Naive lie theory
by John C. Stillwell · first published 2008
60% recommend40% neutral
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics.
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Stillwell is a great author. Naive Lie Theory is a great read, with a big section on quaternions.
on “A View of Mathematics (2005) [pdf]” ↗Seconding this. His other books are great as well (Reverse Mathematics, Naive Lie Theory). Great writer.
on “Ask HN: What kind of math do you study in your free time?” ↗Naive Lie Theory is a great book, and the first chapter teaches quaternions. https://www.goodreads.com/en/book/show/4419538
on “Look, ma, no matrices” ↗I'm currently working through Naive Lie Theory https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math... by Stillwell and there's a lot about quaternions in the first chapter, including their standard matrix representation. You'd need to be…
on “All Hail Geometric Algebra” ↗There is also Naive Lie Theory by Stillwell, which is targeted at an undergraduate level. I haven't read it yet, but it's been on my radar for a while. https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math...
on “Lie groups are crucial to some of the most fundamental theories in physics” ↗