Obviously.

Maybe I'll do your taxes too.

Warren

 

Semigroups, groups (abelian, nonabelian, simple, normal, . . .), integral domains, rings, algebras, fields, vector spaces, field extensions, the Fundamental Theorem of Group Homomorphisms, factor groups, splitting fields, Galois theory, . . . .

Fun stuff!

 

Whoa magician, slow down there We are not that far yet. Last night we proved that some infinities are bigger than other infinities and that in fact their are an infinite number of infinities I am really loving this stuff, but if I have trouble I know who to come to

 

Is the number of infinities countable or uncountable?

 

 

Hmm. Well, we used Cantor's Theorem to "prove" (I am still not convinced of its mathematical fidelity) that the set of Real numbers are not countable and I believe the same was used to show the infinite number of infinities, so I'll say they are uncountable.

 

Continuum Hypothesis.

By the way, this is usually covered in set theory; it's quite odd to find you doing this in a course on abstract algebra.

 

Yeah, I do not think we are covering it much more in depth than this. We learned cardinality and some set theory last class. Before that we did some proofs on the real numbers, then a chapter on complex numbers. The rest of the syllabus looks like this -

Well ordering
Mappings
Semigroups
Group Theory
Isomorphism
Cyclic Groups
Lagrange's Theorem (Gotta love Lagrange )
Rings
Quotient groups

 

i noticed you live near me.. where do you teach stat?

 

I teach review courses for the Chartered Financial Analyst (CFA) exams: some in Irvine (Irvine Marketplace) and some in L.A. (UCLA Extension, downtown). I used to teach the same courses at UCI, and mathematics at CSUF.