Reddit reviews Linear Algebra, 4th Edition

I think the advice given in the rest of the thread is pretty good, though some of it a little naive. The suggestion that differential equations or applied math somehow should not be of interest is silly. A lot of it builds the motivation for some of the abstract stuff which is pretty cool, and a lot of it has very pure problems associated with it. In addition I think after (or rather alongside) your initial calculus education is a good time to look at some other things before moving onto more difficult topics like abstract algebra, topology, analysis etc.

The first course I took in undergrad was a course that introduced logic, writing proofs, as well as basic number theory. The latter was surprisingly useful as it built modular arithmetic which gave us a lot of groups and rings to play with in subsequent algebra courses. Unfortunately the textbook was god awful. I've heard good things about the following two sources and together they seem to cover the content:

How to prove it

Number theory

After this I would take a look at linear algebra. This a field with a large amount of uses in both pure and applied math. It is useful as it will get you used to doing algebraic proofs, it takes a look at some common themes in algebra, matrices (one of the objects studied) are also used thoroughly in physics and applied mathematics and the knowledge is useful for numerical approximations of ordinary and partial differential equations. The book I used Linear Algebra by Friedberg, Insel and Spence, but I've heard there are better.

At this point I think it would be good to move onto Abstract Algebra, Analysis and Topology. I think Farmerje gave a good list.

There's many more topics that you could possibly cover, ODEs and PDEs are very applicable and have a rich theory associated with them, Complex Analysis is a beautiful subject, but I think there's plenty to keep you busy for the time being.

If you are serious about learning, Linear Algebra by Friedberg Insel and Spence, or Linear Algebra by Greub are your best bets. I love both books, but the first one is a bit easier to read.

The course I took as an undergraduate used Friedberg, Insel and Spence. I remember liking it fine, but it's insultingly expensive. Find it in a library or get a used copy if you can. If you're looking for a bargain, it can't hurt to try Shilov. He's Russian, so the book is very terse, but covers a lot of ground.

A graph theory project! I just started today (it was assigned on Friday and this is when I selected my topic). I’m on spring break but next month I have to present a 15-20 minute lecture on graph automorphisms. I don’t necessarily have to, but I want to try and tie it in with some group theory since there is a mix of undergrads who the majority of them have seen some algebra before and probably bored PhD students/algebraists in my class, but I’m not sure where to start. Like, what would the binary operation be, composition of functions? What about the identity and inverse elements, what would those look like? In general, what would the elements of this group look like? What would the group isomorphism be? That means it’s a homomorphism with a bijective function. What would the homomorphism and bijective function look like? These are the questions I’m trying to get answers to.

Last semester I took a first course in Abstract Algebra and I’m currently taking a follow up course in Linear Algebra (I have the same professor for both algebra classes and my graph theory class). I’m curious if I can somehow also bring up some matrix representation theory stuff as that’s what we’re going over in my linear algebra class right now.

This is the textbook I’m using for my graph theory class: Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/1846289696?ref=yo_pop_ma_swf

Here are the other graph theory books I got from my library and am using as references: Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/3662536218?ref=yo_pop_ma_swf

Modern Graph Theory (Graduate Texts in Mathematics) https://www.amazon.com/dp/0387984887?ref=yo_pop_ma_swf

And for funsies, here is my linear algebra text: Linear Algebra, 4th Edition https://www.amazon.com/dp/0130084514?ref=yo_pop_ma_swf

But that’s what I’m working on! :)

And I certainly wouldn’t mind some pointers or ideas or things to investigate for this project! Like I said, I just started today (about 45 minutes ago) and am just trying to get some basic questions answered. From my preliminary investigating in my textbook, it seems a good example to work with in regards to a graph automorphism would be the Peterson Graph.

A First Course in Graph Theory by Chartrand and Zhang

Combinatorics: A Guided Tour by Mazur

Discrete Math by Epp

For Linear Algebra I like these below:

Lecture Notes by Tao

Linear Algebra: An Introduction to Abstract Mathematics by Robert Valenza

Linear Algebra Done Right by Axler

Linear Algebra by Friedberg, Insel and Spence

I am not sure that a pure math textbook is what you want. A lot of the problems that mathematicians think about may not be what you need. Let's take functional analysis for example. Most textbooks focus on bounded/ compact operators, and they only have one chapter at the end dedicated to unbounded operators. Unfortunately, the derivative (momentum) is an unbounded operator, so the part that has the least detail is what you need.

I would recommend a "math for physics students" book. A nice book that tries to paint the intuitive idea of most branches of math relevant to physics (and then some) and show you how to calculate is Goldbart and Stone's book, which they have made freely available online. This book assumes familiarity with linear algebra. If you are weak on this subject, I would highly recommend the book by Friedberg, Insel, and Spence. This is a more traditional math textbook, but it gets you very comfortable with the details of linear algebra (except for tensor products, but you should understand their construction with this background).

You'll usually find the following recommended:

• Axler's Linear Algebra Done Right
  
• Friedberg's Linear Algebra
  
  I've personally used Friedberg's text, and I found it to be pretty well written.

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/

Personally, I would take the time to read them both. A strong linear algebra background will be very helpful in ML. Its especially useful if you want to expand out a little bit more into other areas of signal processing. Make sure you also spend some time getting a good background in probability and statistics.

EDIT: I haven't actually read Axler's book but me and some of my friends are partial to this book.

Almost forgot to reply. Linear Algebra by Friedberg is one of the more mathematically rigorous texts I've seen for undergraduates. My school used it in the honors linear algebra course. I think you'll find that it covers most of what you need. Hope it helps (if you can find it at the library or something).

Linear Algebra (Fourth Edition) by Stephen H. Friedberg

EDIT: I just realized that you already mentioned this book in your comments. I used this book in my upper level course too and it was a real treat.

Linear algebra by Friedberg, Insel and Spence
http://www.amazon.ca/Linear-Algebra-Edition-Stephen-Friedberg/dp/0130084514

I'm a huge fan of linear algebra. My favorite book for a theoretical understanding is this book. A pdf copy of the solutions manual can be found here.

I've been reviewing linear algebra recently and found that I like my old textbook much more now than when I took the course.

https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/dp/0130084514

Its not very good on visual intuition but there are a lot of examples. You could supplement it with the 3blue1brown series for that.

It covers a lot of the topics i needed to review for group theory. For example, it covers dual spaces and the transpose in the second chapter (it stresses invariant subspaces, projection operators, bilinear forms- essentials for group theory.). It's clear, concise and seems popular. One of the prof.s featured on Numberphile said he used it for his course. It might not be a good first linear algebra book for some people. But check it out.

Working through Griffiths is a good idea, but I strongly suggest working through an abstract linear algebra book before you do anything else. It will make your life much better. Doing some of Griffiths in advance might make your homework a bit easier, but you'll be repeating material when you could be learning new things. And learning real linear algebra will benefit you in pretty much every class.

I recommend this book as your primary text and this one for extra problems and and a second opinion.

There is no "one fastest" method to solving them.

Systems of equations are systematic, and it really depends on the problem. The only real way to learn about this is to take a course in Linear Algebra. That is all about systems of linear equations.

But these show up all of the time, here is what I usually do:

If I just need one of the 2-3 variables, Cramer's Rule is a good way to test solvability and extract a single value.

On normal 2x2 systems, I usually do a quick determinant/matrix inverse. Checks the rank as well as the det, and it is always going to work.

On 3x3 or higher systems, it depends. This is why Linear Algebra is important.

Supposedly Linear Algebra Done Right is a good book on the subject, so if you're interested there is one way. The book I used was A custom edition of this one. I thought it was very good as well.

this is the book: http://www.amazon.com/Linear-Algebra-Edition-Stephen-Friedberg/dp/0130084514