Physics & math porn

Alain De Vos

Alain De Vos

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Well, I've got Resnick and Halliday somewhere in my big cardboard box of books; the old edition with the dark green cover. :) And I've got the Fenyman lectures on physics series. But it's all buried under a pile of other stuff, so you'll have to do without a photo this time, sorry.:)

I also do not have ANY books on 'manifolds' 😁
 
I have Signals and Systems on my shelves along with
Digital Signal Processing by Oppenheim and Schafer
The Design of Well Structured and correct programs by Alagic and Arbib
Probability, RandomVariables and Random Signal Principles by Peebles
Properties of Engineering Materials by Murphy (was actually a text book my dad used)

During college all these made sense to me. Now, I pick them up and think "what was I smoking"
 
Alain De Vos said:
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There are some good books in that pile. And some unreadable books. And some that are in both categories (Landau + Lifshitz). I have taught physics using H&R (because our university's standard textbook was not very good), and my father-in-law was a student of Resnick. I hear good things about the Griffiths E&M book you have there, but people say that his QM book is only so-so (I learned from Sakurai's book, and many others). It's not clear to me that a good QM book can even exist, as the topic seems so esoteric (even after you learn to do all the homework problems).

Lenny Susskind has a new series of books out, called the "Theoretical Minimum". They are supposed to be very good, but (a) I haven't bought any of them yet, and (b) even if I did, I wouldn't have time to study them, and (c) to understand them, I would have to spend a year re-learning the fundamentals, which (d) I don't have time for.
 
This is a famous beginner's calculus text book, by Silvanus Thompson. Great book, I worked through the whole thing once many years ago. Someone has made a nice website of the book here.
I think it's been translated into many languages, there is a chinese translation of it on github.

I have an original paper copy of 'calculus made easy' somewhere, if I can find it I'll post a photo.

There is another well-known book called "calculus for the practical man" which was on the bookshelf at home when I was a kid; that's the book richard fenynman said he used to teach himself calculus from.
 
This is my copy. I bought it second hand for 10p (equivalent to a dime US) from a second-hand bookshop, many years ago. I was lucky, I had one particular univ. professor who was an old-school physicist (never used a calculator), and he mentioned it to me as a good book to get one day, so I went and found a copy.

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The book covers both the differential and integral calculus, in just this one small volume. Thompson was a university professor of physics and electrical engineering (and a fellow of the royal society), and this book was a distillation of his experience gained from many years of classroom teaching of calculus. I love his use of dry humor in a technical book, in the english tradition. I think it has to be the most compact book on calculus I have ever seen, so different from many of the huge tomes sold in the bookshops today. They didn't have mathamatica or graphing calculators in those days either! :)

en.wikipedia.org

Silvanus P. Thompson - Wikipedia

en.wikipedia.org en.wikipedia.org
en.wikipedia.org

Calculus Made Easy - Wikipedia

en.wikipedia.org en.wikipedia.org
 
Hahaha. Although actually it's true, the book is very approachable and he does make it easy to learn. But above all it teaches you with a series of practical exercises, you have to work though it on paper and go through all the exercises; it's not a book you can just sit and read. You need a pencil and a thick writing pad, you have to put the time and effort in, and I guarantee the number of pages of working out you will generate will be much larger than the book itself! I still have a thick A4 folder full of notes and working out somewhere.

Hopefully the modern version has been converted to decimal, some of the exercises in the original were in imperial units (feet and inches, etc). If you want to try reading it, I would try that website, it's free https://calculusmadeeasy.org/

The calculus for the practical man book is pretty good too, I worked through that when I was at school.
 
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Compare the size of 'calculus made easy' to a modern textbook like this. Calculus made easy is 300 pages in a small format, my copy measures 12 cm wide x 17 cm high by 1.5 cm thick. The modern book is larger than A4 paper size and has over 1100 pages! It's like comparing K&R "the C programming language" to Barmy Bootstrap's latest huge tome on C++.

I much prefer the older book. Maths is a thing you learn by doing, with lots of practice, not by reading. It helps to think of it as a practical subject, IMHO. A bit like programming. And it helps to have a good teacher. Still, I'm no mathamatician, so maybe you'd better not take too much notice of what I say! Unfortunately I was seduced by the dark side many years ago and became a Z80 programmer.😁
 
Extremely boring book.
hruodr said:
Compare it with Tom M. Apostol's two volumes or with Rudin's Principles of Mathematical Analysis.


No, definitively no! Math you learn by thinking
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OK, I stand corrected! 😁 Well, that just confirms you shouldn't take much notice of what I say. I'll stick to old thinkpads next time.
 
Crivens said:
Math is the language of nature.
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Please, please, do not reduce Math to language! People continuously say it, but it is far from the truth.

Math is the science of exact thinking, it is about thinking, not about nature, it is also not a natural science.

Math is perhaps a collection of sciences (Analysis, Algebra, Geometry, etc) with a common method.

Perhaps you think 'dialectical' when creating new theorems, but you write it down 'analytical'.

And not even the logic is common, because you can do for example constructive Math without tertium non datur.
 
I had a quick look through Apostol Calculus Vol 1, I found it online. Of course that is a very good book, a pure mathamatical approach to the development of the calculus, with proofs. Whereas the Thompson book was intended to be a school textbook, "for 5th form boys", as the author puts it. Which tells you something about the maths that was taught to 16 year olds in 1920's grammar schools, compared to today. Whether what the Thompson book teaches is truly "Mathamatics", or merely a series of calculating techniques, is debatable. But sometimes you need familiarity with techniques before introducing more advanced ideas; learning proceeds in stages, not all at once, at least, in my experience.

I think Maths is the science of the abstract, where 'science' means a systematic, organised body of proven knowledge, developed by logical argument. The 'things' that maths deals with are all pure abstractions. I can have '1' of any concrete object, but I can never have "a 1", which is a pure abstraction; by pure I mean an abstraction that can never be instantiated. Hence maths is the science of pure abstractions. What has always struck me as remarkable is that there appears to be a series of pure abstractions, like the pythagoras theorem and many others, that by logical argument provably 'exist' within the abstract realm; they are eternal and never changing, have a characteristic that we perceive as beauty (which is interesting of itself), and are not subject to the entropy that we have observed in the natural world. Do the pure abstractions of mathamatics, exist independently of consciousness? I don't know the answer; but, perhaps not.

Maths is not a natural science. The natural sciences (sometimes) apply some parts of mathamatics to the natural world, to make arguments about the natural world; for example, newton's laws of motion. You could, for example, develop the entire science of mathamatics, without ever having developed any of the natural sciences, if you so wished.

That is my limited understanding, anyway, speaking as a non-mathamatician.
 
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