Chrystal, Algebra, an Elementary Textbook (1886) - Your opinion?

[Dowland]

Chrystal, "Algebra, an Elementary Textbook" (1886) - Your opinion?

Hey! I'm in high school and have recently discovered how suggestive and ravishing mathematics can be, although I haven't got very far (only basic algebra, geometry and trigonometry - to give you a hint: I'm about to be introduced to derivatives, logarithms and such next semester, so...).

There's one thing about the mathematics education (in my country, Sweden) that has always annoyed me a bit: the lack of rigour. The mathematics education is largely based on mechanical counting by route and recognizing patterns in a quite superficial manner. I would like to get a more solid understanding of why things work as they do; for instance, instead of just presenting a method to solve a linear equation, I would also like to see the deduction of the method itself, using fundamentally derived quantitative properties from the "borderland"(?) between arithmetic and algebra, and learn to do my own derivations (or proofs, or whatever). And I would also like to have a more strict hierarchich evolution of the concepts in mathematics, where one clearly can discover and overlook how to or more concepts can help forming the next concept. Hope you sort of understand what I mean.

I have searched a little for books that would fit my wants, the closest I have got is this one: (warning: large PDF): http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf[Edit: Here's part II of the book: http://djm.cc/library/Algebra_Elementary_Text-Book_Part_II_Chrystal_edited02.pdf)

At Amazon: https://www.amazon.com/dp/0821816489/?tag=pfamazon01-20

My aim with this thread is mainly the following to:
*To hear your opinions regarding the posted textbook. Would you recommend it to a motivated high school student? I have looked into it a little, but it would be nice to here from someone with more experience in mathematics before I invest my time and money in this textbook. I'm grateful for all comments about the book.

*Do you think my aim of getting a solid understanding and conceptualization of the mathematics introduced in high school could be attained in another way instead? (For instance, other books you would recommend instead, e.g. a more modern textbook?)

Oh, and one last thing: Sorry for the not so good language, I hope it's fairly readable! :)

 

[Jorriss]

I would not use that book. Much of the notation would be out of date among other reasons.

https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20

That book is a better choice imo. Another member often recommends it and I gave it a look and it appears excellent.

 

[Dowland]

Thank you Joriss! I think I'll buy that one instead. Never heard of it before but it looks great for my purpose!

 

[epenguin]

I have it. For price I see inside the cover the 2-voume set republ. Chelsea NY cost me £4.15! No doubt more by now, but you can no doubt get it reasonably secondhand and anyway it is available free on the web so price is hardly an issue.

The reason I got it was as a reference - it is rather comprehensive on results and methods that would have been a pain to work out myself when I needed them, or to find in other books, especially when not connected with or near any math library or people. But that does not mean it is a handbook, it is a true expository textbook, and a good one. Whether suitable for you is another question.

I think it was aimed at ambitious students in England in the top years of school (in the past) who were aiming for scholarships at Cambridge and suchlike, studies with strong math content, and then could have served also during their first year or so at University. For many questions that come up here, inequalities, series, it would be fine.

'Algebra' is interpreted very broadly as it includes quite a bit of geometry, number theory, probability, even conformal mapping and Riemann surface get a mensh, etc. etc. - read the contents list.

The approach would now be called 'concrete'. 'Group' and 'matrix' are not in the index. I guess not many university math teachers would recommend it. It is like an archaic, though perfectly intelligible, version of the language they teach you to speak.

For dipping in and occasional use, e.g. when stuck with other authors or on problems. The author himself writes "it by no means follows that the volume should be read through at first reading. Such an attempt would probably sicken the reader both of the author and of the subject."