This review refers to the 1965 Hardcover version of the book.

It's quite apparent that the 40 years that have passed since this book was printed have very much dated it's content. The definitions of many key concepts (such as an ideal) contain the right ideas, but are not formulated in the modern viewpoint. These, however are only minor setbacks. The main flaw of this book is its subject matter. There are 11 chapters, and it was not until the eighth that the ideas start getting deeper. Even these last 4 chapters do not delve very far into the heart of things.

The text is written with the reader in mind (almost excessively so). Useful equations are clearly labeled and the steps in the proof are clearly outlined, though sometimes to an unnecessary degree.

I would recommend this book for a mathematics hobbyist, or perhaps an undergraduate number theory course. For anyone with a stronger background, they wil not glean much.

I don't know how Kolman managed to do it, but he did. He wrote a very basic linear algebra text book for beginners and yet made his explanations so unclear that the book ends up being hard to read. The topics are the very basics of linear algebra: no canonical forms, no infinite dimensional spaces, the underlying field is always R or C, and everything is done in terms of matrices. The explanations of the concepts that are covered could use some coherence and a dash of order.

I wouldn't recommend this book for anyone. It's pretty much garbage.

Topics are explained with exceptional clarity; portions of the book are well tied together; and the order of exposition flows very well. Lie groups are introduced quite early on, but their full power is not revealed until later in the book. I can't laud this book enough. I had a firm, well-developed basis of differential geometry after reading through this book for a course. The excersises are illuminating, as are the examples. Theorems and their proofs are clearly labeled. The motivational explanations prefacing theorems do an excellent job of conveying the intuition behind ideas.

I would recommend this book over Boothby any day. I haven't read Spivak, so I can't compare Lee to it, but Lee definitely seemed like an excellent choice for an intro grad class on differential geometry.

This book has a very particular purpose: to recap some basic concepts from undergraduate mathematics so that you get the "big picture". In other words, for every math course you took as an undergrad, this book provides a good outline of the major ideas and how they fit together. But, it is only an outline; nothing more. If you actually missed out on some topic, or your knowledge of a subject is shaky, then this book won't help much. It will only help by providing a bibliography of some other references for that subject.

This book is meant to organize your undergraduate math knowledge, not to supplement it.

With that said, I'll mention a few words about the content of the book. It is quite well written and definitely extracts the essential ideas for your quick consumption. There are a few topics that I personally feel are missing, such as Gram-Schmidt and Jordan Canonical Forms for Linear Algebra, and UFDs and PIDs from Algebra. In general, it seemed like the book leaned a little more towards analysis than algebra, but the vast majority of important topics were indeed encapsulated in their synopsis.

Good for a very specific audience, but otherwise not wonderfully useful.

This was the book that I learned Complex Analysis from. Definitely made the subject accessible to pretty much any reader. Plenty of exercises: some more theoretical, some more applied. It skillfully straddles the gap between being a theoretical math book and a math book for people with more applied aims (such as engineers). Most topics are covered thoroughly, though certain more complicated subjects such as winding number are left out for simplicity.

This book definitely prepared me for tackling the dense, theoretical, and exceptional "Complex Analysis" by Ahlfors. I'd recommend it as an introductory book for anyone trying to get into the subject who is intimidated by Ahlfors, as well as for anyone who is only interested in the essential commonly-applied tools.

Although this book may be somewhat outdated (published in the mid-70's), it does provide a cohesive view of the developments in logic up until that point. One gets a very strong sense of the status of logical development, while at the same time receiving a historical motivation for the methods employed in developing the theory. Many proofs are shortened or synopsized, however the integrity and technical level of the work is never compromised. In my opinion, the sections on Model Theory, Set Theory, Proof Theory and Recursion Theory provided the reader with a good sense of the major results in those areas. The section on computers (and their limitations) was a hoot to read, because of the limited view provided by the author, but otherwise, Wang has a strong intuition as to where modern developments could have led. Recommended for anyone trying to get a unifying view of the major developments in logic.

KiTH are awesome, and their vision does not stop with this movie. Their offbeat and hilarious brand of comedy is fully unleashed in Brain Candy and I LOVE IT! The subject of the movie is a greatly untapped comedic subject--psychosomatic drugs-- and they rip it to shreds. A lot of classic characters appear in the movie, along with plenty of fun new characters to laugh at. Every time I see this movie, I poo my pants I laugh so hard. Don't you want to poo your pants too??? See this movie!!!

This book provides a great intro to non-standard geometries by creating different axiomatic systems and finding models of them. It then constructs and analyzes operators (addition, multiplication, and the like) on the plane. It devotes a good section to discussing the Desargues and Pappus properties and their fundamentality in most geometries. A good treatise of projective geometry follows, and the book ends with a quick skim of metric geometries and non-euclidean geometries. This is not a good book if you are planning to study Hyperbolic, Spherical or Elliptical geometry, nor does it do a fair treatment of the effects of a metric on a geometry, but it does provide a short, comprehensive intro to axiomatic coordinate geometry.

I am a teacher's assistant for an undergraduate computer science course that uses this book. I have to say that it really is a terrible book for students to learn from who have never had much exposure to non-calculus math and the concept of the "mathematical proof". It skims over topics without providing enough exposition on the topics to allow students to have a fair grasp on the subject. This may just be the nature of teaching discrete math, but there seem to be far too many topics that Truss is trying to squeeze into too small of a space. He tries to throw in some more advanced topics such as formal machines and complexity theory, but only at the cost of having the overall quality of the material be watered down. Sadly, though, from what I have heard, this is the best current intro discrete math book out there.