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I wish I had this when I was learning Linear Algebra. When it was taught to me, both in HS and College, there was not a word of motivation about why we were jug
by randomstring 7y ago
I wish I had this when I was learning Linear Algebra. When it was taught to me, both in HS and College, there was not a word of motivation about why we were juggling numbers around in boxes. It was tedious and had seemed to have no connection to anything.
I developed a strong dislike for LA, if not outright fear and hatred. This from someone who majored in math at university. I later learned from reading Dr Oakley's book, _A Mind For Numbers_, that this is a perfect recipe for not mastering a subject. I was sabotaging my own learning by approaching it from the point of view of something to be despised. It was many years later after reading Oakley's book that I challenged myself to learn Linear Algebra.
I found the Coursera course Coding the Matrix https://codingthematrix.com/ https://codingthematrix.com/ perfect. Not only did Professor Philip Klein explain the subject well, but it was also a programming course in python. Coding the algorithms helped make them that much more concrete. I'm happy to say I finished the online course with 100% grade.
Unfortunately Coding the Matrix is no longer available on Coursera.
I know this thread is more about Strang being a teaching god, and he is. I wanted to add something on alternative ways to learn linear algebra.
- alexhutcheson 7y ago> Unfortunately Coding the Matrix is no longer available on Coursera. The book itself is still for sale, and the website has course slides and auto-grading software for some of the exercises: https://codingthematrix.com/ https://codingthematrix.com/
- roi 7y agoThe course seems to be still mirrored in the Internet Archive: https://archive.org/details/academictorrents_54cd86f3038dfd446b037891406ba4e0b1200d5a https://archive.org/details/academictorrents_54cd86f3038dfd4...
- ofrzeta 7y agoThis is a problem I always had in university. Higher math always seemed to start with "the definition of X is Z etc." and I would never know what's the purpose of doing this. When I attended a talk of Gilbert Strang many years later it was eye opening because it was a totally different approach that always accompanied theoretical concepts with a concrete interpretation. Actually I now think it might also be a cultural thing. If you take a look at the approaches the English Wikipedia takes vs. the German Wikipedia take explaining a vector space you'll know what I mean: https://en.wikipedia.org/wiki/Vector_space#Introduction_and_definition https://en.wikipedia.org/wiki/Vector_space#Introduction_and_... https://de.wikipedia.org/wiki/Vektorraum#Definition https://de.wikipedia.org/wiki/Vektorraum#Definition
- big_chungus 7y agoI'd second the point on different cultures doing it differently. One of my profs once said he had a book written by two mathematicians, one German and another Italian. It was fairly evident who had worked on which part. He also mentioned that the "old style" German books would almost apologize if they "had" to use just a few pictures to illustrate something.
- dkarl 7y agoI had a math professor who told me that advanced math books are like Hoyle's Rules of Games. There are two ways you can use Hoyle's Rules of Games. You can memorize the rules of bridge and stop there, but then you will have a pretty dull experience. Or you can use the book as a tool to start playing bridge, and it will open you up to a rich and engaging activity.
- throwaway6734 7y ago>When it was taught to me, both in HS and College That's so cool that you had access to a linear algebra class in HS!
- rumanator 7y agoTeaching systems of linear equations and using Gauss factorization to solve the equations is quite mundane in HS.
- randomstring 7y agoTo be fair, my HS exposure was in honors Math, and it was very limited exposure: matrixes, determinants, and how to represent systems of equations.
- Al0neStar 7y agovideos from the course are also available here http://cs.brown.edu/courses/cs053/current/lectures.htm http://cs.brown.edu/courses/cs053/current/lectures.htm
- cageface 7y agoHonestly I think we spend way too much teaching students calculus and differential equations and way too little on linear algebra. LA is a lot more useful for most real engineering work, particularly software engineering. I had to build a somewhat basic SVG editor in React recently and the other devs on the team had to leave a lot of the core to me because I was the only one that remembered enough matrix math to do it.
- buzzkillington 7y agoNo, linear algebra is not more useful than calculus or differential equations for any branch of engineering other than computer engineering. Computers engineering is the only discrete engineering discipline.
- cageface 7y agoLinear algebra has many uses beyond computers: http://aix1.uottawa.ca/~jkhoury/app.htm http://aix1.uottawa.ca/~jkhoury/app.htm https://math.stackexchange.com/questions/256682/why-study-linear-algebra https://math.stackexchange.com/questions/256682/why-study-li...
- buzzkillington 7y agoYes, and all of them outside of computer science/engineering are using linear algebra on top of calculus. Computer software/engineering is the only field of science that can use naive linear algebra directly to solve hard problems in the field.
- salty_biscuits 7y agoUmmm, what about say quantum mechanics as the first huge example off the top of my head..
- pergadad 7y agoHow many school graduates will end up studying quantum mechanics?