You are here

Quandles: An Introduction to the Algebra of Knots

Mohamed Elhamdadi and Sam Nelson
American Mathematical Society
Publication Date: 
Number of Pages: 
Student Mathematical Library 74
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Erin E. Bancroft
, on

This book is not for the mathematically faint of heart — just about every other page contains a new definition — but for the motivated reader who is willing to read with pencil and paper in hand it provides a solid introduction to quandle theory.

Knots, combinatorial knot theory and invariants are introduced in chapter 1 while chapter 2 provides a quick background on algebraic structures referred to later in the book, including quotient sets, equivalence relations, modules, groups, and cohomology. The remaining five chapters develop quandle theory starting with the algebraic structures of kei and quandles in chapter 3, continuing with connections to groups, and algebraic topology in chapter 4, generalizing quandles (including racks, bikei, and biquandles) in chapter 5, and finishing with enhancements and applications to generalizations of knots in chapters 6 and 7. As one might expect, diagrams and examples are plentiful and are essential to grasping many of the concepts. The authors do an excellent job of pointing out unifying ideas and motivating questions throughout the text, especially at the start of each section. Chapters are broken up into sections and each section ends with 5–10 challenging exercises without solutions. The bibliography is extensive and the reader is regularly directed to outside resources for more examples, expanded explanations, or origins of a term or theorem.

The authors claim the only prerequisites needed are linear algebra and basic set theory, but most undergraduates will find the text difficult to grasp on their own without having taken a course in Abstract Algebra or Topology. Overall I would highly recommend this book (as the authors do) as a text for an upper division math elective or as a primary resource for a senior capstone project.

Buy Now

Erin E. Bancroft ( is an associate professor of mathematics at Grove City College in Grove City, Pennsylvania who enjoys origami, chocolate, mysteries, and helping her students discover the beauty of mathematics.