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Abstract algebra for developers and people who hate math

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Re: Abstract algebra for developers and people who hate math

#31

Post by wging »

dhaivatpandya wrote: post #16
alex-g wrote: post #15

Earlier quoted context omitted.

Are you also going to fix the assertion that matrices form a group under multiplication? (They don't: not all matrices have inverses. The general linear group is what you are probably looking for.) It's a bit embarrassing that of your three examples of groups, only one is actually a group...

Sorry, again. I'm really trying my best to keep it all correct, but, I do make mistakes.

Another mistake you might want to fix:

>(like, matrix multplication isn't commutative, that means: A∗B≠B∗A when B and A are matrices)

You want to say something like "A∗B isn't necessarily equal to B∗A when B and A are matrices." Neither A∗B≠B∗A nor A∗B=B∗A are true in general when A and B are matrices.

Re: Abstract algebra for developers and people who hate math

#33

Post by dhaivatpandya »

wging wrote: post #31
dhaivatpandya wrote: post #16

Earlier quoted context omitted.

Sorry, again. I'm really trying my best to keep it all correct, but, I do make mistakes.

Another mistake you might want to fix: >(like, matrix multplication isn't commutative, that means: A∗B≠B∗A when B and A are matrices) You want to say something like "A∗B isn't necessarily equal to B∗A when B and A are matrices." Neither A∗B≠B∗A nor A∗B=B∗A are true in general when A and B are matrices.

Fixed. Thanks for telling me these things, it really helps.

Re: Abstract algebra for developers and people who hate math

#34

Post by dhaivatpandya »

vonsydov wrote: post #32

lol you didn't even describe what a 'closure' is ... just drew the equation. i stopped reading after that.

Um. I did. If you read on, I did explain what a closure was. If you don't get it, the concept is pretty simple, if you have two elements in a set S, and you apply the group operation on them, then the result must be in set S for the set in question to be a group.

Re: Abstract algebra for developers and people who hate math

#35

Post by sirclueless »

alex-g wrote: post #9

People who hate math aren't going to be inspired by a collection of axioms and equations. Nor are they likely to be wowed by the examples of matrices and vectors. Some examples from geometry, or permutations, might be more likely to teach the concepts. People who know something about math are going to spot several errors in the presentation. For example, the reals with multiplication don't form a group, since 0 has n…

I think that your last point is a worthy tie-in to the developer's world.

For example, for those who use C# or Java regularly: groups, Abelian groups, and integers under addition are roughly analogous to the Enumerable interface, the List interface, and the ArrayList class.

Obviously they serve different purposes, but their role in their respective professions is approximately the same. Groups appear all over the place in math, and the Enumerable interface is baked right into the for(each) loop. Abelian groups add commutativity to general groups, and the List interface adds indexing and insertion to Enumerables. Meanwhile integers/ArrayLists are basically the go-to concrete implementation that mathematicians/programmers default to when it comes to Abelian groups/lists.

Re: Abstract algebra for developers and people who hate math

#36

Post by dhaivatpandya »

sirclueless wrote: post #35
alex-g wrote: post #9

People who hate math aren't going to be inspired by a collection of axioms and equations. Nor are they likely to be wowed by the examples of matrices and vectors. Some examples from geometry, or permutations, might be more likely to teach the concepts. People who know something about math are going to spot several errors in the presentation. For example, the reals with multiplication don't form a group, since 0 has n…

I think that your last point is a worthy tie-in to the developer's world. For example, for those who use C# or Java regularly: groups, Abelian groups, and integers under addition are roughly analogous to the Enumerable interface, the List interface, and the ArrayList class. Obviously they serve different purposes, but their role in their respective professions is approximately the same. Groups appear all over the pla…

yeah, that's very true.

That analogy works excellently until you consider the implementation of these things, and then its a complete mess because there are side effects all over the place, except in languages like haskell.

Re: Abstract algebra for developers and people who hate math

#37

Post by grot »

An admirable attempt, but -- the formatting and the grammar are distracting detractors from the content.

For anyone who is serious about learning abstract algebra but lacking mathematical background (i.e. an analysis course under the belt), consider the book "Abstract Algebra" by Dummit and Foote. It's at the undergraduate level (so it goes through the motions of rigor that research math texts often omit), and well presented. A more advanced, terse and elegant, text would be Hershtein's Topics in Algebra.

Re: Abstract algebra for developers and people who hate math

#39

Post by dhaivatpandya »

grot wrote: post #37

An admirable attempt, but -- the formatting and the grammar are distracting detractors from the content. For anyone who is serious about learning abstract algebra but lacking mathematical background (i.e. an analysis course under the belt), consider the book "Abstract Algebra" by Dummit and Foote. It's at the undergraduate level (so it goes through the motions of rigor that research math texts often omit), and well p…

If you tell me what's wrong with the formatting and grammar, I'll try my best to fix them for the next time.
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