Algebra Which books provide the best understanding of quaternions for scientists?

[BigFlorida]

I am very much interested in gaining an in-depth knowledge of quaternions, yet I cannot find any reviews of books on quaternions anywhere. Does anyone have any recommendations? Are Hamilton's and Tait's books my best bet?

 

[micromass]

Please tell us all the math you know. Also, please indicate why you are interested in quaternions.

 

[BigFlorida]

@micromass The relevant math courses I have completed (or am taking *) are calculus I through III, Linear Algebra*, Differential Equations I*, Vector Analysis* (Including a brief intro to tensors), and Theoretical physics I*(which covers cal 2, cal 3, linear algebra, complex arithmetic, DE I, DE II, Fourier Analysis, and Vector Analysis). I am self-studying Fourier Analysis, Perturbation Theory, Complex Analysis, Differential Geometry for next semester. I would just like to know more about quaternions because I did a project in my vector analysis course in which I had to give a brief history of William Rowan Hamilton's life, and quaternions have very much captured my interest, but it is hard to find any recommended literature on the subject. Also, I have deduced that an understanding of quaternions will come in handy in QM and this is about the point in the semester that I like to begin preparing for next semester.

 

[micromass]

OK. Well, it seems to be that you will want to study geometric algebra then. This is very related to the quaternions. To study it, I suggest the books by MacDonald, he has two:
https://www.amazon.com/dp/1453854932/?tag=pfamazon01-20
https://www.amazon.com/dp/1480132454/?tag=pfamazon01-20
There are many other texts on geometric algebra though.
If you are mostly interested in the applications to physics, then you have: https://www.amazon.com/dp/0521715954/?tag=pfamazon01-20

 

[BigFlorida]

@micromass Thank you very much! I shall definitely check out all three of them.