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II. Linear Algebra

Sellers, Ph. Reviews Watch First Lecture. Professor Sellers introduces the general topics and themes for the course, describing his approach and recommending a strategy for making the best use of the lessons and supplementary workbook. Warm up with some simple problems that demonstrate signed numbers and operations.

[] Lectures on Randomized Numerical Linear Algebra

An Introduction to the Course. Order of Operations. Percents, Decimals, and Fractions. Variables and Algebraic Expressions. Operations and Expressions. Principles of Graphing in 2 Dimensions. Solving Linear Equations, Part 1. Solving Linear Equations, Part 2.

Abstract Algebra Open Learning Course

Graphing Linear Equations, Part 1. Graphing Linear Equations, Part 2. Parallel and Perpendicular Lines. Solving Word Problems with Linear Equations. This is one of over 2, courses on OCW. Find materials for this course in the pages linked along the left. No enrollment or registration. Freely browse and use OCW materials at your own pace. There's no signup, and no start or end dates.

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Video Lectures. Subscribe to this collection. Need help getting started? Don't show me this again Welcome! My interest was mostly that I was actually doing path integral Monte Carlo calculations for my Chemistry thesis and wanted to make sure I understood the fundamentals.

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The prof, like many most? So the course didn't seem to teach me much about the gotchas that might come up in actual statistics or numerical analysis, and instead more about the ingenuity of mathematicians in constructing absurdly farfetched abuses of e. But besides that cultural mismatch, lack of an explanatory framework sure didn't help. Thus, I was very happy decades later when I ran across Terence Tao's book on measure theory available as a free manuscript online , which had a lot of the same kind of material with quite a good framework of motivation and explanation wrapped around its proofs.

I much preferred this book to the approach in my undergraduate course in statistics.

Lec 01 - Linear Algebra - Princeton University

Again, the difference wasn't only lack of explanations also, e. I have never been motivated to read the proof-heavy parallel book by Vapnik, but I do find it reassuring that it exists in case I ever work with problems that were weird enough to start raising red flags about breaking the comfortable assumptions in my informal understanding of the statistics.

It's honestly harder than it should be to find well-written primers on linear algebra with a geometric focus, which I find to be the most intuitive way to "grasp" the subject and the motivations for it. I'd highly recommend his videos especially the playlist covering linear algebra: "Essence of Linear Algebra" as a supplement to more traditional mediums.

Sorry for being pedantic, your comment is amazing for mentioning him. However, I'm a fanboy of 3B1B and I just have to say this. It's 3Blue1Brown, not the other way around. He named it after his eye color which apparently has 3 parts blue and 1 part brown. Haha, thanks for pointing that out. I've watched literally every video of Grant, and am familiar with the source of the name - but for some reason I always mix it up. The main thesis is that proving everything using determinants hides the intuition for what's really going on.

I'm sadly now convinced that that approach only works for "simple" concepts.

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  7. For instance I am yet to find a single book, course or teacher that can explain measure theory in a way that cultivates intuition. They are simple because they are close to intuition one has already. Mathematical intuition is not something one is born with, it takes time and effort to develop. And this is what gets me about Feynman, why I am a huge admirer of his work.

    Dear Algebra Diary by Geoff Smith (MA10209, 2018)

    Take a look at the footnote. An offhand comment of how to calculate the square root of any N using a short iterative loop that you can compute by hand. I'm no mathematician clearly but I had no idea that this method even existed. I've just had to try it out. And it's a footnote! I have the book of Feynman's computation lectures and they're dated, but most of the theory is still relevant and his writing remains accessible to anyone. There are many stories of how Feynman did fairly profound work in an offhand way. Two that I can remember: 1. A number of times, young professors would visit with him when they were in town to give a lecture, and would discuss a recent result they had come up with, and Feynman would say that reminded him of something, pull out a sheet of paper from his drawer, and say effectively, "yes, looks like your result is correct".

    A more specific version of that was captured in the link below, when Feynman worked out blackhole radiation on a blackboard with some grad students over lunch. The blackboard was erased and the result lost until Hawking published the same result a year later, propelling him to fame deserved, of course. The special case has such a simple expression, though, that I'm tempted to commit it to memory. Yes, yes, I know Carmack didn't invent it. SamReidHughes 40 days ago. If you can find it an audio recording of this lecture is also available and it is one of the best lectures in the series.

    Feynman really brings forward the "soul" of algebra and the illustrates how powerful the art of abstraction is. Audible has all the audio lectures for sale, which is how I got them on my kindle, and I have also seen them floating around the net in other formats.