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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)

#41

Post by dzhiurgis »

I'm from Lithuania.

My dad had present from our relatives in Canada - basketball shoes (eventually stolen) and a calculator. That calculator pulled a lot of favours over time, he was the only one in town to have one. Dad couldn't believe you could just order anything from catalogue in 70s. Anything the world, you can buy. Such a unreal concept. He also got Beatles LP from somewhere (eventually confiscated from teachers).

It's a good point the access to many basics weren't there. I've finished high school in 2006, got my first PC in 1998. Very quickly I've learned to solve math problems using graphing calculator apps. Cheated my German classes by translating from German to English using Babelfish then to Lithuanian.

The only other time I ever had to do derivatives and integrals was math class at university... while studying for management degree!

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#42

Post by google234123 »

tathougies wrote: post #34
agumonkey wrote: post #12

I 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…

I dunno, Rudin, the most popular abstract algebra textbook in English, is quite dense.

"abstract algebra", are you sure you aren't talking about analysis? It's not usually used as an introduction anyway.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#43

Post by gruez »

chii wrote: post #33
agumonkey wrote: post #12

I 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 was very operational, you calculate, you manipulate concrete data it's interesting that some academic approaches focus on the theoretical framework and conceptual depth, with the underlying assumption that the student would "get" it once the fundamentals are understood. The other approach, mostly in the asian schools, teach rote and speed in mechanical/mental manipulation. For example, a student would do 1000 qu…

>But i do believe that being able to manipulate numbers very quickly leads to a quality of its own, and can make understanding harder concepts easier.

Can you elaborate on this? Are you supposed to introspect while you're applying the quadratic formua 1000 times? How does being able to quickly add/subtract/multiply/divide help you better understand abstract concepts?

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#45

Post by philipov »

chii wrote: post #33
agumonkey wrote: post #12

I 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 was very operational, you calculate, you manipulate concrete data it's interesting that some academic approaches focus on the theoretical framework and conceptual depth, with the underlying assumption that the student would "get" it once the fundamentals are understood. The other approach, mostly in the asian schools, teach rote and speed in mechanical/mental manipulation. For example, a student would do 1000 qu…

In fact, the Soviet approach also emphasized solving problems. There are books entirely devoted to problem sets, and there are other books devoted entirely to theory. My grandfather was a Professor of Mathematics at Moscow State University before we emigrated, and as I was growing up, he would always stress that it does one no good to just know about swimming if you can't actually swim. The people who learn the most are the ones who have competency in both theory and application. To get that competency, you alternate between focused practice in one and the other, just like an athlete alternates training different muscle groups.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#46

Post by google234123 »

seibelj wrote: post #6

Soviet body builders only used free weights and a pull-up bar. You don’t need anything but that to get big muscles. Similarly, you don’t need anything except a chalk board to teach math and most other subjects.

I don't believe you that Soviet body builders only used free weights. https://www.rbth.com/history/329827-bodybuilding-outlawed-in...

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#47

Post by julianeon »

agumonkey wrote: post #12

I 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…

I feel like it's worth pointing out here, for Americans who don't know better (no blame implied), that the French have one of the best mathematical pipelines in the world. They have almost as many Nobels (13 vs. 11) despite having 1/5 the population. Guardian article about them here:

https://www.theguardian.com/world/2012/may/31/europa-french-...

So please don't think France is a backwater that just doesn't know how to do math - on the contrary, it may be the best country in the world to be born into, if you want to be a mathematician.

For what it's worth, I'm an American who honestly is pretty bad at math, but I try to keep learning, though I'm past an age where it will matter in college or higher education.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#49

Post by ken »

thaumasiotes wrote: post #28
ngold wrote: post #18

Earlier quoted context omitted.

Thank's for the insight. I struggled with geography until I discovered history...again, after high school of course. I still struggle with algebra, so I look forward to checking your suggestions out. I think my problem as a kid was I was just hyper, all the time. I could cut wood outside for 10 hours but couldn't sit still for a moment.

> I struggled with geography until I discovered history Tangentially, a lot of fantasy authors seem to love maps for their own sake, and provide maps of their world as illustrations. I never saw the point of these; the map never really matters to the story. But history books provide almost the same number of maps -- usually one, before the discussion of whatever -- and it just isn't enough. Those maps really matter t…

My favorite sequence of maps in a book was “Black Hawk Down”. The first chapter begins with a world map, showing Somalia, and it lays the geopolitical setting for the events. The second chapter has a map of Somalia, showing where Mogadishu is, and sets the scene there. It keeps zooming in, until the final chapter shows a map so tight it has individual people (who you have since met) and which side of the street they were on.

Re: Why are Soviet math textbooks so hardcore in comparison to US textbooks? (2017)

#50

Post by Pxtl »

gruez wrote: post #43
chii wrote: post #33

Earlier quoted context omitted.

> It was very operational, you calculate, you manipulate concrete data it's interesting that some academic approaches focus on the theoretical framework and conceptual depth, with the underlying assumption that the student would "get" it once the fundamentals are understood. The other approach, mostly in the asian schools, teach rote and speed in mechanical/mental manipulation. For example, a student would do 1000 qu…

>But i do believe that being able to manipulate numbers very quickly leads to a quality of its own, and can make understanding harder concepts easier. Can you elaborate on this? Are you supposed to introspect while you're applying the quadratic formua 1000 times? How does being able to quickly add/subtract/multiply/divide help you better understand abstract concepts?

In my experience, those rote mental muscles mean that the basics are never slowing you down when tackling a harder problem. It's comparable to having a perfectly organized toolbox vs a mess of tools in your shed - you can do the same things, but you're free to focus on the core of the current task instead of distractions in the trivial parts.
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