Year 1 Algebra Flashcards
1
Q
def complex numbers, properties
A
e
2
Q
polar form
A
e
3
Q
unit circle is a group form
A
e
4
Q
de Moivres theorrem
A
e
5
Q
roots of unity
A
e
6
Q
nth roots prop
A
e
7
Q
fundamental theorem of algebra
A
e
8
Q
order of a root of unity
A
e
9
Q
prime numbers
A
e
10
Q
division properties
A
e
11
Q
product of primes
A
e
12
Q
infinitely many primes
A
ew
13
Q
def lcm gcd
A
e
14
Q
bezout identity
A
e
15
Q
euclid algorthitm (compute gcd)
A
e
16
Q
all bezout identities
A
e
17
Q
euclids lemma
A
e
18
Q
fundamental theorem of arithmetic
A
e
19
Q
gdc lcm properties
A
e
20
Q
def congruence
A
e
21
Q
evcery integer is congruent n to an in within 0,n
A
e
22
Q
congruence classes
A
e
23
Q
well defined sum and propertios on Zn
A
e
24
Q
multiplicative inverse iff coprime
A
e
25
multipicltaion by coprime element is invertible
e
26
Fermats little theorem
e
27
def congruence equation
e
28
Solving congruences
e
29
Chinese remainder theorem
e
30
solving simultaneous congruence equations
e
31
group of units
e
32
phi function
e
33
group odf units is a group
e
34
Euler (a , n coprime phi func)
e
35
cARTESIAN PRODUCT
Q
36
def function
e
37
def graph of a function
em
38
unction space
e
39
graqph property
e
40
image
e
41
inj, surj, bij
e
42
Chinese RT revisited
e
43
def left right inverse
e
44
existence inverses theorem
e
45
inverse maps bbijective
e
46
injective if surjective other way
e
47
composition injsurbij
e
48
m = n iff f is bijective proof
e
49
def cardinality of a fintite set
e
50
pigeonhole principle
e
51
def equivalence relation
e
52
def equivalence classes
q
53
def partition
e
54
equiv part proof
e
55
set of permutations
e
56
equivalence permutation
e
57
def cyclic permutations
e
58
every perm as composition
e
59
even odd perm
e
60
sign
e
61
def fields rings
e
62
field axioms
e
63
integral domains
e
64
cancellation law
e
65
def polynomials
e
66
def leading coefficient
e
67
deg product poly is sum
e
68
irreducible polynomials
e
69
lemma 3.16
e
70
def lcm gcd polynomial
e
71
division for polynomials proof
e
72
Bezout identity polynomial
e
73
Euclids lemma polynomials
e
74
Unique factorisation polynomials
e
75
def matrix
e
76
as a field(mul, add)
e
77
matr mul is ass, bilinear
e
78
def invertible matrixq
e
79
a has left and right then full
e
80
inverting 2x2
e
81
linear map associated to matrix
e
82
def linear map
e
83
mul matrix linear map is linear
e
84
Linear maps come from matrices
e
85
def row checlon form
e
86
def rref
e
87
pivot
e
88
gaussian elimination algorithm
e
89
fundamental lemma
e
90
def linear subspace
e
91
def null space
e
92
def basis linear subspace
e
93
def standard basis
e
94
lemma 4.41
e
95
rank and nullity of matrix
e
96
rank nullity theorem
e
97
the two linear systems have the same solution
e
98
Gauss jordan method
ew
99
0 row means non invertible
e
100
theorem 4.53
e
101
def transpose
e
102
def length, distance, angle
e
103
def orthogonal
e
104
3x3 determinants
