This website contains contains links to lot of these textbooks - https://mirtitles.org
Thanks.
Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
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Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#72I can only assume but culture makes things very different. I often said that French abstract algebra books stopped me from learning for 10 years (after many serious attempts). One book from Garreth Williams unlocked 80% of my issues. The shocking part was the approach. It was very operational, you calculate, you manipulate concrete data. In French books it's all theorems and concepts. Learning curve to make a Haskell…
My experience was the opposite. School in America tried to make me just memorize a bunch of stuff and it didn't work at all, but using resources like Khan Academy to build understanding and working through proofs of everything was all I needed. Lots of shallow exercises did nothing for me compared to a few deep exercises/proofs and reading.
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#73I was comparing my math books (from Soviet university, Physics and Applied Math) and my son's from Canadian university (CS). Huge difference to be honest. Canadian ones (same as in US I think) were more like belletristic texts written with the goal to give basics without too much thought needed by the reader. In contrast you cannot approach Soviet text math book without serious thinking effort. You need to overcome s…
Or perhaps the “hardcore” texts are just poorly written?
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#74I can only assume but culture makes things very different. I often said that French abstract algebra books stopped me from learning for 10 years (after many serious attempts). One book from Garreth Williams unlocked 80% of my issues. The shocking part was the approach. It was very operational, you calculate, you manipulate concrete data. In French books it's all theorems and concepts. Learning curve to make a Haskell…
In my experience with Russian style mathematical thinking, it often involves hardcore theory in pursuit of some hard-nosed applications (where every assumption and approximation in the theory is well-motivated). When the two come together, there’s an ineffable magic and wholesomeness that I’ve seldom seen elsewhere. Some of the Russian Olympiad problems are absolute beauty.
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#75I mean, could it be as simple as "Learning math is more important to Russians than to Americans?" And before you dismiss this as simplistic, consider everything that's competing for attention with "learning math." What things are Americans either preoccupied with or beset with, that Russians esp. Soviet Russians, weren't? I'm thinking, the profit motive. Particularly as concerns textbook publishers. And parents who n…
No, learning math was never more important to an average Russian than it was to an average American. An average Russian has never knew math any better than an average American. Source: attended school in both countries.
Are you in your early, early 20s? Because the Russian education system fell apart recently. Bribes and teachers moving to Europe and all that.
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#76I can only assume but culture makes things very different. I often said that French abstract algebra books stopped me from learning for 10 years (after many serious attempts). One book from Garreth Williams unlocked 80% of my issues. The shocking part was the approach. It was very operational, you calculate, you manipulate concrete data. In French books it's all theorems and concepts. Learning curve to make a Haskell…
> It also correlates with the pragmatic engineering of US history (electricity comes to mind).
I got my math degree in California (at Cal) and the approach was a lot closer to what you describe French books as. Many of my courses were just a semester-long discussion of proof after proof, with breaks for exams that were more proofs.
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#77It's not just math. Physics too. People from India who went through engineering entrance exams like JEE will have fond (or horrific) memories of "Problems in General Physics" by Irodov (https://archive.org/details/IrodovProblemsInGeneralPhysics/m...). Every problem in there was something to wrestle with.
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#78The real question should be is why are US textbooks so hard when most people never need HS math after finishing school, and lack so many other skills that are never taught.
Modern Common Core seems very promising for teaching real number sense and a good foundation to think about things.
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#79My dad took the advanced courses for physics, math, organic chem in first year University of Toronto in 1970. I've seen his textbooks and they were on the same level of this. Much more advanced than what I saw in the 90s/00s. More focus on reasoning from first principles, less focus on easily approachable material. Basically I'm saying that baby boomers had more advanced textbooks in their university period compared…
I find this to be true. It seems like there was more focus on the very, very basics. Now there is a ton of filler and the content gets lost. E.g.:
Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)
#80Disclaimer: I graduated from one of the top math high schools in Moscow in early 90s, I have MS in Math from Moscow State University, and a half finished PhD from the same place.
I think on average the difference between a high school student from Russia and US is negligible. Either country doesn’t really require much to finish school and many kids just do the tests without understanding what is going on. What separates Soviet Union (and now Russian) system is the practice of selecting kids with interest in mathematics / physics into special classes or schools for gifted kids. This government program feeds the mathematics and physics departments in the universities and allows kids who go through this program to get a very early start in mathematics. This is very similar to government sponsored sports programs with talented kids getting help with summer camps, or even all year round training schools.