Naive Lie Theory (Undergraduate Texts in Mathematics)

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.

Let me start by stating my point of view: I'm a math grad student, so I'm not really the nominal audience for the book (the book is targeted toward undergraduates). Having said that, I found this book to be wonderfully conversational in tone, amusing, very honest (if there is slogging to be done in a proof, the author says so, and if the author leaves something out he tells you why), and very useful in gaining an intuitive feel for the material. The prerequisites for this book are very modest: if you've seen linear algebra and calculus, then you could give it a go. Some sort of exposure to abstract algebra of some sort would be useful, but may not be required. Some intuition for manifolds is is similarly useful, but certainly not required. Even with these modest prerequisites, the author manages to do much with Lie Theory. This is a jewel of a book, much like its spiritual predecessor, Halmos's Naive Set Theory (Undergraduate Texts in Mathematics) . So, this book is accessible, well written and useful. What more could you ask for in an introduction?

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'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.

This review is on the textbook Naive Lie Theory by John Stillwell. Recently I purchased this book with hopes of having a study reference to the more elementary parts in preparation for more advanced study of Lie Theory and other theoretical math that involves these ideas. I have not yet finished the book. This book is well written with clear and accurate developments and good examples. There are well placed exercises. One is tempted to try various things, to explore variations based on the readings. I find this exciting the way the book let's me explore ideas. The Author lets you know about the more advanced parts of Lie Theory he is not going to cover so you have an idea what to study later to complete the picture. He decides to use simpler concepts of matrix processes and linear algebra with the understanding that this will allow you to do quite a bit. It is a nice start using the unit circle on the complex plane as an elementary first example. A clear context is given why certain inventions and discoveries were made. I am a mathematician, computer scientist, mathematical physicist, and Formal Languages.

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.

It is not often that I buy a math textbook, read it cover to cover, and long for more. Stillwell is an exceptional writer. What differentiates this textbook from others is (1) the historical background material that seamlessly mixes with the equations, and (2) a clear motivation and exposition of important concepts. For readers with physics background: in my opinion Stillwell is the David Griffiths of math. Stillwell does not cover indefinite groups (Lorentz groups) nor does he cover representations. But it is still the best book to get you going. I found this textbook more interesting than Tapp's Matrix Groups for Undergraduates (Student Mathematical Library,) . I think Tapp's book is somewhat more elementary. I could not read Kosmann-Schwarzbach's Groups and Symmetries: From Finite Groups to Lie Groups (Universitext) (translated) beyond chapter 1, the text was concise but encryptic. Georgi's Lie Algebras In Particle Physics: from Isospin To Unified Theories (Frontiers in Physics) was more advanced and kind of dry. Lipkin's Lie Groups for Pedestrians (Dover Books on Physics) was more advanced also. After finishing Stillwell's book I would recommend Hall's Lie Groups, Lie Algebras, and Representations: An Elementary Introduction .

You don't need much math to wrap your head around this. Even though I studied math, I still appreciate how everything is stated simply and clearly. A "Lie algebra for dummies," I'd you will

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.

This is super book! At every chapter end there is discussion of results, very helpfull.

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Really good book to bridge undergraduate mathematics to results built on quantum mechanics. A must!!!

I am just trying to learn more about Lie groups as a hobby in my retirement (from a life doing chemistry, so I'm used to space groups in molecular symmetry). I have begun reading this book and I can see that it offers a clear explanation of something really quite difficult to grasp. The mathematics linking geometry with algebra, matrices and symmetry is really very beautiful and I feel rewarded for my efforts by this book. I still have rather a long way to go!