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ralqs
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I've seen a number of books and articles touting Geometric Algebra as an important new area of math that will have large application to physics. Is there anything to these claims? Is it worth studying for a physics student?
EWH said:It slices it dices! (Well, it does have a lot of blades, anyway.)
Yes, I have it. I have some mixed feelings about it. The Linear Algebra part is a reasonable review if you already know the material. I would not use it as the only book for a first course, though.jbunniii said:While browsing on Amazon recently, I came across this title: Linear and Geometric Algebra. Based on the "search inside" feature, it looks good and very accessible, not to mention reasonably priced. Has anyone here read it?
EWH said:Sankaku: Yes, that's good for the real mathy-math types, not the place to start unless you eat abstract algebra for breakfast, lunch and dinner.
I've just started a postdoc in geometric algebra and I am reading the book, "Geometric algebra for computer scientists" and I am finding it VERY good, it has a great deal of supplementary material and is actually very good. My one caveat though, is that you should be reasonably familiar and happy with linear algebra first. It really has a great deal of things going for it.EWH said:No, but I read his GA paper a few years back and recall it as pretty good. I'd look at the the primer from Jaap Suter first, and try out the GAViewer software and its tutorials before spending money on books. (links in my previous post) If you're already into linear algebra, then McDonald's book might be the best first book, but take a look at "Geometric Algebra For Computer Science", too.
Geometric algebra is a mathematical framework that extends traditional vector algebra to higher dimensions and allows for the representation of not only scalars and vectors, but also higher-order geometric objects such as planes, spheres, and volumes. It also incorporates the concepts of inner and outer products, which provide a more intuitive and powerful approach to vector and tensor operations.
Geometric algebra has been applied in various fields of physics, including mechanics, electromagnetism, and quantum mechanics. It provides a more elegant and concise way to express and manipulate physical quantities, and has been shown to simplify and unify many mathematical concepts and formulas in physics.
Yes, studying geometric algebra can greatly benefit physicists by providing a deeper understanding of fundamental concepts and simplifying complex calculations. It has also been shown to reveal underlying symmetries and geometries in physical systems, leading to new insights and discoveries in various areas of physics.
Geometric algebra can be challenging at first, especially for those who are not familiar with abstract algebra. However, with patience and practice, it can be learned and applied effectively. Many resources, including textbooks and online tutorials, are available to help in the learning process.
Geometric algebra has been successfully applied in many real-world problems, such as computer graphics, robotics, and computer vision. It has also been used in engineering and physics to solve problems involving rotations, transformations, and vibrations. Its versatility and efficiency make it a valuable tool in various practical applications.