Elementary Algebra and Trigonometry

Question

Hey mathstack community,

recently i came across a 2 volume set of books written by G. Chrystal, and another one by Henry Fine titled "Algebra: An Elementary Text-book Volumes 1-2" and "A College Algebra," respectively.

These works are known for being how do i put it, comprehensive in their coverage and justify the movement from statement to statement, rather than spoon feed to you bits and pieces of math like the common textbook does without any substantiation.

i know that people say "practice, practice, practice" a lot and this is very important, but my experience with the average pre-university textbook is that they are very weak on the theory side but very strong on the rote, drill and kill side. Given this, i have little to no genuine understanding of elementary mathematics at all. After skimming Chrystal and Fine, i wonder if there is any other textbooks like these.

tl;dr: since i'm just a high school student with no genuine understanding of elementary algebra beyond a couple poorly knit techniques, i would like ask the more informed and educated people here whether they know of any other titles for elementary algebra and trigonometry, similar in content to Chrystal and Fine

i also know about the Gelfand series which lack the structure and depth of Chrystal and Fine, but have good content regardless.

Answer 1

I highly recommend Modern Algebra and Trigonometry by Vance.

I can also recommend Trigonometry by Rees and Rees.

These were our textbooks for high school algebra and trigonometry, respectively, at Manila Science High School.

Answer 2

Books suitable for beginners, but with a particular emphasis on proof and justification are:

• Algebra I by Brumfiel. https://archive.org/details/algebrai00brum (Algebra I and II are, I believe, freely viewable on Hathi Trust from within the United States. With some technical knowhow, it should be possible to download them page by page and assemble the pages into a PDF.)

• Volume 1 of A New Algebra by Barnard and Child. https://archive.org/details/newalgebra01barnuoft

The first of these is from the "New Math" period in the United States, so it presents the foundations of algebra in line with the presentation in modern algebra, but leaving out all the difficult parts.

The second, besides teaching the underlying ideas of algebra well, aims for high technical competence in manipulating algebraic expressions. The second volume of A New Algebra comes the closest I've seen to an honest discussion of irrational numbers at this level (though stopping short of full rigor, which is achieved in the sequel Higher Algebra, where irrational numbers are defined via Dedekind cuts).