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1. Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by WalterRudin | |
list price: $132.81
our price: $132.81 (price subject to change: see help) Asin: 007054235X Catlog: Book (1976-01-01) Publisher: McGraw-Hill Science/Engineering/Math Sales Rank: 33187 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Reviews (69)
These Five Stars Need an Explanation Every time I return to this book I discover new and wonderful things in it. For example, in his treatment of the limits of elementary sequences (that are "normally" treated using the log and the exponential function), Rudin uses the binomial theorem with a deftness and facility that contemporary students rarely encounter. Although Rudin's text presents minimal historical background, it is at the same time more faithful to the historical development of the subject than any other text I can think of. That the book is small and easy to carry around is no disadvantage. Who says that a calculus book has to be the size of the Manhattan phone directory to be valuable?
Possibly the best (math) textbook I've seen yet
A Classic "Baby" Analysis Book
If you are serious about doing math... Content: Readability: The real trick to getting in his swing of things is to MAKE SURE YOU COMPLETE HIS PROOFS. They are extremely slick and often are polished in such a way that it's like his little secret. If you can't do one on your own, just ask the prof in office hours or put it aside for later. The proofs are not presented in this way as to imply that you should just accept them, he wants you to dig in and justify the intermediate steps for yourself, so do it and you'll be good by Ch. 3, I promise. Exercises: Suggestions: Finally, DO NOT BE AFRAID! You really have to commit to this book before getting into it, do not be afraid. My best advice to any mathematician is to know your weaknesses, BUT to respond promptly to them.
If you take your mathematics seriously,otherwise runlikehell This book is hyped up a lot by intimidating professors (and competitive students), but does not deliver the goods. Many people feel that Rudin is concise and effective. But to me, Rudin is terse and weak. It is not hard to discover why his book is in fact so ineffective. The reason is that he is trying to cover too much ground in too few pages. The core of this goal, is probably a sick conspiracy: to achieve the impossibe --- to be the most bought math book in history (required text for every math curriculum), yet at the same time cover all the difficult topics that 99% of Math majors will never master without graduate studies. This all reaches a peak in his neglectful treatment of multivariate functions. It would be a shame if a student really had to learn Multivariate analysis from this book. (However, Rudin is good to keep handy if you are doing problems from Spivak's book.) The end result, is that this book is extremely demanding for even the eager student, who is seeing it for the first time. Nobody I know, in result, has benefited much from this book. One final criticism. For those, like myself, who haven't worked all the problems in this book, Rudin is a pretty terrible reference. I once had the misfortune of trying to reference his proof of L'Hospitals. In conclusion, I found it easier to reprove L'Hospital myself than to read his cryptic use of the real axioms. Now with so many criticisms, I must explain why I have given 4 stars. There comes a point in time, for any respectable math student, that he must develop the ability to solve difficult, abstract problems with little explanation of how and why. In this regards, Rudin's book could be an extremely valuable resource. He has left a trail (THE PROBLEMS!!) which goes through many crucial ideas in Mathematics. Few books, at the undergraduate level, have such a vast amount of problems - aimed at the budding math student. In this respect, Rudin should get no less than 5 stars. But I stand at 4. Regretfully, Mathematics departments everywhere have forced the Rudin pedagogy on everyone. I believe the student should make this choice (i.e. which books to study in detail). And since it was forced on me, I have a voice in this matter: This book should not be on the undegraduate curriculum. And in fact, I don't like his style, I don't like this book, and I'll do problems elsewhere, thanks. -TM p.s. If you happening to be struggling through the book at this time, here is some advice: Keep your freshman Cal book handy. Don't become a victim, and don't go through this course not knowing how to prove the limit laws, the definition of a derivative, Mean value theorem, derivative laws the proof of the fundamental theorem of calculus, and theorems involving integrals of continuous functions, convergence divergence tests, power series representations, partial derivatives. Note that all of these topics are indeed in a freshman cal course. (Well, this is what popped into my head, not a formal and complete list..) It is here where calculus actually can become very useful. For example you can define the logarithm, exponential function - and this leads to a definition of a real exponent without using inf / sup 's as Rudin does in a Chapter 1 problem. ... Read more |
2. A First Course in the Finite Element Method by Daryl L. Logan | |
list price: $128.95
our price: $128.95 (price subject to change: see help) Asin: 0534385176 Catlog: Book (2001-04-05) Publisher: Thomson-Engineering Sales Rank: 299669 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (1)
Excellent first course in FEM This book is excellent for whom desires to learn on which basis FEMs work (undergraduate and graduate). ... Read more |
3. Real Analysis (3rd Edition) by Halsey Royden | |
list price: $103.00
our price: $103.00 (price subject to change: see help) Asin: 0024041513 Catlog: Book (1988-02-02) Publisher: Prentice Hall Sales Rank: 236211 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (16)
Excellent Reference, Poor Introduction
This is a pretty average Real Analysis book
this book is just plain good.
Not bad for self-study, excellent for reference
I'm surprised too. |
4. Introduction to Analysis by EdwardD. Gaughan | |
list price: $130.95
our price: $130.95 (price subject to change: see help) Asin: 0534351778 Catlog: Book (1997-12-10) Publisher: Brooks Cole Sales Rank: 229724 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (6)
Excellent Introduction
Extremely unclear
Great book by Great Guru
Excellent
A Good, Rigorous Introduction to Analysis |
5. The Concepts and Practice of Mathematical Finance (Mathematics, Finance and Risk) by Mark S. Joshi | |
list price: $50.00
our price: $39.50 (price subject to change: see help) Asin: 0521823552 Catlog: Book (2003-12-24) Publisher: Cambridge University Press Sales Rank: 56094 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (4)
Good book on the basics If you want to get an inexpensive book then go for this.
An outstanding book in a crowded field Finding the right level of mathematical sophistication is a difficult balancing act in which it is impossible to please all readers. Here, the author has had a clear vision that the principal audience is the practising or potential quantitative analyst (or quant) and writes accordingly; it is impossible to do better than taking an approach of this sort. Such a quant must have a certain minimum level of mathematical background (a good degree in a numerate discipline). By definition, this has to be assumed for a decent understanding of the material, but the author always has an eye on what a quant really needs to know. Integrated into this mathematical work is a good deal of information about how markets, banks and other corporations operate in practice, not found in more academically-oriented books. The first half of the book includes the core material found in any decent first course on the subject including basic stochastic calculus, pricing of European options through discounted expectation under a risk-neutral measure, the Black-Scholes differential equation and so forth. Where this book really stands out, however, is the exceptional clarity with which the key concepts are separated. Not only are three different ways for deriving the Black-Scholes formula presented (through PDEs, expectation, and the limit of discrete tree-models) ; much more significantly, the different roles played by hedging, replication and equivalent martingale measures in enforcing a price are made crystal clear. In whatever way you already think about this material, you will almost certainly come away with something new from reading this treatment. In my case, for example, I gained a much greater understanding of why "risk-neutral" pricing is so called. The second half of the book, roughly speaking, covers a selection of more sophisticated material. The major areas covered include interest-rate derivatives and models; and more complicated models for stock price evolution (such as stochastic-volatility, jump-diffusion and variance-gamma) that have been proposed to correct inadequacies in the Black-Scholes model such as its failure to explain market smiles. Once the core ideas have been so thoroughly explained in the first half, a great deal of interesting and diverse material can be covered rapidly yet with a great deal of clarity and coherence, relating the new models to core ideas such as uniqueness of prices and hedging issues. Those with quantitative finance experience are still likely to find a good deal that is new and worthwhile in this book. And if you a thinking about becoming a quant, I cannot think of a better book to read first.
Most comprehensive
A must read for anyone interested in mathematical finance Mark Joshi's book fills this niche admirably: it is mathematically rigorous In short this is a book which anyone who is interested in mathematical |
6. Probability and Computing : Randomized Algorithms and Probabilistic Analysis by Michael Mitzenmacher, Eli Upfal | |
list price: $55.00
our price: $55.00 (price subject to change: see help) Asin: 0521835402 Catlog: Book (2005-01-31) Publisher: Cambridge University Press Sales Rank: 639049 US | Canada | United Kingdom | Germany | France | Japan | |
Book Description |
7. The Art and Craft of Problem Solving by PaulZeitz | |
list price: $65.95
our price: $65.95 (price subject to change: see help) Asin: 0471135712 Catlog: Book (1999-02-09) Publisher: Wiley Sales Rank: 38955 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (14)
General Problem Solving Strategies. This particular book has very clear explanations of the main problem solving strategies illustrated with carefully sample problems. Reading this book brings to my memory the works of Polya. One of the only things I think the book is lacking is on strategies to solve Geometry problems in particular or to use the same strategies in the book to solve more Geometrically flavor problems. Nevertheless is a Joy to read.
One of the best Now this maybe is the first book written by a member of former MO team, and now a training lecturer. (The author himself won the USAMO and IMO in 1974, and helped train several USA IMO teams, including the 1994 "perfect score team"). So here is the precious experience! Besides, the ratio between the harder problems and the easier problems is really good. In my opinion this is an excellent textbook for ambitious beginners (both teachers and students), for self-studys and problem-solving fans. Highly recommended.
Essential for budding (and experienced) problem-solvers It contains hundreds of problems from various levels of competition, from AIME problems all the way through some of the toughest Putnam problems (which, if you know anything about the Putnam, are about as hard as competition problems come). But the biggest help are the vital insights and exciting ways of looking at these problems. Don't take my word for it-- many past IMO contestants have suggested this book too. You don't have to be a math competition buff to gain from this book, however. If you're simply interested in mathematical puzzles and problems, and looking to expand your repertoire, this book will help you. Anyone with a good dose of intelligence and motivation will benefit. For an additional problem book, check out Mathematical Olympiad Challenges by Andreescu and Gelca. For purely Putnam treatment, there are several volumes written by Kedlaya. And if you're a CS student, looking for honing those CS math skills to be razor sharp, you should definitely look into Concrete Mathematics by Graham, Knuth, and Patashnik. Happy solving.
The Book I wish I had in High School This book is for the exceptionally brilliant and the mentally tough. It is absolutely necessary to approach this book in a different way from a standard math textbook. You MUST attempt the examples BEFORE looking at the example solutions, NO MATTER HOW DIFFICULT OR FRUSTRATING. You may be bamboozled by the problems, but even trying to understand the problems before looking at the solutions and thinking about how a solution might proceed will pay huge dividends in the long run. For example, in the first chapter Zeitz presents an example asking the reader to prove that the product of four consecutive integers cannot be a perfect square. The solution involves some clever algebraic trickery not visible to the inexperienced, but persistence and getting your hands dirty is key. If you persist in spite of the considerable difficulty, you will find that you get better very, very quickly. You will also notice that it isn't just contest problems it helps you solve. I have found that I have solved my homework sets in the Berkeley graduate engineering program much more easily since working these problems. You will start to see creative and clever solutions where they exist in everything problem oriented. PATIENCE PATIENCE PATIENCE!
Brilliant Note: I also bought Problem-Solving Strategies by Arthur Engle. Those, perhaps more advanced, problem-solvers that want even more of a challenge should purchase this book as well (as both books give very challenging problems, but Engel's is undoubtedly more advanced). ... Read more |
8. Schaum's Outline of Calculus by Elliott Mendelson, Frank Ayres | |
list price: $16.95
our price: $11.53 (price subject to change: see help) Asin: 0070419736 Catlog: Book (1999-06-28) Publisher: McGraw-Hill Sales Rank: 7932 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators. ... Read moreReviews (8)
Good for review but errors abound However, the egregious number of serious errors in the book (in a 4th edition?!) can often be frustrating if not misleading. Some errors are misstatements of theorems or errors in the worked problems! Others include mislabeled graphs, incorrect PROBLEMS (yes!), incorrect answers etc. Believe, me, I've spent hours checking my work, assuming I had made the mistake (but have verified using mathematica, graphing calculators etc.) For someone working nearly every problem, this leads to a lot of confusion and a huge waste of time. I estimate that I have found 20-30 major errors already, and I've only finished the chapters covering calculus of a single variable. :( If they had errata published, it might be a little better, but haven't been able to find any. Unfortunately, haven't tried other review texts...probably better just to get a real calculus book. I've forgotten the one I used in high school and subsequently sold. :(
I wish it had more....
Schaum's Calculus garnering an "A". In addition, the Fundamentals of Engineering
An excellent companion to Calculus The Good: 2. Enough practice problems to ensure that the reader will comprehend the material (as is the case with most Schaum Outline books). 3. Lots of graphs for visual learners. 4. A fraction of the price of most calculus books. The Bad: For more detail, check out the list of chapter topics on the back cover of the book (it's a pretty thick paragraph)
Indispensible if you want the "A"... I got a 96/100 on the final, and an "A" for the course. This book saved me. (This sounds ridiculous, I know...but it is absolutely true.) ... Read more |
9. Introduction to Real Analysis, 3rd Edition by Robert G.Bartle, Donald R.Sherbert | |
list price: $113.95
our price: $113.95 (price subject to change: see help) Asin: 0471321486 Catlog: Book (1999-09-21) Publisher: Wiley Sales Rank: 219853 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (11)
Good guidance to the world of analysis
An excellent real analysis text !!!
A concise and to-the-point Real Analysis book However , hints for exercise is not enough , this may create a problem for some beginning~~ undergraduate maths student.~
Masterpiece
It's Not That Good This text while making some improvements over the years, such as providing more 'examples' in an attempt to help the student understand the theory, it really reflects the major problem in the field of mathematics today. This problem is the discipline's fixation on abstraction and technique which alienates some less capable and prepared students (and I might add, people in general). To make my point, the authors, as has been a common complaint, are not really aware of the lack of pedagogy incorporated in the text. This is a major problem with most mathematical and other technical textbooks. In many of the examples and proofs, the authors leave out important information, expecting that the already stressed and overloaded graduate student will figure out on their own. Many of the examples are not instructive at all, but very frustrating because they are too complicated. There is in many places of the text too much information left out, and in other places points/claims made with no explanation. This is true of most mathematical textbooks and renders them worthless in my opinion for learning. This textbook is not suitable, in my opinion, for use in a big university where there is poor instruction along with a major lack of faculty/student support for beginning graduate students. It would be better if there was some tutelage along with the texts overkill of brevity. |
10. The Visual Display of Quantitative Information by Edward R. Tufte | |
list price: $40.00
our price: $25.20 (price subject to change: see help) Asin: 0961392142 Catlog: Book (2001-05-01) Publisher: Graphics Press Sales Rank: 1137 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Reviews (53)
Sets the stage for all information architects
I'd give it 6 stars if they'd let me....
You'll Never Make a Chart the Same Way Again One of the great advances which has made the Information Age possible has been the development of easy-to-use graphing software to swiftly create charts which used to take skilled draftsmen days to produce. Unfortunately, the commoditization and automation of this once-dear skill set has resulted in the proliferation of lies, damned lies, and lousy statistics. Tufte, a Princeton professor and polymath with passionate interest in statistics, information design, and public policy, offers up a thorough diagnosis of what ails our data-rich, information poor society: - Poor graphical integrity, where the visual proportions are out of synch with the data's proportions - Chartjunk, unnecessary clutter which reduces the proportion of data-ink in a graphic - Poor labeling, which robs data of context - Low-density presentations, where complex and nuanced data are "dumbed down" for the sake of a fleeting aesthetic Fear not---Dr. Tufte also provides the reader with a course of treatment (called "Graphical Excellence") thoroughly illuminated with real-world examples drawn throughout history. This is one of those rare works which feeds both your right and left brain. It is a closely-argued work on behalf of clean and clear communications. It is also a wonderful art book depicting the evolution of an often-misunderstood art form. Whether you're an engineer, a statistician, a businessman, or a teacher, this beautifully-designed book will help you become a more effective communicator.
Superb Introduction to Quantitative Information Display
Very Short on Substance; Has Essentially Only A Single Point |
11. An Introduction to Numerical Analysis by KendallAtkinson | |
list price: $109.95
our price: $109.95 (price subject to change: see help) Asin: 0471624896 Catlog: Book (1989-01) Publisher: Wiley Sales Rank: 270674 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (4)
Excellent Book - not for everyone.
Worst Math Book I've ever had to use
thorough, but thoroughly unreadable The typesetting could have been a bit better. I wish the proofs had been set off from the examples and the text a little more. There is also too much referencing to earlier equations. Rather than referring me over and over to equatin (6.2.1), just re-write the equation. Also, this book is starting to show its age. It is now 11 years old, so its bibliography is a bit outdated, as are references to computer programs. My most severe criticism of this book is that it is sorely lacking in explanations. There is little intuition provided here. Definately not an undergrad book. A much better text to learn from--but not as useful as a reference as this book is--is Burden and Faires. B&F make lots of use of pseudo-code and I applaud them for it. It helps detangle some of the math.
Excellent introduction to numerical analysis |
12. Numerical Analysis by Richard L. Burden, J. Douglas Faires | |
list price: $140.95
our price: $134.95 (price subject to change: see help) Asin: 0534382169 Catlog: Book (2000-12-29) Publisher: Brooks Cole Sales Rank: 85773 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (20)
Very moderate calculus is all it takes Very transparent, clear, and straight to the point this book is all I needed to quickly learn about the Gaussian quadrature and understanding both the algorithm itself as well as WHY IT WORKS AND DOES SO EFFICIENTLY. Please disregard the previous author's review, as its poisonous tone alone should suggest that he is trying to blame his own mathematical deficiencies upon the authors of this very worthwhile text.
Numerical Analysis for Dummies its not...
full of errors
Review of Numerical Analysis, 7th edition Even though the book has an initial chapter ("mathematical preliminaries"), reading this chapter is not enough if the student has not a good previous mathematical knowledge. The book introduces modern approximation techniques and explains how, why and when these techniques are expected to work, and allows the reader to understand why one algorithm works better than other for a given problem. The text contains many examples as well as application problems in various areas of science and engineering. The book uses Maple as the standard software for symbolic and approximate calculus, even though Mathematica and Derive are mentioned too and could be used instead with small modifications. The original English edition (7th edition) includes a CD-ROM with all the algorithms, expressed in different formats (C, Fortran, Pascal, Maple, Mathematica and MATLAB), although the Spanish translation (edited by Thomson Learning) does not include the CD-ROM. However, there is an Internet address in which the CD-ROM contents can be accessed. To conclude, the book is a good text that requires a mathematical background from the reader and covers a broad range of modern approximation techniques. It is not a mere numerical methods cookbook, but a text that analyzes and applies the numerical methods instead.
Wordy, poor algorithms, worse code Maybe due to my physics background, but his notation of representing indexes of variables as a _power_ is confusing: Finally, several of the codes on the included CD refused to run, and some of them didn't give correct answers. You will need some programming experience to edit, as none of the codes (at least all of the Matlab and possibly all of the C) adhere to any programming standards or formatting. Mr. Burden (or his programmer) is invited to purchase and use Steve McConnell's "Code Complete"--or hire someone who knows how to write maintainable code well. What is the purpose of supplying code if it cannot be used in other projects? "Gee Wiz, the book includes Code!" one might exclaim. "But what good is it?" is the inevitable response. ... Read more |
13. Topics in Matrix Analysis by Roger A. Horn, Charles R. Johnson | |
list price: $50.00
our price: $50.00 (price subject to change: see help) Asin: 0521467136 Catlog: Book (1994-06-24) Publisher: Cambridge University Press Sales Rank: 323255 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (1)
A great reference source for advanced matrix analysis TOPICS IN MATRIX ANALYSIS contains a lot of stuff including LMI's, Kronecker and Hadamard products of matrices and their properties etc. I found this book indispensible when I was studying Semidefinite Programming. Both these books are now available in paperback (cost around 30+) dollars each. I have recently purchased both copies and can only strongly recommend them to anyone else. ... Read more |
14. Real and Complex Analysis (Higher Mathematics Series) by WalterRudin | |
list price: $135.31
our price: $135.31 (price subject to change: see help) Asin: 0070542341 Catlog: Book (1986-05-01) Publisher: McGraw-Hill Science/Engineering/Math Sales Rank: 80292 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (15)
Best (math) book ever written The book covers the standard material on 'real variable' (measure theory') in a masterful and compact way; then it goes through the standard complex analysis to a level deeper than usual and showing in a very original way its intertwining with real variable. The final third of the book is devoted to more specialized topics. Just a warning: the construction of Lebesgue measure is based on Riesz representation theorem, whose lengthy proof is imposed to the reader in chapter 2. It is really tough, and makes this chapter much harder to read than the rest of the book. If you want to learn REAL mathematics, this is the book for you, you'll learn not only the subject matter, but a great style as well.
Excellent, often intriguing treatment of the subject
Welcome to the self-service analysis center! Also, Rudin does not discuss some of the more advanced or interdisciplinary topics such as distribution theory (Sobolev spaces, weak derivatives, etc.) or applications of measure theory to the probability theory, both explored in the book by Folland. Last but not least, it's worth noting that contrary to the common practice, Folland includes many end-of-chapter notes where he outlines some important historical aspects of the development of the topics, and also gives a few references for further study. For example, in the notes section at the end of the chapter on Lebesgue integration, he mentions --and briefly outlines-- the basics of the theory of "gauge integration" (also called Henstock-Kurzweil theory) which serves to construct a more powerful integral than that of the Lebesgue's. As another instance, having already defined and used "nets" within the chapter on topology, in the end-notes Folland also introduces "filters" and "ultrafilters". These are all machineries which have been developed to play the role of the metric space sequences in general (locally Hausdorff) topological spaces, but for some historical reasons, ultrafilters have nowadays taken a backseat to the nets (the older general topology books usually prove the Tychonoff theorem using ultrafilters). All said, I can recommend taking up Royden as your very first approach to measure theory, then based on how well you think you have learned the first course, move on to either Rudin or Folland for a more advanced treatment. Please note that the other books I have mentioned above do not discuss complex analysis, a subject which is also masterfully presented in Rudin. There are however a few other equally well-written complex analysis books to pick from, for example John B. Conway's classic from the Springer-Verlag graduate series, or L.V. Ahlfors' masterpiece, to name just a couple.
A Comprehensive Guide to Analysis For example, the construction of Lebesgue measure is considered one of the most important topics in graduate analysis courses. After this construction, more abstract measures are developed, and then one proves the Riesz Representation Theorem for positive functionals later. Conversely, Rudin develops a few basic topological tools, such as Urysohn's Theorem and a finite partition of unity, to construct the Radon measure needed in a sweeping proof of Riesz's Theorem. From this, results about regularity follow clearly, and the construction of Lebesgue measure involves little more than a routine check of its invariance properties. Another example of where Rudin takes a more theoretical approach to provide a more elegant, yet less intuitive proof, is the Lebesgue-Radon-Nikodym theorem. Other books generally introduce signed measures with several examples, and use this result, along with properties of measures to derive the proof. On the other hand, since the first half of the book contains an intermission on Hilbert Space, Rudin uses the completeless of L^2 and the Riesz Representation Theorem for a more sweeping proof. In the real analysis section, Rudin covers advanced topics generally not covered in a first course on measure theory. The chapters on differentiation and Fourier analysis are key examples of this. Rudin uses maximal functions to develop the Lebesgue Point theorem and results from complex analysis, and provides an incredibly thorough proof of the change-of-variables theorem. The ninth chapter, on Fourier transforms, relies heavily on convolutions, which are developed as a product of Fubini's theorem. This, in turn, is used to prove Plancherel's theorem and the uniqueness of Fourier transforms as a character homomorphism. The tenth chapter, on basic complex analysis, essentially covers an entire undergraduate course on the subject, with added results based on a solid knowledge of topology on the plane. Once a solid foundation on the topic is laid, Rudin can develop more advanced topics from Harmonic analysis using general results from real analysis like the Hahn-Banach theorem and the Lebesgue Point theorem (for Poisson integrals). Most of the basic results from the power series perspective are covered in the text, but while the geometric view is examined, it is still done in a very analytic, formula-based way that does not allow the reader to gain too much intuition. Nonetheless, all the basic results are covered, and Rudin uses these to develop the main theorems, such as the Mittag-Leffler and Weierstrass theorems on meromorphic functions, and the Monodromy Theorem and a modular function used to prove Picard's Little Theorem. As an introductory text, even for advanced students, Rudin should probably be accompanied by more descriptive texts to develop better intuition. In fact, I would recommend Folland's Real Analysis and Ahlfors' Complex Analysis for self-study, because the problems are easier and one can learn better through those. With a good instructor, though, Rudin's text is concise and elegant enough to be both useful and enjoyable. It is also a good test to see how well one REALLY knows the subject.
The Holy Bible of Real Analysis |
15. Numerical Mathematics and Computing by E. Ward Cheney, David R. Kincaid | |
list price: $111.95
our price: $111.95 (price subject to change: see help) Asin: 0534389937 Catlog: Book (2003-07-25) Publisher: Brooks Cole Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (5)
From a student's view......Garbage The book is not totally at fault in my case. I also have a horrible instructor and have to rely soley on this book to learn the material. This book just makes it very, very hard to teach myself. My only praise of the book is it's pseudocode for implementing the methods explained. They can easily be used to program them in C++ or other languages. Overall the book is very confusing but it is still far better than my instructor who doesn't explain anything or answer questions.
Basic but Good That being said, for my use this book was not detailed enough and failed to go into sufficient detail into many different areas (such as the eigenproblem). It is definantly an undergrad text and would be an excellent choice for a 300-level math or computer science class, it also provides a good general background in numerical computing. In that regard this book is a fine choice.
Reader from Belgium compares to the wrong book
A concise text for introductory numerical analysis
Total piece of crap |
16. An Introduction to the Finite Element Method (Mcgraw Hill Series in Mechanical Engineering) by J. N.Reddy | |
list price: $140.31
our price: $140.31 (price subject to change: see help) Asin: 0072466855 Catlog: Book (2005-01-11) Publisher: McGraw-Hill Science/Engineering/Math Sales Rank: 169173 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description J.N. Reddy's, An Introduction to the Finite Element Method, third edition is an update of one of the most popular FEM textbooks available.The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas. Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world. A supplementary text Web site located at http://www.mhhe.com/reddy3e contains password-protected solutions to end-of-chapter problems, general textbook information, supplementary chapters on the FEM1D and FEM2D computer programs, and more! ... Read more Reviews (9)
a very good book The first s chapters of the book regard the FEm method in general, the 4th focuses on structural mechanics, 5th is about errors in FE analysis, 6th and 7th about numerical integration and 8th is on 2 and 3 dimension FE problem. Actually this is an introductory book, so the 2 and 3 D problems are not deeply trated. The book is never hard to understand, and it's suitable (waw!!) for self study.
It is one of my best list.
THE BOOK
One of the Best Textbooks in FE Samuel K. Kassegne, PhD, PE San Diego, California bikila_97@yahoo.com
Great Introductory Book |
17. Calculus Demystified : A Self Teaching Guide (Demystified) by Steven G. Krantz | |
list price: $19.95
our price: $13.57 (price subject to change: see help) Asin: 0071393080 Catlog: Book (2002-08-01) Publisher: McGraw-Hill Professional Sales Rank: 120711 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description
Reviews (6)
Better look elsewhere... I decided to learn Calculus on my own before I start Cegep, as something to do in my spare time. That being said, I'm having a very hard time with this book. I CAN get through it, but it seems needlessly difficult. The explanations in here aren't the best for the everyday reader. Many concepts and ideas seem to have been omitted, leaving the reader wondering if he's skipped something important or didn't understand well. And the things which are explained are rigorous definitions that just aren't accessible. The book is littered with very hard 'Try it yourself' questions to which the book doesn't give any answers, and even the answers provided for the excersises and final exam are not developped in a way so that you can understand if you get it wrong. There are many other Calculus books out there, so stay away from this one. I guess this book may be alright for someone who just needs a quick revision, but if you're starting from scratch, this book is terrible And I'd like to point out I was releived to see that other people hated this book too ^_^ I'm glad it's not just me...
Demystified? Not likely.
Calculus made Difficult It seriously confuses and complicates simple principles by explaining them in notation only a mathematician could love. Then it gets worse. The author periodically presents the reader with a "Try it yourself problem" that ought to be called a "Puzzle" because it is more complex than any previous example, and no correct solution is tendered. This only leaves the reader wondering if he got it right after all. It shakes the student's confidence, which leads to second guessing destroying any positive reinforcement crucial to learning. Not only is it frustrating, it is detrimental to progress since the student is left on his own to confirm that he has properly grasped the concept and is ready to move on. And what if if the student has taught himself incorrectly....? Some teachers enjoy showing off how well they have mastered a difficult subject. Steven Krantz (the author) seems more interested in demonstrating his own grasp of mathematic notation than teaching the subject of calculus to his students. If I wanted to discourage a student from ever taking any more math, I would send them a copy of this book. On the other hand, the information is all there and it is complete and correct. The format is one that serves well for a for the highly advanced student seeking a challenging brush up, or the casual mathematic genius looking for the equivalent of a crossword puzzle book in calculus. For us mere mortals, don't even open the book. It will do more harm than good.
Calculus Re-mystified
Demystified? Don't Think So. Some may say that calculus is an inherently boring subject - this book will do nothing to disabuse you of that notion. The writing style is almost a parody of the stultifying math teacher who puts everyone to sleep. I have quite a few math texts that I use for my tutoring business, and this is by far the least accessible of the lot. For the calculus novice, I'd recommend "How to Ace Calculus: the Streetwise Guide" as a far more readable text. For the more advanced student who wishes to review the basics or to supplement his or her Calc II or III course, "Calculus Demystified" would fit the bill. ... Read more |
18. Matrix Analysis by Roger A. Horn, Charles R. Johnson | |
list price: $40.00
our price: $40.00 (price subject to change: see help) Asin: 0521386322 Catlog: Book (1990-02-23) Publisher: Cambridge University Press Sales Rank: 226162 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (5)
Not for the uninitiated
An encyclopedic reference for matrix analysis and linear alg
Excellent book.... for the initiated Nonetheless, I really like their take on linear algebra. They motivate you in every subject and problem (for example, the relations between eigenvectors, eigenvalues, and optimization problems). These insights are invaluable and definitely worth the admission price. Together with Golub and Van Loan's "Matrix Computations", this is THE linear algebra book to get, although only if you're sufficiently initiated.
The most comprehensive and up-to-date reference/textbook.
Excellent treatment of the subject matter |
19. Advanced Calculus: A Course in Mathematical Analysis by Patrick M. Fitzpatrick | |
list price: $134.95
our price: $134.95 (price subject to change: see help) Asin: 0534926126 Catlog: Book (1995-08-21) Publisher: Brooks Cole Sales Rank: 59256 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Book Description Reviews (12)
It's not THAT bad...
Good treatment: Unfortunately this is a textbook
Good for streamlined Intro to Multivariable Analysis Sat in on a quarter of undergrad Multivariable Analysis (a previous offering of the same class was cancelled last year before I graduated with the math degree). This book was the assigned text. I did all the class homework. The class covered the Differential part of the multivariable chapters, not the integral part, but skipped the metric spaces chapter. I liked the book despite its several but ususally easily discernable typos. It covered the Multivariable stuff in Rn efficiently for me as an introduction. I can envision many uses in math and econ for the material and approaches used in the book. Now I'll go on to other texts that cover the same material and more but with a higher level of mathematical sophistication (like the Dover published, C.H. Edwards, Calc of Several Variables book they tried two years ago). Also, I'll return to some Optimization texts to get more out of them. In order to get the most out of the multivar part of the book, you definitely need to have good comfort with concepts and proof techniques used in Single-var analysis and in basic set theory.
Not as bad as everyone says Those complaints aside, this text is quite thorough and does a good job motivating and explaining most of the big ideas (which is something that many analysis texts often refrain from doing unfortunately). If you read the reviews on this page you'll see many complaints that Fitzpatrick doesn't baby his readers by cramming tons of examples into the text to illustrate each concept to death. He will also often omit the details of a proof, only giving a sketch and challenging the reader to complete the proof on his or her own. I agree that this can be a bit aggravating if you use this in your first class in rigorous mathematics. But if you've got a few upper level math classes under your belt and these things still bother you, then perhaps mathematics is not the field you should be specializing in. OVERALL OPINION: this is not a bad book for a second undergraduate coarse in analysis. If you are looking for a good single variable analysis text and have not done much in term of rigorous math before, then there are plenty of more user friendly texts out there. If you are looking for a thorough and challenging overview of undergraduate analysis, then this text is one of the many possibilities you should consider.
it's fair, not great tho BTW, if Real Analysis is the reader's first introduction to proof based mathematics, then he might do well to purchase a copy of "An Introduction to Mathematical Reasoning." It's a small book for roughly $30, but it's a wonderful piece to properly develop the skills needed in theoretical math. ... Read more |
20. A Mathematician's Apology (Canto) by G. H. Hardy | |
list price: $16.99
our price: $11.89 (price subject to change: see help) Asin: 0521427061 Catlog: Book (1992-01-31) Publisher: Cambridge University Press Sales Rank: 34439 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan | |
Amazon.com Hardy was, in his own words, "for a short time the fifth best pure mathematician in the world" and knew full well that "no mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." In a long biographical foreword to Apology, C.P. Snow (now best known for The Two Cultures) offers invaluable background and a context for his friend's occasionally brusque tone: "His life remained the life of a brilliant young man until he was old; so did his spirit: his games, his interests, kept the lightness of a young don's. And, like many men who keep a young man's interests into their sixties, his last years were the darker for it." Reading Snow's recollections of Hardy's Cambridge University years only makes Apology more poignant. Hardy was popular, a terrific conversationalist, and a notoriously good cricket player.
When summer came, it was taken for granted that we should meet at the cricket ground.... He used to walk round the cinderpath with a long, loping, clumping-footed stride (he was a slight spare man, physically active even in his late fifties, still playing real tennis), head down, hair, tie, sweaters, papers all flowing, a figure that caught everyone's eyes. "There goes a Greek poet, I'll be bound," once said some cheerful farmer as Hardy passed the score-board. G.H. Hardy's elegant 1940 memoir has provided generations of mathematicians with pithy quotes and examples for their office walls, and plenty of inspiration to either be great or find something else to do. He is a worthy mentor, a man who understood deeply and profoundly the rewards and losses of true devotion. --Therese Littleton ... Read more Reviews (15)
A classic of the mathematical literature
A unique book, should be read by everybody The introduction by C.P. Snow is more like a short biography about Hardy, and it's about the same length as Hardy's actual text. It gives us insights into what one of Hardy's friends thought of him, and it also frames the life Hardy was living in as he wrote this book. Hardy's opinions are strong, and undoubtedly every reader will disagree here and there with him. But he shows the reader some of the gems of mathematics, and perhaps the reader will be able to appreciate those even without formal mathematical training. He also talks about war and what he thinks of it. Whatever the reader thinks about Hardy's opinions, this book gives us the opportunity to glimpse into the mind of an artist - one different than the usual meaning attached to the word, but one nonetheless - and experience a part of human life not experienced by many - the wonders of mathematics.
One should not need an apology But why can't mathematicians study math for the love of the subject? What is so bad about not caring about utilitarian value? Why should we have to justify our existence to others? The fact that Hardy seems so compelled to justify his existence, and all he comes up with is benefiting a pool of knowledge in the platonic realm, is almost pathetic. Why couldn't he have studied math for his own self-interest? This book would have been all the more refreshing if he stated he loved working with Ramanujan and Littlewood, and that this in itself is a justification, and not some means to some cloudy end. Other areas of the book are equally disappointing. We hear the commonplace notion that after 40, one's mathematical abilities are pretty much over. Yet this is a self-fulfilling prophecy. Without confidence in your abilities, how do you expect to get anywhere? What about Erdos, who still actively did math up until his death? Wiles was over 40 when he finally resolved Fermat's Last theorem. You may wonder with this criticism, why I chose 4 stars. This is because, for all its drawbacks, it is at least an interesting account of Hardy's relationship with math. It is however, disheartening how fatalistic he is. It would have been refreshing to hear something of pride, not pretentious or sneering, but pride exclaiming that nobody should ever feel the need to write an apology for their existence.
Motivation for anyone questioning being a Mathematician
Interesting book for the mathematics lover. |
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