The Intuitive Linear Algebra book series offers an exciting approach to linear algebra that stretches the reader in ways most introductory texts would not even consider. Seeing matrices not just as arrays of numbers but as functions from the very beginning, these books illustrate just how intuitive linear algebra really can be.
This book is beyond the normal linear algebra coursework. After touching on differential equations and quaternion rotations, it delves into Galois theory and algebraic number theory. The book culminates with a working example of the General Number Field Sieve for factoring integers. The ideas are completely developed from basic linear algebra learned in the other two books.