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Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced und

by Mimmy 5y ago

Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students. I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.

tptacek 5y ago
Both Strang and D&F are extra-relevant for cryptography (I was struck by how much the earliest parts of D&F --- which I haven't gotten much further beyond --- read like the mathematics background chapter of a cryptography book), and I've been in study groups for both of them with non-mathematicians that went OK. But the D&F study group fell apart for logistical reasons, so maybe it would have hit a wall after a couple more months.
- pvg 5y ago
  read like the mathematics background chapter of a cryptography book A lot of maths-related books, especially ones intended as textbooks will read like that in part because they aren't kidding about the 'abstract' in the title - they're trying to teach/re-summarize key concepts of mathematical abstraction. It's a good and true thing to notice.
dwohnitmok 5y ago
Second Axler. "Linear Algebra Done Right" is probably the pure mathematics textbook I've most enjoyed reading ever (but be warned you will learn very little about applied methods from it if that's what you care about). Also enjoyed Artin's Algebra.
- musgravepeter 5y ago
  +1 for Artin's Algebra. I think is very under appreciated.
- cgriswald 5y ago
  My university course in linear algebra taught me how to manipulate matrices. It was super uninteresting, and easy. I aced every test, but got a B in the course, because the professor assigned an asinine amount of homework (that I either aced or didn't do), perhaps holding the article author's view that: > solving problems is the only way to understand mathematics. There's no way around it. ...without also understanding that doing problems is not a substitute for understanding. (I'm still salty about that course. I've been doing linear algebra based puzzles nearly every day of my life and this professor somehow made the topic a boring chore.) I complained about this to a friend who had also taken the course and he turned me on to Axler. I read through the first chapter, nodding along as I went. I got to the problem questions and couldn't believe what Axler was asking was even related to the material I had read through. I really struggled at first to understand. Axler was heavily juxtaposed to my previous experience. However, when I did understand, I didn't just understand, I grokked. It was just such an awesome experience, and I credit that book in particular with breaking me out of a mathematics plateau and with liberating my mathematics education from a strict reliance on academia. The text is almost magical.
  - dwohnitmok 5y ago
    > I got to the problem questions and couldn't believe what Axler was asking was even related to the material I had read through. I think this is a common first experience when first hitting pure mathematics. Mathematics often feels like very rote applications of rules drilled into one's mind, and then you hit a pure mathematics textbook and the questions become a step change in difficulty where you're expected to derive novel insights on your own that the text doesn't hold your hand in showing. A single problem can easily occupy days of your time before the "aha!" moment, but as you say, once you get the "aha!" you realize your understanding is quite profound as opposed to a shallower understanding of just how to apply a given set of rules.
Py-o7 5y ago
For many years MIT students would go from Strang in year 1 to Artin in year 2. Artin != D&F of course though many would say it does less hand holding than D&F
susanrigetti 5y ago
Gross's review of linear algebra from his MIT algebra course bridges the gap: http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra http://wayback.archive-it.org/3671/20150528171650/https://ww.... A combination of that and then chapter 11 in D&F should cover whatever readers didn't get from Strang. That being said, Axler is an excellent book. I don't know if I would replace Strang with it, but I should add it as a supplement to the next edition of this guide!
selimthegrim 5y ago
I have been using Morris in my class.
selimthegrim 5y ago
Strang's latest book DE&LA is disappointing, it is linear algebra and its applications with the abstraction taken out and mushed together with supplementary notes from ODE videolectures. Mattuck's ODE course is good.
- selimthegrim 5y ago
  I should say his penultimate minus one book, DE&LA is from 2014 and I think he has published a couple more since then. Linear Algebra and its Applications is his 1988 book.
peterhalburt33 5y ago
I’d be hard pressed to recommend D&F to a self study audience. Perhaps it’s just me, but the endless enumeration of examples and counterexamples at the beginnings of most chapters seemed to destroy my intuition rather than reinforce it.

by Mimmy 5y ago

tptacek 5y ago

Both Strang and D&F are extra-relevant for cryptography (I was struck by how much the earliest parts of D&F --- which I haven't gotten much further beyond --- read like the mathematics background chapter of a cryptography book), and I've been in study groups for both of them with non-mathematicians that went OK. But the D&F study group fell apart for logistical reasons, so maybe it would have hit a wall after a couple more months.

pvg 5y ago
read like the mathematics background chapter of a cryptography book A lot of maths-related books, especially ones intended as textbooks will read like that in part because they aren't kidding about the 'abstract' in the title - they're trying to teach/re-summarize key concepts of mathematical abstraction. It's a good and true thing to notice.

dwohnitmok 5y ago

Second Axler. "Linear Algebra Done Right" is probably the pure mathematics textbook I've most enjoyed reading ever (but be warned you will learn very little about applied methods from it if that's what you care about). Also enjoyed Artin's Algebra.

musgravepeter 5y ago
+1 for Artin's Algebra. I think is very under appreciated.
cgriswald 5y ago
My university course in linear algebra taught me how to manipulate matrices. It was super uninteresting, and easy. I aced every test, but got a B in the course, because the professor assigned an asinine amount of homework (that I either aced or didn't do), perhaps holding the article author's view that: > solving problems is the only way to understand mathematics. There's no way around it. ...without also understanding that doing problems is not a substitute for understanding. (I'm still salty about that course. I've been doing linear algebra based puzzles nearly every day of my life and this professor somehow made the topic a boring chore.) I complained about this to a friend who had also taken the course and he turned me on to Axler. I read through the first chapter, nodding along as I went. I got to the problem questions and couldn't believe what Axler was asking was even related to the material I had read through. I really struggled at first to understand. Axler was heavily juxtaposed to my previous experience. However, when I did understand, I didn't just understand, I grokked. It was just such an awesome experience, and I credit that book in particular with breaking me out of a mathematics plateau and with liberating my mathematics education from a strict reliance on academia. The text is almost magical.
- dwohnitmok 5y ago
  > I got to the problem questions and couldn't believe what Axler was asking was even related to the material I had read through. I think this is a common first experience when first hitting pure mathematics. Mathematics often feels like very rote applications of rules drilled into one's mind, and then you hit a pure mathematics textbook and the questions become a step change in difficulty where you're expected to derive novel insights on your own that the text doesn't hold your hand in showing. A single problem can easily occupy days of your time before the "aha!" moment, but as you say, once you get the "aha!" you realize your understanding is quite profound as opposed to a shallower understanding of just how to apply a given set of rules.

Py-o7 5y ago

For many years MIT students would go from Strang in year 1 to Artin in year 2. Artin != D&F of course though many would say it does less hand holding than D&F

susanrigetti 5y ago

Gross's review of linear algebra from his MIT algebra course bridges the gap: http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra http://wayback.archive-it.org/3671/20150528171650/https://ww.... A combination of that and then chapter 11 in D&F should cover whatever readers didn't get from Strang. That being said, Axler is an excellent book. I don't know if I would replace Strang with it, but I should add it as a supplement to the next edition of this guide!

selimthegrim 5y ago

I have been using Morris in my class.

selimthegrim 5y ago

Strang's latest book DE&LA is disappointing, it is linear algebra and its applications with the abstraction taken out and mushed together with supplementary notes from ODE videolectures. Mattuck's ODE course is good.

selimthegrim 5y ago
I should say his penultimate minus one book, DE&LA is from 2014 and I think he has published a couple more since then. Linear Algebra and its Applications is his 1988 book.

peterhalburt33 5y ago

I’d be hard pressed to recommend D&F to a self study audience. Perhaps it’s just me, but the endless enumeration of examples and counterexamples at the beginnings of most chapters seemed to destroy my intuition rather than reinforce it.