Naive Lie Theory (Undergraduate Texts in Mathematics) 2008th Edition by John Stillwell (PDF)

Description

In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called “classical groups” that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra.This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐After a first look through of this book, it quickly becomes apparent that even though this is a naive approach to lie theory, it is still not for the beginner. You will need a good understanding of linear algebra and calculus as the author presents the information of lie theory in terms of these two subjects. Good groundings in group theory and topology would also probably be good before picking this book up. If you know these subjects well, then this book is great to introduce this branch of mathematics. If you are worried about knowing the prerequisites well enough (like I did), look at the contents up to section 2.2, and if you are vaguely familiar with those topics, you should be completely fine reading this.Also after looking at other reviews, it seems that springer has fixed their quality issues on the book. My only complaint on the quality is on the side of Amazon as they put a paper sticker on the back (which I hate) that peels off poorly and left a residue.

⭐As a former math major working my way through this book, I find it delightful: I’d give the contents five stars. The presentation is clear, friendly, and illuminating. The exercises are a good adjunct to the text. The level is perfect for someone with some undergraduate experience looking for an intro to this topic.But the binding is horrid. After relatively light use, the binding has detached from the spine and is starting to peel away from the cover. Some reviewers have complained about the printing; my copy looks fine. But for a hardcover, it feels surprisingly disposable.

⭐The theory is well taught and developed. I found that this book yielded more understanding than the more calculation based references written for physics. As an applied math reader, I feel as if dozens of pages were wasted on proofs that didn’t do much, but I suppose I’ll give in to the pure mathematician point of view here.My biggest criticism is the heavy use of quaternions. The book introduced two concepts that readers likely aren’t familiar with, quaternions and lie groups, and tried to use one to build understand of the other. However, I found this to be of little benefit. The analogies were nice to point out and it was interesting to see the coexistence, but Stillwell took concepts of extreme value and practical use (Lie groups) and obscured them by describing them in terms of often forgotten and little practical use (quaternions.) As if you wanted to learn a second language, Spanish for example, and the instructor insisted that you used an English -> medieval Latin dictionary followed by a medieval Latin -> Spanish dictionary.The book is a very good book, but with the removal of quaternion emphasis and pedantic proofs in exchange for further developed theory, this book would have been one of my favorites.

⭐I didn’t like that there was no answers to the exercises. The theorems were nicely stated and proved.

⭐This book by Stillwell nicely brings Lie groups down to earth as few books do. But I was deeply disappointed by the cheap print quality. Even the cheapest PoD books in my collection are not of such low quality. The printing is very faint and uneven, and the resolution is low. You can see the dots in the smudgy letters caused by some unknown printing process. It’s worse than a home inkjet printer. Most pages are actually quite unpleasant to read because the printing is an uneven grey instead of sharp solid black. Many special mathematical symbols are so thinned out as to be almost unreadable. The paper is also heavy like a PoD book.I generally assume that the high Springer prices are compensated for by the high quality of printing. But in this case, the quality is significantly lower than any cheap Dover book or any PoD book in my collection. I just can’t figure out why Springer would damage their own reputation by using such a low-quality printing process. It probably cost them less than two dollars to print it. (My copy was printed in Lavergne, Tennessee, 2014 Dec 28.)

⭐I’ll write a full review when I’ve finished the book, but given the number of bad reviews of printing quality I want to note that (n = 1) they seem to have sorted that out by this point (Aug 2019). The pages aren’t fancy-fancy glossy pages, they are matte, but print’s great – between normal Springer books and Dover. (And I actually prefer the texture to glossy pages)As for the content: looking it over it’s exciting. I’ll report back in the future. But one thing I must say about this book: it’s short (and hopefully sweet). Full Lie Theory involves differential geometry. If, like me, you plan to get to that, but don’t want to wait, then a very focused volume imbetween makes a lot of sense. Also an excellent follow-up / prelim to a book like Physics from Symmetry by Schwictenberg — where enough Lie Theory to follow basic derivations of modern physics suffices.

⭐Despite having degrees in physics and math, I found some of this hard going.But then, it has been more than half a century.Even when I followed the equations, I did not always grasp their significance.More motivation would be helpful. And more on the related physics.

⭐This is an unusual book in that the topic of Lie Theory is rarely, if at all, covered in an undergraduate course. The author presents Lie theory as a blend between Linear Algebra and Calculus thus you will need a good appreciation of both of these topics. However if that is the case then readers will have no problem at all in reading and understanding Stillwell’s text. It is refreshing to see this topic tackled in a unique way that opens up what is considered to be a subject for graduates. Well recommended if you have the appropriate background and have an interest in expanding and discovering this interesting topic.

⭐Good book

⭐Got the Kindle version. Met my needs.

⭐I read now approximately the first 3 chapters, so maybe I will revise my opinion when I finished it.My experience so far:I appreciate a lot the way the author gives a short and relative comprehensive, structured introduction in the subject of Lie theory and Quaternions. Just 2 points of criticism:- The title is a bit misleading: This book is dedicated to an experienced colleague who owns already a master in mathematics or at least a bachelor with some special knowledge in algebra. In this sense it is not ‘naive’ in the sense of Halmos “Naive Set Theory” which everyone can read without pre-knowledge. However, I can understand that one cannot give a short introduction to this subject without making preconditions about the reader’s knowledge: The topic is far too advanced, it would extend this book beyond scope.- I miss some rigorous and short definitions of the objects the author is introducing: Also the colleague, not familiar with this topic (and to whom the book is apparently dedicated), cannot memorize all definitions right from the beginning: The notations are confusing (which is not the fault of the author though, e.g. unit circle S^1 is an object in R^2) so it would be a great help to have some kind of definition or table where to look up these objects when you run across them later on in the text. Instead objects are defined somewhere in the text which makes it difficult to look them up later. For this one star less.Else a very good book with which a scientist, not specialized in the topic, can get a quick overview what Lie theory is about and for what it can be used.

⭐Ich kann den Rezensionen nur sehr wenig hinzufügen. Dieses Buch ist unter anderem Physikstudenten zu empfehlen,da hier in sehr einfacher Weise die Grundlagen zu den Gruppen SU(n), SO(n),Sp(n) e.t.c und deren Algebren zu erfahren sind.Irgendwann stößt man ja unweigerlich auf die Gruppen SU(2), Pauli-Matrizen oder Majorana- Spinoren,oder die SO(3) Drehgruppe.Unter anderem ermöglicht dieses Buch, das man sich an die klaren Schreibweisen der Mathematiker gewöhnt.Ich hatte früher meine Schwierigkeiten mit Begriffen wie Einfache oder halbeinfache Liealgebren.Die Kapitel 8 und 9 motivieren die Hintergründe. Jedes Kapitel enthält einen orientierungsgebenden Vorspann.Dieses Buch ist mittlerweile erfreulicherweise für ca. 20 Euro zu erwerben.

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