Overview 18.701
                   ---------------
                      Fall 2004
                      ---------



Material in this course: Everything discussed in the lectures which
corresponds roughly to the following sections of the book


	Chapter		|	Sections
	--------------------------------
		I	|	all
		II	|	all
		III	|	all but 5
		IV	|	all but 5,7,8
		V	|	5,6,7,8
		VI	|	1,2,3,4,6
		X	|	all but 8
		XI	|	1,2,3,4
		XII	|	all but 8


Things you should know how to define (at least,there may be more this
seems like a fairly complete list which I got by simply reading
through my notes, in other words I did your preparation for you lewt
me know if I should add something)


matrix
vector
	operations on matrices and vectors
	inverse matrix
	elementary row operations
	elementary matrices
	system of linear equations
	determinant function, determinant
	adjoint matrix
group
	permutation group
		symmetric group
		cycle (notation)
		permutation matrices
		sign of a permuation
	subgroups
	subgroup generated by
	cyclic (sub) group
	order of element
	order of group
	Klein four group
	Quaternion group
	homomorphism of groups
		isomorphism of groups
		isomorphic groups
		automorphisms of groups
			inner automorphisms & conjugation
		kernel & image of a homomorphism of groups
	conjugates 
	normal subgroups
	central element of a group
	center of a group
	relation on a set
		equivalence relation
		partition on a set
		equivalence class
		equivalence relation defined by a map
	cosets (left and right)
	congruence relation
	products of groups
	quotient groups
field
	prime field
	characteristic of a field
vector space
	subspace
	linear map or linear transformation
		endomorphism
		isomorphism
		automorphism
		kernel
		image
	subspace spanned by
	linear combination
	V spanned by S
	linearly (in)dependent
	basis
	coordinates
	finite dimension(al)
	direct sums
	matrix of T with respect to bases
	matrix of change of base
	determinant of a linear endomorphism
	eigenvector
	eigenvalue
	invariant subspace
	diagonal matrix
	similar matrices
	diagonalizable matrix (or linear endomorphism)
	characteristic polynomial of a linear endomorphism 
	scalar matrix
more group
	operation or action of a group on a set
		orbit
		transitive action
		stabilizer
		fixed point
	centralizer of x \in G
	simple group
	solvable group
	Sylow p-subgroup or p-Sylow subgroup or ...
ring
	commutative ring (OK: all rings are commutative)
	subring
	homomorphism of rings
		isomorphism
		automorphism
		kernel
		image
	ideal (of a ring)
		principal ideal
		ideal generated by
		quotient ring
		maximal ideal
	special elements
		unit
		nilpotent
		zero divisor
		prime element
		irreducible element
	Gaussian integers
polynomials
	polynomial over a field
	polynomials over rings
	polynomial rings
	degree of a polynomial
	evaluation of a polynomial
	constant polynomial
	monomial
	multi-index
ring (continued)
	integral domain
	fraction field
	maximal ideal
factorization (happens in domains)
	prime element
	irreducible elements
	factorization
	Noetherian ring
	Principal ideal domain
	Euclidean domain
	Unique factorization domain
module
	free module
	submodule
	homomorphism
		isomorphism
		endomorphism
		automorphism
		kernel
		image
	submodule generated by
	elements generating M
	fintely generated
	presentation of M
classification of finite dimensional vector spaces endowed with an
endomorphism: rational canonical form, Jordan block, Jordan canonical
form