[HN Gopher] Free Math Books
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Free Math Books
Author : blewboarwastake
Score : 291 points
Date : 2021-01-19 09:12 UTC (13 hours ago)
(HTM) web link (klkuttler.com)
(TXT) w3m dump (klkuttler.com)
| tomcam wrote:
| What an amazing amount of work to give the world for free. Thank
| you.
| phonebucket wrote:
| Another solid source of free math resources:
| https://realnotcomplex.com/
| cpp_frog wrote:
| 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.
| lr1970 wrote:
| The best, by far, book on Linear Algebra that elegantly teaches
| it from Vector Spaces and Linear Operators point of view is
|
| Paul Halmos "Finite-Dimensional Vector Spaces"
|
| For instance, the way Halmos introduces the determinant of a
| matrix (or an operator) is the most consistent, elegant and
| simple way I ever encountered. OTOH, in Kenneth Kuttler's
| LinAlg books the determinant is pulled out of the thin air like
| in 1000+ other similar books.
| cpp_frog wrote:
| Thanks, I'll look it up. The best textbook from which I
| studied (operators) was Elon Lima's Algebra Linear. Sadly the
| only physical copies are sold in Brazil.
| spekcular wrote:
| If you want to see the matrix point of view done well,
| there's _Linear Algebra Done Wrong_ :
| https://www.math.brown.edu/streil/papers/LADW/LADW.html.
| You can read a bit about the motivation for doing it that
| way on that website.
|
| The title is a reference to a somewhat well-known book,
| _Linear Algebra Done Right_ , which avoids using
| determinants to develop the theory (resulting in a somewhat
| novel/cleaner presentation). It's unfortunately not freely
| available online (published by Springer - I would suspect
| most university students can get it freely through their
| library's website, however).
| Tomte wrote:
| LADR was freely available at Springer at least at some
| point in time. Under their open access program. I
| couldn't find it again in a few minutes' search, so it
| may be gone.
| in9 wrote:
| Ah yes, a fellow Brazillian. I've alwys found Elon's book
| on Linear Algebra a masterpiece. Coupled with the exercises
| book, going through it is an eye opening experience.
| enriquto wrote:
| While Halmos' book is lovely, I still prefer the geometric
| definition of determinant to the algebraic one: The
| determinant of a matrix is the signed volume (or area) of the
| parallellepiped spanned by its columns. Equivalently, the
| determinant of a linear map is the volume of the image of a
| unit cube by that map (or any arbitrary shape of volume one,
| not necessarily a cube). All the algebraic properties of the
| determinant follow easily from the geometric definition
| (multi-linearity, anti-symmetry, etc).
|
| Really, I don't see what you like about Halmos definition of
| the determinant... I have just read it (page 99 of my copy)
| and he admits that it is a "somewhat roundabout procedure",
| just after giving the definition! There's other references
| that seem much cleaner (e.g. Spivak's calculus on manifolds,
| using exterior algebra).
| lr1970 wrote:
| > Really, I don't see what you like about Halmos definition
| of the determinant...
|
| Halmos shows (it is almost trivial) that the space of anti-
| symmetric n-forms Wn over L_n is 1-dimensional.
| Wn(Ae1,...,Aen) = const*Wn(e1,...,en). This scalar const is
| called determinant. It has all the properties you would
| ascribe to Volume like volume spanned by collinear column-
| vectors is zero. This is a nice bridge to geometry in Ln.
| Also, in a space of just one page (p.99) he introduces
| determinant and proves its main properties like det(A*B) =
| det(A)*det(B) and therefore det(A^-1) = 1/det(A).
| jacobolus wrote:
| The determinant of n vectors {vi} relative to a
| particular basis {ei} in an n-dimensional vector space is
| the scalar-valued ratio:
|
| ( v1 [?] v2 [?] *** [?] vn ) / ( e1 [?] e2 [?] *** [?] en
| )
|
| The signed volume per se is just the n-vector: v1 [?] v2
| [?] *** [?] vn
|
| Generally working with the wedge product is more pleasant
| and conceptually clearer than working with determinants.
| Among other things we don't need to make an arbitrary
| choice of basis or unit n-vector. There's also no reason
| to limit ourselves to n terms. v1 [?] v2 is also a
| reasonable quantity to use, etc.
| lr1970 wrote:
| The beauty of Halmos' derivation, which is similar but
| not identical to exterior algebra (wedge product), is
| that his approach is basis independent. A determinant by
| his definition is scalar invariant over all bases. It is
| very geometrical in nature.
| jacobolus wrote:
| The determinant inherently involves a basis (or at the
| very least a choice of unit n-vector). Or if you like you
| can think of the determinant as a function of a square
| matrix (grid of numbers), rather than a function of a
| collection of vectors.
|
| When you take the basis out, that's the wedge product,
| which inherently includes the orientation. Conveniently,
| there is only one degree of freedom for n-vectors in
| n-dimensional space. When we take the quotient of two
| n-vectors in n-dimensional space we therefore get a
| scalar.
| The_suffocated wrote:
| If you define determinant as volume, how do you define
| volume? I agree that it's pedagogically sound to _motivate_
| the notion of determinant by the volume of a
| parallelepiped, but using volume as the _definition_ of
| determinant just doesn 't sound right.
|
| And strictly speaking, determinant is not volume because
| the former is dimensionless. It is the scaling factor of
| the volume when a geometric entity is transformed by a
| linear map.
| enriquto wrote:
| > If you define determinant as volume, how do you define
| volume?
|
| How do you define "length" and "area"? I guess that if
| you don't have already a very firm grasp of these basic
| concepts, then there's no business for you (yet) in
| studying determinants. Much later, once you master
| thoroughly lengths, areas, volumes and hypervolumes; and
| also linear algebra and determinants (however they are
| defined), then you can embark in the elegant definitions
| using exterior algebra and the like. Notice that Halmos
| itself says that his treatment is appropriate for a
| *second* course in linear algebra, preparing the field
| for the later study of infinite-dimensional spaces.
|
| > And strictly speaking, determinant is not volume
| because the former is dimensionless.
|
| This really depends on the context. If you are working on
| euclidean space, you already have "units" and the
| determinant makes sense in itself, as the volume spanned
| by sets of vectors.
| [deleted]
| ABeeSea wrote:
| I find both the geometric and algebraic definitions quoted
| here unsatisfying. What is a "volume" spanned by a vector
| space of polynomials or co-tangent functionals?
|
| *A* determinate function (not the) is simply a skew symmetric
| n-linear map into the underlying field.
|
| Done. Now we get the volume interpretation when it's
| appropriate, the wedge product interpretation, and the
| generalization to finitely generated projective modules (if a
| determinate function exists, there are additional conditions
| needed for the existence.)
| mhh__ wrote:
| 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.
| cpp_frog wrote:
| I understand, I too had a similar experience in high school.
| My comment was largely referring to my context: This semester
| I'll finish a mathematical engineering degree (in my country
| engs. are 12 semesters long) and the abstract way is
| rewarding but without applications can only be endured so
| far. It does not help that a large fraction of mathematical
| engineers after they graduate end up doing some software work
| consisting in statistics, optimization or some other advanced
| mathetical concept. With a dropout rate of ~80%, not many
| people are willing to put themselves through rigorous
| analysis classes on top of the engineering requirements for
| so many years to get a job doing something you could have
| learned in a more practical way. But we are very well paid
| and the unemployment rate is 0% since there are maybe 10
| graduates in the whole country each year.
| 2wrist wrote:
| 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.
| mhh__ wrote:
| No negativity measured, actually
| [deleted]
| fangyrn wrote:
| Could you please talk about alternative ways of learning about
| linear algebra?
| amelius wrote:
| Are the answers to the exercises to be found somewhere?
| AlphENsign_Tech wrote:
| wolfram alpha?
| AcademicHamster wrote:
| Probably not. That's why most of these books are useless for
| people that self-study. There isn't an external feedback
| mechanism to check your work. I'd recommend hiring a tutor. You
| can post online too, but the answers to your questions may
| vary.
| commandlinefan wrote:
| I never understood why they do that - especially for
| something like this that's offered for free. What's the point
| of even including the exercises if there's no way to check
| the answers?
| AcademicHamster wrote:
| I wondered the same. I have no idea, other than to
| speculate. In this case, it might be out of habit (since
| this is usually how textbooks are written) or laziness. I
| can't recommend any of these books for self-studies unless
| the person studying is fine with posting every exercise
| they do online for correctness checks or can hire a tutor.
| carapace wrote:
| It's really hard to do (at all, let alone well) but the
| point is to encode more information in the problems such
| that, by solving them oneself, the student gains direct
| understanding of some technique or application or
| extension that wasn't covered in the main text. In a
| (well-written) textbook there might be five or tens times
| as much information latent in the (solving of the)
| exercises than in the entire preceding chapter. Writing
| these kinds of sets of exercises is very challenging,
| much harder than just writing a textbook.
| visarga wrote:
| Off topic: nice PDF rendering I wish normal PDF would be as
| fluent.
| lightspot21 wrote:
| Indeed, LaTeX makes for really awesome results if you can put
| in the time to learn it (which is not a lot for basic usage).
| Plus it helps enforce a common style in all docs, and works
| well with Git.
| xanax wrote:
| I like this. The more free information the better.
| amilein7minutes wrote:
| Did the same person write all these books, which altogether
| amount to upwards of 10k pages? From his website, he is quite an
| active research mathematician too. While just writing so many
| textbooks is a huge accomplishment in itself, the author has also
| made them available for free; I am lost for words at how prolific
| as well as generous the author is. I really want to know how this
| was possible, how long it took, and more about their motivation.
| opheliate wrote:
| Wow, these look great! Does anyone know of any similar resources
| for mechanics, specifically the Hamiltonian & Lagrangian
| formulations? I've had a bit of trouble finding good resources
| online to supplement my mechanics modules at uni.
| posix_me_less wrote:
| 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).
| mhh__ wrote:
| 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.
|
| 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
| enriquto wrote:
| > 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.
| mhh__ wrote:
| 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).
| spekcular wrote:
| To amplify this point, all the negative Amazon reviews
| praise the book but excoriate the print quality.
| enriquto wrote:
| This must concern some paperback English print? My copy
| in French from "Editions MIR Moscou, 1969", hardcover,
| masterfully typeset and in bible paper is one of the
| finest books that I have.
| spekcular wrote:
| Yes, I think it's specific to the English version. You
| can see examples if you use the Amazon.com "look inside"
| feature. For instance in volume 3, in the first pages
| already some of the footnotes are hardly readable.
|
| For one of the volumes, a reviewer even posted a picture
| of his edition with subscripts printed so faint/partially
| that they were basically missing, and he had to Google
| the proper formulas!
| mhh__ wrote:
| Yes, I literally have RF engineering books (interesting
| reads actually) that are as old as my grandfather that
| have clean equations and beautiful text, in a lovely
| binding, but my L&L copies are both like an n-th order
| photocopy.
| posix_me_less wrote:
| 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.
| mhh__ wrote:
| 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.
| spekcular wrote:
| What are the titles of the two Oxford books you
| mentioned? I'd like to look at them.
| mhh__ wrote:
| Quantum Field Theory for the gifted amateur (well not
| quite...)
|
| Concepts in thermal physics
|
| Not at the same level as L&L but they are absolute
| masterpieces in pedagogy and the formula should be
| extended to a 800page tome to cover more material. It's
| the way MTW should be written...
| spekcular wrote:
| Yeah, I liked the mechanics and quantum volumes, but the
| choice of material in the stat mech books (both volumes)
| just seemed weird compared to what's usually done in a
| modern graduate course.
|
| Do you have any recommendations for good stat mech books? I
| guess the two volume set by Kardar is trendy right now, but
| I'm always curious about other options.
| mhh__ wrote:
| I'm remiss to recommend as I'm still learning, but I
| absolutely love "Concepts in Thermal physics". It's
| embarrassingly well written and structured.
|
| Beyond that the usual suspects are good enough for me, I
| just don't _like_ L &L. I'm probably forgetting
| something.
|
| It's not exactly statmech but I really like McComb's
| introductory renormalization methods book.
| spekcular wrote:
| Thank you for the recommendations!
|
| While I have not seen either of those books before, I
| have another book by the author of the first one, Stephen
| Blundell. It's _Quantum Field Theory for the Gifted
| Amateur_ , and I think you might like it. Not as a
| standalone quantum book, but perhaps as a supplement to a
| more "serious" treatment.
|
| edit: I just saw you recommended this below!
| mhh__ wrote:
| QFTFTGA is really great. Surprisingly hard as well.
|
| I got it when I was 17 and it was an absolute godsend as
| its really cheap.
| mhh__ wrote:
| Based on "uni" I'm guessing you are at a UK institution (as am
| I).
|
| The notes are utter dogshit because there's no culture of
| publishing them online for the public.
|
| Kibble's classical mechanics book is deep, easy to read and
| cheap, I'd start there. Most physics books past a certain level
| end up with an increasingly hand-wavy derivation of the Euler-
| lagrange equations in some context
| abhinav22 wrote:
| Look for Dover books, particularly from Russian authors. Cheap
| and good!
| Tomte wrote:
| For linear algebra: Shilov.
| blewboarwastake wrote:
| I found these lecture notes by David Tong to be really good at
| a glance [1]. A free introductory physics book [2]. I don't
| have much physics stuff and I know almost nothing about it, I
| mostly focus on Math/CS, this is some stuff that I had
| bookmarked. Maybe someone else here can share some good
| Mechanics resources.
|
| [1] http://www.damtp.cam.ac.uk/user/tong/dynamics.html [2]
| http://www.lightandmatter.com
| posix_me_less wrote:
| Does anybody know of an awesome list that has more of these kinds
| of "pdf textbooks" on math/phys/engineering?
| ivan_ah wrote:
| Not sure if you needed PDF specifically, but this site has a
| lot of good OER textbooks, digitized nicely as HTML + MathJax:
| https://math.libretexts.org/Bookshelves
| mvalcic wrote:
| Check out the Open Textbook Library:
|
| https://open.umn.edu/opentextbooks/
| aungmyohtet wrote:
| Thank you.
| enriquto wrote:
| > 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.
| human4fter4ll wrote:
| Thank you so much!
| mathnmusic wrote:
| 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
| mattowen_uk wrote:
| Oooh this is like a dmoz.org list from yesteryear when the
| web was _useful_. Bookmarked, Cheers!
| Spooky23 wrote:
| Nerds love to bike shed crap like this and bite the hand that
| feeds.
|
| To paraphrase a typical rant: "Making knowledge free and
| accessible is useless unless a libre format is used like
| Markdown." Lol
|
| The PDF beef is funnier in that people usually don't know why
| they are morally opposed to PDF, it usually boils down to not
| liking Adobe Acrobat a decade ago, not accepting that page
| format preservation is a thing, or some beef with zooming or
| something. End of the day, it seeks to be digital paper.
|
| End of the day, it's an open standard with multiple
| implementations. Just by virtue of the US Federal Courts
| using it for millions of documents it will be usable for the
| foreseeable future, well beyond our lifetimes. (And there are
| many similar or even bigger examples)
| ravi-delia wrote:
| Not just that, but if you actually look at the
| implementation its pretty understandable. 90% of use cases
| are covered by the easiest parts to parse too. PDF might
| not be perfect, but honestly not much comes close.
| gmfawcett wrote:
| https://www.reddit.com/r/mathbooks/ is a good place to find
| free titles.
| ithrow wrote:
| openstax.org
| asicsp wrote:
| https://github.com/EbookFoundation/free-science-books/blob/m...
|
| Kenneth Kuttler's books doesn't seem to be there though.
| wwwhizz wrote:
| Under which license are these books published?
| chrismorgan wrote:
| At the end of the _One Variable Advanced Calculus_ table of
| contents is this text:
|
| > Copyright (c) 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.
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