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Free Math Books

klkuttler.com

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Re: Free Math Books

#11

Post by mhh__ »

posix_me_less wrote: post #8
mhh__ wrote: post #7

Earlier quoted context omitted.

Although I have immense respect for them I really don't like L&L all that much. The first one is pretty beautiful but it could use some material on the "deeper" side of things, particularly the connection with geometry and Noether's theorem. As for the others, they're just too "russian" - I like how oddly practical they are, but they're just not structured properly - StatPhys in particular just doesn't flow very well…

Regarding geometry and Noether's theorem, I disagree. That stuff is way overblown in general, it gives you very little ( in classical mechanics) for the time and page count the subject requires. I had a lecture on this topic from enthusiast well-respected physicist, and I kept thinking, this stuff is interesting math but completely useless to a physicist.

Classical mechanics is ultimately just masturbation compared to the "real thing", it's all a warm-up for the mind rather than teaching you how to calculate stresses on a beam - Full on symplectic geometry is niche but the basics of Noether's theorem and symmetries are central to classical and quantum field theories which are ultimately the language in which the cutting edge of fundamental physics speaks.

So I sort of agree, but take the two Oxford books on QFT and Statistical physics - they pack in enormous amounts of detail in a 3 or 4 hundred pages. There's room to spare if the book is the right shape.

Re: Free Math Books

#12

Post by enriquto »

posix_me_less wrote: post #9

Does anybody know of an awesome list that has more of these kinds of "pdf textbooks" on math/phys/engineering?

> Does anybody know of an awesome list that has more of these kinds of "pdf textbooks" on math/phys/engineering?

Go to John Baez's awesome list "How to Learn Math and Physics":

https://math.ucr.edu/home/baez/books.html

And then to Library Genesis.

Re: Free Math Books

#13

Post by mbustamanter »

In college I was taught Linear Algebra from the operator point of view, rather than with matrices. That way theorems are clearer and the student's understanding is deeper, but for applications it's better to study from the matrix point of view and with lots of examples. Kuttler's book was refreshing in that sense. His other books are excellent, too. If you have been studying pure math (or french-style applied math which is just pure math with a concentration in Analysis) they are a light and fun complementary read.

Re: Free Math Books

#14

Post by enriquto »

mhh__ wrote: post #7
posix_me_less wrote: post #6

Earlier quoted context omitted.

Tong is good, most appropriate if you already know a little about the subject. However, it is a "fast-track" kind of resource, it is good to read some standard textbooks on the subject, i.e. Landau & Lifshitz (the most efficient book on theoretical mechanics ever) and Goldstein (broad and interesting).

Although I have immense respect for them I really don't like L&L all that much. The first one is pretty beautiful but it could use some material on the "deeper" side of things, particularly the connection with geometry and Noether's theorem. As for the others, they're just too "russian" - I like how oddly practical they are, but they're just not structured properly - StatPhys in particular just doesn't flow very well…

> could use some material on the "deeper" side of things

The first few chapters are precisely about the extraction of concrete conserved quantities from symmetries. A sufficiently "russian" reader will be able to see immediately the general case from these very complete examples. Noether's theorem is only missing in name, not in content.

> The typesetting is also a crime against humanity - they should be done similarly to the Feynman lectures, so typed up in LaTeX rather than whatever they are now

The typeseting of the french edition of L&L is extraordinarily beautiful. I'm not sure that is is possible to reach this typographical elegance with freely available LaTeX packages. On the other hand, the re-typed Feynman lectures are a disgrace, and an objectively worsening in quality from the first editions.

Re: Free Math Books

#15

Post by mhh__ »

enriquto wrote: post #14
mhh__ wrote: post #7

Earlier quoted context omitted.

Although I have immense respect for them I really don't like L&L all that much. The first one is pretty beautiful but it could use some material on the "deeper" side of things, particularly the connection with geometry and Noether's theorem. As for the others, they're just too "russian" - I like how oddly practical they are, but they're just not structured properly - StatPhys in particular just doesn't flow very well…

> could use some material on the "deeper" side of things The first few chapters are precisely about the extraction of concrete conserved quantities from symmetries. A sufficiently "russian" reader will be able to see immediately the general case from these very complete examples. Noether's theorem is only missing in name, not in content. > The typesetting is also a crime against humanity - they should be done similar…

I liked that section a lot but I want a jumping off point. I don't think symmetries of the action or groups are discussed, IIRC.

I may have been a little vague when I said typesetting - the actual typesetting is a bit dull but the thing that is a disgrace, I should clarify, is that the fonts are terrible, and the text has that "Cheap Dover book" print quality (not far off a good typewriter).

Re: Free Math Books

#16

Post by mhh__ »

mbustamanter wrote: post #13

In college I was taught Linear Algebra from the operator point of view, rather than with matrices. That way theorems are clearer and the student's understanding is deeper, but for applications it's better to study from the matrix point of view and with lots of examples. Kuttler's book was refreshing in that sense. His other books are excellent, too. If you have been studying pure math (or french-style applied math wh…

Although I understand that matrix-soup is kind of the entropic endstate of all high school mathematics pedagogy, I think it is a real tragedy: In the UK especially even the best and brightest barely touch any real mathematics until after they leave secondary school so they leave with almost literally no idea of what university mathematics consists of. It's all well and good training people to be engineers, but the universities end up teaching the whole syllabus to them again in about 6 weeks. It's just shit.

The only reason why I am now doing theoretical physics (I was in the dumb group initially and worked my way up largely by myself) is because I read a calculus textbook by accident and got hooked when I was 14. Even when I made it to the top of the pile I still wasn't allowed to do anything more than calculus because the module system means we had to choose as a class whether to do group theory or not.

Re: Free Math Books

#17

Post by chrismorgan »

wwwhizz wrote: post #10

Under which license are these books published?

At the end of the One Variable Advanced Calculus table of contents is this text:

> Copyright © 2018, You are welcome to use this, including copying it for use in classes or referring to it on line but not to publish it for money. I do constantly upgrade it when I find things which could be improved.

Re: Free Math Books

#18

Post by 2wrist »

mhh__ wrote: post #16
mbustamanter wrote: post #13

In college I was taught Linear Algebra from the operator point of view, rather than with matrices. That way theorems are clearer and the student's understanding is deeper, but for applications it's better to study from the matrix point of view and with lots of examples. Kuttler's book was refreshing in that sense. His other books are excellent, too. If you have been studying pure math (or french-style applied math wh…

Although I understand that matrix-soup is kind of the entropic endstate of all high school mathematics pedagogy, I think it is a real tragedy: In the UK especially even the best and brightest barely touch any real mathematics until after they leave secondary school so they leave with almost literally no idea of what university mathematics consists of. It's all well and good training people to be engineers, but the un…

Good luck to you. I wish you every success. The education in this country has been shit for such a long time. It is and has been pretty devastating for so long.

Apologies for the negative waves.

Re: Free Math Books

#19

Post by mathnmusic »

posix_me_less wrote: post #9

Does anybody know of an awesome list that has more of these kinds of "pdf textbooks" on math/phys/engineering?

I have been adding a number of these free books at https://learnawesome.org/

Do you really care about the format being PDF or is it about the books being FREE? I'd like to make common queries like yours easier. LearnAwesome is open-source, so of course you're free to contribute: https://github.com/learn-awesome/learn

Re: Free Math Books

#20

Post by mhh__ »

2wrist wrote: post #18
mhh__ wrote: post #16

Earlier quoted context omitted.

Although I understand that matrix-soup is kind of the entropic endstate of all high school mathematics pedagogy, I think it is a real tragedy: In the UK especially even the best and brightest barely touch any real mathematics until after they leave secondary school so they leave with almost literally no idea of what university mathematics consists of. It's all well and good training people to be engineers, but the un…

Good luck to you. I wish you every success. The education in this country has been shit for such a long time. It is and has been pretty devastating for so long. Apologies for the negative waves.

No negativity measured, actually
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