{"id":1529,"date":"2022-01-27T01:00:37","date_gmt":"2022-01-27T06:00:37","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=1529"},"modified":"2022-01-17T17:42:22","modified_gmt":"2022-01-17T22:42:22","slug":"exterior-algebra","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/01\/27\/exterior-algebra\/","title":{"rendered":"Lecture 3: Exterior Algebra"},"content":{"rendered":"<p><a href=\"https:\/\/youtu.be\/paEKgbiCyPk\"><img loading=\"lazy\" src=\"http:\/\/brickisland.net\/DDGSpring2021\/wp-content\/uploads\/2021\/02\/03_ExteriorAlgebra.png\" width=\"480\" height=\"270\" \/><\/a><\/p>\n<p>Our next lecture will cover one of the basic tools we&#8217;ll use throughout the rest of the course: <em>exterior algebra<\/em>. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about <em>volumes<\/em> rather than just vectors. If you felt ok working with things like the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cross_product\">cross product<\/a> and the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Determinant\">determinant<\/a> in your linear algebra\/vector calculus courses, this shouldn&#8217;t be too big of a leap. (If not, could be a good moment for a <a href=\"http:\/\/brickisland.net\/DDGFall2017\/2017\/09\/03\/linear-algebra-and-vector-calculus-review\/\">review<\/a>!)<\/p>\n<ul>\n<li><a href=\"https:\/\/youtu.be\/paEKgbiCyPk\">Video<\/a><\/li>\n<li><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2021\/02\/03_ExteriorAlgebra.pdf\">Slides<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Our next lecture will cover one of the basic tools we&#8217;ll use throughout the rest of the course: exterior algebra. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about volumes rather than just vectors. If &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/01\/27\/exterior-algebra\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 3: Exterior Algebra&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[7,3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1529"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/comments?post=1529"}],"version-history":[{"count":5,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1529\/revisions"}],"predecessor-version":[{"id":3439,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1529\/revisions\/3439"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=1529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=1529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=1529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}