Reddit reviews Linear Algebra Done Right (Undergraduate Texts in Mathematics)
We found 19 Reddit comments about Linear Algebra Done Right (Undergraduate Texts in Mathematics). Here are the top ones, ranked by their Reddit score.
Springer
Pick up mathematics. Now if you have never done math past the high school and are an "average person" you probably cringed.
Math (an "actual kind") is nothing like the kind of shit you've seen back in grade school. To break into this incredible world all you need is to know math at the level of, say, 6th grade.
Intro to Math:
These books only serve as samplers because they don't even begin to scratch the surface of math. After you familiarized yourself with the basics of writing proofs you can get started with intro to the largest subsets of math like:
Intro to Abstract Algebra:
There are tons more books on abstract/modern algebra. Just search them on Amazon. Some of the famous, but less accessible ones are
Intro to Real Analysis:
Again, there are tons of more famous and less accessible books on this subject. There are books by Rudin, Royden, Kolmogorov etc.
Ideally, after this you would follow it up with a nice course on rigorous multivariable calculus. Easiest and most approachable and totally doable one at this point is
At this point it's clear there are tons of more famous and less accessible books on this subject :) I won't list them because if you are at this point of math development you can definitely find them yourself :)
From here you can graduate to studying category theory, differential geometry, algebraic geometry, more advanced texts on combinatorics, graph theory, number theory, complex analysis, probability, topology, algorithms, functional analysis etc
Most listed books and more can be found on libgen if you can't afford to buy them. If you are stuck on homework, you'll find help on [MathStackexchange] (https://math.stackexchange.com/questions).
Good luck.
I found Axler's Linear Algebra Done Right to be a very easy to digest introduction to abstract linear algebra.
I think the most important part of being able to see beauty in mathematics is transitioning to texts which are based on proofs rather than application. A side effect of gaining the ability to read and write proofs is that you're forced to deeply understand the theory of the math you're learning, as well as actively using your intuition to solve problems, rather than dry route calculations found in most application based textbooks. Based on what you've written, I feel you may enjoy taking this path.
Along these lines, you could start of with Book of Proof (free) or How to Prove It. From there, I would recommend starting off with a lighter proof based text, like Calculus by Spivak, Linear Algebra Done Right by Axler, or Pinter's book as you mentioned. Doing any intro proofs book plus another book at the level I mentioned here would have you well prepared to read any standard book at the undergraduate level (Analysis, Algebra, Topology, etc).
Yes!
If you don't know any calculus Stewart Calculus is the typical primer in colleges. Combine this with Khan Academy for easy mode cruise control.
After that, you want to look at The Big Orange Book, which is essentially the bible for undergrad astrophysics and 100% useful beyond that. This book could, alone, tell you everything you need to know.
As for other topics like differential equations and linear algebra you can shop around. I liked Linear Algebra Done Right for linear personally. No recommendations from me on differential equations though, never found a book that I loved.
If it's too simple, stop wasting your time and start reading something more your speed. Say, Linear Algebra Done Right by Axler. If you're still unimpressed, try Advanced Linear Algebra by Roman. If you can solve most problems in this book cold, just drop everything you're doing now and walk straight into the nearest best grad school.
If you are still an undergrad and your school offers a "how to prove stuff and how to think about abstract maths" course take it anyway. No matter how far along you have come.
An example text for such a course is this one:
https://www.amazon.com/Introduction-Mathematical-Reasoning-Numbers-Functions/dp/0521597188
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As for Linear Algebra (the most useful part of all higher mathematics for sure (R/math: if you disagree, fight me on this one...i'll win) ) I will tell you i learned a LOT from these two texts:
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https://www.amazon.com/Linear-Algebra-Introduction-Mathematics-Undergraduate/dp/0387940995
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https://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/3319110799/ref=pd_lpo_sbs_14_img_0?_encoding=UTF8&psc=1&refRID=APH3PQE76V9YXKWWGCR9
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You'll usually find the following recommended:
I've personally used Friedberg's text, and I found it to be pretty well written.
Where I teach they use Linear Algebra by Lay for the introductory class. I'm not sure what level you need but Linear Algebra Done Right is also commonly recommended; could be more abstract than what you need?
This webpage has a solid list of recommended textbooks: https://mathblog.com/mathematics-books/
For Linear Algebra, Linear Algebra Done Right (3rd Ed.).
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.
Book of proof is a more gentle introduction to proofs then How to Prove it.
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No bullshit guide to linear algebra is a gentle introduction to linear algebra when compared to the popular Linear Algebra Done Right.
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An Illustrated Theory of Numbers is a fantastic introduction book to number theory in a similar style to the popular Visual Complex Analysis.
A matrix "times" a vector is a vector. This is how the matrix behaves as a linear transformation. (Hence why everyone is telling you you're talking about linear transformations.) To get a matrix to behave like a tensor, you need to compare it to two vectors to get a number, in the way I outlined above.
I would suggest that you focus on linear algebra vocabulary and notation. It is easy to get things confused without something solid to fall back on. I suggest reading through this cheap book, and working on the problems.
EDIT: Probably shouldn't link pirated copies of things.
Not much, the nice thing for upper math courses is they do a good job of building up from bare bones. If you have some linear algebra and a multivariable calc course you should be good. The big requirement is however mathematical maturity. You should be able to read, understand, and write proof.
A very basic intro to proofs course is usually taught to first year math students, this covers set notations, logic, and some basic proof techniques. A common reference is "How to prove it: a structured approach", I learned from Intro to mathematical thinking. The latter isn't as liked, it does seem to cover some material that I think should be taught early. A lot of classical number theory and algebra, for example fundamental theorem of arithmetic, and Fermat's little (not last) theorem are proven. Try to find a reference for that stuff if you can.
It's really important to do a proof based linear algebra class. It helps build the maturity I mentioned and will make life easier with topology. But even more importantly teaching linear algebra in a more abstract way is important for a physics undergrad as it can serve as a foundation for functional analysis, the theory upon which quantum mechanics is built. And in general it is good to stop thinking of vectors as arrows in R^n as soon as possible. A great reference is Axler's LADR.
Again not strictly required, but it helps build maturity and it serves as a good motivation for many of the concepts introduced in a topology class. You will see the practical side of compact sets (namely they are closed and bounded sets in R^(n)), and prove that using the abstract definition (which is the preferred one in topology). You will also prove some facts about continuous functions which will motivate the definition of continuity used in topology, and generally seeing proofs about open sets will show you why open sets are important and why you may wish to look at spaces described only by their open sets (as you will in topology). The reference for real analysis is typically Rudin, but that can be a little tough (I'm sorry, I can't remember the easier book at the moment)
Edit: I will remove this as it doesn't meet the requirements for an /r/askscience question, we usually answer questions about the science rather than learning references. If you feel my answer wasn't comprehensive enough feel free to ask on /r/math or /r/learnmath
I keep seeing this book recommended in a lot of places. How is it different from the one by Axler and one by Roman?
I like this book a lot: http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/3319110799/
The professor who assigned it preferred Linear Algebra Done Wrong but he's a robot.
Like 50 on amazon but could also try Abebooks and see if there's a cheaper used or international copy.
I don't know much about AI, though I do know that (there's a theme, here) linear algebra gets a starring role. So, if you're currently enjoying linear algebra, continue with that. Axler is frequently recommended, if you want a textbook to go through.
After that it's really up to you what you want to go for next, since you have many paths available. Sipser is a great intro to theoretical CS, but, again, don't spend $200 on it. Try to find it in a library, or use something like this to find a much cheaper international edition.
Edit: Forgot to mention, CLRS is the standard for algorithms, but I'm not sure how useful it is as a primary source for learning. Maybe try to borrow a copy to see if you like it.
What do you want to do, though? Is your goal to read math textbooks and later, maybe, math papers or is it for science/engineering? If it's the former, I'd simply ditch all that calc business and get started with "actual" math. There are about a million books designed to get you in the game. For one, try Book of Proof by Richard Hammack. It's free and designed to get your feet wet. Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand/Polimeni/Zhang is my favorite when it comes to books of this kind. You'll also pick up a lot of math from Discrete Math by Susanna Epp. These books assume no math background and will give you the coveted "math maturity".
There is also absolutely no shortage of subject books that will nurse you into maturity. For example, check out [The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Grinberg](https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Princeton/dp/0691172935/ref=sr_1_1?ie=UTF8&qid=1486754571&sr=8-1&keywords=real+analysis+lifesaver() and Book of Abstract Algebra by Pinter. There's also Linear Algebra by Singh. It's roughly at the level of more famous LADR by Axler, but doesn't require you have done time with lower level LA book first. The reason I recommend this book is because every theorem/lemma/proposition is illustrated with a concrete example. Sort of uncommon in a proof based math book. Its only drawback is its solution manual. Some of its proofs are sloppy, messy. But there's mathstackexchange for that. In short, every subject of math has dozens and dozens of intro books designed to be as gentle as possible. Heck, these days even grad level subjects are ungrad-ized: The Lebesgue Integral for Undergraduates by Johnson. I am sure there are such books even on subjects like differential geometry and algebraic geometry. Basically, you have choice. Good Luck!
Sorry, I went on vacation and totally blanked about posting these for you!
Anyway, here are some books
Linear Algebra Done Right (Undergraduate Texts in Mathematics) https://www.amazon.com/dp/3319110799/ref=cm_sw_r_cp_api_1L8Byb5M5W9D3
This one is actually for analysis but depending on your appetite, it might help greatly with the proof side of your class. You can buy it here: Counterexamples in Analysis (Dover Books on Mathematics) https://www.amazon.com/dp/0486428753/ref=cm_sw_r_cp_api_GS8BybQWYBFXX
But there's also a PDF hosted here: http://www.kryakin.org/am2/_Olmsted.pdf