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

In summary, this book is an older, more comprehensive textbook that is aimed at more experienced students. It is not a modern, handbook-style book that would be suitable for most students.
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Dowland
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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! :)
 
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Thank you Joriss! I think I'll buy that one instead. Never heard of it before but it looks great for my purpose!
 
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I have it. For price I see inside the cover the 2-voume set republ. Chelsea NY cost me £4.15! :biggrin: 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."
 
  • #5


I believe that gaining a solid understanding and conceptualization of mathematics is crucial for success in any scientific field. It is important to not just memorize formulas and methods, but to truly understand the underlying concepts and principles.

In regards to the textbook "Algebra, an Elementary Textbook" by Chrystal, I have not personally read it but I have heard good things about it. From what I have seen, it seems to cover the topics in a rigorous and logical manner, which aligns with your desire for a more strict hierarchical evolution of concepts. I believe it would be a good resource for a motivated high school student looking to deepen their understanding of algebra.

However, I also want to emphasize that there are many resources available for self-study and deepening one's understanding of mathematics. It may be worth exploring other textbooks or online courses to find one that aligns with your learning style and goals. Additionally, seeking out a mentor or tutor who can guide you through the more rigorous understanding of concepts may also be helpful.

In summary, I believe that "Algebra, an Elementary Textbook" could be a valuable resource for your goals, but I also encourage you to explore other options and find what works best for you. Keep up your motivation and curiosity in mathematics, it will serve you well in your future scientific endeavors.
 

1. What makes "Chrystal, Algebra, an Elementary Textbook (1886)" a significant book in the field of mathematics?

"Chrystal, Algebra, an Elementary Textbook (1886)" is considered a significant book in mathematics because it was one of the first textbooks to present algebra in a systematic and comprehensive manner. It also introduced many new concepts and techniques, and was widely used in schools and universities for over a century.

2. What makes this textbook different from other algebra textbooks?

This textbook stands out from others because it was one of the first to use the modern notation and symbols for algebraic expressions. It also includes many real-life examples and exercises, making it more practical and applicable for students.

3. How relevant is this textbook in today's mathematics education?

Although this textbook was published over 130 years ago, many of the concepts and techniques it covers are still relevant in modern mathematics education. A solid understanding of algebra is essential for higher level math courses, and this textbook provides a strong foundation in the subject.

4. Is "Chrystal, Algebra, an Elementary Textbook (1886)" suitable for self-study?

Yes, this textbook is suitable for self-study as it is well-structured and covers all the necessary topics in a clear and concise manner. However, it is recommended to have some basic knowledge of algebra before attempting to use this textbook.

5. In your opinion, what makes this textbook a timeless classic?

In my opinion, this textbook's timeless classic status is due to its ability to effectively teach algebra to students of all levels. It has stood the test of time and is still used by many educators today. Its clear explanations, practical examples, and comprehensive coverage of algebra make it a valuable resource for anyone interested in the subject.

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