Groups and Their Graphs (New Mathematical Library 14) by Israel Grossman (PDF)

Description

The abstract nature of group theory makes its exposition, at an elementary level, difficult. The authors of the present volume have overcome this obstacle by leading the reader slowly from the concrete to the abstract, from the simple to the complex, employing effectively graphs or Cayley diagrams to help the student visualize some of the structural properties of groups. Among the concrete examples of groups, the authors include groups of congruence motions and groups of permutations. A conscientious reader will acquire a good intuitive grasp of this powerful subject.

User’s Reviews

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

⭐The American Mathematical Society publications provide an excellent math education for junior high and high school students as they make for excellent self-study texts at the introductory level. This book is an excellent example of their quality publications. Recommended as a companion book would be either Pinter’s

⭐or Herstein’s

⭐.Also recommended are the various introductory abstract algebra lecture courses (for free) on the internet.

⭐A good standard to build mathematics reading skills.

⭐This elementary introduction to group theory is supposed to be unique in its use of graphs to represent groups (Cayley diagrams), which would be an interesting and fresh approach to teaching group theory. But no, the authors don’t deliver what they promised. It’s the same old group theory, with a few Cayley diagrams thrown in here and there. Of the few Cayley diagrams that actually appear, many are so very trivial that they just seem stupid (C_n, Z, etc.). In fact there are only two nontrivial Cayley diagrams in the whole book: the quaternion group and the icosahedral group (last page).

⭐Graphs are a superb tool for understanding groups and for some reason are not usually taught in the usual introduction to group theory. This book is strictly an elementary introduction to group theory, but I believe it is the best introduction around. If you don’t know any group theory and want to get into it, start here. If you know some group theory, but not about graphs of groups, then pick this book up.

⭐This is one of the best books for self study on group theory. It is useful as a class text book for students in high school or freshman undergraduates. Highly recommend this book along with Pinter’s. Of course, if you have sound knowledge of fundamentals, this book will not be much use to you except for a few graph interpretations of groups.

⭐群の図形表現(グラフ)を基礎に具体例から抽象へ導くユニークな群論入門。邦訳：浅野敬三、”群とグラフ”,河出書房新社(1970)がある。この原書ではR.H.Crowell,”Introduction to Knot Theory”(1963,182page)を結び目理論の参考書(邦訳あり)として詳しく説明している。高校生や一般人むけにかかれた、本格的な入門書である。確かに群とグラフを同時に説明する教授法は読者の理解を徹底させるのに効果的なようだ。抽象性の故に群論の学習に挫折した経験のある読者もこの本であれば展望がひらけるかもしれない。

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