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I have the version of this book in Spanish (Editorial MIR), the translated title is 2000 Problems in Linear Algebra. This publishing house (MIR) doesn't exist

I have the version of this book in Spanish (Editorial MIR), the translated title is 2000 Problems in Linear Algebra. This publishing house (MIR) doesn't exist anymore but now goes under the name of URSS [0] and publishes modern versions of these same books, at least in Spanish and Russian. It has several books on problem solving, which was probably a pathway to demonstrating true "elite" status in eastern europe at the time (hence the known romanian, hungarian and russian way of teaching). It also contains several books on theory too, be it mathematics, physics or engineering. The important thing with textbooks on theory is, unlike the custom of modern textbooks to have few problems and often disconnected or that require to make a few "leaps" in the sense that the exposition does not clearly pave a way to solve harder problems, the amount of exercises is large and they frequently build on top of one another, thus making learning much more enjoyable in my opinion. Some books also worth looking at in mathematics: (1) Anti-Demidovich series (2) Combinatorial Analysis, Ribnikov (3) Problem series by Suprun (4) Probability Theory, Zolotarievskaya (5) Discrete Mathematics Problems, Evnin (6) Theory of Surfaces, Finikov ... and several other problem book series for university mathematics. Engineering (mechanics): (1) Anti-Mescherski series (2) Theoretical Mechanics, V. M. Starzhinski (3) Strength of Materials, Stiopin (4) Problems in Strength of Materials, Volmir [0] https://urss.ru/cgi-bin/db.pl?lang=sp&blang=en&page=Bookstore https://urss.ru/cgi-bin/db.pl?lang=sp&blang=en&page=Bookstor... (apparently the headquarters are in Peru now)

azalemeth 4y ago
At a glance, probably Western equivalent of these are Schaum's Outline Series, which start by telling you something, giving you some worked examples on it, and then setting you lose on them. It's a great way to learn, quickly, particularly for a student. I remember distinctly learning (as a teenager) Schaum's Outline Series of Vector Calculus teaching me quickly and in detail "grad div curl and all that" very effectively, so much so that I got basically 100% on all of my A-level maths and further maths papers because, well, if you can do a big book of problems like that, then exams really are just more of the same. At the time, I absolutely loved them -- big brown books, some of which are currently by my ankles. I'm not sure it actually helped that much beyond early university though. Exams select for a very specific skill. What isn't taught is why something was discovered, or is useful, or how an idea came to be. Many more advanced ideas in mathematics are downright bizarre and it's the basic idea that you need to be able to come up with something similar to, not necessarily the detail.
- mbustamanter 4y ago
  I completely agree with you. A corollary of my comment is that while not necessarily providing theoretical justification, sometimes doing this whole problem solving thing helps seeing why a field of knowledge came to study some of its problems, fast. For example, I have a strong abstract foundation in Functional Analysis, Measure Theory and Optimization and my field is Numerical Analysis of PDE. I didn't understand 1. some mechanical properties of materials, 2. some properties of tensors and differential geometry that I needed. But I didn't have so much time to devote and work out the proofs for all the abstract apparatus on my own. So I took an engineering textbook on tensors, some notes on relativity (because they use tensors and Christoffel symbols) and in a few weeks I had almost understood everything I needed. On the other hand, there is an extremely rigorous book with all the proofs for differential geometry, by Kennington. It has 2400 pages. For tensors I would guess that I need more Algebra, specifically, modules. And to review smoothness and differentiability classes.
  - dls2016 4y ago
    Re: Kennington… I check in every year or so to see his progress. For those interested: topology.org
- rg111 4y ago
  By that book, do you mean the one authored by Spiegel? I went over that book fully. From cover to cover. It was absolutely fantastic, and as good as a "problems book" can be. I loved it and would recommend it to anyone who is looking to get their feet wet with problems in Vector Calculus. Although it is neither a rigorous treatment (look into Arfken, Weber, Harris for that), nor it is greatly healpful pedagogically (look into Mary L. Boas for that), nor is it easy (look into Riley, Hobson, Bence for that). The greatest intro material into Linear Algebra still remains the one by Gilbert Strang.
  - azalemeth 4y ago
    Yes, it was (is) the one by Spiegel! All of those are classic texts. Riley Hobson & Bence (or RHB) in particular was my first year of university text – it's very useful and well written, but I think it is not as "easy" as Boas. But for passing exams, Spiegel's problem book can't be beat :-).
lfmunoz4 4y ago
pvg 4y ago
For easier googling, the names of some of these authors in their slightly different English transliteration: Rybnikov Zolotarevskaya Stepin
mananaysiempre 4y ago
Note though that URSS is a ruthlessly commercial enterprise, and in the absence of any real competition, their printing is frequently bad, covers tasteless, translation and editing passable (which is better than can be said for more generalist Russian publishing houses’ attempts at technical literature) but only just, and prices high. (Before this February, the EUR prices before shipping were about 250% of the already-substantial RUB ones per the official conversion rates; nowadays I don’t know.) If you can at all help it, try the MCCME / IUM press and bookshop[1] first; unfortunately they do not deal in second-hand books (or rather they do, a bit, but people will pick those up in person in a day or two, before anybody even bothers entering them into the online catalogue). Let me also add a recommendation for the calculus problems book by Günther (Gyunter) and Kuzmin (I don’t think it was ever translated, but how much translation do you really need in one?). It will not train you—every idea occurs once or maybe twice; it is not a book of exercises. (The joke goes that Demidovich is G&K with every problem repeated ten times.) But it is a book of problems, and it will teach you. [1] https://biblio.mccme.ru/ https://biblio.mccme.ru/

azalemeth 4y ago

At a glance, probably Western equivalent of these are Schaum's Outline Series, which start by telling you something, giving you some worked examples on it, and then setting you lose on them. It's a great way to learn, quickly, particularly for a student. I remember distinctly learning (as a teenager) Schaum's Outline Series of Vector Calculus teaching me quickly and in detail "grad div curl and all that" very effectively, so much so that I got basically 100% on all of my A-level maths and further maths papers because, well, if you can do a big book of problems like that, then exams really are just more of the same. At the time, I absolutely loved them -- big brown books, some of which are currently by my ankles. I'm not sure it actually helped that much beyond early university though. Exams select for a very specific skill. What isn't taught is why something was discovered, or is useful, or how an idea came to be. Many more advanced ideas in mathematics are downright bizarre and it's the basic idea that you need to be able to come up with something similar to, not necessarily the detail.

mbustamanter 4y ago
I completely agree with you. A corollary of my comment is that while not necessarily providing theoretical justification, sometimes doing this whole problem solving thing helps seeing why a field of knowledge came to study some of its problems, fast. For example, I have a strong abstract foundation in Functional Analysis, Measure Theory and Optimization and my field is Numerical Analysis of PDE. I didn't understand 1. some mechanical properties of materials, 2. some properties of tensors and differential geometry that I needed. But I didn't have so much time to devote and work out the proofs for all the abstract apparatus on my own. So I took an engineering textbook on tensors, some notes on relativity (because they use tensors and Christoffel symbols) and in a few weeks I had almost understood everything I needed. On the other hand, there is an extremely rigorous book with all the proofs for differential geometry, by Kennington. It has 2400 pages. For tensors I would guess that I need more Algebra, specifically, modules. And to review smoothness and differentiability classes.
- dls2016 4y ago
  Re: Kennington… I check in every year or so to see his progress. For those interested: topology.org
rg111 4y ago
By that book, do you mean the one authored by Spiegel? I went over that book fully. From cover to cover. It was absolutely fantastic, and as good as a "problems book" can be. I loved it and would recommend it to anyone who is looking to get their feet wet with problems in Vector Calculus. Although it is neither a rigorous treatment (look into Arfken, Weber, Harris for that), nor it is greatly healpful pedagogically (look into Mary L. Boas for that), nor is it easy (look into Riley, Hobson, Bence for that). The greatest intro material into Linear Algebra still remains the one by Gilbert Strang.
- azalemeth 4y ago
  Yes, it was (is) the one by Spiegel! All of those are classic texts. Riley Hobson & Bence (or RHB) in particular was my first year of university text – it's very useful and well written, but I think it is not as "easy" as Boas. But for passing exams, Spiegel's problem book can't be beat :-).

lfmunoz4 4y ago

pvg 4y ago

For easier googling, the names of some of these authors in their slightly different English transliteration: Rybnikov Zolotarevskaya Stepin

mananaysiempre 4y ago

Note though that URSS is a ruthlessly commercial enterprise, and in the absence of any real competition, their printing is frequently bad, covers tasteless, translation and editing passable (which is better than can be said for more generalist Russian publishing houses’ attempts at technical literature) but only just, and prices high. (Before this February, the EUR prices before shipping were about 250% of the already-substantial RUB ones per the official conversion rates; nowadays I don’t know.) If you can at all help it, try the MCCME / IUM press and bookshop[1] first; unfortunately they do not deal in second-hand books (or rather they do, a bit, but people will pick those up in person in a day or two, before anybody even bothers entering them into the online catalogue). Let me also add a recommendation for the calculus problems book by Günther (Gyunter) and Kuzmin (I don’t think it was ever translated, but how much translation do you really need in one?). It will not train you—every idea occurs once or maybe twice; it is not a book of exercises. (The joke goes that Demidovich is G&K with every problem repeated ten times.) But it is a book of problems, and it will teach you. [1] https://biblio.mccme.ru/ https://biblio.mccme.ru/