(Part 2) Best linear algebra books according to redditors
We found 297 Reddit comments discussing the best linear algebra books. We ranked the 80 resulting products by number of redditors who mentioned them. Here are the products ranked 21-40. You can also go back to the previous section.
Gilbert Stang Linear Algebra Third Edition optical illusion is my favorite.
https://www.amazon.com/Linear-Algebra-Its-Applications-3rd/dp/0155510053/ref=sr_1_1?s=books&ie=UTF8&qid=1492964393&sr=1-1&keywords=gilbert+strang+3rd+edition
When I've got a clear aim in view for where I want to get to with a self-study project, I tend to work backwards.
Now, I don't know quantum mechanics, but here's how I might approach it if I decided I was going to learn (which, BTW, I'd love to get to one day):
First choose the book you'd like to read. For the sake of argument, say you've picked Griffiths, Introduction to Quantum Mechanics.
Now have a look at the preface / introduction and see if the author says what they assume of their readers. This often happens in university-level maths books. Griffiths says this:
> The reader must be familiar with the rudiments of linear algebra (as summarized in the Appendix), complex numbers, and calculus up to partial derivatives; some acquaintance with Fourier analysis and the Dirac delta function would help. Elementary classical mechanics is essential, of course, and a little electrodynamics would be useful in places.
So now you have a list of things you need to know. Assuming you don't know any of them, the next step would be to find out what are the standard "first course" textbooks on these subjects: examples might be Poole's Linear Algebra: A Modern Introduction and Stewart's Calculus: Early Transcendentals (though Griffiths tells us we don't need all of it, just "up to partial derivatives"). There are lots of books on classical mechanics; for self-study I would pick a modern textbook with lots of examples, pictures and exercises with solutions.
We also need something on "complex numbers", but Griffiths is a bit vague on what's required; if I didn't know what a complex number is than I'd be inclined to look at some basic material on them in the web rather than diving into a 500-page complex analysis book right away.
There's a lot to work on here, but it fits together into a "programme" that you can probably carry through in about 6 months with a bit of determination, maybe even less. Then take a run at Griffiths and see how tough it is; probably you'll get into difficulties and have to go away and read something else, but probably by this stage you'll be able to figure out what to read for yourself (or come back here and ask!).
With some projects you may have to do "another level" of background reading (e.g., you might need to read a precalculus book if the opening chapters of Stewart were incomprehensible). That's OK, just organise everything in dependency order and you should be fine.
I'll repeat my caveat: I don't know QM, and don't know whether Griffiths is a good book to use. This is just intended as an example of one way of working.
[EDIT: A trap for the unwary: authors don't always mention everything you need to know to read their book. For example, on p.2 Griffiths talks about the Schrodinger wave equation as a probability distribution. If you'd literally never seen continuous probability before, that's where you'd run aground even though he doesn't mention that in the preface.
But like I say, once you've taken care of the definite prerequisites you take a run at it, fall somewhere, pick yourself up and go away to fill in whatever caused a problem. Also, having more than one book on the subject is often valuable, because one author's explanation might be completely baffling to you whereas another puts it a different way that "clicks".]
I have a B.S. in mathematics, statistics emphasis - and am currently in the second semester of Linear Models in a M.S. Statistics program.
Contrary to popular opinion, I don't think Linear Algebra Done Right is suitable for learning linear algebra. Statistics - as far as I've gathered - is more focused on what is called "numerical linear algebra," rather than the more algebraic (and more abstract) approach that Axler takes.
It took a lot of research on my part to find better books. I personally believe that these resources are much better for covering the linear algebra needed for linear models (I recommend these after a first-course treatment in linear algebra):
I have also heard that Matrix Algebra Useful for Statistics by Searle is good, but I haven't read it yet.
If you feel like your linear algebra is particularly strong (i.e., you're comfortable with vector spaces, matrix operations, eigenvalues), you could try diving right into linear models. My personal favorite is Plane Answers to Complex Questions by Christensen. I reviewed this book on Amazon:
>It's a decent text. If you want to understand any part of this text, you need to have at least a first course in linear algebra covering matrices and vector spaces, some probability, and some "mathematical maturity."
>READ THE APPENDICES before you read any part of this text. READ THE APPENDICES. Take good notes on them and learn the appendices well. Then proceed to Chapter 1.
>Definitely one of the most readable books I've read, but it does take a long time to digest everything. If you don't have a teacher to take you through this material and you're completely new to it, you will find that some details are omitted, but these details aren't complicated enough that someone with an undergraduate degree in math wouldn't be able to figure them out.
>Highly recommended. The only thing I don't like about this text is some of its notation. It uses Cov(A) to mean the variance-covariance matrix of a random vector A, and Cov(A, B) to mean E[(A-E[A])(B-E[B])^transpose ]. I prefer using Var(A) for the former case. Furthermore, it uses ' instead of T to denote the transpose of a matrix.
No linear models text will cover all of the linear algebra used, however. If you get a linear models text, you should get your hands on one of the above linear algebra texts as well.
If you need a first course's treatment in Linear Algebra, I prefer [Linear Algebra and Its Applications](http://www.amazon.com/Linear-Algebra-Its-Applications-Edition/dp/0201709708) by Lay. The 3rd edition will suffice, although I think it's in the 5th edition now. Larson's [Elementary Linear Algebra*](http://www.amazon.com/Elementary-Linear-Algebra-Ron-Larson/dp/1133110878/ref=sr_1_1?s=books&ie=UTF8&qid=1458047961&sr=1-1&keywords=larson+linear+algebra) is also a decent text; older editions are likely cheaper, but will likely give you a similar treatment as well, so you may want to look into these too. I learned from the 6th edition in my undergrad.
Transistor-level IC designer.
The elective that benefited me the most was "Minimization of Functions" in the Applied Math department. This is a course in nonlinear optimization, where you learn how to find (numerically) the maxima and minima of highly nonlinear functions. It has been incredibly useful throughout my career, even in the simplest cases a/k/a curve-fitting.
The follow-on course, "Minimization of Functionals" was for the aero/astro Optimal Control types, people who want to shoot down ballistic missiles using ballistic missiles -- although the course catalog expressed it slightly differently. I skipped that one.
The book by Gill, Murray, and Wright gives a wonderful overview of the field (amazon link) but I recommend you buy a used copy or a previous-edition used copy. There ain't much that's changed in 40 years, except the cost of a trillion floating point operations has fallen by a factor of a million.
While that is a useful application of linear algebra, IMO, it's not a good way to actually learn linear algebra. There's far more to linear algebra than you'd immediately use in a graphics programming course.
For example, it'll be a little while before you need to invert matrices (and all the related work that comes with that). And I haven't had to use eigenvectors at all so far (and I'm just completing a graphics class now).
It's very possible to learn linear algebra and useful applications without the CS related aspects. For example, resolving systems of equations is something that you probably learned in high school, if not using matrices at that time. Projections are also very easy to understand the uses of.
Frankly, there's a lot of math that you'll learn without an application at the time. This is somewhat of a hindrance, but shouldn't prevent you from learning the theory behind things. For example, most calculus courses don't make it very clear as to why you'd want to find a derivative, yet it should still be understandable that you're finding the slope of the tangent line.
All that said, applications are helpful. My linear algebra class used this text and I thought it was pretty good. It tried to give real world applications of many things, and does include a brief mention of application to computer graphics (along with things like balancing chemistry equations).
I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done.
If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try.
Basics
I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW.
Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving.
From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done.
This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on.
Intermediate
At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better.
This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point.
Advanced
Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev.
Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time.
Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject.
Intro Calculus, in American sense, could as well be renamed "Physics 101" or some such since it's not a very mathematical course. Since Intro Calculus won't teach you how to think you're gonna need a book like How to Solve Word Problems in Calculus by Eugene Don and Benay Don pretty soon.
Aside from that, try these:
Excursions In Calculus by Robert Young.
Calculus:A Liberal Art by William McGowen Priestley.
Calculus for the Ambitious by T. W. KORNER.
Calculus: Concepts and Methods by Ken Binmore and Joan Davies
You can also start with "Calculus proper" = Analysis. The Bible of not-quite-analysis is:
[Calculus by Michael Spivak] (http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1413311074&sr=1-1&keywords=spivak+calculus).
Also, Analysis is all about inequalities as opposed to Algebra(identities), so you want to be familiar with them:
Introduction to Inequalities by Edwin F. Beckenbach, R. Bellman.
Analytic Inequalities by Nicholas D. Kazarinoff.
As for Linear Algebra, this subject is all over the place. There is about a million books of all levels written every year on this subject, many of which is trash.
My plan would go like this:
1. Learn the geometry of LA and how to prove things in LA:
Linear Algebra Through Geometry by Thomas Banchoff and John Wermer.
Linear Algebra, Third Edition: Algorithms, Applications, and Techniques
by Richard Bronson and Gabriel B. Costa.
2. Getting a bit more sophisticated:
Linear Algebra Done Right by Sheldon Axler.
Linear Algebra: An Introduction to Abstract Mathematics by Robert J. Valenza.
Linear Algebra Done Wrong by Sergei Treil.
3. Turn into the LinAl's 1% :)
Advanced Linear Algebra by Steven Roman.
Good Luck.
(co)Homology is useful whenever you have a ring and a module. Homological Algebra is, very roughly, linear algebra for a general ring over a module. (co)Homology problems turn up when you do something "linear" to an exact sequence of modules and they don't remain exact. Some examples that come to mind are:
Group Theory: Group Cohomology via Peter Webb's notes: The second cohomology group classifies certain kinds of group extensions.
Number Theory: Galois Cohomology a flavor of Group Coho, Class Field Theory which can be thought of, among other interpretations, as a vast extension of quadratic reciprocity,
Commutative Algebra: e.g. Local Cohomology ala Huneke, Gorenstein Rings, see page 6 and lots more...
Combinatorics: e.g. R.P. Stanley's Combinatorics and Commutative Algebra or his intro also in Lattices
If you want to get a feel for these and more, you could no better IMO than to pick up Weibel's History of Homological Algebra. If you want to start to learn this material I'd also suggest Weibel's Introduction to Homological Algebra.
Somehow no one mentioned it (also in the referred math.stackexchange), but from abstract mathematical point of view, this is an awesome book IMO:
http://www.amazon.com/Multilinear-Algebra-Universitext-Werner-Greub/dp/0387902848
This should keep you busy, but I can suggest books in other areas if you want.
Math books:
Algebra: http://www.amazon.com/Algebra-I-M-Gelfand/dp/0817636773/ref=sr_1_1?ie=UTF8&s=books&qid=1251516690&sr=8
Calc: http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1356152827&sr=1-1&keywords=spivak+calculus
Calc: http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
Linear algebra: http://www.amazon.com/Linear-Algebra-Modern-Introduction-CD-ROM/dp/0534998453/ref=sr_1_4?ie=UTF8&s=books&qid=1255703167&sr=8-4
Linear algebra: http://www.amazon.com/Linear-Algebra-Dover-Mathematics-ebook/dp/B00A73IXRC/ref=zg_bs_158739011_2
Beginning physics:
http://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/0465023827
Advanced stuff, if you make it through the beginning books:
E&M: http://www.amazon.com/Introduction-Electrodynamics-Edition-David-Griffiths/dp/0321856562/ref=sr_1_1?ie=UTF8&qid=1375653392&sr=8-1&keywords=griffiths+electrodynamics
Mechanics: http://www.amazon.com/Classical-Dynamics-Particles-Systems-Thornton/dp/0534408966/ref=sr_1_1?ie=UTF8&qid=1375653415&sr=8-1&keywords=marion+thornton
Quantum: http://www.amazon.com/Principles-Quantum-Mechanics-2nd-Edition/dp/0306447908/ref=sr_1_1?ie=UTF8&qid=1375653438&sr=8-1&keywords=shankar
Cosmology -- these are both low level and low math, and you can probably handle them now:
http://www.amazon.com/Spacetime-Physics-Edwin-F-Taylor/dp/0716723271
http://www.amazon.com/The-First-Three-Minutes-Universe/dp/0465024378/ref=sr_1_1?ie=UTF8&qid=1356155850&sr=8-1&keywords=the+first+three+minutes
I dunno about “undergraduate”, but you could try Birkhoff & Mac Lane or Greub. Those are both kind of old, so someone else may have a better idea.
Although I've never read it myself, this might interest you.
CS 1 & 2, Discrete Mathematics don't have textbooks.
These are the amazon sites that you can choose to purchase them from. They contain the ISBN for the corresponding books on the market site, so you can look for them on more morally ambiguous sites.
This book: http://www.amazon.com/Linear-Algebra-Applications-Bretscher-Third/dp/B000UTKDN0/
"The proof is left to the reader" is the ultimate way to troll your innocent introductory linear algebra students.
Linear Algebra and its applications.
http://www.amazon.com/Linear-Algebra-Its-Applications-3rd/dp/0201709708
is a great introductory text. lots of examples, lots of diagrams to illustrate important concepts. it'll take you from zero to the singular value decomposition.
i have a softcover version but couldn't find it on amazon.
You might like Hassani 1 better (or more readable) compared to Boas (Boas has more problems though). Though I'm not suggesting it as a preparation for your test next week (although you never know; you might pick it up from the library tomorrow and find out it answered many of your questions). It's one of the books that you shouldn't rush through (a whole summer working through it, solving 70-80% of the problems, would be a good idea).
Bra Ket notation shouldn't be too difficult if you've taken 'linear algebra' already (again Hassani has a few chapters on LA, but I used Leon when I took LA class). Schmidt ortho is covered in an LA class (again also is in Hassani).
Other stuff you mentioned seem like special topics in Diff. Eq, save for Complex Fourier which should be under 'complex analysis' I guess.
I hope this helps FWIW.
Si estás hablando de Algebra Lineal, los libros de Serge Lang son buenísimos. Conciso explicando, pero no deja la intuición detrás. Tiene muchos ejercicios también si querés practicar.
Los libros son:
https://www.amazon.com/Introduction-Linear-Algebra-Undergraduate-Mathematics/dp/0387962050
https://www.amazon.com/Linear-Algebra-Undergraduate-Texts-Mathematics/dp/0387964126/ref=pd_bxgy_14_img_2?_encoding=UTF8&pd_rd_i=0387964126&pd_rd_r=JFJYRBF3JXJN1T8SNXK7&pd_rd_w=Ym5Mi&pd_rd_wg=d1H0O&psc=1&refRID=JFJYRBF3JXJN1T8SNXK7
Por ahí los podés encontrar en genlib para descargar.
edit: si podés ir a una clase de consulta mejor aún para cerrar un tema en particular, de ahí generalmente te vas con todo clarisimo
I think Linear Algebra by Kuldeep Singh is the best fit for newcomers to LA. It's unpretentious and meant to be actually read by students (can you imagine?). This book will take you from someone who just discovered there exists such a thing as LA to someone who solves problems in Linear Algebra Done Right By Axler cold. After Kuldeep Singh you can pick up Advanced Linear Algebra by Steven Roman which is an extreme overkill even for mathematicians.
Basically, once you get the basics of LA down, you can simply read up on the newest matrix algos for machine learning on ArXiv or something. BTW, if your goal is working with data you need to learn some probability.
There's like a million textbooks and online courses on the subject, and I can't really speak to which ones are good and which ones are not. I've had some success suggesting that people watch this lecture series, but it starts off assuming a fair amount of background. If you're just planning to have some fun noodling around I strongly recommend that you look up a tutorial that suits you on the Keras library for Python, which will let you get started building cat/dog classifiers very easily but which scales up to exploiting the full power of Tensorflow. If you're interested in getting a bit more serious I'd suggest getting comfortable with linear algebra (great book) and making sure you really understand backpropagation. It might sound elitist, but if you can't derive it from scratch on a whiteboard you don't actually understand it, and it will limit your ability to understand why many other techniques are useful.
From there you should have the grounding to understand basically all of the entry-level stuff in the field, from support vector machines to convolutional neural networks.
These are listed in the order I'd recommend reading them. Also, I've purposely recommended older editions since they're much cheaper and still as good as newer ones. If you want the latest edition of some book, you can search for that and get it.
The Humongous Book of Basic Math and Pre-Algebra Problems https://www.amazon.com/dp/1615640835/ref=cm_sw_r_cp_api_pHZdzbHARBT0A
Intermediate Algebra https://www.amazon.com/dp/0072934735/ref=cm_sw_r_cp_api_UIZdzbVD73KC9
College Algebra https://www.amazon.com/dp/0618643109/ref=cm_sw_r_cp_api_hKZdzb3TPRPH9
Trigonometry (2nd Edition) https://www.amazon.com/dp/032135690X/ref=cm_sw_r_cp_api_eLZdzbXGVGY6P
Reading this whole book from beginning to end will cover calculus 1, 2, and 3.
Calculus: Early Transcendental Functions https://www.amazon.com/dp/0073229733/ref=cm_sw_r_cp_api_PLZdzbW28XVBW
You can do LinAlg concurrently with calculus.
Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) https://www.amazon.com/dp/0538735457/ref=cm_sw_r_cp_api_dNZdzb7TPVBJJ
You can do this after calculus. Or you can also get a book that's specific to statistics (be sure to get the one requiring calc, as some are made for non-science/eng students and are pretty basic) and then another book specific to probability. This one combines the two.
Probability and Statistics for Engineering and the Sciences https://www.amazon.com/dp/1305251806/ref=cm_sw_r_cp_api_QXZdzb1J095Y1
Differential Equations with Boundary-Value Problems, 8th Edition https://www.amazon.com/dp/1111827060/ref=cm_sw_r_cp_api_sSZdzbDKD0TQ9
After doing all of the above, you'd have the equivalent most engineering majors have to take. You can go further by exploring partial diff EQs, real analysis (which is usually required by math majors for more advanced topics), and an intro to higher math which usually includes logic, set theory, and abstract algebra.
If you want to get into higher math topics you can use this fantastic book on the topic:
This book is also available for free online, but since you won't have internet here's the hard copy.
Book of Proof https://www.amazon.com/dp/0989472108/ref=cm_sw_r_cp_api_MUZdzbP64AWEW
From there you can go on to number theory, combinatorics, graph theory, numerical analysis, higher geometries, algorithms, more in depth in modern algebra, topology and so on. Good luck!
Linear Algebra can be of different levels of difficulty:
Book of proof is a more gentle introduction to proofs then How to Prove it.
​
No bullshit guide to linear algebra is a gentle introduction to linear algebra when compared to the popular Linear Algebra Done Right.
​
An Illustrated Theory of Numbers is a fantastic introduction book to number theory in a similar style to the popular Visual Complex Analysis.
The No-Bullshit Guide to Linear Algebra by Ivan Savov.
I would recommend Physics from Symmetry as it builds almost everything from the ground up and does an amazing job of explaining things clearly.
From there, to go into more detail, you can try QFT for the gifted amateur or QFT and the standard model by Schwartz.
Here you go:
> Calculus is the foundation for modern math. Always a good thing to have.
> Linear Algebra is the foundation for 3d mathematics in games. Things such as perspective projection, arbitrary rotation, and more exotic things such as quaternions come around here.
> Essential Math for Games is a most excellent book that, after having built your mathematical foundation through the previous two books, provides you pretty much everything you need to know about making a 3d renderer, which is probably one of the most educational experiences that you can undergo in game development.
This is how I taught myself http://math.stanford.edu/~vakil/725/course.html
This book is a great help too http://www.amazon.com/Introduction-Homological-Cambridge-Advanced-Mathematics/dp/0521559871
Good luck, there is A LOT for you to learn.
you're going to struggle with mathematics until you get a better handle on stuff like proofs. it gets a little better once you've paid your dues.
book wise i'd recommend Linear Algebra and Its Applications by Peter Lax really just because i'm a huge fan of his. additionally, i'd recommend reading (or trying to read) every book you can get your hands on.
Usual hierarchy of what comes after what is simply artificial. They like to teach Linear Algebra before Abstract Algebra, but it doesn't mean that it is all there's to Linear Algebra especially because Linear Algebra is a part of Abstract Algebra.
Example,
Linear Algebra for freshmen: some books that talk about manipulating matrices at length.
Linear Algebra for 2nd/3rd year undergrads: Linear Algebra Done Right by Axler
Linear Algebra for grad students(aka overkill): Advanced Linear Algebra by Roman
Basically, math is all interconnected and it doesn't matter where exactly you enter it.
Coming in cold might be a bit of a shocker, so studying up on foundational stuff before plunging into modern math is probably great.
Books you might like:
Discrete Mathematics with Applications by Susanna Epp
Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers
Building Proofs: A Practical Guide by Oliveira/Stewart
Book Of Proof by Hammack
Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al
How to Prove It: A Structured Approach by Velleman
The Nuts and Bolts of Proofs by Antonella Cupillary
How To Think About Analysis by Alcock
Principles and Techniques in Combinatorics by Khee-Meng Koh , Chuan Chong Chen
The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!) by Carol Ash
Problems and Proofs in Numbers and Algebra by Millman et al
Theorems, Corollaries, Lemmas, and Methods of Proof by Rossi
Mathematical Concepts by Jost - can't wait to start reading this
Proof Patterns by Joshi
...and about a billion other books like that I can't remember right now.
Good Luck.
he's okay.
just don't come into class late.
the textbook for linear algebra wasn't great
some additional resources:
https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
https://open.math.uwaterloo.ca/2?gid=395
http://joshua.smcvt.edu/linearalgebra/
https://www.amazon.ca/dp/3319307657
https://www.math.brown.edu/~treil/papers/LADW/LADW.html
https://www.amazon.ca/dp/0130084514/
Since you are a practicing engieer with plenty of experience, I will suggest the right way to learn rather than the speed-of-the-internet , show-me-a-web-page way to acquire jargon.
Buy and read textbooks.
Start with Numerical Recipes by Press et al (Link 1). It has a couple of chapters on optimization and some very VERY excellent discussion. It will teach you the way academics formulate these problems, and how they solve them today.
Then read Gill, Murray, and Wright "Practical Optimization" (Link 2).
Next comes Roger Fletcher, "Practical Methods of Optimization". This book has been published two different ways: as a single volume, and also split into two volumes. Since Amazon Used Books sells the two volumes for considerably less money, I recommend that path: (Link 3) and (Link 4) .
After you have read those books, you will be able to appreciate the following paragraph:
I myself have found, in practice, that some of the old 1960's approaches to optimization work DELIGHTFULLY WELL on 2015 real world engineering problems, using 2015 computer power. In fifty years the problems have become 10,000 times more difficult and the computers have become 2^(50/3) times more powerful. The computers are winning the tug of war.
Make an honest try to solve your problem using no-derivative unconstrained optimizers, plus penalty functions or barrier functions for the constraints. I think you will be very pleasantly surprised. If you have honestly done your best and tried your hardest to get this to work, and failed, then your fallback is to implement the full stochastic miasma. Start with the TOMS paper by Corana, Marchesi, Martini, and Ridella. It is the most engineering-results oriented discussion I know of. If you are a masochist, try (just try!) to read the various publications and white papers by Lester Ingber. You will regret it.
I'm no physicist. My degree is in computer science, but I'm in a somewhat similar boat. I read all these pop-science books that got me pumped (same ones you've read), so I decided to actually dive into the math.
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Luckily I already had training in electromagnetics and calculus, differential equations, and linear algebra so I was not going in totally blind, though tbh i had forgotten most of it by the time I had this itch.
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I've been at it for about a year now and I'm still nowhere close to where I want to be, but I'll share the books I've read and recommend them:
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I'm available if you want to PM me directly. I love talking to others about this stuff.
For calc MATH 1300/1014 and 1310/1014 you need , buy it new from the bookstore cause you will need the online code for assignments also it’s useful for calc 3 if you wanna take that. Man Wong is a good prof I had him for both 1300 and 13010
For EECS 1019 you need it’s not that useful and PDF can be found online for free and no online assignments so no need to buy it new. I had Zhihua Chang he’s a new prof but really nice but his lectures are boring. Trev tutor on YouTube is really helping with the course.
For Math 1025/1021 you need I found the book helpful but unlike calc some profs tend not to use this book so I’d hold out of buying it but most profs use lyryz which is an online assignment program so you will need to buy that. I had Paul Skoufranis, amazing prof but had tests. The book is also useful for linear 2 but again depend if the prof uses it
For EECS 1022 you need
It’s a good book and the guy you wrote it teaches the class.
PM if you have any other questions
Hey, I have found a nice text book called no bullshit guide with math and physics.
https://www.amazon.ca/No-bullshit-guide-math-physics/dp/0992001005
No bullshit guide to math and physics: Ivan Savov ... - Amazon.ca
So far it's the best I've ever read. The author made another one only for linear algebra as well.
https://www.amazon.ca/No-bullshit-guide-linear-algebra/dp/0992001021
No bullshit guide to linear algebra: Ivan Savov ... - Amazon.ca
Schaum's Outlines - Linear Algebra provides a lot of useful proofs and theory behind abstract vector spaces if that's the kind of stuff you need. It also goes into Hermition forms and various complex applications
Without knowing anything else about you, the 3 best places to start with data science, in my most humble opinion, are here, here and finally here.
Strang's course is a great introduction. I feel that his explanations provide great intuition into how and why certain methods in linear algebra work.
Here is a link to the OCW course page: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm
And the book website: http://math.mit.edu/~gs/linearalgebra/
By the way, used copies of previous editions of the book can be obtained at a significant discount: http://www.amazon.com/Linear-Algebra-Its-Applications-3rd/dp/0155510053/ref=sr_1_4?s=books&ie=UTF8&qid=1459432805&sr=1-4&keywords=Introduction+to+Linear+Algebra%2C+Third+Edition
People seem to really like Fraleigh. I can't vouch for it. I've never had a good standalone linear algebra book.
While I agree with your comments on the importance of the conceptual side of linear algebra, I really don't like Axler's book. It reads, to me, as `here is the only perspective to take on this issue, read my proof and that is all.' So, you might augment it with something like Gil Strang's Linear Algebra and Its Applications.
>Peter Lax turned out to be too concise for me.
You prefer a math text that rambled on and doesn't get to the point? I would think concision is a good thing in a text.