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Read and work through <em>Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach</em> by Hubbard and Hubbard - can be bought pretty cheaply used. It's a book that starts at introductory linear algebra and infinite series and ends by covering vector calculus with a treatment of differential manifolds.
Greatest introductory university maths book I've ever taught from or read. Has enough material to take you through at least 3 academic semesters of work if you go through it slowly and will put you in a great position to understand a more rigorous analytical text like Walter Rudin's Principles of Mathematical Analysis upon completion.
I'm a big fan of Sheldon Axler's Linear Algebra Done Right though it tends to be a might more towards the theory side than applications really. As a physics (assuming undergrad) I think you'll be doing more applied stuff.
If you can lookup the website/syllabus from a previous semester of the course to see what textbook they used or even the main topics the course focuses on, you can get a bit of a jump start on something more focused.
With all the uncertainty about opening and how classes are being run, an announcement of the text through official challenges might be delayed. Back in my day, you had to rely on what info had been sent to the Uni bookstore if you wanted to know the textbook before getting the syllabus on the first day of class. You might try emailing the professor. She might be able to tell you the textbook sooner and/or suggest some additional resources that might be helpful.
According to amazon on Hubbard and Hubbard:
>Using a dual-presentation that is rigorous and comprehensive--yet exceptionally "student-friendly" in approach--this text covers most of the standard topics in multivariate calculus and a substantial part of a standard first course in linear algebra. It focuses on underlying ideas, integrates theory and applications, offers a host of pedagogical aids, and features coverage of differential forms. There is an emphasis on numerical methods to prepare students for modern applications of mathematics.
That sounds amazing. I want a do-over so I can do it that way.
If anything NTU CS/CE courses would be, they are not math heavy. They are simply a regurgitation of math mechanics passed down by PYPs from years to years. That being said, try these resources out:
Math Videos:
-3blue1brown (Essence of Linear Algebra is solid series, u may check out his complex number video as well)
-Numberphile and maybe Computerphile(some nerd stuffs)
- Khan Academy (of course)
Some books:
- Linear Algebra Done Right (link)
- The matrix cookbook
Last but not least, even if you don't like math, don't screw up your year 1 math mods, as they are the foundation for almost every buzz modules u gotta learn in the future (if you plan to research too).
-CE Grad-
The fourth edition of this book is good:
https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/dp/0130084514
Pdfs of it are available online (at libgen in particular).
I took a class in college called "Scientific Revolutions" about the shifts in scientific paradigm throughout history. One of the textbooks in the course was The Structure of Scientific Revolutions by Thomas S. Kuhn. It was rather enjoyable and extremely informative. I wish I kept my copy. Amazon has a bunch of related suggestions as well. (https://www.amazon.com/Structure-Scientific-Revolutions-Thomas-Kuhn/dp/0226458083) Perhaps this will spark some ideas?
This is the linear algebra textbook I had. Loved it. It's very theory heavy and proof based.
For example: a bunch of my peers just now realized, while studying for the GRE, that matrix multiplication is defined the way it is because it's just a composition of linear transformations, and that's the way you preserve the right properties (sorry about vagueness, it's been a little while since that class). That kind of intuition was built into me by the time I got to the dry stuff, so it was much more fun.
https://www.amazon.com/Quantum-Mechanics-Theoretical-Leonard-Susskind/dp/0465062903
book on quantum mechanics
Yeah I find this comes up for me a lot. I don't have a science background, dropped physics in highschool, can't do math without a spreadsheet to save my damn life.
That being said, a couple of these authors here were a huge jumping off point for me to become excited and energized at the concept; they may not go into the nuts and bolts of things but in terms of illuminating concepts and translating nearly undefinable ideas to a brain like mine it's essential.
I don't know, I think people like to pass judgement, but I find with QM there's as much art to the explanations as science, at least when you're starting to learn; you can hear the same explanation ten times, and then the right author comes along and number 11 is the one that breaks the concept wide open for you.
For what it's worth, that Halpern book I think is pretty well regarded as a historical account, I think the Carroll one is also good. Both little books are meant to be summations.
If you're anything like me and want to go "next level" on this stuff, I started with the Theoretical Minimum by Susskind and Friedman. It seems to hold up to a lot of scrutiny and is a text that appears in first year classes a lot. I'd be lying if I told you I understood it and it didn't kick my ass, but it may be what you're looking for as a next foray.
Finally Rovelli is a damn treasure and his face should be on money. Fight me.
You believe Tesla sales are exponential? yeah. It’s time for you to pack it up and and order this book No bullshit guide to linear algebra https://www.amazon.com/dp/0992001021/ref=cm_sw_r_cp_api_glt_fabc_EBVYMVAYMHS6CG8PC6H0
<u>The Structure of Scientific Revolutions</u> could fall out of the sky and land square on his head -- he would just call it an ad hominem.
As others have said, no need for an actual credit course. I think Strang's course is good as well as LAFF.
I also found the No BS book good as well (you can find it free online somewhere usually):
https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0992001021
This sub will be overwhelmingly supportive of any idea you have (which is typically a very good thing), but it sounds like you may benefit a lot from reading books meant for an audience of people without a background in physics before you jump into this. This one is great, and there are other books with fewer equations you might also like. Getting a physics degree will require a very strong math background, and on top of that it’ll be two years or so of slogging along before you get to the sorts of things you’re envisioning (quantum mechanics, particle physics). If you’re worried your interest may be gone by then, it may be good to step back and do more thinking first.
Susskind’s book (Quantum Mechanics: The Theoretical Minimum https://www.amazon.com/dp/0465062903/ref=cm_sw_r_cp_api_glc_fabc_n5f9FbT9VTEFY ) and the corresponding free lectures which cover the same material (https://theoreticalminimum.com/courses/quantum-mechanics/2012/winter).
I also took a course on the subject which used Griffith’s text, but I feel I got more out of The Theoretical Minimum, honestly.
Just to add to this, section 3.F of Linear Algebra Done Right gives a great discussion of dual maps and how they work. It has an accompanying video on youtube.
I always wondered what was on the cover of the Theoretical Minimum books, it's a meccano set! Also I highly recommend the books if you are competent in advanced mathematics and want to learn more about theoretical physics.
I think you should read this if you're interested in Quantum Mechanics.
Otherwise, please quit talking about quantum mechanics like it's magic.
Like 50 on amazon but could also try Abebooks and see if there's a cheaper used or international copy.
I recommend Leonard Susskind's Quantum Mechanics: the Theoretical Minimum. It's a serious, non-dumbed-down lectures for interested layperson. After that, it depends on what you would like to know about quantum computing (algorithms? implementations? error correction? foundations?) and on what level.
This is not EXACTLY what you are looking for, but it's a great read that will provide an instereting perspective on how science has "evolved" over the generations: The Structure of Scientific Revolutions by Thomas S. Kuhn
https://www.amazon.com/Structure-Scientific-Revolutions-Thomas-Kuhn/dp/0226458083
> Is the Friedber, etc. Linear Algebra book one that eschews matrices and uses Bra-Ket notation?
Not at all. They do not use Bra-Ket notation, and while most of the material is phrased in terms of linear transformations, matrices are used extensively.
> Is there somewhere we can learn more about that book? The publishers page and the Amazon page aren't very helpful.
What do you want to know that isn't covered on the Amazon page or the table of contents?
I really like this book by Gilbert Strang. It's a little expensive, so if you want to save a few bucks you could look for the third edition.
It's not necessarily material prerequisites. What you need going into it is a somewhat developed sense of mathematical maturity. You need to be comfortable with proofs (usually you can develop this skill by going through the stuff that you do need, like logic, sets and arithmetic) and also should be comfortable with a certain level of abstraction.
As a resource, the book Linear Algebra Done Right is a good, solid introduction to the field.
Strang's book looks nice, and I noticed he has accompanying lectures which is good. I found this version, which is more or less in my price range but appears a bit outdated. https://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gilbert/dp/0980232716
There are a lot of good linear algebra books. For example https://www.amazon.com/gp/aw/d/0387982582/ref=mp_s_a_1_2?ie=UTF8&amp;qid=1477260449&amp;sr=8-2&amp;pi=SL75_QL70&amp;keywords=linear+algebra+done+right and https://www.amazon.com/Linear-Algebra-Its-Applications-4th/dp/0030105676 . The latter book's author's lectures are on ocw.mit.edu and he does a great job of explaining the topic.
I learned about data structures/algorithms on my own and didn't use any textbooks. But for linear algebra, I found this book to be very helpful: https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/dp/0130084514
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.
I've heard pretty good things about Quantum Mechanics: The Theoretical Minimum by Leonard Susskind. I imagine it also has the added advantage of matching the Standford course he did that can be found on YouTube
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.