Symbol |
Description |
Location |
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is in the set
|
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the natural numbers |
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the integers |
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|
the rational numbers |
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the real numbers |
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the complex numbers |
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is a subset of
|
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the empty set |
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the union of sets and
|
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the intersection of sets and
|
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complement of the set
|
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difference between sets and
|
Paragraph |
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Cartesian product of sets and
|
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( times) |
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identity mapping |
Paragraph |
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inverse of the function
|
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is congruent to modulo
|
Example 1.30 |
|
factorial |
Example 2.4 |
|
binomial coefficient
|
Example 2.4 |
|
divides
|
Paragraph |
|
greatest common divisor of and
|
Paragraph |
|
power set of
|
Exercise 2.4.12 |
|
the least common multiple of and
|
Exercise 2.4.23 |
|
the integers modulo
|
Paragraph |
|
group of units in
|
Example 3.11 |
|
the matrices with entries in
|
Example 3.14 |
|
the determinant of
|
Example 3.14 |
|
the general linear group |
Example 3.14 |
|
the group of quaternions |
Example 3.15 |
|
the multiplicative group of complex numbers |
Example 3.16 |
|
the order of a group |
Paragraph |
|
the multiplicative group of real numbers |
Example 3.24 |
|
the multiplicative group of rational numbers |
Example 3.24 |
|
the special linear group |
Example 3.26 |
|
the center of a group |
Exercise 3.5.48 |
|
cyclic group generated by
|
Theorem 4.3 |
|
the order of an element
|
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|
|
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|
the circle group |
Paragraph |
|
the symmetric group on letters |
Paragraph |
|
cycle of length
|
Paragraph |
|
the alternating group on letters |
Paragraph |
|
the dihedral group |
Paragraph |
|
index of a subgroup in a group
|
Paragraph |
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the set of left cosets of a subgroup in a group
|
Theorem 6.8 |
|
the set of right cosets of a subgroup in a group
|
Theorem 6.8 |
|
does not divide
|
Theorem 6.19 |
|
Hamming distance between and
|
Paragraph |
|
the minimum distance of a code |
Paragraph |
|
the weight of
|
Paragraph |
|
the set of matrices with entries in
|
Paragraph |
|
null space of a matrix
|
Paragraph |
|
Kronecker delta |
Lemma 8.27 |
|
is isomorphic to a group
|
Paragraph |
|
automorphism group of a group
|
Exercise 9.4.37 |
|
|
Exercise 9.4.41 |
|
inner automorphism group of a group
|
Exercise 9.4.41 |
|
right regular representation |
Exercise 9.4.44 |
|
factor group of mod
|
Paragraph |
|
commutator subgroup of
|
Exercise 10.4.14 |
|
kernel of
|
Paragraph |
|
matrix |
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orthogonal group |
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|
length of a vector
|
Paragraph |
|
special orthogonal group |
Paragraph |
|
Euclidean group |
Paragraph |
|
orbit of
|
Paragraph |
|
fixed point set of
|
Paragraph |
|
isotropy subgroup of
|
Paragraph |
|
normalizer of s subgroup
|
Paragraph |
|
the ring of quaternions |
Example 16.7 |
|
the Gaussian integers |
Example 16.12 |
|
characteristic of a ring
|
Paragraph |
|
ring of integers localized at
|
Exercise 16.7.33 |
|
degree of a polynomial |
Paragraph |
|
ring of polynomials over a ring
|
Paragraph |
|
ring of polynomials in indeterminants |
Paragraph |
|
evaluation homomorphism at
|
Theorem 17.5 |
|
field of rational functions over
|
Example 18.5 |
|
Euclidean valuation of
|
Paragraph |
|
field of rational functions in
|
Item 18.4.7.a |
|
field of rational functions in
|
Item 18.4.7.b |
|
is less than
|
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join of and
|
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meet of and
|
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|
largest element in a lattice |
Paragraph |
|
smallest element in a lattice |
Paragraph |
|
complement of in a lattice |
Paragraph |
|
dimension of a vector space
|
Paragraph |
|
direct sum of vector spaces and
|
Item 20.5.17.b |
|
set of all linear transformations from into
|
Item 20.5.18.a |
|
dual of a vector space
|
Item 20.5.18.b |
|
smallest field containing and
|
Paragraph |
|
dimension of a field extension of over
|
Paragraph |
|
Galois field of order
|
Paragraph |
|
multiplicative group of a field
|
Paragraph |
|
Galois group of over
|
Paragraph |
|
field fixed by the automorphism
|
Proposition 23.14 |
|
field fixed by the automorphism group
|
Corollary 23.15 |
|
discriminant of a polynomial |
Exercise 23.5.22 |