Groups and Symmetry 2nd Edition by M. A. Armstrong (PDF)

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User’s Reviews

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

⭐Armstrong is ridiculously laconic. He also writes as if you’re fluent in the language of abstract pure mathematics. He also assumes you remember theorems proved in homework exercises and uses them in the main text of later chapters. Do yourselves a favor and take an intermediate level algebra course before picking up this book (if you even have to pick up this book, which I wouldn’t have, but it was required for my course). Applications happen on a rare basis, until the last handful of chapters. Worse still, Armstrong decides to only allude (at most) to scientific applications of the material, and instead focuses the “applied” chapters on things such as block problems (how many blocks can be produced if you have two colors of paint and paint pattern x) and wallpaper patterns (whereas he could have focused on the numerous applications of group theory to chemistry and even physics). Don’t let the easy going and easy to understand first 3 or 4 chapters fool you, this is really a poor text except perhaps for those who already know group theory, know high level algebra, and just want a book explaining the intersections in a not-so-rigorous, often hand-wavy way (this also adds to frustration because your professor will probably tell you your proof is weak if you mimic the proofs in the chapter text).

⭐good

⭐Some authors like to expound, some like to dazzle and some like to teach. Armstrong falls easily into the latter category. If you are looking for a clear and motivating book to start learning about group theory, you will not find a better book. It is a short book but covers the essentials. The range of topics covers the necessary ground for an introduction: Sylow’s theorems, free groups, matrix groups, presentations are all there with a strong geometric content. He even proves the Nielsen-Schrier Theorem in an accessible manner. All you really need to know is some basic undergraduate algebra to understand this little gem and it will certainly give you the foundation to move deeper. Highly recommended for a starting point.

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