Great Resource! But a good primer to Linear Algebra would be Gilbert Strangs course at MIT OCW.
Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
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Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#92You might be interested in the Open Textbook Initiative by the American Institute of Mathematics:
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#93Earlier quoted context omitted.
There's a practical course for this http://www.datasciencecourse.org/lectures/ anything you don't know, like linear algebra, look up the topics here for a 1-2hr crash course https://www.youtube.com/playlist?list=PLm3J0oaFux3aafQm568bl... There's a playlist for a math background in ML for anybody who wants to try a more rigorous ML course https://www.youtube.com/playlist?list=PL7y-1rk2cCsA339crwXMW... More information…
> There's no answers because the author gives thanks to a grad course in evidenced based teaching where he claims the only way to really know something and remember it is to figure it out for yourself. Math stackexchange can help too. This is a cop out; of course to really know something and remember you have to figure it out for yourself. But answers allow you to check whether your work was right, and if not, allow…
He has extensive posts on his reasons, but it's also used for a course so only letting other professors have the answers to allow reuse of exercises is another reason. Those Art of Problem solving olympiad books don't have answers either with authors claiming same reasoning and in their defense I did learn a lot figuring it out myself. Personally I too like gratification of solving something then seeing the answers and finding a different and almost always more elegant/clear proof to compare to mine.
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#94Earlier quoted context omitted.
There's a practical course for this http://www.datasciencecourse.org/lectures/ anything you don't know, like linear algebra, look up the topics here for a 1-2hr crash course https://www.youtube.com/playlist?list=PLm3J0oaFux3aafQm568bl... There's a playlist for a math background in ML for anybody who wants to try a more rigorous ML course https://www.youtube.com/playlist?list=PL7y-1rk2cCsA339crwXMW... More information…
> There's no answers because the author gives thanks to a grad course in evidenced based teaching where he claims the only way to really know something and remember it is to figure it out for yourself. Math stackexchange can help too. This is a cop out; of course to really know something and remember you have to figure it out for yourself. But answers allow you to check whether your work was right, and if not, allow…
In short, by not providing an answer key, you are denying the disciplined student the opportunity to efficiently learn.
I agree with you 100%. But let me add this: in most cases, if you're studying with a book that doesn't have an answer key, you can supplement that text with exercises taken from somewhere else. For example, lots of course websites around the 'net post previous years exams / homework with answers. There are also books like Schaum's 3,000 Solved Problems in Calculus[1], The Humongous Book of Calculus Problems[2], 3,000 Solved Problems in Linear Algebra[3], etc.
Also, with books that are used as textbooks, and that provide an answer key but only to instructors... if you aren't averse to violating copyright and using certain pirate websites, those "instructor only" answer keys can often be found.
[1]: https://www.amazon.com/Schaums-Solved-Problems-Calculus-Outl...
[2]: https://www.amazon.com/Humongous-Book-Calculus-Problems-Book...
[3]: https://www.amazon.com/000-Solved-Problems-Linear-Algebra/dp...
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#95Earlier quoted context omitted.
Would be interested to hear why you’re studying machine learning. Do you see important problems you think it can solve, are you looking to make more $$ as an ML data scientist, or just generally interested in stats/data?
Part of a broader effort - I committed to learning to code about 3 years ago. At that point in time, I didn't really know why I was doing it... really out of curiosity. I kept going because it was addicting, and really an antithesis to my day job at the time (investment banking) - which I felt was corporate / bureaucratic and unintellectual. That said, eventually, I want to start a startup. I'm building out small sid…
Thanks for sharing, good luck on your journey
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#96I'm e-learning Linear Algebra right now to have a good math foundation for Machine Learning. I was a History and Sociology major in college - so I didn't take any math. If you are like me, and working off an initial base of high school math, I would recommend the following (all free): Linear Algebra Foundations to Frontiers (UT Austin) Course: https://www.edx.org/course/linear-algebra-foundations-to-fro... Comments:…
3blue1brown has a great youtube series on both Calculus and Linear Algebra that provide excellent intuitive backing for the concepts in both areas.
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#97Somehow I found linear algebra easier than calculus, but I don't know why. I did both at the same time in university, but failed calculus 3 times and aced linear algebra at the first try. I'd expect being either good or bad at math, not both at the same time
Math professor here --- Quality of teaching might have something to do with it. But, also, calculus is much harder to understand at a rigorous, formal level than at an informal level. On one level you can try to understand what the main concepts are about, be able to compute derivatives and integrals, solve optimization and related rates problems, and so on. I'd recommend Silvanus Thompson's Calculus Made Easy over a…
> - Why are limits defined the way they are (with epsilons and deltas)?
> - The book will probably touch lightly upon the Mean Value Theorem -- why is this important? What's the point?
> - Why is the chain rule true? It reads dy/dx = (dy/du) (du/dx). Yay! This is just cancelling fractions, right? Any "respectable" calculus book will insist that it's not, but most students will cheerfully ignore this, still get correct answers to the homework problems, and sleep fine at night.
Which "respectable" book(s) would you recommend for those who want to dive into this details? Is Tom Apostol's Mathematical Analysis? good for learning these kind of details? (They say this book is "respectable", but I would like to hear your thoughts about it. Thanks).
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#98Sort of off topic - but I was a math major in college and I always had a broad, casual categorization of the types of classes I took.
Linear Algebra - felt like it required you to be able to hold really long trains of thought in your head
Probability - felt like you had to be clever
Analysis - felt like you just had to think critically and approach things from all angles
I always preferred Algebra - felt like I was writing essays not doing math
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#99I'm e-learning Linear Algebra right now to have a good math foundation for Machine Learning. I was a History and Sociology major in college - so I didn't take any math. If you are like me, and working off an initial base of high school math, I would recommend the following (all free): Linear Algebra Foundations to Frontiers (UT Austin) Course: https://www.edx.org/course/linear-algebra-foundations-to-fro... Comments:…
That's a pretty good list, here are some things I'd add. Amazing js visualizations/manipulatives for many LA concepts: http://immersivemath.com/ila/index.html LA Concept map: https://minireference.com/static/tutorials/conceptmap.pdf#pa... (so you'll know what there is to learn) Condensed 4-page tutorial: https://minireference.com/static/tutorials/linear_algebra_in... (in case you're short on time) And here is an exce…
Wow - nice stuff. I'm a fan of the reference map.
Re: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares
#100Earlier quoted context omitted.
The definition (calling those unit vectors which are members of the standard basis “standard unit vectors”) sounds perfectly reasonable to me. You haven’t given any good reason why you think it’s “completely bogus” or “plain wrong”.
What is your personal definition of the term "unit vector?" Do you suppose there's a reason why no other textbook or Web site defines it the way these authors do? Are there only N unit N-vectors, as the book says, or are there an infinite number of them?
My definition of unit vectors is the same as yours. However, the book does not say there are only N unit N-vectors. It says there are only N STANDARD unit N-vectors.
In math, “Adjective X” usually means something more specific than “X”. “Prime numbers” are a subset of “numbers”, and so on. Just like in this case, “standard unit vectors” are a subset of “unit vectors”.