Classical Advice on Algebra for High School

[Trying2Learn]

Good Morning

While I am an engineer, my math training was deficient. On my own, I made up for it, but it was a struggle.

For example, I always thought Algebra was the study of rate problems (e.g.: "If a train is going one way at one speed and the other is going that way at another, where will they meet?"). It was later that I realized that algebra was about sets, groups, fields, rings, etc., among so many other ideas.

With that in mind as the study of symbols and the rules for their manipulations... Can someone suggest an introductory site about algebra for a precocious eigth grade student?

I do not want my son to experience what I did.

It would be great to find a free PDF online somewhere, if possible.

EDIT: yes, some people posted response, but please note that my son does NOT want (sets of equations, solving them, polynomials, exponents, etc.) He wants ALGEBRA (sets, groups, fields, rings, etc.)

 

[symbolipoint]

Introductory Algebra, like in what the student would have in high school or a beginner's course at a community college? Does the information NEED to be a website or webpage? You can easily find good Algebra 1 books at public library booksales. Books of this traditional sort would be more comfortable to use, and to learn and study from. Titles like Basic Algebra, or Elementary Algebra would usually be good. If this sort seem right, do you want other details?

 

[Trying2Learn]

I am spending a few years abroad, and do not have easy access to english textbooks for my son. Thus the request for an online site, or a PDF

I found a good online PDF for Calculus and he is reading it to teach himself. But now he wants to learn more about algebra.

And most books or tutorials I see on the net are about the train-type problems (or if one farmer plowed two fields in one day, how many days for... blah blah blah)

He is interested in the foundations of Algebra (set, rings, fields, etc.)

But many of those are too advanced.

If I try to google "high school algebra" I get a list of sites that solve those rate problems. So I do not know what to google.

(I think he is going to be smarter than me, and I would rather not undermine his learning with a bastardization of algebra as it is taught in schools. I wouldrather he see and experience the theoretical beauty of it.)

 

[BvU]

Check out:

https://tutorial.math.lamar.edu/pdf/Alg/Alg_Complete.pdf
https://tutorial.math.lamar.edu/

Site has it all: .htm AND .pdf (bit of drilling down required)

 

[Trying2Learn]

Check out:

https://tutorial.math.lamar.edu/pdf/Alg/Alg_Complete.pdf
https://tutorial.math.lamar.edu/

Site has it all: .htm AND .pdf (bit of drilling down required)

Thanks, BUT that is exactly what I do NOT want.

he algebra discussed there is solving sets of equations, and polynomials and exponents and all that.

He wants to learn Algebra: set theory, bounds of sets, topology, limits, fields, rings, algebras, sets, groups, etc.

Is there no book (if I have to order, I will order it online) or site (preferred) that does this for a high school student?

 

[PeroK]

Is there no book (if I have to order, I will order it online) or site (preferred) that does this for a high school student?

Abstract algebra is not a high-school subject. It took me ten seconds to find:

https://math.berkeley.edu/~apaulin/AbstractAlgebra.pdf

 

[BvU]

https://link.springer.com/book/10.1007/978-3-319-77649-1
can still be downloaded

I agree with @PeroK -- but then again, I'm a physicist -- who knows

 

[Trying2Learn]

Abstract algebra is not a high-school subject. It took me ten seconds to find:

https://math.berkeley.edu/~apaulin/AbstractAlgebra.pdf

Yes, that one I found. But it is too advanced for him.

Yes, you are right, it is not a high school subject.

So I assume you are suggsting that my hope of finding some book that can teach some of these things to an advanced student, is just not possible?

It almost seems like there could be a market for a book like that (but maybe the market is not that big).

That is why I am hoping for some on-line site, written by a prof who does recognize the need for such a treatment.

 

[PeroK]

Yes, that one I found. But it is too advanced for him.

Yes, you are right, it is not a high school subject.

So I assume you are suggsting that my hope of finding some book that can teach some of these things to an advanced student, is just not possible?

If a subject is too advanced then you need to learn the prerequisites first.

 

[BvU]

Browsed both (Paulin and Lee). The latter seems more accessible (and even a bit if fun). But then again, I hit some abstraction level ceiling .

 

[hutchphd]

I recommend that the OP look at the first lecture in the Harvard online course for abstract algebra to understand the scope. There is apparently "no royal road to abstract algebra" either ! (my apologies to Euclid).

 

[vanhees71]

I don't know very much about English math literature, because I learned most of my math out of German textbooks, but from my own experience I can only say: Stay away from high school math books. I don't know any American or British math schoolbooks, but the German ones are about something I cannot name. It's not about math. Usually they give some vague short explanation about a subject and then a lot of problems to be solved by some fixed set of recepies. It's perfectly the opposite of what math is about, namely to learn to derive and prove everything from some set of axioms.

The revelation for me was when I looked at our local city library for some mathbook to learn geometry/trigonometry from, because I couldn't understand what they told me at high school nor what was in the schoolbook. I found some book with a title like "geometry for engineers". All of a sudden, I understood very quickly, how math really works, of course on a more applied level than with rigorous proofs of pure math, which came later when I started to study math further for myself, because all of a sudden I liked the subject. That said, indeed it may be a good idea to look for good introductory university-level undergraduate textbooks. Concerning algebra you usually start with linear algebra, which I think is a good starting point also for the more advanced and more abstract kind of books.

 

[FactChecker]

For your son, make sure that he has complete mastery of pre-calculus algebra before you worry about abstract algebra. He will certainly need the former very soon, but he may never need the latter.

 

[FactChecker]

If your son has a good understanding of pre-calculus algebra and wants something more advanced, has he mastered trig, calculus, linear algebra? It is disturbing that abstract algebra texts are too advanced for him, yet that is what he wants to study. There are more traditional subjects to study after pre-calculous algebra -- namely pre-calculus trig and calculus. And there are good reasons for that.

 

[Mondayman]

I've seen the book A Book of Abstract Algebra by Charles Pinter be mentioned as a good introduction to abstract algebra and proofs for high school students that have a good grasp of basic algebra.