I've read this book. It's definitely one of the more interesting and readable maths texts out there. I wasn't exactly sure I'd use the methods. Working as a mechanical engineer I probably go straight to numerical methods, or approximate things even more crudely and approximately than a mathematician's 'rough' work. Though "replace a complicated function with a rectangle" definitely resonated. Overall the impression was that it was full of great techniques for mathematicians and scientists puzzling out every bit of meaning they can from a situation whose true features aren't yet known.
That's kind of how I do maths, too. Working out the lengths of antenna feeders, for example, where a coil of cable is about 30cm across. One turn of that is about one metre, so a coil with ten turns is about ten metres. Roughly. Close enough. I can coil it up shorter but I can't coil it up longer.
If I'm doing really precise stuff, I'm either doing it on a computer already or it's something that's just going to have to be "adjusted" into place when it's done.
In high school my maths teacher said "You'll need to learn all this, you won't always have a calculator!"
My dude, I am walking around with a supercomputer the size of half a slice of bread in my pocket, that probably has a sizeable fraction of the total computing power available in the world when you told me that.
It turns out I don't need either of these things, I just need a good sense of "yeah that feels about right".
This is a good book. Also, any time this kind of book becomes available (be it a 100 year old one or a new one), it is worth looking into - great improvements in isnight and simplicity are possible above the "baseline" of US math education today.
So for example, I posit that the engineers or scientists you might admire from the 1950's didn't learn calculus or linear algebra the way you did.
I skimmed the chapter on operators (7) and always liked that way of thinking (plug things like the derivative operation D into things that expect numbers instead, and see what happens). So plugging into 1/x and getting integrals. Dattoli and Tom Copeland do serious stuff starting from that kind of considerations that go way beyond cocktail party tricks.
I've read this book. It's definitely one of the more interesting and readable maths texts out there. I wasn't exactly sure I'd use the methods. Working as a mechanical engineer I probably go straight to numerical methods, or approximate things even more crudely and approximately than a mathematician's 'rough' work. Though "replace a complicated function with a rectangle" definitely resonated. Overall the impression was that it was full of great techniques for mathematicians and scientists puzzling out every bit of meaning they can from a situation whose true features aren't yet known.
That's kind of how I do maths, too. Working out the lengths of antenna feeders, for example, where a coil of cable is about 30cm across. One turn of that is about one metre, so a coil with ten turns is about ten metres. Roughly. Close enough. I can coil it up shorter but I can't coil it up longer.
If I'm doing really precise stuff, I'm either doing it on a computer already or it's something that's just going to have to be "adjusted" into place when it's done.
In high school my maths teacher said "You'll need to learn all this, you won't always have a calculator!"
My dude, I am walking around with a supercomputer the size of half a slice of bread in my pocket, that probably has a sizeable fraction of the total computing power available in the world when you told me that.
It turns out I don't need either of these things, I just need a good sense of "yeah that feels about right".
Not to mention instant and searchable access to more subject matter than he’d seen in his whole lifetime.
Book PDF is here: https://direct.mit.edu/books/oa-monograph-pdf/2284035/book_9...
This is the draft, not the current version.
edit: and for the current unfortunately there's only a dead dropbox link.
This is a good book. Also, any time this kind of book becomes available (be it a 100 year old one or a new one), it is worth looking into - great improvements in isnight and simplicity are possible above the "baseline" of US math education today.
So for example, I posit that the engineers or scientists you might admire from the 1950's didn't learn calculus or linear algebra the way you did.
Feynman learned calculus from the textbook "Calculus for the Practical Man".
I also quite liked https://ocw.mit.edu/courses/res-6-011-the-art-of-insight-in-...
Which is, I think, the successor and quite useful.
I skimmed the chapter on operators (7) and always liked that way of thinking (plug things like the derivative operation D into things that expect numbers instead, and see what happens). So plugging into 1/x and getting integrals. Dattoli and Tom Copeland do serious stuff starting from that kind of considerations that go way beyond cocktail party tricks.
Another book title aimed at getting people who haven’t read their pile of books to buy another.
what is it about?
how to distribute fighters so that your team defeats-in-detail your opponents?
It is about useful tricks you can usually not learn in university classes.
tricks of what kind
fast multiplying for example