mathematics for Business Economics, Life Sciences and Social Sciences (10th Edition)
- NOT USER FRIENDLY!
- Sound choice for a finite math textbook
- Many exercises in economics, life and the social sciences
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Finite Mathematics for Business Economics, Life Sciences and Social Sciences (10th Edition)
Raymond A. Barnett ,
Michael R. Ziegler , and
Karl E. Byleen
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ASIN: 0131139622 |
Book Description
Designed to be accessible, this book develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.
This book features a collection of important topics from mathematics of finance, linear algebra, linear programming, probability, and statistics, with an emphasis on cross-discipline principles and practices.
For the professional who wants to acquire essential mathematical tools for application in business, economics, and the life and social sciences.
Customer Reviews:
Lacking in going from abstract to application.......2007-09-23
This review is for the 11th edition of the book. I am using this for a business math course and overall the book is lacking. Many of the examples presented in the chapters are simplistic and have no relation to the difficulty of the application examples. It's unfortunate that the solutions manual while containing the solutions to the examples does not go into more detail in how to solve these type of problems. While it appears the authors goal is to go from abstract to application, he misses the mark. I find myself consulting external resources for almost every chapter. Not recommended.
Finite Mathematics for Business Economics, Life Sciences and Social Sciences (10th Edition).......2005-09-17
They sent me the wrong book. I ordered the Finite Mathematics for Business Economics, Life Sciences and Social Sciences (10th Edition)by Raymond A. Barnett and received the solution manual. I feel very disapointed with this purchase.
NOT USER FRIENDLY!.......2005-09-08
I am using this textbook for my Math for Business and Economics class and it is terrible. This book is not written taking into consideration the audience "Business Majors". Concepts are better explained in the Chapter review than under the sections they are being presented. There is only 1 example for each new concept and definitions are written using one or two definitions of new concepts within it. If this book is intended to take the student from the abstract concept to the real world it sure doesn't do this. I understood the material better in my Intermediate Algebra class than I do now.
Sound choice for a finite math textbook.......2004-06-27
This is a very sound choice as a textbook for a course in finite mathematics. The coverage is appropriate, the level suitable for the non-math major, the explanations are excellent and the authors take the title seriously.
The topics are covered in the following order:
* Elementary functions and their graphs.
* The mathematics of finance.
* Matrices and systems of linear equations.
* Linear inequalities and linear programming.
* Logic, set theory and basic counting.
* Probability and probability distributions.
* Basic game and decision theory.
* Markov chains.
There are many exercises and at the end of each section there is a set of basic exercises followed by a collection of applied problems. The set of applied problems is split into three categories: business & economics, life sciences and social sciences. Since finite mathematics is often a preparation for students to work in these fields, this format is what impressed me the most. With all of these "real world" problems to work as part of their study, no student using this book could ever legitimately say that they see no purpose to their studies. Solutions to the odd-numbered problems are included.
I came into contact with this book after my choice of textbook was irrevocable. Had I seen it earlier, it would have been the one I used.
Many exercises in economics, life and the social sciences.......2004-06-26
This is a very sound choice as a textbook for a course in finite mathematics. The coverage is appropriate, the level suitable for the non-math major, the explanations are excellent and the authors take the title seriously.
The topics are covered in the following order:
* Elementary functions and their graphs.
* The mathematics of finance.
* Matrices and systems of linear equations.
* Linear inequalities and linear programming.
* Logic, set theory and basic counting.
* Probability and probability distributions.
* Basic game and decision theory.
* Markov chains.
There are many exercises and at the end of each section there is a set of basic exercises followed by a collection of applied problems. The set of applied problems is split into three categories: business & economics, life sciences and social sciences. Since finite mathematics is often a preparation for students to work in these fields, this format is what impressed me the most. With all of these "real world" problems to work as part of their study, no student using this book could ever legitimately say that they see no purpose to their studies. Solutions to the odd-numbered problems are included.
I came into contact with this book after my choice of textbook was irrevocable. Had I seen it earlier, it would have been the one I used.
Book Description
Designed to be accessible, this book develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.
This book features a collection of important topics from mathematics of finance, linear algebra, linear programming, probability, and statistics, with an emphasis on cross-discipline principles and practices.
For the professional who wants to acquire essential mathematical tools for application in business, economics, and the life and social sciences.
Customer Reviews:
Like a telephone book.......2006-04-17
I was very dissappointed in this math textbook. I purchased it full price from the university, because they didn't have any used copies, and regretted it. It's basically like a telephone book of math information. You look something up, there's a short entry, and then tons and tons of problems. It contains everything, but the writing style is very dense, like they are trying to cram everything in. Its supposedly for applications oriented work, but I actually find more "theoretical" textbooks to have better and more well-described applications. A lot of the applications are just problems to solve that I question the real world relevance of. Bottom line, if you take a class that requires this book, I'd try to get a used copy or share a copy with some classmates, xerox the problem sets required for your homeworks, and get some other calculus textbooks to study from (one that I think is very interesting, if underutilized, is "Calculus In Context". Also take good notes in class and make sure you know the topics that are covered, so you can learn them somewhere else. Finally, unlike the previous reviewer, I do not hope the authors get cancer, but I do hope universities start carrying other textbooks instead of this one.
OUCH!.......2004-10-03
It assumes that you know a lot about math already so it does _not_ contain step by step. Mostly it just says "Here, this is the problem and this is the answer". How you get from point 'A' to point 'B' is a total mystery.
Bottom line, if the instructor had known that the book was this bad, he would have changed it to something better so that we could actually go through more stuff then we did.
Poorly Written Piece.......2004-05-06
It's simply a bad math text. I hope the authors get cancer.
Do you like the Matrix??.......2002-08-18
Did you like The Matrix? If you did you will love this book, it is filled with Matricies (the plural version of matrix). So buying this book is like having all three of the Matrix movies at once. All the excitement and all of knowledge, with this book you are "The One" and will never have to wonder what the Matrix is again. If you don't like the Matrix maybe you have wondered what the answer to f(x,y)= 4x + 5y - 6 is. Well I'm not going to ruin the ending of the book for you but the answer can be found in the back of this book(pg. A-90). Oh the suspense!!! Either way this book is a great read and if you are taking the class related to this book, you will never pass without it.
~Tyrell
Book Description
Designed to be accessible, this book develops a thorough, functional understanding of calculus in preparation for its application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving.
Chapter topics include The Derivative; Graphing and Optimization; Integration; Multivariable Calculus; Trigonometric Functions; and more.
For the professional who wants to acquire a knowledge of calculus for application in business, economics, and the life and social sciences.
Customer Reviews:
Applied calculus.......there is a method to the madness.......2000-05-08
I used this textbook in my first calculus class. The applied calculus class showed me some of the things this stuff can actually be used for. The authors and editors have combined excellent graphics, and outstanding homework problems. If you are a gluton for punishment from word problems, or if you need help at the most basic level of calculus, this is the book you'll need.
Book Description
Mathematical Physiology provides an introduction into physiology using the tools and perspectives of mathematical modeling and analysis. It describes ways in which mathematical theory may be used to give insights into physiological questions and how physiological questions can in turn lead to new mathematical problems.
The book is divided in two parts, the first dealing with the fundamental principles of cell physiology, and the second with the physiology of systems. In the first part, after an introduction to basic biochemistry and enzyme reactions, the authors discuss volume control, the membrane potential, ionic flow through channels, excitability, calcium dynamics, and electrical bursting. This first part concludes with spatial aspects such as synaptic transmission, gap junctions, the linear cable equation, nonlinear wave propagation in neurons, and calcium waves. In the second part, the human body is studied piece by piece, beginning with an introduction to electrocardiology, followed by the physiology of the circulatory system, blood muscle, hormones, and kindeys. Finally, the authors examine the digestive system and the visual system, ending with the inner ear. This book will be of interest to researchers, to graduate students and advanced undergraduate students in applied mathematics who wish to learn how to build and analyze mathematical models and become familiar with new areas of applications, as well as to physiologists interested in learning about theoretical approaches to their work.
Mathematical Reviews, 2000: "This is neither a physiology book nor a mathematics book, but it is probably the best book ever written on the interdisciplinary field of mathematical physiology, i.e. mathematics applied to modelling physiological phenomena. The book is highly recommended to anybody interested in mathematical or theoretical physiology."
Customer Reviews:
Poor explanations.......2007-01-15
I used this book in a graduate school course. I found myself checking out other mathematical physiology books to understand what they were talking about. There's poor explanations, and they skip certain steps that would help the reader get a better understanding of what's going on. Save your money and skip this book.
this is the book about systems biology!!!.......2005-09-24
If you would like to delve into the true complexity of systems biology (physiology), get this book. It's even much better than computational cell biology book by JJ Tyson et al since it's described in depth. But I'd rephrase Tyson's comment: "The regulatory system is so complex that it defies understanding by verbal arguments alone."
All of it fascinating...........2001-05-23
This book is an excellent overview of the major research into the mathematics of physiological processes. The first part of the book covers cellular physiology beginning with a discussion of biochemical reactions in the first chapter. Some of the applications of dynamical systems are nicely illustrated here, especially bifurcation theory.
Applications of the diffusion equation follow in the next chapter on cellular homeostasis. The Nernst-Planck electrodiffusion equation is discussed but not derived, and is solved in the constant field approximation.
This is complicated somewthat in the next chapter on membrane ion channels, where the potential across the membrane is not assumed to have a constant gradient. There is a discussion of channel blocking drugs in the last section, but unfortunately it is too short. This is an important area of application, with the experimental validation of the mathematical results of upmost importance.
The Hodgkin-Huxley and the FitzHugh-Nagumo equations dominate the next chapter on electrical signaling in cells. The phase space analysis of these models is discussed, along with an interesting treatment of the excitability of cardiac cells in the Appendix of the chapter.
A very well-written treatment, along with helpful diagrams, of calcium dynamics is given in Chapter 5. The authors show how ignoring the fast variables and transients lead one to a solution of they dynamical problem of the receptor model.
Phase space analysis is used extensively in the next chapter on electrical bursting, with emphasis on bursting in pancreatic beta-cells. An interesting discussion on the classification of bursting oscillations is given purely in terms of bifurcation theory.
That synaptic transimission is quantal in nature is one of the topics of the next chapter on intercellular communication. This is the first time in the book that probabilistic methods are introduced into the modeling. The authors quote some very old references on the experimental verification of the quantal model, leaving the reader wondering if more modern experiments have been done. In calculating the effective diffusion coefficients, the authors introduce the technique of homogenization, and give a explanation of the rationale behind the technique. The strategy of determining the behavior at a particular scale without solving completely the details at a finer scale is one that has proven to be quite productive, especially in physics.
The use of partial differential equations is increased in the next chapter on electrical flow in neurons, with the linear cable equation playing the dominant role. The authors use transform methods to obtain the solutions in the main text and exercises, giving references for the reader not familiar with these techniques.
The nonlinear cable equation is the subject of the next chapter, with traveling waves solutions of the bistable equation given the main emphasis. Shooting methods are employed in the solution of this equation, and the authors also treat the more difficult case of the discrete bistable equation.
Wave propagation in higher dimensions is the subject of the next chapter, with spiral waves discussed along with a brief discussion of scroll waves.
The fascinating subject of cardiac propagation is the subject of Chapter 11. The mathematical techniques are not much more complicated, but mathematicians coming to cardiac biology for the first time will need to pay attention to the details. One of the most interesting subjects of the book is treated in Chapter 13 on cell function regulation. Mathematical models of the G1 and G2 checkpoint processes are given.
Part two of the book emphasizes the mathematical modeling of the biological systems, rather than at the cellular level. This part begins with a consideration of how cellular activity can be coordinated to produce a regular heartbeat and how failure can occur. Interestingly, a Schrodinger-like equation appears when linearizing the FitzHugh-Nagumo equations for oscillating cells. And, interestingly, dynamical systems via circle maps appear in the model of the AV modal signal. This is followed by a lengthy and fascinating discussion of the mathematics of the circulatory system. Unfortunately, the discussion on the dangers of high blood pressure is not justified by any mathematical models in the book. It would have been very interesting to see a model developed that would predict the effects of hypertension on the heart, kidneys, etc and one that would be compared with historical and clinical data.
The next chapters discuss physiology of the blood, respiration, and muscles. A very interesting discussion of hormone physiology and mammal ovulation is given. The mathematical models of the kidneys and gastrointestinal systems are very detailed and very enlightening for individuals not in these fields.
The book ends with chapters on the physiology of sight and hearing. The discussion of the light reflex mechanism is very interesting as the authors use linear stability analysis. The oscillations of the basilar membrane in the inner ear are good reading for the physicist.
This book would be of great interest to mathematicians who are entering the field of computational physiology or computational biologists who need an understanding of the modeling required. Very captivating reading........
Graduate level Mathematical Physiology text.......2000-04-12
This is a very good graduate level text on mathematical physiology. It covers a broad range of topics from cardiac electrophysiology to the cell cycle. The authors have written the closest thing to a mathematical version of Guyton's Human Physiology text that I have seen. The prospective reader of this text should be aware that it assumes a background in PDE ,ODE, and asymptotics, as well as introductory molecular Biology. The structure of DNA, RNA, and the central dogma DNA to RNA to Protein are described in less than 3 pages without diagrams. Terms from Biochemistry are used at times without definition or explanation. Each Chapter concludes with a very nice collection of interesting problems. Supplement the text with the outstanding elementary text by Leah - Edelstein - Keshet , lecture notes by C. Peskin ,the applied math texts by Keener and Cole, Molecular biology texts by Lodish et al or Baltimore et al ,and of course Guyton's Human Physiology for a fascinating introduction to mathematical biology with an emphasis on differential equation models in physiology.
Book Description
Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences.
A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling.
This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology. A background in calculus and differential equations is assumed, although the main results required are collected in the appendices. A dedicated website at
www.springer.co.uk/britton/ accompanies the book and provides further exercises, more detailed solutions to exercises in the book, and links to other useful sites.
Average customer rating:
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Biomathematics
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ASIN: 0444502734 |
Book Description
This book presents new mathematics for the description of structure and dynamics in molecular and cellular biology. On an exponential scale it is possible to combine functions describing inner organisation, including finite periodicity, with functions for outside morphology into a complete definition of structure. This mathematics is particularly fruitful to apply at molecular and atomic distances. The structure descriptions can then be related to atomic and molecular forces and provide information on structural mechanisms. The calculations have been focussed on lipid membranes forming the surface layers of cell organelles. Calculated surfaces represent the mid-surface of the lipid bilayer. Membrane dynamics such as vesicle transport are described in this new language. Periodic membrane assemblies exhibit conformations based on the standing wave oscillations of the bilayer, considered to reflect the true dynamic nature of periodic membrane structures. As an illustration the structure of an endoplasmatic reticulum has been calculated. The transformation of such cell membrane assemblies into cubosomes seems to reflect a transition into vegetative states. The organisation of the lipid bilayer of nerve cells is analyzed, taking into account an earlier observed lipid bilayer phase transition associated with the depolarisation of the membrane. Evidence is given for a new structure of the alveolar surface, relating the mathematical surface defining the bilayer organisation to new experimental data. The surface layer is proposed to consist of a coherent phase, consisting of a lipid-protein bilayer curved according to a classical surface - the CLP surface. Without employing this new mathematics it would not be possible to give an analytical description of this structure and its deformation during the respiration cycle. In more general terms this mathematics is applied to the description of the structure and dynamic properties of motor proteins, cytoskeleton proteins, and RNA/DNA. On a macroscopic scale the motions of cilia, sperm and flagella are modelled.
This mathematical description of biological structure and dynamics, biomathematics, also provides significant new information in order to understand the mechanisms governing shape of living organisms.
Book Description
The study of complex systems in a unified framework has become recognized in recent years as a new scientific discipline, the ultimate in the interdisciplinary fields. Breaking down the barriers between physics, chemistry, and biology and the so-called soft sciences of psychology, sociology, economics and anthropology, this text explores the universal physical and mathematical principles that govern the emergence of complex systems from simple components. Dynamics of Complex Systems is the first text describing the modern unified study of complex systems. It is designed for upper-undergraduate/beginning graduate level students, and covers a broad range of applications in a broad array of disciplines. A central goal of this text is to develop models and modeling techniques that are useful when applied to all complex systems. This is done by adopting both analytic tools, including statistical mechanics and stochastic dynamics, and computer simulation techniques, such as cellular automata and Monte Carlo. In four sets of paired, self-contained chapters, Yaneer Bar-Yam discusses complex systems in the context of neural networks, protein folding, living organisms, and finally, human civilization itself. He explores fundamental questions about the structure, dynamics, evolution, development and quantitative complexity that apply to all complex systems. In the first chapter, mathematical foundations such as iterative maps and chaos, probability theory and random walks, thermodynamics, information and computation theory, fractals and scaling, are reviewed to enable the text to be read by students and researchers with a variety of backgrounds.
Customer Reviews:
beautifully written and highly useful.......2007-07-16
This is a beautifully written and thought-provoking work that presents the field of complex systems in a unified manner. The writing is highly engaging and stimulating with a broad range of topics. The material is pitched at just the right level, focusing on the concepts without getting buried in unnecessary details, while avoiding superficiality. I highly recommend this excellent book.
The worst side of normal science.......2007-04-24
The book is a tour around the paradigms used by scientists in
Complex Systems. While normal science is about using and re-using the paradigms without much creativity or true aportation to knowledge or understanding, the situation is worse in complex systems, since, as an emerging area it has multiple (competing?) paradigms, to the point that it is not possible to define a "complex system" in a form that encompases all the paradigms. The book certainly does not solve this problem, yet the author acknowledges the difficulty present in saying what a complex system is.
Complex systems is not an area of research but a community of researchers united by their interests.
The book is then a compilation of the "how to" and the believes for each paradigm, several of them carry very little science and have left the idea of "refutation" burried under piles of meaningless papers. Not surprissingly, some authors claim that complex systems is a postmodern scienceComplexity and Postmodernism: Understanding Complex Systems. And truly, the complex systems of Bar-Yam are only possible after we have buried reason and have accepted that science has nothing to do with truth.
Too much for me, not a book I recommend to my students.
Perpetuates the usual myths.......2007-04-03
that information is the opposite of entropy which is a measure of disorder or uncertainty. However because this book is about complexity and not information per se, I will only briefly refer to his mistakes with the latter as I have explained them further in other reviews that are specifically on that topic.
Shannon's information rate from communications theory, R, is an entropy like formula but most critically it is a state function difference of the uncertainty reduction to a recognizer after a measurement. Entropy is not a proper measure of disorder or uncertainty; the 2nd law of entropy increase of the universe applied long before there were any observers. It is a measure of the dispersal of energy. Going back in time is not going back to perfect order, but quite the opposite. I have not seen proper definitions in any book but there are PhD level articles available on the internet with proper definitions such as the Principia Cybernetica Web and molecular biologist Dr Thomas Schneider's website. Biologist Richard Dawkins also has an accurate short article on the internet. Most physicists have the definitions wrong unfortunately and believe information evolved before life, which is false. (A recognizer is required, whether a ribosome or mind etc.) Instead a better definition of complexity than the present author offers would indicate that the universe has increased in complexity through gravitational clumping (among other things). By making the mistake then the physicists and present author believe maximum information is randomness or equilibrium. This is the definition of algorithmic complexity.
As the author adapts algorithmic theory to his complexity profile he arrives at formulas that are observer dependant: "the complexity profile [is] the length of the description [of] the error allowed [as] the description increases." This is of little or no practical use. Again the universe has grown in complexity (or at least in pockets or we wouldn't be here) without relying on the degree of focus of any observer. A crystal is highly ordered relative to say a human cell whose complexity is a result of a multitude of interactions of chemical agents and macro molecules. This is where his analysis falls silent, in fact wrong. He says (page 741) "short-range correlations decrease the microstate complexity..." Well that's because he has a flawed method of using statistical mechanics. There is likely no universal complexity algorithm. Consider that a single gene can yield up to thousands of different proteins. One should be wary however of any formula that treats correlations as reduced complexity! Again the crystal vs the cell!
However there are ways of measuring the critical biological requirement of interactions that in fact increase complexity, the opposite of equilibrium statistical mechanics, a flawed tool. For instance in a recent article at lanl.arXiv.org, authors Edwin Wang et. al. apply Pearson's correlation coefficient to show that "genes with higher cis-regulation complexity are more coordinately regulated by transcription factors at the transcriptional level and by micro RNA's at the post-transcriptional level. This is a potentially novel discovery of a mechanism for coordinated regulation of gene expression...We found a positive correlation between these two groups of transcriptional regulators... " Measures of correlations are key in studying biological complexity and are not based on an observer's focus ability.
For a layman's guide to the issue of correlations for life see Irun Cohen's book 'Tending Adam's Garden' (though it has no quantitative aspect).
Interesting but incomplete.......2006-10-14
That physical systems are complex has been acknowledged for centuries, but only in recent decades has the scientific community, especially physicists and biologists, directly confronted complexity. This book discusses complex systems from the dynamical systems perspective, and as such can be read by physicists, mathematicians, and mathematical biologists. Biologists in particular will find the discussion of `emergence' the most important one, especially systems biologists. Physicists and mathematicians who study dynamical systems tend to not be concerned with their origins, whether they are in biology or some other area. But physicists do concern themselves with the experimental relevance of dynamical systems, unlike mathematicians who are sorely concerned with their formal properties, and do not care at all if they can find expression in the real world. But it goes without saying that the theory of complex systems has found application in finance, genetic engineering, cryptography, network engineering, and many other areas. This book gives a good overview of the techniques used to study complex systems, and can be read by anyone with the necessary mathematical preparation, consisting of probability theory and elementary calculus.
Systems that are simple can become complex by only a slight alteration in their configuration. The gravitational three-body system in classical mechanics is a good example of this. The dynamics of two objects interacting gravitationally can be solved explicitly, but the system consisting of three bodies cannot. The complexity in these two cases is measured by the availability of solutions to the dynamics of the system. The author is very aware that more involved measures of complexity are needed and he gives examples of these in the book. Mathematical techniques from probability and statistics are of course used throughout the book to frame these measures more quantitatively. This reflects the author's stated strategy throughout the book, namely to describe the essential characteristics of a class of systems, and employ statistical techniques to find the properties and behaviors of these systems.
The concepts of emergence and complexity are fundamental to a study of complex systems, the author argues and early on in the book he clears up some of the confusions behind the use of these terms in the scientific literature. A `complex system' is one which is constructed from many components and whose behavior cannot be determined from the behavior of these components, i.e. the behavior of the system is `emergent.' The `complexity' of a system, on the other hand, is the amount of information needed to describe the system. This is a somewhat subtle definition, and quite a few proposals have been put forward in the literature for measuring complexity. The author settles on a familiar method, the `entropy' for measuring complexity, but with a warning to the reader that the calculation of the entropy is dependent on the particular length or time scale over which the system is observed. For extremely long time scales (of observation), one can get away with describing systems as always in equilibrium. In this case the entropy would be maximum but the system would not be viewed as being complex. For very short time scales (of observation) , the entropy of the system is very small but due to the ability to observe the microscopic dynamics of the system it would be viewed as highly complex.
These considerations lead the author to introduce the concept of a 'complexity profile' of a system, which he discusses at some length in the last pages of the book. The complexity profile is designed to study the the dependence of complexity on both length and time scales. The concept is dependent on the notion of a sequence of observers that are ordered according to their ability to distinguish microstates. The author calculates the complexity profile of the ideal gas and shows that the complexity of a microstate for this case is simply the entropy, but as the number of microstates with a given region increases, the complexity approaches zero. Other examples of the complexity profile are discussed, one being for observers that only measure the positions of particles and not the momentum. The author also studies the connection between the complexity profile and the predictability or chaotic behavior of the system, where chaotic systems are viewed as being ones where information from a particular scale can be transferred to a larger scale, as contrasted with dissipative systems where information on a large scale is transferred to a smaller scale. The author gives various arguments and calculations that illustrate the difference in complexity profiles between chaotic systems and those of conservative, nonchaotic systems. The discussion is fairly convincing but if the complexity profile is important in complex systems, its defintion and properties should have been included at the beginning of the book, and serve as a central theme behind the discussions throughout the entire book. As it stands the complexity profile comes across as a concept that is purely ancillary to the study of complex systems. It certainly does not appear to be indispensable in discussing irreversibility of physical systems, this problem still being the most pressing one in statistical mechanics and is still hotly debated at the present time.
How complicated are we?.......2005-04-04
This book is designed as a text to introduce graduate students in science to the concepts and methods in the ``science of complexity'' which comprises studies in mathematics, physics, chemistry, biology, computer science, sociology, psychology, economics, anthropology, and philosophy. Written from the perspectives of a physicist, definitions are informal; thus a concise definition of a complex system is not given. The concept of a complex system is introduced through examples, and informally described as having ``a large number of interacting parts'' although ``even a few interacting objects can behave in complex ways.'' More precisely, complexity is defined as ``the amount of information necessary to describe a system.'' Another key concept is the phenomenon of emergence which arises when ``the collective behavior [of a complex system] is not readily understood from the behavior of its parts.''
Dynamics of Complex Systems opens with a long chapter (278 pages) of ``introduction and preliminaries'' which surveys iterative maps; thermodynamics and statistical mechanics; activated processes (glasses); cellular automata; statistical fields; computer simulations; information theory; computation; and fractals, scaling and renormalization. It is suggested that this chapter can serve as the basis for a one-semester course. This introductory chapter is followed by eight chapters devoted two each to four different subjects: neural networks, protein folding, biological evolution, and human civilization. In each of these pairs of chapters, the first is more detailed and the second more general. Thus the first of the two chapters on neural networks describes neural network models (Hopfield's attactor models) whereas the second discusses the phenomenon of sleep and models of mind, with similar divisions of labor in the pairs of chapters on protein folding and on biological evolution. In the final chapter, it is noted that ``human civilization is more complex than we are as individuals.''
Alwyn Scott
http://personal.riverusers.com/~rover/
Average customer rating:
- An Illustrated Tour of Mathematical Patterns in Nature.
- Required reading for everyone learning math.
- Mathematics deserves four colour
- A Universe Full of Mathematics
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What Shape is a Snowflake?
Ian Stewart
Manufacturer: W. H. Freeman
ProductGroup: Book
Binding: Hardcover
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Why Beauty Is Truth: A History of Symmetry
ASIN: 0716747944 |
Book Description
The stripes of a zebra...the complexities of a spider's web...the waves of the ocean...and the shape of a snowflake. These and other natural patterns have been recognized by scientists for centuries. What do they have in common? They can all be accounted for mathematically.
In What Shape is a Snowflake? internationally acclaimed mathematician Ian Stewart shows how life on earth develops not simply from genetic processes, but also from the principles of mathematics. Starting with the simplest symmetrical patterns, each chapter looks at a different kind of patterning system and the key scientific issues that underlie it. Patterns can embrace chaos, fractals, dislocations, even statistical regularities, and are found in many things that at first seem irregular or featurless. A constant wind blowing over a flat expanse of sand, for example will develop ripples, which eventually lead to sand dunes that are often arranged in long parallel rows or other geometric forms. And the smooth surface of a growing organism will develop beautiful patterns, of spots, stripes and colors.
Beautifully illustrated, What Shape is a Snowflake? is an illuminating and engaging vision of how the apparently cold laws of mathematics find organic expression in the beauty of nature.
Customer Reviews:
An Illustrated Tour of Mathematical Patterns in Nature........2006-05-17
In "What Shape Is a Snowflake?: Magical Numbers in Nature", author Ian Stewart uses a quest to understand why snowflakes form in unique six-sided designs to take the reader on a tour of mathematical patterns in nature. "Snowflakes are a showcase for the mathematics of pattern formation," he says. "What Shape Is a Snowflake?" is an overview of the mathematics behind nature's patterns, from the microscopic to astronomical. Stewart starts by hinting at the depth and implications of his seemingly simple question about snowflakes, presenting a little history of mathematicians' efforts to understand patterns, and explaining the significance of symmetry.
Then he delves into the Why and How of patterns that manifest themselves in everything around us: big and small, living and non-living, spirals, wiggles, cycles, mirror symmetry, rotational symmetry, tiling patterns, spots and stripes, waves, lattices, and even patterns in time. When reading about patterns in living things, I could not help but doubt mathematical explanations of biological processes. But Stewart acknowledges this problem and makes the case that the principles underlying which patterns can and will occur may be governed by mathematics, though the patterns are coded in genetics.
The book's final section delves into some apparent inconsistencies in the links between mathematical laws and nature's patterns and mathematicians' continuing efforts to explain them with theories of bifurcation, symmetry-breaking, and fractal geometry. Finally, Ian Stewart answers that question about snowflakes -but not before he has posed a new question: What Shape Is the Universe? "What Shape is a Snowflake?" is a nice introduction to the mathematics of pattern formation for the layperson. It presents the ideas behind the patterns without mathematical formulae and with a great many color photographs and illustrations. It will pique the reader's interest in everything from ancient Pythagorean math to modern chaos theory by giving us a sense of what humans have learned about patterns and what continues to elude us.
Required reading for everyone learning math........2005-08-24
Rob Hardy's review is an excellent summation of this excellent book. "What Shape is a Snowflake?" is a book about the big picture, about the meanings behind and the connections between big ideas. This book is not about details of applying or calculating under these frameworks. As has been stated before, this is an excellently illustrated and formatted book. The pictures and text dance with each other, nicely balancing and building interest in each other.
As Mr. Stewart says, he sees mathematics and beauty as attached ideas and this book is an effort to show the beauty of mathematics. "Most people's mental image of mathematics is page upon page of complicated `sums' - not an especially beautiful sight. I sympathize, believe me. But that's arithmetic, not mathematics (I'm quite passionate about this). Those symbols on the page come no closer to the subject's true beauty than the staves and semiquavers of musical notation come to a Beethoven symphony." As such, this is definitely a book about mathematics and definitely not about arithmetic. There are many references in the book to original publications and theories, and there is a short section at the end for further reading so anyone who wants more detail has a place to start looking. For me this book provided a clear and concise description of the ideas at the foundation of various mathematical principles. Mr. Stewart focuses his book on patterns and their implications. He talks about the different dimensions, scale, and symmetry of patterns, he talks about bifurcation, fractals, chaos, randomness, complexity and phase transitions. He also showed how these ideas and principles thread their way through literally everything in the universe.
This book should be approachable for any child in junior high or high school. Additionally, I think it is an excellent introduction for any adult interested in understanding the world around us.
Mathematics deserves four colour.......2002-07-19
I must admit I was looking for more detail from this book than it contains. I was looking for more detail on hexagonal systems.
Instead there is less detail and less formal mathematics. I found it to be rather similar to other publications by Ian Stewart, such as the book Fearful Symetry which contains many of the same ideas.
Despite my personal desires I am glad to see that Ian has finally been granted lots and lots of expensive four colour illustrations with which to explain how interesting mathmatics really is.
I immediately found a use for it in the workshops I run for children. It is the best illustrated book Mr Stewart has yet produced.
A Universe Full of Mathematics.......2001-11-07
In _What Shape is a Snowflake? Magical Numbers in Nature_ (W. H. Freeman), Ian Stewart has managed to write a wonderfully comprehensive and colorful mathematical tour of the universe from top to bottom without putting a single equation into his book. In fact, there aren't really many numbers. He gets to show what happens when a mathematician looks at the infinite aspects of the world. He writes, "I am a mathematician. I experience these wonders through a mind that has spent a lifetime learning how to detect patterns, how to understand patterns, how to find new patterns... I stand on the shoulders (and lean on the elbows) of giants, on five thousand years of mathematical history that has been groping toward such understanding. I see what all humans see, and in a few respects perhaps I see more. I see clues to rules, laws, regularities."
The snowflake is key to his tour, and there is plenty to learn specifically from it, but since Stewart is keen to draw on patterns all over the place, the range of his book is amazing. In well connected chapters, looking closely at snowflakes takes him to the leafy patterns of frost on the window, the organization of leaves around spirals and Fibonacci numbers, the spiral of the nautilus shell, the stripes and amazing triangle patterns on other sea shells, the patterns of stripes on zebras and fish, the grooves in sand dunes and the lines of dunes themselves, the lines a sidewinder leaves in the sand, the synchrony of a millipede's legs and a horse's at different gaits, the oscillations of the legs of robots, the ups and downs of animal populations, the chaotic variations of weather and of the planets in the solar system, and the shape of the universe. It is clear that Stewart sees connections everywhere, and is only using the snowflake as an excuse to look at the foundations of physical laws, the nature of time, space, and matter, and why patterns in one field give clues to patterns in something entirely different. "I'm going on a journey in search of the snowflake's secret," he says, "and, with it, the deeper secrets of our astonishing universe. And you're coming with me." It's a beguiling invitation from a masterful guide.
Naturally a tour of this type, with all it encompasses, is not going to be long on detail, and anyway, one would have to start getting into equations for that. There is a useful list for further reading at the back of the book, for those who insist on stronger doses of such stuff. Stewart's book, however, is an exhilarating, accessible, vividly illustrated voyage through classic and current mathematical ideas. By the end of it, a reader will understand that the snowflake's shape is determined by phase transition, bifurcation, symmetry-breaking, chaos, fractals, and other complexities. Oh, and the book does eventually reveal what shape a snowflake is.
Average customer rating:
- Not recomended
- Best Laboratory Math Book on the Market!!
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Laboratory Mathematics: Medical and Biological Applications
Joe Bill Campbell , and
June Mundy Campbell
Manufacturer: Mosby
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Tietz Fundamentals of Clinical Chemistry
ASIN: 0815113978 |
Book Description
The best laboratory math text on the market for almost 20 years, this title covers both the general principles of mathematics and specific equations, formulas, and calculations used for laboratory testing. It provides simple, easily understood explanations of calculations commonly used in clinical and biological laboratories. Contains more than 1000 practice problems.
Customer Reviews:
Not recomended.......2006-07-13
This book is horrible in understanding Lab Math. It does help in some areas such as molarity, but the solution dilutions and trying to decipher what they want in the word problems are very difficult.
Best Laboratory Math Book on the Market!!.......2001-01-17
I am a Math Phobic person and for me this book is practically My Laboratory Math Bible. This book alone helped me, a Math Phobic, to finally understand laboratory math. The Campbell's are truly gifted when it comes to making things understandable to the nonmathematically inclined Labortorian.
This book has almost every imaginable formula that you could possibly need in the clinical lab. There's tons of examples and exercises coupled with clear concise explanations throughout. This is the best book on the market for Laboratory Science students and for those who need a brush up on lab math.
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