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Year 1 - Algebra > Definitions > Flashcards

Definitions Flashcards

1
Q

Roots of unity

A
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2
Q

Order of a root of unity

A
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3
Q

Primitive root of unity

A
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4
Q

Prime number

A
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5
Q

Lcm, gcd

A
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6
Q

Congruent modulo n

A
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7
Q

Congruence classes

A
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8
Q

Congruence equations

A
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9
Q

Groups of units

A
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10
Q
A

Number of integers

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11
Q

Sets

A

A collection of elements

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12
Q

Cartesian product

A
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13
Q

Functions

A
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14
Q

Graph of a function

A
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15
Q

Identity map

A
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16
Q

Composition

A
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17
Q

Inverse

A
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18
Q

Function spaces

A
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19
Q

Image of a function
(Compare 2 sets as well)

A
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20
Q

Injective

A
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21
Q

Surjective

A
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22
Q

Bijective

A
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23
Q

Left and right inverse

A
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24
Q

Finite set

A
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25
Q

Cardinality

A
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26
Q

Countable sets

A
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27
Q

Equivalence relation

A
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28
Q

Equivalence classes

A
29
Q

Partition of a set

A
30
Q

The set of permutation on n letters

A
31
Q

Cyclic permutations / cycle

A
32
Q

Transposition

A
33
Q

Even and odd permutations

A
34
Q

Sign of a permutation

A
35
Q

Field

A
36
Q

Additive group

A
37
Q

Ring

A
38
Q

Commutative ring

A
39
Q

Integral domains

A
40
Q

Polynomials in x

A
41
Q

Equal polynomials

A
42
Q

Addition of polynomials

A
43
Q

Multiplication of polynomials

A
44
Q
A

With coefficients in f

45
Q

Leading coefficients

A
46
Q

Degree of f

A
47
Q

Monic

A

If the leading coefficient is 1

48
Q

Irreducible polynomials

A
49
Q

lcm of a polynomial

A
50
Q

gcd of a polynomial

A
51
Q

Equal matrices

A
52
Q
A

Wrong way around (too obvious to change)

53
Q

Compact matrix multiplication

A
54
Q
A
55
Q

Invertible matrix

A
56
Q

Linear maps associated with a matrix
Include formula

A
57
Q

Linear map

A
58
Q

Row Echelon form

A

Eg the 0 matrix

59
Q

RREF

A
60
Q

Linear subspace

A
61
Q

Null space of a matrix

A
62
Q

Basis of a linear subspace

A
63
Q

Standard basis

A
64
Q

Nullity of a matrix

A
65
Q

Rank of a matrix

A
66
Q

Transposition

A
67
Q

Dot product / the angle

A
68
Q

Euclidean length
Euclidean distance

A
69
Q

Orthogonal matrix

A

Year 1 - Algebra (6 decks)

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