No comments about Geometry Part 2 (Quickstudy Reference Guides - Academic).

5 comments about General Topology (Graduate Texts in Mathematics).

1. John Kelley wanted the title to be "What every young analyst should know", but was convinced (by Halmos, among others) not to use it. Still, it is a very good description of the book. Barry Simon calls it "superb" and recommends that you read it by trying to do the exercises, recurring to the text as needed. But then you would perhaps not pay attention to how wonderful the text is. I believe this is the best-written modern mathematical text. The proofs are clean and extremely elegant. The prose itself is beautiful and frequently witty. Treats topological and uniform spaces at depth and in detail, so as to be both a textbook and a reference. Excels in both capacities. This is mathematics close to poetry.



2. I cannot agree with the other reviewers on this. Back in the days when there were hardly any general texts on topology this may have been good. Nowadays there are at least a dozen such that are far better than this. The printing fonts and layout are spidery and primitive and not easy on the eye. The style is rather formal and dry for a subject as rich as this and little effort is put into illustrating the material with background, diagrams or examples. As I said before there is no shortage of better texts amongst which Hocking & Young is worth special mention.



3. I don't hesitate to give this book 5 stars. It is solid! Many reviewers allow too much personal judgement to cloud their appraisal of a certain book. To me I believe it is important to be as dispassionate as possible so that a prospective buyer can make an unbiased decision. Rather than label a book as "bad" or "good" one should focus on some factors such as:
   (1) Content: a summary of the main point covered by the book (this is optional). In the case of this book, this is obvious from the title.
   (2) the author's approach: Kelly took what I call the "analyst's approach" to topology. This is fine for those who love analysis but don't really care for topology for it's own sake (like me!) By using this approach, those like me are much more inclined to find topology motivating because ones sees it as abstractions of what one is familiar with
   (3) the presentation: Kelly gave a simple but "sophisticated" presentation. You will not describe him as very expository but the presentation is excellent. Some people seem to prefer this style and some don't. No, this has nothing to do with the so-called "mathematical maturity" (how do you define that by the way?) What the author expects you to know to understand the book - that is, the intended audience - is usually stated clearly in the preface



4. This is a great book. The proofs are clearly presented, and generally it is easy to understand the motivation behind definitions and theorems. Exercises are relevant, interesting, and well designed, often allowing the reader to discover things that other texts describe in dull detail. Unfortunately, a few exercises (such as "Integration Theory: Junior Grade") seem to pop out of nowhere. I consider this a minor defect. A much larger annoyance is that Kelley defines partial and linear orders in an utterly non-standard and somewhat clumsy way, which ends up affecting a large number of exercises. If you already know something about orderings, you will encounter many surprises; if you know nothing about them, you may get the wrong idea.



5. I was motivated to read this book while in grad school, becasue I needed to understand the French literature in my field (probability). One particular concern is the metrizability of a general topological space. I would say Kelley's book has a spendid presentation on this subject.
   
   Other things in this book are also practically useful. Convergence in the general sense (net or filter) is useful in mathematical finance. The part on locally compactness and paracompactness is a must for anyone working in differential geometry. And if you work in analysis, then the chapter on space of continuous functions is a good reference to look up.
   
   The exercise problems are also good resources when you need some help. I still remember one cute problem on the neighbourhood systems. It helped me understand how a family of seminorms would yield a topology on a linear space.
   
   Evetually, I read this book from cover to cover. And I would say this is one of the best education I've ever received.
   
   If there has to be a complain, the proofs are somewhat hard to read. But this is more or less determined by the nature of the subjects. And when you are well-motivated and equipped with certain mathematical maturity, this problem will gradually go off.
   
   In summary, this book is comprehensive, useful and beautifully written. It is a treasure that every mathematician's library should have.

2 comments about The Mathematics of Juggling.

1. Polster manages to take the innocuous pastime of juggling and segue from it into number theory. The movement of balls is shown to map naturally into the concepts of finite state graphs. Bringing in ideas of permutations. And introducing juggling matrices!
   
   Plus, he points out that the founder of Information Theory, Claude Shannon, was also interested in the theory of juggling. Several crucial juggling theorems were discovered by Shannon and are named after him. For readers familiar with Shannon in computing, the book gives a look at relatively little known research by him.



2. I am a mathematical dunce. I have a better than average IQ, I passed high school algebra, I have been juggling for 35 years, and I even came up with diagrams on my own to remember and devise patterns. I thought I would enjoy this book, and I imagine I would if it were at all comprehensible to me. Though the book is hyped as "useful," "accessible" and "entertaining," buyers should be warned that Polster's book is about math and is written entirely in the language of math. There is no effort to bridge the gap between a practical understanding of juggling logic and his numeric abstractions. He writes in plain English prose until 3/4 of the way down page 8, and by the bottom of that page he has ditched you and disappeared into a world of opaque notation that might as well have been written by G.E. Moore and Bertrand Russell. If page after page of greek letters, academic jargon and abstract equations is easy reading for you, get this book. If you don't already speak higher math, Polster isn't going to teach you how.
   
   For a book that does what Polster does not, find Laws of Form by G. Spencer Brown.

2 comments about Sacred Geometry Oracle.

1. I highly recommend this Sacred Geometry Oracle. The cards are fantastic and the companion book helps understand how each symbol may significant to you. This book can help guide you if you are a begineer, regular practioner or advanced.
   
   In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. These inevitably follow geometrical archetypes, which reveal to us the nature of each form and its vibrational resonances. They are also symbolic of the underlying metaphysical principle of the inseparable relationship of the part to the whole. It is this principle of oneness underlying all geometry that permeates the architecture of all form in its myriad diversity. This principle of interconnectedness, inseparability and union provides us with a continuous reminder of our relationship to the whole, a blueprint for the mind to the sacred foundation of all things created.



2. My advise is, don't buy this deck. There are better ones on the market.

No comments about Intuitive Topology (Mathematical World, Vol 4) (Mathematical World).

3 comments about Topology Now! (Classroom Resource Material).

1. If you are looking for a text for an undergraduate course in topology, then this book is Goldilocks in disguise. The amount and level of the material are both just right. Chapter 1 begins the process by introducing topological equivalence and topological invariance. This is followed by chapters on knots and links, surfaces, three-dimensional manifolds, fixed points, the fundamental group and metric and topological spaces. The background mathematics needed to understand the contents of this book are all well within the skill set of an advanced undergraduate. There is the occasional appearance of a derivative, but an understanding of calculus is not needed.
   The most significant skill is a through understanding of functions as mappings, and the special characteristics, such as homeomorphism, that functions can have. There are a large number of exercises at the end of the sections, further increasing its' value as a textbook. Topology is a branch of mathematics where one can sometimes engage in hands-on demonstrations. Problem 6 on page 38 is a demonstration involving cutting the toe off an old sock, sewing the ends together and then turning it inside out. Some of the other questions are a bit silly. The best is problem 6 on page 24, "Homeo, Homeo, wherefore art thou Homeo?"
   The authors should be nominated for a prize in expository writing for this book, if it were in my power to do so I would. Understandable is an understatement of the quality of the explanations.
   
   Published in Journal of Recreational Mathematics, reprinted with permission



2. What more can I say ... I ordered this for a friend who requested it, and who finds it invaluable. And it came very quickly. Can't do better than that. Sorry I'm not qualified to comment on the book's academic content.



3. This book is bad on many levels, possibly uncountably infinite levels. Nowhere in this book is there any motivation for the material, the author just throws various topics from topology at you and expects you to be interested, which I wasn't. The assignment's in the book are dull and boring and the entire book is entirely confusion. I find it slightly ironic that the book is called topology now, when every chapter I was waiting for the topology to begin. The only chapter in the book that is at least mediocre was the last chapter in the book. Other than that the author spends 25% of the book (right in the middle) discussing knot theory, a concept that he never relates to the rest of the book, or gives any motivation to learning he just throws it out there. Overall this book is too confusing for non-math majors and not rigorous enough for math-majors, so if you're looking for a good introductory topology book try Introduction to Topology by Colin Adams.

No comments about Generalized Hypergeometric Functions.

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 Topological Methods in Hydrodynamics (Applied Mathematical Sciences).

1 comments about Young Tableaux: With Applications to Representation Theory and Geometry (London Mathematical Society Student Texts).

1. With his usual lucidity, Fulton brings together the surprisingly wide area of mathematics concerned with Young tableaux. These are combinatorial patterns which index basis vectors of group representations (either of the symmetric group or the general linear group). These vectors can be seen as Plucker coordinate functions on non-linear representations, namely homogeneous spaces (Grassmannians and flag varieties). Thus, Young tableaux form an invaluable tool to examine these representations and varieties in concrete detail. Fulton also gives a good exposition of the combinatorial operations on tableaux which reflect the crystal basis structure from quantum GL(n), though Fulton does not explicitly discuss quantum groups. Other good expositions of these topics, from a more algebraic and combinatorial point of view, are Sagan's newly revised "The Symmetric Group", and Stanley's "Enumerative Combinatorics", Vol 2.