5 comments about Modern Graph Theory.

1. My profile is the following: I am a phD student in theoretical computer science and I needed a good introduction book to graph theory.

   This book is just what I needed...




2. Bela Bollobas has the rare gift of having both deep mathematical insights, and the ability to eloquently communicate them in a way that is accessible to the average graduate student. In his book "Modern Graph Theory", Bollobas covers just about every exciting area of the subject, and does so in an up-to-date fashion that gives the reader a big picture of each sub-area of the field. The ability to do this not only seems difficult, but also essential, since he himself has written entire books on two of the chapters (extremal graph theory, and random graphs). Just about every major important theorem (including max-flow/min-cut Theorem, and theorems by Menger, Szemeredi, Kuratowski, Erdos/Stone, and Tutte) can be found here, and thus makes this book indispensable for anyone who does research in graph theory, combinatorics, and/or complexity theory. In my opinion the true highlights of this book are indeed those areas he knows best: extremal graph theory, random graphs, and random walks on graphs, the latter of which may be the best introduction to that subject that one will find in a textbook.

   My only complaint, at the cost of perhaps half a star, is that his discussions and proofs often seem difficult to follow, as he will state something that to him seems quite obvious, yet to this reader often seemed a bit subtle, and would hence slow down the reading. Indeed, if these off-handed remarks were included as exercises at the end of each chapter, then the number of excercises would have swelled from the current 600 to well over one thousand ! Speaking of which, these 600+ exercises, although also representing another blessing of this book in that they add another degree of depth, tend to lack "starter" exercises, and go straight to the theory. But this is to be expected from a graduate text.

   Finally, for the reader whose research significantly intersects with graph theory, but may not be ready or willing to be initiated by Bollabas into the world of graph theory, I would recommend Dietsel's graduate text on the subject. His book covers similar topics, but may be more clearly and transparently, but with less depth and insight.




3. I am, what Prof. Bollobas would call a hobby mathematician. Some popular science book arouse my interest in graph theory, and the author of that popular science book recommended this book. I feel it was a vey good introduction to the subject, even though the proofs become challenging at times. His motivation for the subject is always concise but precise, one cannot but notice, that a master of the subject is writing about it.
   
   The only distraction are the enormous number of typographical errors: I counted over 60, and this in a third corrected printing!?!



4. This book is absolutely precious! It is a little bit weird, but you can get used to it. This book's strongest points are that it is easy to jump around in it, and it contains a wealth of material. It also has incredible numbers of exercises, of greatly varying difficulty levels.
   
   The author's clarity of writing comes out particularly well in the later chapters. In particular, my favourite parts are the discussion of algebraic graph theory, and the discussion of the Tutte polynomial and connections with knot theory. There is also some beautiful use of linear algebra in various parts of the book; some rather strange and difficult results are presented very clearly.
   
   I think this book would be a great purchase for anyone wanting to engage in some self-study in graph theory, or anyone wanting a good reference on graph theory, or anyone wanting to work some hard problems (or easy problems) in graph theory, or someone choosing a textbook for a graph theory course...or...in short, anyone who wants anything to do with graph theory at all.



5. This is a very well structured book. However, this book is not amenable to easy reading. The theorem proofs are short and concise with no overt explanations. Bottom line is that reading this book is a an exercise for the brain.
   
   Being an engineer my only grouse about this book is that this book is written for mathematicians and as the author himself claims there are very few practical applications accompanying the theory. But this being a graduate text in mathematics it really cannot be expected to fulfill this need.

5 comments about Calculus of A Single Variable, Seventh Edition.

1. This book is good because it give you clear (easy) examples of the material it is explaining. The practice problems are also very good because they start off from the most basic then progress to advanced. This books has a lot of practical real world problems. Some of the material can be difficult at times, that's why I suggest you purchase "3,000 Solved Problems in Calculus (Schaums Solved Problems Series)" in addition to this book. The Solved Problems Series helps when you're studying quick examples just before the test.



2. This is your average math textbook. I haven't had any problems with it. It gives pretty good examples and explanations for each section.



3. This book is pretty nice. It provides you a lot useful concepts with brief explanation. Your job is to study and do the homework to digest that such concepts ( you'd better have a solution book that comes along with it). Don't blame for the book not covering everything as you expected, like other science courses, you should have a fair understanding the basics before go up to higher level.



4. This book has almost no differences from the 8th edition other than it is an older edition. Larson covers virtually all topics in calculus with multiple approaches preparing students for success whether it's on the AP exam or taking a course in Calculus. The authors focus on concepts and not just calculations enabling a deeper understanding of calculus. As a teacher, I appreciate this author's work.



5. Because this was a requirement for class, this book served me very well. It is clear and easy to understand if one has the time to concentrate while reading and complete the practice problems.

5 comments about Advanced Calculus Problem Solver (REA) (Problem Solvers).

1. This book is great help for the university student. I have two books the problem solver REA and I sure that the exercises in this book will my salvation for Calculus I and I recommend shipp this book



2. All math students get stuck on a problem, while that maybe irritating enough, looking for the answer in this book doesn't make your situation any better. So if you're anyway like me, you don't want to spend 1 hour racking your brain on one math problem when you have billions of other things to do and another millenium looking for a problem that remotely resembles yours in this waste of paper. I'm not trying to be discouraging to anyone looking for help, but I suggest that you just continue your search. I bought this book and I am now sending it back. So be your own judge. If you don't believe me, then my second suggestion would be to find the book in a book store and check it out yourself before buying it. Just being honest.



3. If you are taking a course covering the theory of Advanced Calculus or perhaps in introductory Real Analysis, this book is a great buy. There is alot of material covered, but make sure that you compare the syllabus of your couse and the contents of this book before buying. This book contains fully (and I mean fully) worked out solutions to very difficult problems that you may encounter in such courses. My only complaint is that there should have been included more of the proof-type questions for infinte suequences and series. However, if you taking merely an introductory calculus course, you would be better off buying REA's "Calulus Problem Solver", which is another great book.



4. This book contains a wealth of useful information. My only complaint is that REA hasn't re-set the book in a decent type face. Instead, they continue to publish these books that look like they were typeset on a manual typewriter. Very hard on the eyes...



5. The book was received in good condition and on time. Very satisfied with the service.

5 comments about Undergraduate Analysis (Undergraduate Texts in Mathematics).

1. Lang's book is an excellent introduction to real analysis that tries to build the reader's knowledge from the ground up. Lang starts with fundamental ideas from calculus and then proceeds in a logical way. Having taken Lang's course, for which this book was designed, it is clear to me that this book is a result of Lang's many years of experience teaching undergrads. I highly recommend this book to anyone who wants a solid foundation in analysis.



2. I personally don't care much for this book. It's too terse, and there are nowhere near enough examples. I have about 6 analysis books and this is the one I look in the least. It seems to cover a lot of stuff, but maybe too much-- it wouldve been better to focus more on some more elementary topics. For instance, he spends about one and a half pages introducing the derivative. So if you want a book that glosses over more elementary concepts and leans heavily toward a graduate level, this book's for you. At my school we were supposed to learn advanced calculus from this and it is not good for that at all. For advanced calc try robert stritchart's Way of Analysis (the best book on analysis I've ever read) and for analysis Intro to real analysis by kolmogrov (only 10 bucks or so and actually better than most books costing a 100)



3. Serge Lang's "Undergraduate Analysis" offers an impeccable selection of topics and exercises for the student wishing to broaden his/her knowledge of analysis. The proofs of theorems can be terse at times, but a hardworking student will gain much through a thorough reading of the text. Also, Lang concentrates many of his exercises on estimates, which is an art form that is slowly dying among undergraduates (and graduate students as well, sad to say). Many of his problems require only the triangle inequality (the basic tool of estimation) and ingenuity (and hard work) from the student. I would strongly recommend this text for anyone who wishes to fully understand and appreciate the results and techniques of basic real analysis.



4. This book typifies Lang's style. If you enjoyed any of his other books you'll enjoy this too. Like seemingly all of his texts, it has a section on the inverse function theorem and makes quite a deal out of it. Overall, it is quite comprehensive, but there's little motivation for the proofs so things can be a bit boring. Both Rudin and Browder cover the same amout of material in far fewer pages, and they have better excerises too.



5. I learned this material years ago but when I need to
   look things up, this book has everything, well written.
   For example the Taylor expansion with multinomial notation
   is given here. The writer treats the undergraduate student's
   intellect with respect. This is a serious book.

4 comments about Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis).

1. This book is the best book on real analysis I have ever studied. It does a wonderful job in bridging undergraduate level with graduate level analysis. I have not seen any book that makes measure and Lebesgue theory so easy to understand.
   
   The books begins by defining what a "measure" is all about. And the description is so intuitive and geometrical that you would wonder why you weren't taught it this way before. The book then goes into Lebesgue theory and all of it suddenly becomes so easy.
   
   The book has plenty of wonderful examples and a good set of over 30 problems per chapter.
   
   Elias Stein (one of the authors) is a very renowned mathematician, and one need not worry about the accuracy of the proofs in the book--they are "bullet-proof", and at the same time succinct.
   
   If you are struggling with W. Rudin's book on Analysis, this book is a MUST for you.



2. This book has a lot of problems. Several sections are poorly written/edited. Several important named theorems are not clearly labeled. Also some of the proofs contain typos or errors. The chapter on differentiation is particularly lacking. The chapter is poorly organized and presented. There is also a glaring TeX error in the chapter.
   
   At Princeton this book is used as part of an undergraduate course, and it shows. This is not the ideal book for a graduate level course in real analysis(though I think it would be very well suited for advanced undergrads). Too much time is spent on Lebesgue measure and integration in the first 2 chapters, and abstract measure theory is not intoduced until chapter 6. Also the Monotone Class theorem is lacking from the chapter on abstract measure theory. Also, the book only touches on functional analysis in the two chapters on Hilbert spaces (where they assume all Hilbert spaces are separable).
   
   On the other hand, the presentations of Lebesgue measure/integration and Hilbert spaces in the book are pretty good. The exercises and problems in teh book (when stated properly) are very good and instructive. Overall this book has a lot of potential to be very good, but seems to be suffering from a lack of revision. Hopefully these issues will be fixed in later editions.



3. Easy to read. My university is using this book to get the graduate students ready for the real analysis qualifying exam. So go ahead and buy this book if you're planning to work on a PhD in mathematics. If you're not planning to work on a PhD in math, this is still a good book to read if you enjoy studying about the real line.
   
   The book begins with measure theory, integration and differentiation. These are included in Chapters 1 to 3. Then in Chapters 4 and 5, we look into Hilbert spaces. This is similar to studying finite-dimensional inner-product spaces, but here, Hilbert space is infinite-dimensional. However, the analysis is very similar. If you know some linear algebra, it should feel like as if you have already read these two chapters.
   
   Finally in Chapters 6 and 7, we see abstract measure theory, including Hausdorff measure, and we study fractals and self-similar sets. And this concludes the book.
   
   Also recommend Walter Rudin's Real Analysis.



4. i found the first three chapters of this book very clear and well written. i'd strongly recommend it for someone looking to learn about analysis on the real line.

1 comments about Real Analysis and Foundations, Second Edition (Studies in Advanced Mathematics).

1. This book is an excellent text for understanding the foundations of Analysis. I have used this book as a suplement for several math classes. It is a good refrence tool for math majors.

1 comments about A Course of Pure Mathematics Centenary edition (Cambridge Mathematical Library).

1. This is the book for a serious student to begin his study of analysis. This is Hardy's timeless masterpiece. There is no other Calculus book even remotely close it. The collection of the problems in this book is superb. After you wade through this book, your command of Calculus will be unshakable and your whole view of mathematics could also alter.
   
   This is one of few math and science books that are a joy to read even after you have mastered the material. What Hardy does for mathematics in this book is what Feynman does for physics in Lectures of Physics.

2 comments about Louis Bachelier's Theory of Speculation: The Origins of Modern Finance.

1. This is an excellent book on the origins of computational finance. It discusses the academic beginnings in the early twentieth century. Finance is a strange subject that is hard to study because people are usually not too willing to share their discoveries- they would rather make massive profits off of them! This book discusses Bachelier's incredible thesis on several levels. He has some very interesting stochastic analysis, but more importantly he discovered a method for the valuation of options- the basis of modern finance.



2. Finally, a worthy title, a worthy edition and binding, and worthy translation of the forgotten paper that transformed the world of finance long after its genius author had passed from this mortal coil. Louis Bachelier's "The Theory of Speculation" was previously only available in French (online at NUMDAM, under Théorie de la spéculation. Annales scientifiques de l'École Normale Supérieure) and in English in the obscure 1971 book "The Random Character of the Stock Market" edited by MIT's Paul Cootner.
   
   Davis and Etheridge's commentary and background and helpful timeline are all welcome, but a thorough biography of Bachelier and his sad life remains to be written. The index is adequate for such a slender volume.

4 comments about Convex Analysis (Princeton Landmarks in Mathematics and Physics).

1. This is a good book for the first year in PhD studies. I recommend amply this book, it's very clear in the explanation, if you have any doubts about topology, Rockafellar explained in this book very simple the theory and all you need about Topology.



2. convex programming is a beautiful topic which admits amazing geometric interpretation.
   
   books like this manage to destroy one's appreciation of the topic by not providing even one (gasp!) figure. damn Bourbaki style.



3. This book perhaps ranks with Halmos' "Finite Dimensional Vector Spaces" as an unusually clear description of its subject. Rockafellar's book has been through numerous printings in 40 years. The theorem proofs can be intricate. But the thread of logical development makes reading it worthwhile. Certainly, it is beautiful how the crucial assumption of convexity makes all the derivations possible.
   
   The level of discussion is suitable for a 3rd year undergrad [or higher], who is majoring in maths.
   
   By current standards of maths texts, it does lack diagrams. In fact, there doesn't seem to be a single one! Something to get used to, if you are a current undergrad weaned on recent texts. [Since the author is still alive, perhaps he might consider adding diagrams to a future edition.]



4. This book is a classic. It is probably the best reference book although it is tough to read from the beginning untill the end. The style is heavy and you need strong mathematical background to understand it.
   Anyway, if you need a result on convex functions or convex analysis it is very likely that you will find it in ths book.

5 comments about Calculus: Single and Multivariable, 2nd Edition.

1. I bought this book to brush up, that's all. I found the examples confusing and the explanations poor, even for someone with experience.



2. I agree with the earlier comment regarding this text which points out its confusing explanations and lack of examples. Even in the case of someone looking to review calculus this text is not at all useful and a very expensive waste of money.



3. When I took Multivariable Calculus, we used "Multivariable Calculus" by James Steward in class. I personal like Steward's book very much because it made me understand without the help of my professor. With a supplement of this book, I found I understand Multivariable Calculus in a more comprehensive way. All in all, I like this book a lot.



4. The book is a disaster. I had to suffer with it for 2 semesters. None of the other students in my Calc I and Calc II courses got anything from it either, as far as I can tell. I had to scramble and seek information from other calc books in order to understand what differentiation and integration was all about. The text in no way prepares one for the exercises. There's no connection between the text and the exercises. In the exercises there appear some inane, open-ended questions that seem to be trying to make some unfathomable point. This is not a book anyone can learn from. I would strongly advise any student who must use this book as their course textbook to CHANGE COLLEGES. There are many great calculus books out there, on all levels. For those who prefer a 'calculus reform' approach, I would recommend Calculus Lite, by Frank Morgan. For the more traditional approach, I got a lot out of Anton's classic.



5. Teaching with this text - which I've been doing for the past two semesters - is an uphill battle, to say the least. It's a text designed for non-majors; I teach business and social science students. Instructors of these sorts of students need to convince their pupils that they DO need to know how to reason mathematically, and that math IS relevant to their life plans - they can't just rely on their calculators to do all their work for them. When the textbook seems to disagree, our job is all the more difficult.

   The authors of _Calculus_ don't seem to have made up their minds regarding whether or not it is necessary to introduce the notion of mathematical justification in this book. On the one hand, the examples feature sound arguments for why a curve looks the way it does, or why a critical point is a maximum or minimum - but on the other hand, alongside Newton's Method and the Bisection Method for estimating roots, is a "Using the Zoom Function on Your Calculator" primer on how to estimate the zeroes of functions. Offhand remarks about "and you can use your graphing calculator for this and that" serve to seriously undermine any attempt to explain to first-year students the concept of mathematical argument - which is unfamiliar to many.

   The organization of the chapters is also somewhat questionable. Differentiation is broken up into two sections: one dealing with the concept of a derivative (complete with pictures), and the other pertaining to computing them. While the idea of introducing differentiation through a concrete example - measuring instantaneous velocity given a displacement function - is a good one, by the time students actually get to work with derivatives, they're no longer focused on what they actually represent. Curve sketching is introduced vaguely at the end of the second chapter - before the shortcuts to differentiation are mentioned - and then revisited only in chapter 4.

   The section on integration is even worse: again, it's introduced in a concrete manner - this time, by asking how displacement can be computed from a velocity function. But for some bizarre reason, the authors don't take this opportunity to explain that the area under a velocity curve - the integral - is that same displacement function whose derivative was the velocity. It's a perfect opportunity to do so, as it's an interesting and surprising (to the beginner) result, and one that's accessible at this point in the course. But instead, the Fundamental Theorem of Calculus is relegated to a later section, long after the "integral as an area" idea has been abandoned and students are just working with integrals as antiderivatives. (Even more curiously, there's a section entitled "The Second Fundamental Theorem of Calculus", but none called "The First Fundamental Theorem of Calculus".)

   I'd highly recommend James Stewart's _Calculus_ instead of this text for a first-year calc course: the material is far better explained, and there's even a section on the inadequacies of graphing calculators (which are expensive, and which most first year students don't have the mathematical background to use properly).