#### Comment Preferences

• ##### Too bad I don't live closer(none)
I'd be knocking at your doorstep to explain Abstract Algebra to me.  Right now it's like reading a Greek text when you don't know how to read greek.

(And I'm not even to the tricky parts yet)

America works best in spreading democracy when people over the world see something they want to emulate. Richard

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• ##### On one level...(none)
...it's about learning how to prove things, about the nature of what constitutes a proof, and about how to use words which have very precise meanings in a logically coherent manner.

On another level, you are learning about different mathematical objects, sets which have operations acting upon them that follow certain rules.  Logical questions arise:

• What rules do you minimally have to have in order to prove a desired result?
• If a set has an operation that adheres to those rules, what else must necessarily be true?
• Given a set with an operation that generates certain properties being true, what can you say about the rules that the operation must satisfy?  What can you say about the structure of the set?
• What about sets with multiple operations and a way in which the operations are intertwined (i.e. the distributive law)?
• What can you say about the class of sets that have operations that satisfy certain rules (here, we enter something called Category Theory)?
• Robyn

Teacher's Lounge opens each Saturday, sometime between 10am and 11am EST

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"abstract algebra".  Lol.  I just glanced through some stuff, and said, "Oh, set theory."

It sounds like the issues are similar to those called "meta-logic" in philosophy.  (Sorry, I know I should know this already, but I'm a lowly grad student.)

"In the beginning the universe was created. This has been widely criticized and generally regarded as a bad move." -- Douglas Adams

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• ##### Me too...(none)
Because I don't know the meaning of english words !
What I saw on google seems to be what we call the "Théorie des Ensembles" (or why this blog cannot be an Abelian ring, because it's not commutative... :-) )

Oh well... I really don't have the vocabulary for some low joke !

An older friend of mine was a math searcher (US Navy) and a bench astronaut for Gemini... He's retired and makes a nice living in translating mathematic books from english to french and vice-versa... It did surprise me at first, as I always thought that mathematics were a sort of universal language, but his explanations convinced me that, even in formulas, we don't really write it the same way !

Too bad the poor Evariste Galois was killed too young!

"What can I do, What can I write, Against the fall of Night" A.E. Housman

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• ##### Abelian...(none)
...is derived from Henrik Abel, a contemporary of Galois.  Both worked on the same problem.   Both sent their work to Cauchy to have it reviewed.  Cauchy screwed them both.  Galois outlined a theory about how to find the roots of polynomials, then went out and got killed in a duel, which although nominally about a woman, was more probably about his politics.  Cauchy supressed the work, because he disagreed with Evariste's politics.  Abel, a Norwegian, submitted a proof that there can be no general method created to find the roots of polynomials of degree greater than 4 that uses only the operations common to arithmetic (+, -, *, /) and the extraction of nth roots (called Abel's Theorem).  Cauchy misplaced the paper.  Abel died of consumption before receiving notice that he had obtained a faculty position.

Robyn

Teacher's Lounge opens each Saturday, sometime between 10am and 11am EST

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• ##### Time flies...(none)
And we still have all those "Cauchy"..!
While I'm not at all in algebra (learned that long, long ago), I still find pleasure in re-reading the Bourbaki books... Made for fun and enlightenment by several mathematicians and writers... I wonder if there is a english translation ?

"What can I do, What can I write, Against the fall of Night" A.E. Housman

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• ##### It is every bit the study of logic and meta-logic(none)
There was a joke among my colleagues in grad school, which I mentioned the other day.
When the engineer has questions, he asks the physicist.  When the physicist has questions, he asks the mathematical analysist.  When the analysist has questions, he asks the algebraist.  When the algebraist has questions, he asks God.  If physicist's questions concern quantum theory, insert the statistician between the physicist and the analysist.  The topologist points out that the problem is either more or less complex than it appears, depending on one's point of view.
The part about the algeraist talking to God is really about the algebraist consulting the foundations of mathematics and logic.

Teacher's Lounge opens each Saturday, sometime between 10am and 11am EST

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