quark Posted February 24, 2015 Share Posted February 24, 2015 It's ON this summer! :hurray: http://www.artofproblemsolving.com/School/classlist.php?#cd_grouptheoryseminar Anyone else's DC signed up? :D ETA: More info. 2 Quote Link to comment Share on other sites More sharing options...
kiana Posted February 24, 2015 Share Posted February 24, 2015 Oh my, and they've got a first draft of a group theory book. I really want it even though I doubt it would be suitable for the class I teach in that area :P 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted February 24, 2015 Share Posted February 24, 2015 I first read that as group therapy. I thought...with AoPS...yes please! 8 Quote Link to comment Share on other sites More sharing options...
quark Posted February 24, 2015 Author Share Posted February 24, 2015 :lol: I think for my son group theory IS a form of group therapy. :lol: It's the branch of math that makes him happiest. Intermediate Number Theory really kicked his you-know-what so I am not optimistic that this course will be easy for him, but he is definitely a lot more enthusiastic about this than he was for InterNT. Fingers crossed! 1 Quote Link to comment Share on other sites More sharing options...
wapiti Posted February 24, 2015 Share Posted February 24, 2015 Dumb question... is "group" theory the same as set theory, or is it something different? Quote Link to comment Share on other sites More sharing options...
quark Posted February 24, 2015 Author Share Posted February 24, 2015 Dumb question... is "group" theory the same as set theory, or is it something different? See here! DS says there is some overlap (he says ALL math is related!). 1 Quote Link to comment Share on other sites More sharing options...
kiana Posted February 25, 2015 Share Posted February 25, 2015 Dumb question... is "group" theory the same as set theory, or is it something different? Related and yet not the same. Definition: A binary operation on a set is basically an operation that takes two inputs from the set and returns one output, also in the set. Common examples: Addition and multiplication on integers, rational numbers, real numbers, and complex numbers. Addition and multiplication on nxn matrices with entries from the above sets. Addition, multiplication, and composition of real-valued functions Examples of things that are not binary operations: Division on the integers -- 1/2 is not an integer. Division on the real numbers -- to define it as a binary operation you need to specify the non-zero real numbers. A group, then, is a set together with a binary operation (let us use * for the operation) defined on that set that satisfies three properties: 1) The binary operation is associative -- a*(b*c) = (a*b)*c 2) There is an identity element, denoted by e, such that a*e = e*a = a for every a in the set. 3) Every element in the set has an inverse in the set -- that is, for every a in the set, there is a b in the set such that a*b = b*a = e. Basic examples of groups: The integers under addition. It is a set with a binary operation, addition is associative, the identity element is 0, and the inverse of a is -a. The non-zero rational numbers under multiplication. It is a set with a binary operation, multiplication is associative, the identity element is 1, and the inverse of a is 1/a. Note that the restriction to non-zero rational numbers is required as otherwise 0 would not have an inverse. Much cooler example - symmetry group! This is not my page, but it's correct and putting images in here is obnoxious. http://dogschool.tripod.com/trianglegroup.html Anyway, so group theory studies groups and their properties. (btw, we usually spend about 1.5 weeks of lecture getting to everything that I put in this post, including doing lots of examples and some basic set theory as a lead-in). 2 Quote Link to comment Share on other sites More sharing options...
quark Posted February 25, 2015 Author Share Posted February 25, 2015 If you want a basic idea of group theory, and would love a laugh while learning it, read Simon: The Genius in My Basement by Alexander Masters. 1 Quote Link to comment Share on other sites More sharing options...
SeaConquest Posted February 25, 2015 Share Posted February 25, 2015 If you want a basic idea of group theory, and would love a laugh while learning it, read Simon: The Genius in My Basement by Alexander Masters. What a fun read! Adding to my wish list for later. :) 1 Quote Link to comment Share on other sites More sharing options...
avilma Posted February 25, 2015 Share Posted February 25, 2015 I took group theory my freshman year in college as part of an abstract algebra course but couldn't figure out what it was for. Subsequently in 3 different courses (Theoretical Mechanics, Cristalography, Quantum Mechanics) we did mention that group theory could be used but we didn't use it. Not knowing group theory is one of the things that I consider as a hole in my education. Quote Link to comment Share on other sites More sharing options...
kiwik Posted February 26, 2015 Share Posted February 26, 2015 If you want a basic idea of group theory, and would love a laugh while learning it, read Simon: The Genius in My Basement by Alexander Masters. This comes up as not available for purchase. Does it do that for you or is it a living in NZ thing? Quote Link to comment Share on other sites More sharing options...
kiana Posted February 26, 2015 Share Posted February 26, 2015 This comes up as not available for purchase. Does it do that for you or is it a living in NZ thing? Is it the ebook that's making it unavailable? Here's the print copy -- http://www.amazon.com/Simon-The-Genius-My-Basement/dp/0385341083 1 Quote Link to comment Share on other sites More sharing options...
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