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Free Math Books

klkuttler.com

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Re: Free Math Books

#41

Post by enriquto »

lr1970 wrote: post #35
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…

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 100…

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).

Re: Free Math Books

#42

Post by spekcular »

mhh__ wrote: post #39
spekcular wrote: post #32

Earlier quoted context omitted.

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.

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.

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!

Re: Free Math Books

#43

Post by mhh__ »

enriquto wrote: post #34
spekcular wrote: post #33

Earlier quoted context omitted.

To amplify this point, all the negative Amazon reviews praise the book but excoriate the print quality.

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.

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.

Re: Free Math Books

#44

Post by mhh__ »

spekcular wrote: post #42
mhh__ wrote: post #39

Earlier quoted context omitted.

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.

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!

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.

Re: Free Math Books

#45

Post by lr1970 »

enriquto wrote: post #41
lr1970 wrote: post #35

Earlier quoted context omitted.

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 100…

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 determi…

> 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).

Re: Free Math Books

#46

Post by in9 »

mbustamanter wrote: post #37
lr1970 wrote: post #35

Earlier quoted context omitted.

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 100…

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.

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.

Re: Free Math Books

#47

Post by AcademicHamster »

amelius wrote: post #27

Are the answers to the exercises to be found somewhere?

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.

Re: Free Math Books

#48

Post by commandlinefan »

AcademicHamster wrote: post #47
amelius wrote: post #27

Are the answers to the exercises to be found somewhere?

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.

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?
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