Reddit reviews Linear Algebra and Its Applications, 4th Edition

I think it is silly that this requires much of an explanation. I recall this question being asked in a fucking linear algebra book! http://www.amazon.com/Linear-Algebra-Applications-Gilbert-Strang/dp/0030105676/ref=dp_ob_title_bk

I haven't used it myself, but you might appreciate Gilbert Strang's Linear Algebra and Its Applications.

My favorite linear algebra text is Paul Halmos' Finite-Dimensional Vector Spaces. As far as textbooks go, it's cheap, and it's written very well. It does expect a certain amount of mathematical maturity (a familiarity with proof techniques).

Gilbert Strang's book, Linear Algebra and Its Applications might be better for someone looking into applied mathematics than Halmos'. He makes frequent references to applications and uses geometric arguments fairly liberally. It is 3 times the price of Halmos' text as well, but I'm sure your university library has a copy or two.

I agree with urish, that learning linear algebra fairly well, especially considering the fields that you're interested in.

Hope this helps.

Wow, do you go to some school where mathochism is cool? This is not a junior-level course in my academic worldview. It was not too too long ago that linear algebra was almost exclusively a graduate course. It was pushed down to the undergraduate level because of its extreme usefulness in ODEs and DSP, among other things. Undergraduates did not get that much smarter, instead the curriculum for linear algebra just got that much more streamlined. Your prof is either ignorant of or doesn't care about that evolution. If this is supposed to be a "regular" class, then you might voice a complaint to the chairperson of the department. Junior level courses usually are the introduction to mathematical rigor, not the launchpad for the study of Lie Algebras or other specialized areas. However if you are in an honors class or a hardcore mathematics school, you'll just have to strap in and enjoy the ride.

So here's some rope. All my references are old because I am old(ish). However, you can probably do better with keyword searches in Wikipedia and WolframAlpha based on your lecture notes. Do something like a mind map of the connections. The only thing you are missing online will be problems.

Go to your library and get Linear Algebra and Its Applications. I learned from an earlier edition of the book, but I can't imagine it getting worse. The people who hate the book are the ones who didn't do the exercises. If you stick with it, it is very cool and things start to build and just make sense. Strang is an excellent, excellent expositor, but you have to be a big picture person. He also tells you exactly what the core of the book is, The Fundamental Theorem of Linear Algebra. Grok that and linear algebra is your oyster, e.g., Gram-Schmidt will seem like an obvious thing. (And wouldn't you know, a reference on that Wikipedia page is to a paper by Strang on just that(pdf).)

If you can put up with older notation, you will find a lot in the famous book by Halmos, Finite Dimensional Vector Spaces.

A lot of this carries through to graduate algebra and functional analysis, so find whatever texts your graduate courses require and check their indices. From the above it sounds like your prof is trying to hit all the connections to other areas.

This next book will probably not help you, but it is just crazy enough to make me think you may find some of your professor's thoughts hidden there, Mathematical Physics by Geroch. You don't have time to learn category theory, but his exposition ends up at the spectral theorem, I seem to recall. Seeing another presentation of those powerful theorems might be illuminating. (It's a beautiful book, but I've never heard of it being used in a class.)

If you don't have MATLAB, get a (free?/cheap?) student edition and play with it for "real" examples of what you are doing. Going through the Theorem-Proof process never worked for me with things like linear algebra: Seeing how you can pull things apart and put them back together is what makes the power of linear algebra come alive and gives you some motivation.

The last piece of advice is not a guarantee, but has always worked for me when in a draconian course: Drill yourself on your old tests and quizzes and homework. When everyone is failing and the final comes around, chances are good (for various reasons, including pity and laziness) that the earlier exams are almost exactly recapitulated. Use your prof's office hours to go over the subtleties of the exam problems. If you are engaged with the material, the chances are good that he will extend the scope of discussion and pull in examples from the current lectures. That's a very handy insight to have.

If the notes of your class do make it online, please think of linking it back here. I'm curious as to how deep this course is since it is pretty wide.

That helps a little. I'm not too familiar with that world (I'm a physics major), but I took a look at a sample civil engineering course curriculum. If you like learning but the material in high school is boring, you could try self-teaching yourself basic physics, basic applied mathematics, or some chemistry, that way you could focus more on engineering in college. I don't know much about engineering literature, but this book is good for learning ODE methods (I own it) and this book is good for introductory classical mechanics (I bought and looked over it for a family member). The last one will definitely challenge you. Linear Algebra is also incredibly useful knowledge, in case you want to do virtually anything. Considering you like engineering, a book less focused on proofs and more focused on applications would be better for you. I looked around on Amazon, and I found this book that focuses on applications in computer science, and I found this book focusing on applications in general. I don't own any of those books, but they seem to be fine. You should do your own personal vetting though. Considering you are in high school, most of those books should be relatively affordable. I would personally go for the ODE or classical mechanics book first. They should both be very accessible to you. Reading through them and doing exercises that you find interesting would definitely give you an edge over other people in your class. I don't know if this applies to engineering, but using LaTeX is an essential skill for physicists and mathematicians. I don't feel confident in recommending any engineering texts, since I could easily send you down the wrong road due to my lack of knowledge. If you look at an engineering stack exchange, they could help you with that.

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You may also want to invest some time into learning a computer language. Doing some casual googling, I arrived at the conclusion that programming is useful in civil engineering today. There are a multitude of ways to go about learning programming. You can try to teach yourself, or you can try and find a class outside of school. I learned to program in such a class that my parents thankfully paid for. If you are fortunate enough to be in a similar situation, that might be a fun use of your time as well. To save you the trouble, any of these languages would be suitable: Python, C#, or VB.NET. Learning C# first will give you a more rigorous understanding of programming as compared to learning Python, but Python might be easier. I chose these three candidates based off of quick application potential rather than furthering knowledge in programming. This is its own separate topic, but my personal two cents are you will spend more time deliberating between programming languages rather than programming if you don't choose one quickly.

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What might be the best option is contacting a professor at the college you will be attending and asking for advice. You could email said professor with something along the lines of, "Hi Professor X! I'm a recently accepted student to Y college, and I'm really excited to study engineering. I want to do some rigorous learning about Z subject, but I don't know where to start. Could you help me?" Your message would be more formal than that, but I suspect you get the gist. Being known by your professors in college is especially good, and starting in high school is even better. These are the people who will write you recommendations for a job, write you recommendations for graduate school (if you plan on it), put you in contact with potential employers, help you in office hours, or end up as a friend. At my school at least, we are on a first name basis with professors, and I have had dinner with a few of mine. If your professors like you, that's excellent. Don't stress it though; it's not a game you have to psychopathically play. A lot of these relationships will develop naturally.

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That more or less covers educational things. If your laziness stems from material boredom, everything related to engineering I can advise on should be covered up there. Your laziness may also just originate from general apathy due to high school not having much impact on your life anymore. You've submitted college applications, and provided you don't fail your classes, your second semester will probably not have much bearing on your life. This general line of thought is what develops classic second semester senioritis. The common response is to blow off school, hang out with your friends, go to parties, and in general waste your time. I'm not saying don't go to parties, hang out with friends, etc., but what I am saying is you will feel regret eventually about doing only frivolous and passing things. This could be material to guilt trip yourself back into caring.

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For something more positive, try to think about some of your fun days at school before this semester. What made those days enjoyable? You could try to reproduce those underlying conditions. You could also go to school with the thought "today I'm going to accomplish X goal, and X goal will make me happy because of Y and Z." It always feels good to accomplish goals. If you think about it, second semester senioritis tends to make school boring because there are no more goals to accomplish. As an analogy, think about your favorite video game. If you have already completed the story, acquired the best items, played the interesting types of characters/party combinations, then why play the game? That's a deep question I won't fully unpack, but the simple answer is not playing the game because all of the goals have been completed. In a way, this is a lot like second semester of senior year. In the case of real life, you can think of second semester high school as the waiting period between the release of the first title and its sequel. Just because you are waiting doesn't mean you do nothing. You play another game, and in this case it's up to you to decide exactly what game you play.

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Alternatively, you could just skip the more elegant analysis from the last few paragraphs and tell yourself, "If I am not studying, then someone else is." This type of thinking is very risky, and most likely, it will make you unhappy, but it is a possibility. Fair warning, you will be miserable in college and misuse your 4 years if the only thing you do is study. I guarantee that you will have excellent grades, but I don't think the price you pay is worth it.

I used these lectures and skipped 23-28 and all of the review lectures. Though, you may want to review if there is any material in there that would be on the exam. I just ran out of time / got lazy towards the end. It helped me to buy the book and do homework assignments in the relevant chapters as I watched each video. It's not the same book used in the lectures, but for the most part it follows, and if it doesn't it was just out of order. The textbook is okay but is more or less the video lectures with the chalkboard diagrams and examples in print; there's not that much additional information. Doing practice problems is invaluable. Much of Math 415 is algorithmic.

Strang's Linear Algebra.