No comments about Fourier Analysis (Graduate Studies in Mathematics) (Graduate Studies in Mathematics).

2 comments about Calculus Mysteries and Thrillers (Classroom Resource Materials).

1. Even though they may be well-written, most mathematics books follow a set formula of presentation that is stale to many. While it may be an alien language to the uninitiated, the theorem - proof style has proven to be a very effective method of data transfer. However, not everyone understands these protocols, which is where books like this are worth their weight in ancient antiquities. Writing good problems that have a clear relevance to something that might actually happen is difficult, but not impossible, and this book is an existence proof of that.
   Eleven problems are given in the book, with the solution presented in the context of an official summary or report of how the conclusions were arrived at. In the first part of the book, there are short summaries of the problems with a list of what the precise mathematical requirements are for solution. This is an invaluable guide to anyone considering using the book as a classroom supplement. All problems require some topic commonly covered in a full year course of calculus. Topics such as the intermediate value theorem, the chain rule, Newton's method, the quotient rule, Newton's Law of Cooling and the Fundamental Theorem of Calculus are needed for solution. The first problem deals with the possibility of a fraud in connection with a parabolically shaped pool table and is presented as evidence to be used in a court of law.
   While the teaching of calculus has been invigorated somewhat recently with the introduction of sophisticated mathematical software, it still lacks some real-world applicability. If you are searching for problems to present to a class that will really be of interest, you will find none better than the eleven in this book.
   
   Published in Journal of Recreational Mathematics, reprinted with permission.



2. While this book is useful to see how one can apply Calculus to everyday life, the solutions were sometimes more complicated than the problem itself. This book is definately not for the novice calculus student. The book uses many formulas that you may not find in a Calculus textbook and it just assumes that you know them. At times, I found it difficult to understand simply because it doesn't explain the problems as thoroughly as I would have liked it to.

4 comments about Functions and Graphs.

1. Great book to help you remember how to do graphs. It has many pictures to keep you in track with what you are doing. It also has many examples and problems to illustrate the material.



2. I tend to look at elementary books like this one from the point of someone who doesn't need to learn from it but might want to use it as a text if teaching or tutoring someone. I learned almost nothing from this book, but I didn't expect to, as it's all material I learned ages ago. But for someone encountering this material for the first time, this would be an excellent book.

   I see this book as used primarily in a pre-calculus math class or for tutoring someone about to take calculus. It gives a good exposition of material that will be encountered at the time a student takes calculus, but at a level that assumes the student has only the algebra that most students entering a calculus course have taken. And from that point, it explains the elements of drawing graphs of algebraic functions and the ideas of tangency that are so critical to differential calculus, and does so in a clear way, with helpful diagrams. It is a slim book, and probably by itself could not be the only text in a pre-calculus math class, but on the subjects it covers, it is the best I have seen. (And that is underrating it, because there aren't many books on the subject. So one might say that "the best there is" isn't really as high praise as it deserves.)

   This book certainly deserves a 5-star rating.




3. This brief text provides a clear introduction to analytic geometry. Its scope is narrow. The authors discuss the graphs and properties of linear functions, absolute value functions, quadratic functions, linear fractional functions, power functions, and rational functions (trigonometric functions are discussed in another volume of the Gelfand School Outreach Program). What distinguishes this book from other treatments of the same topics is the extent to which the authors go to explain, using both words and diagrams, why the graphs of the functions they discuss have the form they do and the many challenging exercises they include.
   
   This book concludes with a chapter length exercise set full of challenging problems. The reader who completes these problems will gain a much fuller understanding of analytic geometry than one who reads a typical precalculus text. While calculus is not required to complete the exercises, the reader may wish to revisit these problems once she or he has had calculus in order to analyze the properties of the graphs more fully.
   
   The text was written initially for a correspondence course in the Soviet Union. Since students could send their solutions to the authors when they were at the University of Moscow, answers or hints to only a few of the exercises are included in the back of the text.
   
   I also highly recommend the other volumes in the Gelfand School Outreach Program. They include The Method of Coordinates, Algebra, and Trigonometry.



4. In this slim, 100 page volume, Gelfand, Glagoleva and Shnol have a wonderful review of graphing.
   
   There is nothing here incredibly advanced; they only cover linear, quadratic, polynomial, and rational (ie, f(x) = P(x)/Q(x) ) functions. But they systematically explain how to transform, how to combine, how to shift, how to reflect... They consider asymptotes (vertical and horizontal), zeros, symmetries. They spend more time with absolute value then one might expect.
   
   They treat these limited topics in depth. I read this book on vacation, cover to cover, completing every single exercise. It was a great refresher, and led me to think about several graphing-skill topics from new perspectives.
   
   I am a teacher, and this book has informed my teaching. Also, I intend to use it with my math team. I do not think you could use this book to teach graphing from scratch. Rather, I see it as a source of enrichment.
   
   The major drawback to this book is the lack of answers in the back. But if you are really stuck, the judicious use of a graphing calculator (or checking with friends or colleagues) should be good enough. At the price, there is no reason not to own "Functions and Graphs."

2 comments about A First Course in Integral Equations.

1. This was almost my first book which I had read about integral equations. The real advantage of it is that this book is not an abstract one, but really teaches you several practical equation solving methods and contains lots of examples and exercises with the answers provided at the end of the book. Simply great !



2. A little background. I am taking an inverse problem graduate level course, which makes use of Gelfand-Levitan equations, Marchenko equations, etc. I had never studied integral equations, and I was looking to get an intuitive understanding of how to solve and approach the G-L and Marchenko equations. One of the main problems I was having was understanding the notation of the G-L equations. This book gave me a lot of the basics that I was missing in how to solve Fredholm and Volterra equations and also where some of the more advanced theory came from. So, I would recommend this book as a great introduction to integral equations, as the name suggests.
   
   For a more theoretical approach, I would first go through Abdul Jerri's book on integral equations, and then, if you want to learn some applications or more theory, I would recommend books by Chadan, Sabatier, Marchenko, etc.

5 comments about Complex Variables with Applications (3rd Edition).

1. Free of fancy pedagogical "features," such as color-coded regions of text and useless chapter summaries. You actually have to read (or at least skim) the book to find a few of the important points. Once you find them, you are treated to very well written (and also very clear and exact) definitions, explanations, and examples.



2. I learned complex variable theory on my own from this book and it was a very fun process. The treatment proceeds similar to a normal calculus textbook. Clear examples, and interesting problems are also included. In fact, this book has more info here than most others. At 600+ pp. it's a solid reference.

   Also, this is the only such book I've seen with exercise answers included in the back. No other complex variable book out there (that i've seen) does this for some reason.

   I highly recommend this title.




3. ...
   The writer introduces the subject from elementary to difficult subects. Partiuclarly good is the section on the integration of complex variables. The writer first introduce the concept of line integrals so the readers have a concept on that before going furhter.



4. My comments here are for the second edition of this book as I do not have the third edition. This is one of the most elegant books on the subject of complex variables. The author uses very clear language to explain complicated topics such as contour integration and conformal mapping. It contains both elementary and advanced topics. This book has several interesting properties: First, It is virtually void of errors. Second, there are a lot of examples worked out in detail. Most of these examples are from physics or engineering. Third, the book contains an excellent collection of homework problems with varying degree of difficulty and the author actually leads you to the solution step by step. This is a great book for self study or any introductory undergraduate course on the subject



5. This book is a great way to learn complex variable analysis. The text is generally very clear and concise and there a plenty of good examples. The problems at the end of each section are particularly useful. I agree with other reviews that it is an excellent book to use for self-study or as a reference. I highly recommend it.

No comments about Counterexamples in Probability and Real Analysis.

No comments about Quantum Field Theory I: Basics in Mathematics and Physics: A Bridge between Mathematicians and Physicists.

5 comments about Differential Equations (with CD-ROM).

1. So i really hate this book... it give maybe one example of certain concepts and they are not even that descriptive. i might just be use to my other math books... but coming from a girl who is a math major, i would stay away!!!



2. Great for learning. Poor for reference.
   
   This book is unique. Most differential equations textbooks simply provide formulae for different types of problems, but you don't really see the big picture. This book lets you see the big picture, but omits many of the most useful formulae that you may need in your career. This for that. It would be nice to see a book with the best of both worlds, but if you simply want to learn and understand the topic, this book is the way to go. Also, there is a good emphasis on qualitative and numerical techniques. Students often feel like they get less out of a mathematics class when qualitative and numerical techniques are emphasised over more analytic approaches. However, those of us who have worked in the "real world" know that the qualitative and numerical techniques are probably even more important. I have worked as a research statistician and my research areas emphasise computing. When I'm presented with real problems and real data (which, in my career, usually comes in large, unmanageable quantities), do I usually pull out my notebook and tackle the problem in a very precise manner, working out an exact solution? No, quite often I cannot realistically do that. Now I'll admit that I don't use much from this particular field on the job, but it still applies. Moving on, I must also mention that the book does a very good job at explaining these qualitative and numerical techniques in addition to things that are more analytic, although it is sometimes a little too verbose.
   
   Regarding applications, the book covers a lot of fields and does put a big emphasis on applications. Physics, biology (especially population growth models), and electrical/computer engineering receive the most treatment. Overall, I would say that the book does an excellent job at including plenty of applications and choosing meaningful ones.
   
   I don't have much to say about the exercises. Most aren't too contrived and they mixed up the difficulty fairly well. However, I would have liked to see more "hard" problems.
   
   In summary, I'd recommend that you pick up a different book if you need a reference for work or research, but pick this one up if you actually want to learn and UNDERSTAND the basics of differential equations.



3. Worst. Book. Ever.
   I am not exaggerating.
   Insufficient depth and poor examples that do not coincide with problems. Proofs are round-about.



4. If you have an instructor like mine who does not like to cover all the minor details of this subject, you need this solutions manual to show you how to do the hw problems. It's worth the money but try to get a used one if you can.



5. I am taking Differential equations for the first time as a college student and we are using this book. Previous to taking this class I purchased an old Dover publication reprint by Tenenbaum and Pollard, and read it over the summer.
   
   Picked up this new book due to the homework problems and the fact that my teacher(if you could call him that) reads directly from the book.
   
   Well needless to say this new book is "magical". They expect the new student to start creating equations on your own and they also expect you to intuitively derive solutions from these differential equations with no experience. What really grinds my gears is when they use the words "simple" and "easy" to describe what they are teaching. It isn't always simple and easy unless you practice practice practice, and with the short amount of problems to work in this book its impossible.
   
   Do yourself a favor...get a good teacher and use the Tenebaum/Pollard book if you are serious about learning Differential equations.
   
   Stay away from this BOOK at all COSTS...I warned you!

5 comments about Numerical Methods Using MATLAB (3rd Edition).

1. The book covers most of the traditional methods. It is a good choice for learning numerical methods. The book has plenty of examples and are very easy to follow. I would recommend some background on calculus and some knoledge about matlab



2. This book was a waste of time for me. It's a decent numerical methods book but it's basically a textbook in Numerical Methods (which I already have).
   
   Sprinkling a few lines of Matlab code in does not make it a Matlab book.



3. Whether you are an instructor for an Engineering class, Life Sciences, Statistics, Mathematics, or simply want to add practical mathematical analysis and programming, this book is the book you should use. I have been using Matlab for a number of years, and I had to pick up my Matlab knowledge from the manuals, man pages, the Internet, etc... and finding out the ins and outs of how to do something was not always an easy task nor accurate. Mathews and Fink's book put all you need to know about the most popular Mathematical methods at your finger tips. The book is tailored such that it can be used alone in a Mathematics course, or as reference in an Engineering course. One field of study that has enjoyed the power and flexibility of Matlab in the recent years is Computational Biology or Bioinformatics. Even though there are plenty of applications popping up here and there for this area of research, the area is still very much untapped and algorithms need to be developed for it as we go forward. Matlab is the best way to try out these new or improved algorithms, and use some of the available tools out there to generate C source code from your Matlab files. This method of algorithms development could save you tons of time, since Matlab makes numerical programming very simple.
   
   The authors start with the basics in Numerical Methods; assuming that this book will be used as the primary text book in the course. A very good assumption, and the instructors who choose otherwise, can always skip the preliminaries. The context of text aims to provide a good balance of theory and application. One way that the authors try to keep this balance is to talk about "error" rate for the algorithms in question. The students are thought the limitations of Matlab along with the strengths of the software, and error analysis is one way to show the students that the results of numerical analysis is Matlab is not perfect, and more importantly why. This error analysis is done for every major algorithm and method presented in the text, and a number of methodologies are presented to help the student in figuring out this rate.
   
   Authors start the main contents of the book with a representation of basic Linear Systems followed by a more complicated topic of Polynomial Approximation. Taylor Series and Lagrange Approximations are thoroughly covered in theory followed by examples that are solved by "hand" and by Matlab. The examples are complete, and can even be used, at least to start with, for the problem sets at the end of the chapter. As one would guess, curve fitting is the next topic of discussion. As you know, numerical techniques in science and engineering often requires curve fitting of experimental data. Starting with simple techniques of Least-Squares Lines, non-Linear Least-Square Methods and ending with the four different flavors of Spline Functions. The Matlab examples becomes more advanced as the topic progresses, and more and more examples are given as the topics get more complicated as well.
   
   One can not learn Numerical Methods without a deep understanding of Numerical Differentiation and Numerical Integrations. Numerical methods for Differentiation are used to solve boundary value problems in ordinary differential equations and partial differential equations. Heat Transfer, Semiconductor Physics and Device Modeling, an Physical modeling of Molecules are just some of the examples that use these numerical differentiation techniques to solve problems. As is the case with the book, the authors start talking the theory behind how numerical differentiation works, and then, they go into the Matlab representation of the problem. Various approximation methods are presented, and error rate for each approximation method is also calculated in detail - both by hand and using Matlab.
   Numerical Integration is a bit more difficult, as there are a number of ways to calculate the area under a curve. The authors present four numerical methods in detail: quadrature, composite trapezoidal, adaptive quadrature and Gauss-Legendre Integration. Each theory is followed by an example Matlab programs. The authors wrap up the text by talking about differential equations and partials differential equations. These two topics are difficult without using numerical methods, and it is even harder to follow the numerical theory of these topics. The authors take a slightly different approach to these topics. They start with examples from the get go. Instead of laying down the theory, they start each chapter with relevant examples from simple to more complex and abstract. Wave Equations and Heat Transfer equations are well known applications of PDE that are presented in detail. Eigenvalues, eigenvectors and the Jacodi's Meothod wrap up this text by j. H. Mathews and K. D. Fink.
   
   I would recommend this book to be used for second year Mathematics, Physical Sciences or Engineering students. A course in Numerical Methods would benefit greatly from this book. Other students can certainly use this text to assist them with modeling, simulation and statistical problems in Electrical Engineering, Mechanical Engineering and various Applied Chemistry and Physics courses.



4. This book goes straight to the heart of the numerical methods without unnecessary distracting fancy pictures and layout that some numerical methods textbook for engineers have. Also, the book has enough Matlab programs for a reader/student to understand essentials of Matlab programming and then tweak/modify the programs for further applications.
   
   I wish author incorporates numerical methods for nonlinear ODE boundary value problems and eigenvalue problems related to ODE in the future edition.
   
   Overall, it is an excellent introductory numerical methods textbook for science and engineering students. After grasping the fundamentals in this textbook, student/reader will tend to be more confident and enthusiastic while studying Numerical Analysis.



5. The Math Part:
   I have to use this as the main text for a college math class, and while it may be a good reference book or engineering text, I don't think it's the best choice for a math course. It's written in such a way that you can flip to the section/topic you need and immediately get the main points and the formulas. But the authors don't necessarily teach their materials in the most intuitive way and frankly, don't seem that concerned with intuition at all. This makes the book quite sufficient as reference for your computations in your bioinformatics research project and such, but for a math text I would be more interested in really owning the intuition and tricky ideas so I can generalize to new cases or derive the formulas, rather than discovering 20 gazillion technical details/equations that will magically spew out an answer for who knows what reason. See the bajillion formulas on cubic splines for what I mean. Or see how instead of simple example + intuition, the authors chose to do 20 pages demonstrating Gaussian elimination.
   
   The Matlab Part:
   I learned Matlab in a few weeks from "Mastering MATLAB 7" and playing around with it on my own. It's very easy to just use the built-in manual or find all kinds of solutions to common problems using Google. There's really nothing wrong or tedious with picking up Matlab knowledge "from the manuals, man pages, the Internet, etc..." as one reviewer complained, because a language is necessarily something you pick up gradually and continually. Personally I think the reviewer was misleading in implying that this book does a good job teaching beginners Matlab. There's 1-2 programs per section, and no explanations in terms of the programming. Honestly, what are the chances that these programs will just drop into your lap and fit perfectly whatever application it is that you presumably need these numerical methods for? You will need to tailor the programs to your objectives or at least, understand WHY and HOW they work, in order to really take advantage of them, and that is outside the scope of this book. What this book really offers are the algorithms behind the programs, and not the programs themselves that are useful. In my opinion the Matlab programs were just a selling point, that's all.
   
   There were also lots of little things that I personally just did not like about the book, where I felt the authors cut corners in their explanations or didn't phrase certain things in the best ways or used slightly funky notation or were not organized enough. Not a great math book in my opinion. But objectively speaking most people probably don't mind those kinds of details and aren't necessarily looking for a math book. So with that in mind I give it a 4.

5 comments about Introduction to Wavelets and Wavelet Transforms: A Primer.

1. This book is a crafted piece as opposed to one of those collections of journal articles that usually leave you wondering. It appears to have a sound theoretical foundation with some clearly presented definitions and theorems. I wouldn't hesitate to spend time with this one.



2. The introduction to Wavelets and Wavelets transform aplications.



3. I have examined most of the popluar books printed on the subject of Wavelet Analysis and this is the best book for those who want to understand what a wavelet is, where is comes from, and how is it is useful for performing Time Scale signal analysis. I strongly suggest starting with this book.



4. Before reading this book, read the wavelet chapter from
   
   Digital Image Processing (2nd Edition)
   by Rafael C. Gonzalez, Richard E. Woods



5. If you studied Mathematical Physics or if you like the mathematical approach that physicists used to write their papers and lectures, it 's a pleasant book to understand wavelets.