Are the (translated) High School Japanese maths textbooks by Kodaira Good?

[whatevs]

I'm trying to review some high school maths and work my way to Calculus and Linear Algebra, and I found these three translations of Japanese maths textbooks translated by the AMS and edited by Kunihiko Kodaira. The AMS links to them are:

https://bookstore.ams.org/cdn-1669378252560/mawrld-8/

https://bookstore.ams.org/cdn-1655774305546/mawrld-10/

https://bookstore.ams.org/cdn-1669377777869/mawrld-11/

Does anyone have any experience with these books and whether they are good for self teaching? The reason I bring them up is because I already have the hard I found them at a garage sale for 10$ for all three volumes (there are no online pdfs on libgen or anywhere that I could find, other than for the first one, which is available as a pdf), and when I researched them many people said that they cover up to basic linear algebra and calculus, and have many proof based exercises.

They also seem not to be too long which makes them less intimidating somewhat(though I know that it won't affect how fast I go through them).

tl;dr:

1) Are you familiar with these books?
2) Are they good for self teaching from Algebra 1 to Calc and LA?
3) Any other advice is welcome.

P.S: I know there are books like Basic Mathematics that cover roughly the same terrain (a little bit less actually), but since I already have these books it'd be nice to use them.

 

[jedishrfu]

Well not knowing or seeing these books. It would seem that the American Mathematical Society has endorsed them by virtue of selling them.

In any event, for any kind of study it’s good to have more than one reference to fall back on.

 

[whatevs]

Here is a link to the first one if you want to check it out:

https://cloudflare-ipfs.com/ipfs/ba...Chicago School Mathematics Project (1996).pdf

Thanks anyways for your reply, and if you do check it out I’d love to hear some of your opinions on it.

 

[MidgetDwarf]

they appear like good books from a quick perusal

 

[whatevs]

Thank you!

 

[MidgetDwarf]

I would like to add, just from the first volume. its a bit more formal compared to the run of the mill books of today. it wouldn't hurt to supplement them with any of the modern offerings.

 

[whatevs]

I would like to add, just from the first volume. its a bit more formal compared to the run of the mill books of today. it wouldn't hurt to supplement them with any of the modern offerings.

Isn't formality supposed to be a good thing? I apologise if I seem somewhat confused, but what I was looking for was something similar to Basic Mathematics by Serge Lang, with proofs and all. I had tried Lang's book before and the writing didn't mesh well with my style.

The teaching through proofs and definitions was something I really enjoyed however. And when I found these books they just seemed to satisfy what I was looking for, except for Euclidean Geometry and such which I'll be supplementing with the Moise/Downs book.

I tried Khan Academy, but the questions were very easy, and the format bothered me somewhat(I prefer books over videos).

What would you recommend I supplement with?

 

[MidgetDwarf]

Isn't formality supposed to be a good thing? I apologise if I seem somewhat confused, but what I was looking for was something similar to Basic Mathematics by Serge Lang, with proofs and all. I had tried Lang's book before and the writing didn't mesh well with my style.

The teaching through proofs and definitions was something I really enjoyed however. And when I found these books they just seemed to satisfy what I was looking for, except for Euclidean Geometry and such which I'll be supplementing with the Moise/Downs book.

I tried Khan Academy, but the questions were very easy, and the format bothered me somewhat(I prefer books over videos).

What would you recommend I supplement with?

yes, depending on mathematical maturity. since you are asking for basic math, it is fair to assume you do not have mathematical maturity. that is why I mentioned, maybe SUPPLEMENTING with an easier book. This is very common when one learns mathematics/physics at all levels.

Do you know what supplement means?

 

[jedishrfu]

I looked at the book you posted, and it looks excellent. Compared to today's US math books, it's very dry. There are no side stories or brief biographies of mathematicians of the past. I do like the brevity of the pages though.

As a student, I would try to do the problems first, and when I couldn't, I'd go back and read the relevant book sections looking for examples, seldom reading the full chapter until test time came up (not a good approach in hindsight).

Now, if I were to look back, I would try the problems and go back to read the chapter until I found the relevant section and go back to the problems, thus working my way through the chapter more consistently.

But as a student, you have to find what works for you.

As a supplement, you could consider the Jan Gullberg book:

https://www.amazon.com/dp/039304002X/?tag=pfamazon01-20

It covers math and math history with photos and illustrations in an exciting read, up to first-year college. The author was a medical doctor who wrote it to support his son's engineering studies in college.

https://en.wikipedia.org/wiki/Jan_Gullberg

 

[vela]

Isn't formality supposed to be a good thing?

In addition to your level of mathematical maturity, it also depends on what you're trying to learn. As the joke goes, mathematicians are good at spending a long time to come up with an answer that is 100% correct but still utterly useless. If your goal is to be able to prove theorems about integration but not know how to evaluate an integral, then formality might be a good thing. If not, a more informal text might be better to learn from.

If you've already learned these subjects and now want to review the material with more rigor, then formality would be good. If it's your first exposure to these topics, maybe not so much.

 

[whatevs]

In addition to your level of mathematical maturity, it also depends on what you're trying to learn. As the joke goes, mathematicians are good at spending a long time to come up with an answer that is 100% correct but still utterly useless. If your goal is to be able to prove theorems about integration but not know how to evaluate an integral, then formality might be a good thing. If not, a more informal text might be better to learn from.

If you've already learned these subjects and now want to review the material with more rigor, then formality would be good. If it's your first exposure to these topics, maybe not so much.

I see, that makes sense.

In my case, I know computation, it's all I've ever studied. But I'm really interested in proofs and I want to learn how people take an abstract idea, render it in mathematical terms, then proceed to prove or disprove it.

Part of this would be review, since I'm already familiar with all the topics, but the other part would be having a springboard to launch my studies into further mathematics later on, whether by changing from an engineering degree to a maths degree, or just studying it as a hobby and doing some recreational maths.

And the reason why I'm using these books is because I want a foundation as solid as it can get (I noticed I sometimes have trouble with basic algebraic manipulation that I'd like to fix) and I also want to do it while studying some proofs, instead of endless drill questions.

I hope this reply has somewhat illustrated my motives, and thank you for your reply(I think I should've said that in the beginning).

 

[whatevs]

I looked at the book you posted, and it looks excellent. Compared to today's US math books, it's very dry. There are no side stories or brief biographies of mathematicians of the past. I do like the brevity of the pages though.

As a student, I would try to do the problems first, and when I couldn't, I'd go back and read the relevant book sections looking for examples, seldom reading the full chapter until test time came up (not a good approach in hindsight).

Now, if I were to look back, I would try the problems and go back to read the chapter until I found the relevant section and go back to the problems, thus working my way through the chapter more consistently.

But as a student, you have to find what works for you.

As a supplement, you could consider the Jan Gullberg book:

https://www.amazon.com/dp/039304002X/?tag=pfamazon01-20

It covers math and math history with photos and illustrations in an exciting read, up to first-year college. The author was a medical doctor who wrote it to support his son's engineering studies in college.

https://en.wikipedia.org/wiki/Jan_Gullberg

I don't mind the dryness honestly. I dislike the books with so many colours and useless information sprinkled throughout the text(I have ADHD, amongst other things and information overload is a thing for me). Which is why I was attracted towards these books.

I am guilty of doing what you used to do, but I've been trying to fix that, I guess having problems interspersed through the text make this a little harder to do as I must search for them and inadvertently read the explanations.

The book you recommended seems right up my alley. Contrary to what might have been implied by my first paragraph, I do enjoy history, just not when it's mixed with a technical book. To see it from a bird's eye view such as from the book you mentioned is very appealing however.

Thank you for the advice and recommendation. I needed an opinion from someone who knows more than me before I could invest my time and effort into this, and now that I have it, I feel a certain comfort with starting my studies from the books.

 

[whatevs]

yes, depending on mathematical maturity. since you are asking for basic math, it is fair to assume you do not have mathematical maturity.

Not with proofs no, I have studied all this however, this is mainly for review and solidifying my foundations. I don't believe computation counts for much mathematical maturity, I do believe however that it surely is different from not having ever seen the material before.

that is why I mentioned, maybe SUPPLEMENTING with an easier book.

To which I replied with,

What would you recommend I supplement with?

As for,

Do you know what supplement means?

No, I don't. Please feel free to tell me. I'm always down to learn something new.

 

[vela]

In my case, I know computation, it's all I've ever studied. But I'm really interested in proofs and I want to learn how people take an abstract idea, render it in mathematical terms, then proceed to prove or disprove it.

Makes sense. If you've already had a first pass at the subjects, you might find it useful to proceed toward books geared at upper-division math students. The others can tell you what books might be appropriate for that level.

I hope this reply has somewhat illustrated my motives, and thank you for your reply(I think I should've said that in the beginning).

It's very helpful to know where you're coming from and what your goals are.

 

[MidgetDwarf]

Those are fine for the stated purpose. What does an engineering background mean? Engineering undergrad major, BS in Engineering, MS, PHD?

I am assuming undergrad major, who has not completed a degree.

https://www.people.vcu.edu/~rhammack/BookOfProof/

This is probably one of the easiest intros to proof writing. It is a free legal download, and a physical copy can be purchased very cheaply.

Continue reading through those books if you are lacking in "fundamentals", and read the book I linked to simultaneously. If you are okay with fundamentals, then you can skip those algebra books, and either read Moise's book and hammock together, or read hammock and some other beginner proof book in a math field.

 

[Muu9]

If you want some more rigorous texts on elementary topics, see this page: https://faculty.utrgv.edu/eleftherios.gkioulekas/OGS/santos.html or the texts by hung-hsi wu