It's an interesting approach. They do like the classic sources.
I've at least skimmed more than half of those titles, long after college.
It's amusing that they have students read Pikkety's "Capital" before Marx's "Capital".
You don't want to learn geometry from Euclid. You read Euclid after you already know geometry, to see how he built it up. Similarly, you don't want to learn calculus from Newton. Or physics from Aristotle. What you're seeing there is people trying to figure something out before the tools for the job were developed.
There are great papers in engineering, where a theoretical advance changed the world. They're not well known. These should be as well known as the "Great Books".
* Maxwell's paper "On Governors". In a few pages, he invents feedback control theory. People were building steam engine governors but didn't understand stability and lag. It's a milestone in that it's one of the first times abstract math met practical engineering and the result worked.
* Shannon's discovery that telephone toll switches could be reduced from needing O(N^2) relays to O(N log N) was one. Suddenly, combinatorics went from a useless abstraction to a huge financial win for AT&T.
* "Rational Psychrometric Formulae", by Willis Carrier. Least click-bait title ever.
Basis of air conditioning. It's how you make an air conditioner and control both temperature and humidity at the cold end, rather than getting cold, humid air out.
* Von Neumann's Report on the EDVAC. That's better known. It's how to make a CPU. He got all the basic architecture right, except for index registers.
Is Euclid just about geometry? I have not read it, but others have written it is a good introduction to mathematical proofs. A few comments on HN over the years said Hammack's "Book Of Proof" or Velleman's "How To Prove It" are more thorough, but are intended for 3rd/4th year math undergrad, and Euclid is easier to get through.
My last math course was stats and business calc about 30 years ago.
Are you looking for a book to learn proofs from? Are you looking to learn any math topics in particular?
I think you can go through any of the books you listed and get an understanding of proofs. The proofs books usually use basic number theory or set theory for examples because the point is to learn the logic and structure of proofs. (If the book isn't enough for you, you can use Khan Academy as a refresher.) Learning more math is left to other books.
I looked through the table of contents for the ones you've linked, but neither looks like an upper year math book. Typically, if there is an explicit course on proofs, it's covered in the lower division.
The proofs course I took used "Mathematical Proofs: A Transition to Advanced Mathematics" by Chartrand, Polimeni, and Zhang. It's ridiculously expensive on Amazon right now, so I'm not sure I can recommend it for the cost. But it does cover more areas of math using proofs. It covers proofs in set theory, number theory, combinatorics, calculus, and group theory at a very basic level. The books you linked seem to cover less of those topics, so I think Chartrand et al. is a more gentle intro to different branches of upper division math.
You can take four terms of calculus using the Stewart book and not need to do any proofs. You do need to review algebra and have a good grounding in that, though.
You can also cover linear algebra without proofs.
There are, of course, books that do cover proofs for calculus and linear algebra, but it depends on what you’re trying to get out of the material.
Books 1, 2 and 6 are plane geometry, books 3 and 4 are what we now call trig, book 5 is on what we now call real numbers, books 7-9 are on integer number theory, book 10 is on irrationals, and books 11-13 are on solid geometry.
Those are excellent suggestions. I think we are probably at the point where you could do a Great Books curriculum in Computer Science. Would be interesting to put together that list: 10-20 foundational primary texts in Algorithms, Programming/Software Engineering, Logic, AI, and Computer Architecture.
But, as you note, it'd probably be a terrible way to actually learn how to engineer software. More intellectually satisfying, though :)
> It's amusing that they have students read Pikkety's "Capital" before Marx's "Capital".
I get why it's amusing, but it also makes sense. Marx's "Capital" is kind of a beast. Pikkety's is written more-or-less toward a modern general audience. If I were sequencing these books in a student's intellectual development, Pikkety definitely comes before Marx.
> I think we are probably at the point where you could do a Great Books curriculum in Computer Science. Would be interesting to put together that list: 10-20 foundational primary texts in Algorithms, Programming/Software Engineering, Logic, AI, and Computer Architecture.
I graduated before Piketty wrote Capital, but that sounded weird so I looked. All the "Elective Work(s)" at the bottom of Junior and Senior years are part of the Junior/Senior elective preceptorials which not every student reads and that list changes every year. The Program definitely doesn't have you read Piketty before Marx.
You don't want to learn geometry from Euclid. You read Euclid after you already know geometry, to see how he built it up. Similarly, you don't want to learn calculus from Newton. Or physics from Aristotle. What you're seeing there is people trying to figure something out before the tools for the job were developed.
There are great papers in engineering, where a theoretical advance changed the world. They're not well known. These should be as well known as the "Great Books".
* Maxwell's paper "On Governors". In a few pages, he invents feedback control theory. People were building steam engine governors but didn't understand stability and lag. It's a milestone in that it's one of the first times abstract math met practical engineering and the result worked.
* Shannon's discovery that telephone toll switches could be reduced from needing O(N^2) relays to O(N log N) was one. Suddenly, combinatorics went from a useless abstraction to a huge financial win for AT&T.
* "Rational Psychrometric Formulae", by Willis Carrier. Least click-bait title ever. Basis of air conditioning. It's how you make an air conditioner and control both temperature and humidity at the cold end, rather than getting cold, humid air out.
* Von Neumann's Report on the EDVAC. That's better known. It's how to make a CPU. He got all the basic architecture right, except for index registers.