date

description

reading

Sept 10 
why abstract algebra? five motivations: historical, higher mathematics, applications to other scientific disciplines, abstraction of the familiar, because it's there 
Herstein sections 1.2, 1.3, and Scott LaLonde's set theory handout 
Sept 11 (xhour) 
proof writing workshop part 1: logic, proof by contradiction 

Sept 12 
some number theory basics; modular arithmetic: two points of view 
Herstein p. 2326 (Euclidean algorithm), p. 4041, and section 2.2 
Sept 14 
modular arithmetic, definition of group 

Sept 17 
examples of groups, definitions, first theorems 
Herstein section 2.1 and 2.3 
Sept 18 (xhour) 
proof writing workshop part 2: techniques, examples, style 

Sept 19 
the mattress group, cyclic groups, subgroups 
Fraleigh section 5 and Herstein p. 6163 
Sept 21 
the integers mod n: addition and multiplication 
Herstein section 3.1 
Sept 24 
integers mod n under multiplication, dihedral groups 

Sept 26 
equivalence relations, symmetric groups 
Herstein section 2.4 
Sept 28 
cosets and Lagrange's theorem 

Oct 1 
cosets, Lagrange, homomorphism 
Herstein section 2.5 
Oct 2 (xhour) 
symmetry group of the tetrahedron 

Oct 3 
tetrahedron, permutations, cycle decomposition, homomorphism yoga 

Oct 5 
a counterexample to the converse of Lagrange, homomorphisms, isomorphisms 
Herstein section 2.6 
Oct 8 
isomorphism, quaternions 

Oct 10 
quotient groups, quaternions 

Oct 12 
isomorphism theorem, quaternions 
Herstein theorem 2.6.4, p. 9698 
Oct 15 
Cauchy's theorem, direct products 

Oct 16 (xhour) 
midterm study session 
bring questions 
Oct 17 
direct products, structure theorem for finite abelian groups 

Oct 19 
in class portion of midterm 
Herstein section 4.1 
Oct 22 
applications of group theory to elliptic curves, rings 

Oct 24 
rings: examples and basic definitions 
Herstein 4.2, 4.3 
Oct 26 
fields, oddtown, quadratic rings 

Oct 29 
ring homomorphisms, ideals 
Herstein 4.4 
Oct 30 (xhour) 
optional: midterm debrief 

Oct 31 
halloween, quotient rings, maximal ideals 
Herstein 5.1 
Nov 2 
ideals, quadratic rings 
Herstein 4.6 
Nov 5 
polynomial rings 
tomorrow is election day: please go vote 
Nov 7 
irreducibles, polynomials 
Herstein 5.3 
Nov 9 
roots of polynomials, field extensions 
Herstein 5.4, 5.5 
Nov 12 
field extensions, constructibility 
Herstein 5.6 
Nov 13 (xhour) 
a bit of galois theory 
enjoy your take home final 