4 ms·
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
by 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 agoI 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 agoRe: Kennington… I check in every year or so to see his progress. For those interested: topology.org
- rg111 4y agoBy 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 agoYes, 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 :-).
- rg111 4y agoExactly. I got perfect scores in both of the Mathematical Physics papers in college. Many problems, with some variations did appear directly from Spiegel. Best VC problems book ever.