No comments about Shape Up!.

2 comments about Vectors And Tensors In Engineering And Physics: Second Edition.

1. It's a good-level book in tensors' algebra and calculus. Besides, physical examples help you better understand the mathematical concepts. On the other hand, I think it does not have enough applications about vector calculus (Frenet formulas, scalar potentials, Maxwell equations...).I would have also preffered it to contain more about general tensor theory: pseudotensors, curvilineal coordinates, and also about Riemann spaces. Despite this, it's an excellent book where you can see mathematics aplied to science; this is the important thing for physicist and engineers



2. I've not come across another book that introduces tensors successfully to non-mathematics graduates. It would not be easy to appreciate and comprehend every part of the book as it covers a wide range of physics & engineering applications. (not many of us are experts in all fields) However, the book is an excellent platform to start learning about tensors, after which one can go on to read the classics on tensors. I'd recommend the book to any senior or graduate engineering student (physics and maths students might find the book "less challenging").

1 comments about Methods of Homological Algebra.

1. Homological algebra is one of those subjects that in order to understand, you need to know already. Category theory wouldn't hurt either, nor some algebraic geometry and algebraic topology. Unfortunately, you need to know homological algebra to do some of these things as well. The great strength of Gelfand and Manin's work is that it ties together examples from all of these areas and coherently integrates them into some of the best mathematical prose I've ever read. The book is recent enough that its authors write from a position of vast perspective on fifty years of research, and the subject as they present it is about as up-to-date as possible, yet cleanly developed and not overwhelming. Unlike many books whose subject matter was influenced by modern algebraic geometry, this one does not merely pay lip service to standard references on its vast prerequisites, but systematically develops them (specifically, the ideas of category theory and abelian categories) in an entire, large chapter.
   
   The book's only tangible drawback is the presence of errors, despite the revision. The previous edition was said to be riddled with them, and the authors have indeed brought the count down to a nearly respectable level, with those remaining relatively minor. The remaining errors are more jarring than confusing, however, and this is not a sticking point.
   
   Finally, I would like to emphasize that neither this book nor any other is suitable for beginners in homological algebra. This is an aspect of the field, and its remedy is to study the applications, algebraic geometry and algebraic topology most of all. The ideas of homological algebra are derived not from first principles but from mathematicians' experiences doing mathematics, and both the subject matter and the many excellent examples in the book will resonate more with a student whose knowledge they cast in a new light.

No comments about Non-Linear Elliptic Equations in Conformal Geometry (Zurich Lectures in Advanced Mathematics).

2 comments about The Golden Ratio and Fibonacci Numbers.

1. Well, I have studied these numbers and other fascinating phenomena in mathematics, and I never found it enough. So, every book I read about this stuff I found a new set of new things, or at least a new view/review of the old things I knew. After my short study (7 years now) in the field of Number theory and Related topics, I dare say, that this book was another addition to my knowledge that -thanks GOD- I didn't waste.



2. This book is not absolutely perfect, but it is so much better than any other one on the subject that it deserves a 5-star rating. The majority of books on Fibonacci numbers and the golden ratio fall into three categories: (1) Books for children, (2) Mystical mumbo-jumbo, and (3) Books claiming you can use Fibonacci numbers to win in the stock market (!). Even Mario Livio's book, which is better than most, uses so much of its space to _debunk_ some of the mystical mumbo-jumbo that it de-emphasizes the wonderful patterns that can be found in the Fibonacci sequence, which is beautiful enough in its mathematical properties that one doesn't need to make such digressions. Dunlap's book, by contrast, _does_ emphasize those patterns. And when it's not directly addressing the Fibonacci sequence's properties, it's discussing things like the golden ratio and Penrose tilings, which are completely within the category of mathematics related to the topic.
   
   I really enjoyed the book, even though it has some typographical errors and minor omissions. The formulas collected in the third appendix alone justify buying the book. I could wish that there were more given, but this is the best collection I have seen.

No comments about Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing).

1 comments about A Catalog of Special Plane Curves.

1. This book presented information regarding plane curves in a clear, concise manner. The illustrations add to the book's quality. This is a good reference for people who work with plane curves.

No comments about Calculus with Analytic Geometry.

No comments about Convex Bodies: The Brunn-Minkowski Theory (Encyclopedia of Mathematics and its Applications).

1 comments about Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors (Cambridge Texts in Applied Mathematics).

1. I am using this book in filling in the gaps in my knowledge of PDEs for my masters project and it is great. I have to agree with this author that this is a great book for a beginning student in the field. The way the auther builds up the material of functional analysis for the study of PDEs really cleared up a lot for me.