Book Description

This concise introduction to probability theory carries on the success of previous editions, offering readers a logical, well-organized look at the fundamental of the subject--includes applications that strengthen engineers' grasp of probability concepts. New! Coverage of discrete-time random processes and sequences, and other general topics related to digital signal processing. ... Read more

Reviews (3)

4.5 stars as an undergraduate textbook for EE students
This book is one of the best undergradute textbooks for EE students, especially students having focus on physical-layer communication engineering. The highlight of this book is the enormous amount of well-written problems at the end of each chapter. These problems really help students fully understand abstract definitions and theorems which otherwise will not be easily cracked.

This book, however, has the following drawbacks:
1. The author should have emphasized in the first chapter the importance of real analysis and measure theory in order to motivate the students planning graduate research to study and prepare for the math courses during their undergraduate study.
2. No section for complex Gaussian random variable and vector, which are very important in digital communications.
3. No limit theorems except CLT.
4. No handling of convergence of a random sequence.

Even with above drawbacks, this book is still the classic. I recommend ambitious students to read a little bit advanced books along with this book to better understand the subject.

Poorly writtin and Incomprenhensible.
This book does a very poor job of explaining principles and concepts involved in this subject after chapter number one. This book has examples that are poorly explained and infrequent. The examples seem to consist of one the formulae two the answer with no explanation of the reasoning or the how of the intermediate steps required to obtain the solution. Also example problems are full of subitutions without explanation of these "clever tricks" subistutions. Additionally this work has no given answers to the given problems at the back of the chapters. As all students know trying to solve problems this is essential to check ones work for understanding of the course material and problem questions.
For example I always do some problems at the back chapter and check to see if I have arrived at correct answers. If I do I can assume I have a pretty good understanding of the material. This seems to always work for me.
In summary this books lack of detailed explained examples,lack of details on those examples and lack of answers in the back of the book makes me wonder if the author expects the students to use the ouji board to understand his example problems, the Pshchic friends hotline for the written material and random guess process for the problems at the back of the chapters.

A very good book for beginners.
I am a novice. I've been reading some other books of probability before, and I've found that this one is much clearer than the others. ... Read more

Book Description

As the power of Bayesian techniques have become more fully realized, the field of artificial intelligence (AI) has embraced Bayesian methodology and integrated it to the point where an introduction to Bayesian techniques is now a core course in many computer science programs. Unlike other books on the subject, Bayesian Artificial Intelligence keeps mathematical detail to a minimum and covers a broad range of topics. The authors integrate all of Bayesian net technology and learning Bayesian net technology and apply them both to knowledge engineering. They emphasize understanding and intuition, but also provide the algorithms and technical background needed for applications. Software, exercises, and solutions are available on the authors' Web site. ... Read more

Reviews (1)

Bayesian Networks for Undergrads and Practicioners
Despite its name "Bayesian Artificial Intelligence" covers Bayesian network (BN) techniques only. Other Bayesian techniques useful for AI are not treated.
The content is divided in three main sections: (1) The basics of probabilistic reasoning with BNs, (2) Causal discovery (finding BNs from data), and (3) "Knowledge engineering".
The first part covers the fundamental concepts and algorithms around BNs and (simple) decision networks. It is well-written and clear, but readers who are not totally new to the field might find only little new information (e.g., loopy belief propagation, continuous densities, large decision networks, etc. are not covered).
The second part is on how to deduce causal relationships from observational data. Constrained-based and Bayesian approaches are covered, but on a rather general level. I am not sure how easy it is to implement the algorithms from the descriptions provided. When it comes to details of the algorithms, proofs, or mathematical background the authors very often refer to the literature due to "lack of space". From a practical standpoint, it is unfortunate that the different methods are compared to each other only superfiscially. For instance, one method presented performs a large number of statistical tests; one would expect that this requires large amounts of data in order to avoid false positive results. Is this a problem? With questions like these the reader is often left alone.
I am not competent to talk about part three (knowledge engineering), so I end with my general impression of the book: I would have appreciated if the authors had treated some the algorithms in greater detail and had spent a few pages on advanced concepts and current research directions. On the other hand, some information provided could have easily been left out. (For instance, how to download and install certain software packages from the internet, Kevin Murphy's well-known survey on BN software packages, screenshots of user dialogs, etc. just eat pages. Providing the URLs to the corresponding sites on the internet is completely sufficient, and the information there is more likely to be up-to-date.) The saved pages could then be spent on information which is not readily available elsewhere.
To summarize: The book provides a mostly well-written general overview of the basic concepts and could serve as a first introduction to the field. However, it leaves the reader often alone when it comes to the mathematical background, potential practical pittfalls, or advanced algorithms. ... Read more

Reviews (5)

for serious non-mathematicians
This is a serious book. Stewart explains clearly and concisely for a non-mathematician some of the central ideas of mathematics. Perfect for those willing to put in some thought. I'd also recommend it to anyone in first year pure math. And especially to anyone who teaches math.

A classic - the first version of this book appeared in 1975.
This charming book was written by a man who knows how to teach, and how to have fun. For example, as each successive topic is discussed, Mr. Stewart is careful to furnish the reader with an intuitive grasp of its main points. Only then, does he delve into the topic's details. However, what really makes this book readable is the author's wit, and sense of delight, as he illuminates--one-by-one--the abstract concepts of modern mathematics. Amazingly, this book can be read by almost anyone, and they will come away with an understanding of the why, and the wherefore, of modern math.

In theory at least, having a degree in pure math meant that I had insights that most engineers don't have. In reality, it meant I was more aware of what I didn't understand. When I got this book, I went straight to the topics I'd never gotten the point of: set theory, topology, and hyperspace. I was not disappointed, but it was not until I settled down and read the whole book that I really got the point. Modern mathematics (modern meaning the late 1800s on) provides a framework for all math. That is why it is--of necessity--more abstract, generalized, and rigorous.

Interestingly, the figures in this book are hand drawn. Perhaps its because this book has a way of transporting the reader to a university classroom - somewhere. It wouldn't have seemed right if the figures were anything but hand drawn.

outstanding guide to higher math for the layman
This book is very much in the same spirit as more recent books such as Keith Devlin's "Mathematics, the New Golden Age" (which I also recommend). It explains various subjects in pure mathematics in order to make them accessible and interesting to non-mathematicians. A great variety of subjects are covered, including abstract algebra, group theory, number theory, and especially topology, to which the author devotes several chapters. The links between different branches of mathematics (e.g. topology and group theory) are given special attention, and one of the central themes of the book is the fundamental unity of mathematics. I strongly recommend this book to anyone with a serious interest in mathematics. Plus, the price is definitely right!

One of the most lucid and enjoyable math books available
If you want great mathematical puzzles, you buy a Terry Stickels puzzle book. If you want to read about the universe from the world's best amateur mathematician and physicist, you read Martin Gardner. If you want a professional's point of view of all the above, you read anything by Ian Stewart. This is simply a must read for all clear thinking people.

Absolutely brilliant!
Deserves 10 stars. Here is an author who understands so many advanced concepts and who can write smoothly, clearly and convincingly, bearing the reader along with his keen and interesting mind. Convincingly demonstrates the interrelationships between different areas of modern mathematics. Great mathematics for the layman without being in the slightest bit condescending. I have had an amateur's interest in mathematics since high school but was never able to follow it up professionally. This book is the best I have read in the 30 years I have had this interest. A delight to read, educational and informative. ... Read more

Book Description

This book is an introduction to mathematics--in particular, it is an introduction to discrete mathematics.There are two primary goals for this book: students will learn to reading and writing proofs, and students will learn the fundamental concepts of discrete mathematics. ... Read more

Reviews (3)

This book is sabotage for university students
This book was a required textbook for a discrete mathematics course I am taking in school. Be warned, this book is terrible and is filled with logic holes and gaps!

There are COUNTLESS times in the book where there will be a large proof about a major concept that will take you hours to wrap your head around, only to discover that afterwards it tells you that it is incorrect and suggests that you try to figure it out for yourself!!

From page 372, following a large proof: "Nice proof, huh? Not really. The above proof is incorrect! What went wrong? Try to figure out the difficulty for yourself."

From page 464, following a proof: "Read this proof carefully. When you spot the error, you will know how to answer this problem." A smiley face follows.

Professors, suggest this book to your students if you wish to sabotage their academic careers.

Wonderful book!
This book is very clear. It explains most of the fundamentals of discrete mathematics, including logic, combinatorics, graph theory, probability, number theory, cryptography, and more. Things are clearly explained, and students are taught the basics of proof writing. Proof templates give the reader a skeleton for different proofs (such as direct, contradiction, induction, contrapositive, etc.). A great book!

Simplistic explanation for complex material
This book explains, with simple examples complex material. He includes proof templates, that are helpful in the understanding of the material. ... Read more

Book Description

This book provides an integrated presentation of mathematics and its application to problems in medical imaging.Key topics include data collection, signal processing and noise analysis.The book should be suitable for self study by a motivated person with a solid mathematical background interested in medical imaging. ... Read more

Amazon.com

If Barbie thinks math class is tough, what could she possibly think about math as a class of metaphorical thought? Cognitive scientists George Lakoff and Rafael Nuñez explore that theme in great depth in Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being.This book is not for the faint of heart or those with an aversion to heavy abstraction--Lakoff and Nuñez pull no punches in their analysis of mathematical thinking. Their basic premise, that all of mathematics is derived from the metaphors we use to maneuver in the world around us, is easy enough to grasp, but following the reasoning requires a willingness to approach complex mathematical and linguistic concepts--a combination that is sure to alienate a fair number of readers.

Those willing to brave its rigors will find Where Mathematics Comes From rewarding and profoundly thought-provoking. The heart of the book wrestles with the important concept of infinity and tries to explain how our limited experience in a seemingly finite world can lead to such a crazy idea. The authors know their math and their cognitive theory. While those who want their abstractions to reflect the real world rather than merely the insides of their skulls will have trouble reading while rolling their eyes, most readers will take to the new conception of mathematical thinking as a satisfying, if challenging, solution. --Rob Lightner ... Read more

Reviews (18)

Mathematics as a product of the human mind
While I agree with the previous reviewer that the authors may at times suggest a little too much credit for a work that does have its predecessors, I still consider this a great book.

By attacking the transcendental nature of mathematics, and elaborating the grounding of mathematical thought in the metaphorical mapping of the mind, many important implications arise ranging from the meaning of mathematics, the way mathematics is practiced and proofs are formulated, to the way mathematics should be taught. The authors formulate their intention to link the fields of mathematical thought and cognitive sciences to generate the field of mathematical idea analysis. They stress the point that their work should be considered as an initial step and in no way as the final word. In the analysis of the thought process a number important aspects of mathematical thought get visited. Having recently read Aczel's book about Cantor and Infinity- I now feel I over-rated it at 2 stars- Lakoff and Nunez give a treatment of the concept of infinity based on the basic metaphor of infinity (BMI) that simply ridicules Aczel's. Masterful.

Is this book perfect? It's excellent, but could (and will) be improved.

Little attention is paid to the idea of linearization that is such a central concept in much of mathematics. In attempt to save the best for last, the authors conclude with a detailed analysis of the ideas behind Euler's famous formula: e^ip = -1. They claim that such a treatment would be very helpful to develop a better understanding of the formula, than a more standard approach. It may be that my former Dutch high school education, blessed with a great math teacher, deviates from the current US standard. Yet, I must say that the analysis of Lakoff and Nunez is simply not as clear and thorough as the one I received in my teens. Not only did my high school analysis include all the metaphors but a much clearer link between the e^ip and the sin(t) + i sin(t) functions based on the Taylor expansions. It is especially in this last section that the authors undermine their cause, by making statements that an expression e^p would be devoid of implicit meaning.

While I agree with the author's central dogma of mathematics as one of the human mind's most beautiful and enduring products they sometimes take their argument just a little too far. By a careful analysis and conceptualization of simple ideas mathematics has generated formalized concepts that allowed extrapolation into conclusions that initially appeared non- or even counter-intuitive. I think, that this process has been so crucial in establishing the magic or romance of mathematics.

No matter what the authors may say, wherever in the Universe any group of beings draw the line connecting the series of points that share the same distance, r, to this center, the resulting circle will always have a 2pr circumference. They may conceptualize it completely differently, but will come to the same conclusion.

Refreshing approach to the ideas of mathematics
As a physicist and recreational mathematician, I found this book stimulating and reassuring. The connection of mathematics to human realities in our embodied world gives a new way to understand the conceptual and practical power of mathematics, as well as approach its limitations. I also found it helps to explain my preference for "seat of the pants" approach to some subjects, as contrasted to the proof-driven esthetic of many professional mathematicians. I think this book may encourage new ideas in mathematics education as well. If you're a Platonist, you'll find a lot to scream about, but its a great read for any math nut.

classic lakoff
this book is a linguist's assessment of the origin of our cognitive mathematical faculties. it is a good read, and is more satisfying than most pop-sci type books. I highly recommend reading George Gamow's 1,2,3...Infinity! along with this book.

An interesting view of the nature of mathematics
For as long as Western mathematics has been around, it has generally been viewed as having an existence independent of human experience, as belonging to a Platonic realm of forms and ideas. To make it embodied in the human psyche, as the authors attempt to do in this book, would be a sacrilege to many mathematicians. Such a move would deny the 'eternal truth' of mathematics some would argue.

But the last few decades have seen the rise of cognitive science, and this field has led to many interesting insights into the operation of mind and has demystified its status in the world. The authors though see cognitive science as being deficient in one respect: it has omitted the study of mathematical ideas from a cognitive perspective. There is no cognitive science of mathematics, they say, and hence they endeavor in the book to correct this deficiency. Such a project is definitely worth the effort, for mathematics has to be interpreted in the light of what is known about the mind, or as the authors put it, "it should study precise nature of clear mathematical intuitions".

The book is very interesting to read, and the justifications for the assertions put forward by the authors are certainly the most optimal if viewed in the context of what is currently known in cognitive science. Further work must be done however, particularly in tying their ideas to the very intensive research in neuroscience that is being done at the present time. The prospect of having a science of mathematical thought is an exciting one. This book is the best that is currently available.

The attitude of the authors is most refreshing, in that they not only show great enthusiasm throughout the book, but they are not nervous about discarding what they view as the "romance" of mathematics. They list several statements illustrating this "beautiful romance", such as the view that mathematics has an objective existence, which transcends the existence of human beings; or that human mathematics is merely a part of abstract, transcendent mathematics, and that reason is a form of mathematics. These romantic beliefs appear to be false, the authors say. Instead, they argue, the nature of mathematical ideas is that they are inherently metaphorical in nature. They give several examples of this in the first few pages of the book, with the rest of the book elaborating in great detail their reasons for asserting this.

This is certainly an exciting time to be involved in mathematics, and assuming more evidence is accumulated that supports the authors opinions on the embodied nature of mathematics, it will be even more interesting to be engaged in mathematical research and in the teaching of mathematics. Mathematical thinking will then viewed as part of us, not some abstract collection of statements existing in some vaguely defined realm. Viewing mathematics as purely embodied may also give much more insight into teaching non-human machines how to do mathematics. This is the most exciting prospect of all.

you must read this book
If you hate math, you must read this book.
If you love math, you must read this book.
If you live in the deadly icy Platonic realms, you must save your life by reading this book.
If your math teacher is confusing the hell out of you, get this book for your math teacher. ... Read more

Book Description

Authors Wayne Winston and Munirpallam Venkataramanan emphasize model-formulation and model-building skills as well as interpretation of computer software output. Focusing on deterministic models, this book is designed for the first half of an operations research sequence. A subset of Winston's best-selling OPERATIONS RESEARCH, INTRODUCTION TO MATHEMATICAL PROGRAMMING offers self-contained chapters that make it flexible enough for one- or two-semester courses ranging from advanced beginning to intermediate in level. The book has a strong computer orientation and emphasizes model-formulation and model-building skills. Every topic includes a corresponding computer-based modeling and solution method and every chapter presents the software tools needed to solve realistic problems. LINDO, LINGO, and Premium Solver for Education software packages are available with the book. ... Read more

Book Description

Statistics for the Life Sciences presents the key concepts of statistics as applied to the life sciences, while incorporating tools and themes of modern data analysis. The book emphasizes interpretation of results using real data, which facilitates an understanding of statistics and data through the use of graphical data and analysis. The Third Edition has added many new sections to cover probability rules, random variables, the Wilcoxon Signed-Rank Test, and two-way ANOVA and ANOVA for randomized blocks designs. In addition, there is expanded treatment of logistic regression in Chapter 12. This book is an essential statistics reference for professionals and scientists in biology, agronomy, medical and health sciences, nutrition, pharmacy, animal science, physical education, forestry, and other life sciences.

Reviews (3)

I DON'T HAVE IT YET
I wish I knew where my book was...

easy introductory to statistics
I recently finished using Samuel's book in a dual level statistics course. As an undergraduate I found the material basic and extremely easy to follow. From the perspective of a student who has never had a formal statistics course, I found this book to be simple. Problems are relevant to the life sciences. I perhaps expected more challenging concepts and problems to have been presented-a bit disappointing.

very good stat book
Great examples, great problems, and a great writer sum up this book written by a Purdue Professor. If you deal with statistics and have a career in the health sciences, this is the book for you. ... Read more

Book Description

Students and research workers in mathematics, physics, engineering and other sciences will find this compilation of more than 2000 mathematical formulas and tables invaluable. They will see quickly why half a million copies were sold of the first edition! All the information included is practical -- rarely used results are excluded. Topics range from elementary to advanced-from algebra, trigonometry and calculus to vector analysis, Bessel functions, Legendre polynomials and elliptic integrals. Great care has been taken to present all results concisely and clearly. Excellent to keep as a handy reference! ... Read more

Reviews (8)

Indispensible for the physicist
A fantastic summation of neccesary mathematics for any engineer or physicist...the only reason for 4 stars is that it's integral table is a little short.

Not as much help as it should be
I bought this book as an aid to EM theory and Quantum Mechanics. I found little really useful stuff. The series expansion didn't have (1+u)^-3/2 for example, or the curl operator in cylindrical and spherical coordinates. The integral table is limited. The authors should look at books like Dwight, for example, and make sure their coverage is more complete. I am disapointed in it. For the money, it should be much better.

Inexpensive reference!
As an undergraduate physics major, it is necessary to have some sort of mathematical handbook containing tables of integrals, trig identities, differentiation rules, vector identities, etc. As such, I cannot give this book higher praise! While does not contain as many features as the CRC Handbook of Tables and Formulae, or many of the other big famous hardcovers, it makes up for this in many ways. It is compact, lightweight and fits in most bookbags. It contains the tables and rules which will be most used in undergraduate homework problems. Most importantly, it is affordable on a student budget! I carry this with me to study groups and tutoring sessions.

You are crazy if you don't have this book!
Great reference for formulas and identities that you have forgotten. Integral table is awsome. This book is week on more advanced stuff like bessel functions etc...This is some of the best money I have ever spent. Used it all the time in my physics classes and ALWAYS carry it with me. How did I ever get on without it?

Best money i've ever spent
This handbook was pretty much all I ever needed from college through my Ph.D. in physics. An extremely valuable resources. If the formula you need isn't in here, chances are you did the problem wrong ... Read more

Book Description

The book aims to introduce the reader to DEA in the most accessible manner possible. It is specifically aimed at those who have had no prior exposure to DEA and wish to learn its essentials, how it works, its key uses, and the mechanics of using it. The latter will include using DEA software. Students on degree or training courses will find the book especially helpful. The same is true of practitioners engaging in comparative efficiency assessments and performance management within their organisation. Examples are used throughout the book to help the reader consolidate the concepts covered. ... Read more

Book Description

"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." ---Applied Mechanics Review (Review of First Edition)  This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership.Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition is an exceptionally complete and accessible text/reference for graduate students, researchers, and professionals in mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference. ... Read more

Book Description

This Seventh Edition explains in plain English the basic concepts and procedures of statistical analysis and makes a special effort to clarify such topics as the standard deviation, variance interpretation of the correlation coefficient, hypothesis tests, degrees of freedom, p-values, and estimates of effect size.
* Highly interesting and engaging exercises include how standard scores might explain the disappearance of .400 hitters in Major League Baseball, probability calculations that recreate the chillingly high likelihood of the space shuttle Challenger disaster, and a chi-square test of the survival rates of cabin and steerage passengers aboard the Titanic.
* Avoids unnecessary math, computational busy work, and subtle technical distinctions, without sacrificing either accuracy or realism.
* Each chapter begins with an overview and ends with a summary, a list of important terms, and numerous exercises. ... Read more

Reviews (2)

Statistics
Very easy to use. Open airy text. Well defined formulas and examples provide clear instruction on how to perform each test.

User Friendly
The chapters are very easy to read and understand. Each chapter includes exercises to do after each new concept is explained. Most answers to the exercises are included in the back of the book. The step-by-step instructions make concepts and exercises user friendly. A great Stats book. ... Read more

Book Description

Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization.Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place. ... Read more

Reviews (2)

An essential component of all mathematical libraries
Until I read this book, I had no perspective on the number of significant constants there are in mathematics. Finch describes in complete detail a large number of constants of interest in mathematics, I didn't count how many are covered, but a list of one per line covers twenty four pages. It was also interesting to note that twelve of the pages list constants between zero and one. I couldn't help but wonder if this cluster represents a bias of the author or that mathematics is somehow naturally biased into this interval.
The coverage of each constant or group of constants follows the pattern of an explanation of how the constant arose, the formulas that are used to define it and an extensive set of references. So extensive that at times the paper devoted to the reference list rivals the amount spent in the explanation of the constant.
There are eight chapters, which group the constants into the following categories:

1) Well-known constants, which covers constants such as Ð, e and the golden mean.
2) Constants associated with number theory.
3) Constants associated with analytic inequalities.
4) Constants associated with the approximation of functions.
5) Constants associated with enumerating discrete structures.
6) Constants associated with functional iteration.
7) Constants associated with complex analysis.
8) Constants associated with geometry.

Separate subject and author indexes are in the back, a most sensible approach as many of the constants are named after the person who first described them.
I consider this book to be an essential component of all mathematical libraries. I have placed it on my "within the grasp" shelf and have strongly recommended to the college library that it be added to the reference collection.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

An Instant Classic
This is an instant classic of mathematical exposition, a superb addition to the series Encyclopedia of Mathematics and Its Applications. Steven Finch's engaging style and lucid, self-contained essays on an amazing variety of topics will appeal to a wide audience. Beginners and experts alike will find a treasure trove of stories, unexpected appearances of numbers, connections between different subjects, and unsolved problems (e.g., if x is the square root of 2, is the tower of powers x^x^x irrational?).

From the Preface: "Material about well-known constants appears early and carefully, for the sake of readers without much mathematical background." The well-known constants include Pythagoras' square root of 2, the Golden Mean, Euler's e and gamma, Archimedes' pi, Apery's zeta(3), Catalan's G, Khintchine's K, Feigenbaum's delta, Madelung's M, and Chaitin's Omega.

There are chapters on constants associated with the fields of number theory, real and complex analysis, approximation of functions, enumeration of discrete structures (some from physics), functional iteration (e.g., paper folding), and geometry. A Table of Constants in decimal form directs the reader to sections of the book. Many sections have extensive lists of references, and Finch indicates exactly where in the literature one should look for rigorous proofs and further elaboration. Author and Subject Indexes complement each other. More than sixty figures illuminate the text.

This book shows the mysterious ubiquity and "unreasonable effectiveness" of certain universal constants. Anyone interested in mathematics will benefit from reading it. ... Read more

Book Description

Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis.What's new in the Second Edition?Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The author has also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress.He discusses three different linearization techniques to solve nonlinear differential equations.Also included are new sections on shell formulations and MATLAB programs.These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists. ... Read more

Reviews (4)

There has to be a better book to learn FE.
Professor Young Kwon teaches at the Naval Postgraduate School in Monterey, CA. I used this book in his class and found little difference when I compared it to the first edition. The first edition has some minor errors, but the problem sets for each chapter along with the Matlab programs provided are very much the same. The first chapter has some basic Matlab necessities and the second chapter covers weighted residual methods (strong / weak formulation, least squares, collocation, and Galerkin). There is a one paragraph summary of the Raleigh-Ritz method (derived from Calculus of Variations), which is more accurate but not as popular as Galerkin. I found a much better explanation of these weighted residual methods in an undergraduate numerical analysis book. The remainder of the book covered shape functions, isoparametric functions, numerical integration techniques, boundary and initial value problems, eigenvalue problems, beams, shell and plates, and trusses.

Caution:
- If you are planning to use this book as a reference or to educate yourself. STOP! This is a boring and merciless graduate-level book. At times we (study groups) would spend anywhere from half an hour to an hour trying to decipher the sample problems. Don't waste your time looking for the solutions manual; it is harder to follow than the sample problems.

- If you want to learn the core of FE and can program easily, this book would help -- but it won't be easy.

- If you want to learn FE for practical applications, spend your energy using a commercial or open-source FE package.

More general comments:
- If asked to describe this book, I would reply with "grueling".

- The Matlab code is far from being easy to understand. Maybe it's easy to follow the logic, but there is very little documentation to support the code. You will spend A LOT of time figuring out the variables alone, which has a lot to do with how well you understand the code.

- Someone with a non-engineer background would NOT be able to understand this book. Someone with a technical background and a strong math foundation may be able to. For example, this book contains a few topics from Theory of Elasticity. This theory is taught in advanced solid mechanics classes -- not even the undergraduate Mech-E's cover it. You should also have a good handle on matrix algebra, integral calculus, and basic ODE's.

Bottom Line:
I did not like how this book presents the FE Method. If you really need it...good luck!

understanding the finite element method
This book carries on from the first edition, lots of new theories and programs have been added. The errors in the last edition(1996) have been corrected. This book is a must for people who want to understand the finite element method and for people who want to learn how to program it using 'Matlab'. Matlab is one of the most widely used programming tool.

I have the old edition but i find this new edition refreshing. The new theories and programs help in digesting the book better.

overall this is an indispensable book for people trying to learn to program the finite element method because it gives a clear understanding of how a finite element code works.

thanks,

kartik srinivas

Excellent finite element text
This book is extremely useful, especially for those new to the finite element methods. Despite the fact that it puts a lot of emphasis on matlab, the code is easy to understand and translate into other powerful languages like fortran 90. It took me a few days to start writting my own FEM code after buying the book. I would strongly recommend it even for those with a non-engineering background.

bug into fetruss2.m
Dear Sir There is little mistake into file fetruss2.m. The matrices consistent and lumped are not correct. wrong matrix: m=(rho*area*leng/6)*[ 2*c*c+2*s*s 0 c*c+s*s 0;... 0 2*c*c+2*s*s 0 c*c+s*s;... c*c+s*s 0 2*c*c+2*s*s 0;... 0 c*c+s*s 0 2*c*c+2*s*s]; rigth matrix: m=(rho*area*leng/6)*[ 2*c*c 2*c*s c*c c*s;... 2*c*s 2*s*s c*s s*s;... c*c c*s 2*c*c 2*c*s;... c*s s*s 2*c*s 2*s*s]; % lumped mass matrix wrong matrix: m=(rho*area*leng/2)*[ c*c+s*s 0 0 0;... 0 c*c+s*s 0 0;... 0 0 c*c+s*s 0;... 0 0 0 c*c+s*s]; rigth matrix: m=(rho*area*leng/2)*[ c*c c*s 0 0;... c*s s*s 0 0;... 0 0 c*c c*s;... 0 0 c*s s*s]; The consistent and lumped mass matrices shown in page 209 - 210 are not consistent with the correspondent problem. (example 7.4.1). The matrices do not consider the angle corrections. ... Read more

Book Description

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses.
* Reduced mathematical rigour to fit the needs of undergraduate students ... Read more

Reviews (4)

Very Good.
I read the FIRST EDITION. This is definitely the best introductory mathematical logic book I've seen. It's the most rigorous, most advanced (a reasonably strong form of Godel's theorem is given), and is well-organized and very clearly written. It would be suitable as 1)an introduction for students with some mathematical experience- say a little abstract algebra and perhaps some previous exposure to logic. 2)a refresher for advanced students 3)a nice reference for basic topics. The exposition is great- Enderton always clearly explains what he's doing and why, keeping the reader focused on the big picture while going through the details. He helps to place topics in perspective, and has organized the book so readers can skip some of the more involved proofs and sections on the first reading. Chapter 1 covers propositional logic, with a general-purpose discussion of inductively defined sets, unique readability, and recursion. Many books these days do a sloppy job justifying recursive definition, or dont bother at all- Enderton does it right and is fairly detailed. Chapter 2 begins first order logic and has the most detailed proof of the completeness theorem I've seen. Sect 2.7 concerns translating between theories in different languages, something i hadnt seen developed explicitly before. 2.8 is a great exposure to nonstandard analysis- long enough to give you an idea how it works and why its useful. Chapter 3 begins with an analysis of some reducts of number theory- (N,0,S) (N,0,S,<) and (N,0,S,<,+) and shows how to eliminate quantifiers in them. Next, toward Godel's theorem, a finite set of axioms for a subtheory of number theory is given, and a host of relations and functions are shown to be representable in this theory. In 3.5 we get the fixed-point theorem, Tarskis thm, a weak Godels thm, a stronger Godels thm, and Church's Undecidability thm, and an introduction to the arithmetic hierarchy. 3.6 lifts Godels thm to show set theory is incomplete, and discusses Godels 2cd thm. Chap 4 is 2cd order logic, skolem normal form, many-sorted logic (a first order logic with different sets of variables ranging over different universes), and general 2cd order logic (restrictions are placed on the subsets "X" ranges over in the 2cd order formula \all X \phi). Basic recursion theory is developed throughout the book- Enderton begins with informal notions of computation, then defines a relation R as recursive iff it is representable in some consistent finitely axiomatizable theory, and discusses Church's thesis. 3.8 quickly covers universal computers, partial functions, Kleene normal form, unsolvability of the halting problem, the smn thm, Rice's them, and a register machine model. All this seemed a bit disorganized, so familiarity with computation and automata theory would be a plus. Heres the contents for the first edition, c1972:

Chapter Zero - USEFUL FACTS ABOUT SETS . . . .1
Chapter One - SENTENTIAL LOGIC
1.0 Informal Remarks on Formal Languages 14
1.1 The Language of Sentential Logic . . . . . 17
1.2 Induction and Recursion . . . . . . . . .22
1.3 Truth Assignments . . . . . . . . . . . .30
1.4 Unique Readability . . . . . . . . . . .39
1.5 Sentential Connectives . . . . . . . . . .44
1.6 Switching Circuits . . . . . . . . . . . .53
1.7 Compactness and Effectiveness . . . . . 58
Chapter Two - FIRST-ORDER LOGIC
2.0 Preliminary Remarks . . . . . . . . . .65

2.1 First-Order Languages . . . . . . . . . .67
2.2 Truth and Models . . . . . . . . . . . 79
2.3 Unique Readability . . . . . . . . . . . 97
2.4 A Deductive Calculus . . . . . . . . . .101
2.5 Soundness and Completeness Theorems . .124
2.6 Models of Theories . . . . . . . . . . . 140
2.7 Interpretations between Theories . . . ... 154
2.8 Nonstandard Analysis . . . . . . . . . . .164
Chapter Three - UNDECIDABILITY
3.0 Number Theory . . . . . . . . . . . . 174
3.1 Natural Numbers with Successor . . . . 178
3.2 Other Reducts of Number Theory . . . . 184
3.3 A Subtheory of Number Theory . . . . . . 193
3.4 Arithmetization of Syntax . . . . . . . . .217
3.5 Incompleteness and Undecidability . . . 227
3.6 Applications to Set Theory . . . . . . . .239
3.7 Representing Exponentiation . . . . . . .245
3.8 Recursive Functions . . . . . . . . . . .251
Chapter Four - SECOND-ORDER LOGIC
4.1 Second-Order Languages . . . . . . . . . 268
4.2 Skolem Functions . . . . . . . . . . . . 274
4.3 Many-Sorted Logic . . . . . . . . . . . . 277
4.4 General Structures . . . . . . . . . . . . 281
Index . . . . . . . . . . . . 291

Excellent Textbook with lots of examples
I used this book for self study of Mathematical Logic with the aim of understanding Godel's incompleteness theorem. I also referred to other introductory Mathematical Logic books. In my opinion, this book is by far the best among them. Very readable and contains lots of carefully selected examples.

Excellent introduction to logic
One of the very best introductions to logic, combining readability and depth. An excellent book.

Great Book
This is a great introductory book. Some set theory, sentential logic, first-order logic, metatheory/model theory,number theory, undecidability and Godel's Incompleteness, and Second-Order Logic. You still have to take a lot of time trying to soak in the stuff, but that's because of the complex nature of the material, not the book. The book itself is really good. ... Read more

Book Description

Mathematicians and scientists have been closely tied to many famous disasters. The Challenger explosion, the failure of the Mars Orbiter, and the Kansas City Hyatt Regency walkway collapse all involved thinking errors. This book presents the ten things our future mathematicians and scientists must know to prevent these kinds of tragedies from occurring. Because science and mathematics instruction is often dominated by facts and calculation, children are rarely exposed to these important concepts. Over 50 stories are included that show children the strong connections between mathematics and science and the real world.

a)Sister Elizabeth Kenny discovered an effective treatment for polio, but it was ignored by the medical establishment for 30 years.

b)Engineers tried to stop the Challenger launch because of concerns that the o-rings might fail in the cold temperatures. They were ignored.

c)Dr. Semmelweis discovered why thousands of women who gave birth at hospitals were dying and a simple way to stop the deaths. His colleagues ignored his discovery and thousands of women continued to die.

d)How a simple design mistake led to 114 deaths when a walkway collapsed at the Kansas City Regency Hotel.

Questions are included at the end of each chapter to test the reader’s understanding of each concept. ... Read more

Book Description

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.

The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.

In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.

The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Reviews (3)

Not application oriented
I am working on my research which involves applications of Fourier transforms. I spent the whole weekend reading the first five chapters of the book and briefly looking at the exercises, hoping to get a general picture of Fourier analysis and its applications. While theories are actually well presented, I didn't find interesting applications. The book does talk about "applications", like the area enclosed by a simple curve is maximized when the curve is a circle, or that you can find a continuous but nowhere differentiable function using fourier analysis, and other examples in NUMBER THEORY. This kind of applications may be interesting to mathematics students (I was), but obviously not to engineers (I am now). Plus, a lot of nice results are actually placed in the exerciese. I would have missed those if I didn't look at the exercises. So this might be a good text book for mathematics students (if they really do all exercises), it is obviously not for those who are interested in computations and applications.

Excellent, if you've got some experience in analysis
I used this book for an undergraduate-level course in Fourier analysis. It is an excellent text, although I would recommend the prospective learner to take a basic course in real analysis first (or perhaps concurrently, if the learner dares!). With my experience in analysis, it proved very readable. In fact, it strengthened my understanding of (and even interest in!) analysis, as it provides a fruitful application of the subject--one gets to see various important analysis ideas and techniques used in context. One could almost say that the text is an excellent complement to real analysis to help the ideas jell. On the other hand, perhaps it is theoretically possible to use this book as a springboard into learning analysis. The proofs do gloss over some details, which as the previous reviewer noted, can make things tough going at times... I actually found this useful (again, perhaps because of analysis experience), as it omits just enough detail to stay focused on the subject at hand (being too pedantic is likely to make those of shorter attention spans, such as myself, want to wander away), and yet supplies enough detail to remind the reader of the underlying theory, and that all this stuff is mathematically rigorously justified.

The course I took was actually a brand-new course created at the undergraduate level, and was structured around the book, which had also just come out at the time. I can say with confidence that the course was a success, which is pretty unusual for something hot off the press (true, the book itself was based on lectures, but every university has its quirks...).

Challenging
I have just finished a class with the book as its main textbook.The book is well written, but you honestly have to work through each page with pen and paper in hand filling in the omitted steps.Nothing is spoon-fed to you.The exercises are very challenging while the problems develop small theories.If you work through the pain and sweat through the exercises, you will at the end of the book greatly improve your skills and intuition.

The author Stein is a leader in his field and has provided plenty of depth and breadth.This also means that he is on a different level and an argument that he calls "simple" has quite often taken me two pages to justify.However, if you put in the effort it will pay off tenfold. ... Read more

Book Description

Continuing its rich tradition of engaging students and demonstrating how mathematics applies to various fields of study, the new edition of this text is packed with real data and real-life applications to business, economics, social and life sciences. Users continually praise Sullivan and Mizrahi for their attention to conceptual development, well-graded and applied examples and exercise sets that include CPA, CMA, and Actuarial exam questions. The new Eighth Edition also features a new full color design and improved goal-oriented pedagogy to facilitate understanding, including:

• More opportunities for the use of graphing calculator, including screen shots and instructions.
• Icons clearly identify each opportunity for the use of spreadsheets or graphing calculator.
• Work problems appear throughout the text, giving the student the chance to immediately reinforce the concept or skill they have just learned.
• Chapter Reviews contain a variety of features to help synthesize the ideas of the chapter, including: Objectives Check, Important Terms and Concepts, True-False Items,Fill in the Blanks, Review Exercises, Mathematical Questions from Professional Exams (CPA).

Book Description

This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. This is one of very few books to deal extensively with the mathematics of Late Antiquity. It sees Pappus' text as part of a wider context and relates it to other contemporary cultural practices and opens new avenues to research into the public understanding of mathematics and mathematical disciplines in antiquity. ... Read more

Reviews (1)

Interesting project
Cuomo starts this book by suggesting we don't understand the late-classical era, that great confusing muddle which starts around 300 AD when Constantine transferred the capital of the Roman Empire to Constantinople and legalized Christianity. It ends with the Muslim conquest of Alexandria. In crude terms, it is what Gibbon called the 'fall of the Roman Empire.' Cuomo uses the 'Arch of Constantine' as a metaphoric reference. For most contemporary art historians, the arch is a pastiche of scavenged sculptures from earlier and finer artistic efforts. Scavenged is the key word here. The late-antiquity (according to Gibbon) was the moral equivalent of Sodom and Gomorrah.

I don't know how many people still take "Rome's Fall' as a moral litmus test, but I suspect the story still holds a lot of weight. It's this icon that Cuomo targets.

In general terms, I couldn't be more pleased with the project. Unfortunately, it doesn't really get off the ground. Cuomo isn't very forth coming on what she makes of the era. It seems she simply likes pastiche.

She starts her iconoclastic journey well, suggesting the subject of her book might never have existed. It is hard to argue the point. We know almost nothing about Pappus, the man. Unfortunately, the fictional Pappus concept seems to have been mentioned for shock value, and not pursued seriously. I would have been interested in hearing details on the process of putting mathematic lectures on scrolls for academic, social or bureaucratic purposes. Maybe ghost writing was a common practice. This emphasis on the 'media' itself seems critical to Cuomo's case (a role the Arch of Constantine served), but it is entirely ignored.

Cuomo then takes us down an entertaining bunny hole involving legal torture and highly paid astrologers. By taking this route, she hopes to convince us that mathematics was about as important to our late-classical delinquents as, well, ourselves. The legal discussion shows mathematical knowledge put one socially above those who could expect torture during any legal cross-examination. The astrological references show desperate young parents prayed for their off-spring to become mathematicians.

So far, so good, but Cuomo then launches into a book by book deconstruction of the works ascribed to Pappus (whoever he was), and in this the reader starts to wonder just what she wants to say. The less than stunning conclusion is that Pappus had careerist interests and said different things to target groups in hopes of enhancing his authority.

I was less than impressed.

One might surmise Cuomo has a bigger goal, but if it exists, it is very subtle. Of these subtle arguments, the chief seems to be that the standard historiography associates the development of Greek mathematics exclusively with Plato's philosophy (the Proclus (411-485) perspective). Cuomo points out contradictions in this line of reasoning made by Pappus (? 320 ?) and Iamblichus (250?-330?). In this, Cuomo hints at disputing the role of the Neo-Platonic synthesis. Proclus, as the heir to Plato's academy, plays a pivotal role in this. Cuomo seeks to uncover the real mathematician hidden by Proclus and later Neo-Platonic Christians.

If this is really what she hints at, I would be surprised. I am just grasping at straws... The unfortunate fate of the interested reader. ... Read more

Book Description

Mathematical forms rendered visually can give aesthetic pleasure; certain works of art -- Max Bill's Moebius band sculpture, for example -- can seem to be mathematics made visible. This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993.

Mathematicians throughout history have created shapes, forms, and relationships, and some of these can be expressed visually. Computer technology allows us to visualize mathematical forms and relationships in new detail using, among other techniques, 3D modeling and animation. The Visual Mind proposes to compare the visual ideas of artists and mathematicians -- not to collect abstract thoughts on a general theme, but to allow one point of view to encounter another. The contributors, who include art historian Linda Dalrymple Henderson and filmmaker Peter Greenaway, examine mathematics and aesthetics; geometry and art; mathematics and art; geometry, computer graphics, and art; and visualization and cinema. They discuss such topics as aesthetics for computers, the Guggenheim Museum in Bilbao, cubism and relativity in twentieth-century art, the aesthetic value of optimal geometry, and mathematics and cinema. ... Read more