mẫu câu toán học anh-việt

alpha plus beta is gamma, alpha plus beta equals gamma, alpha plus beta is equal to gamma, alpha plus beta makes gamma 38.. alpha is equal to the ratio of beta to gamma.. beta divided by

Nguyễn Hữu Điển

MẪU CÂU TOÁN HỌC

ANH - VIỆT

Bản 1.0

51

Lời nói đầu

Đây là bản nháp các thuật ngữ toán học Mục đích khởi đầu cho các bạn mới viết bài cho các báo Tập sách gồm các phần

1 Phần các thuật ngữ

2 Phần một số chú ý ngữ pháp

3 Một số các đọc ký hiệu và công thức

4 Các ký hiệu toán chuẩn soạn bằng LaTeX

5 Những ý kiến hay về viết báo tiếng anh và cách trình bầy chúng

Đây chỉ là bản nháp, còn rất nhiều nội dung chưa đưa vào đây và cũng chưa được chọn lọc, mong các bạn cho ý kiến

Mục lục

Lời nói đầu 3

Mục lục 4

Chương 9 Một số quy tắc đọc ký hiệu 5 9.1 Các ký hiệu công thức chung 5

9.2 Ký hiệu chuyên ngành 8

9.2.1 Logic 8

9.2.2 Set 8

9.2.3 Order 9

9.2.4 Algebra 9

9.2.5 Topology 9

9.2.6 Function 10

9.2.7 Probability 10

Chương 9

Một số quy tắc đọc ký hiệu

9.1 Các ký hiệu công thức chung

1 + 1 plus

4 × 4 multiplication sign (sign of multiplication)

5 : 5 division sign (sign of division)

10 ' 10 congruent to , is isomorphic to

11 α = β 11 alpha equals beta, alpha is equal to beta

12 α6= β 12 alpha is not beta, alpha is not equal to beta

13 α≈ β 13 alpha approximately equals beta

14 α± β 14 alpha plus or minus beta

15 α > β 15 alpha is greater than beta

16 α β 16 alpha is substantially greater than beta

17 α < β 17 alpha is less than beta

18 α β 18 alpha is substantially less than beta

19 α2> αn 19. alpha second is greater than alpha n-th

20 x−→ ∞ 20 x lends to infinity

21 x =∞ 21 x approaches infinity

24 α00 24 alpha double prime, alpha second prime

25 α0000 25 alpha triple prime

26 α 26 alpha vector, the mean value of alpha

9.1 Các ký hiệu công thức chung 6

30 α1 30 alpha first, alpha sub one, alpha suffix one

31 αn 31. alpha n-th, alpha sub n, alpha suffix n

32 f0

c 32. f prime sub c, f prime suffix c, f suffix c prime

33 α00

2 33 alpha second double prime, alpha double prime second

36 1000 36 ten seconds (ten inches)

37 α + β = γ 37 alpha plus beta is gamma, alpha plus beta equals gamma,

alpha plus beta is equal to gamma, alpha plus beta makes gamma

38 (α + β)2 38 alpha plus beta all squared

39 α− β = γ 39 alpha minus beta is gamma; alpha minus beta leaves

gamma

40 (2x− y) 40 bracket two x minus y close the brackets

41 2× 2 = 4 41 twice two in four

42 5× 5 = 25 42 five times five is twenty five, five multiplied by five equals

twenty five

43 S = v ˙t 43 S is equal to v multiplied by t; S equals v times t

44 α = β

γ 44. alpha is equal to the ratio of beta to gamma

45 β

γ = α 45. beta divided by gamma is alpha; beta by gamma equals

alpha

46 αβ2

β = αβ 46. alpha beta square (divided) by beta equals alpha beta

47 α

∞ = 0 47. alpha by infinity is equal to zero.

48 α

∞ = 0 48. alpha by infinity is equal to zero.

49 x±px2

− y2

y 49. x plus or minus square root of x square minus y square all

over y

50 α

β =

a

b 50. the ratio of alpha to beta equals the ratio of a to b; alpha to

beta is as a to b

51 1

52 1

53 1

54 3

55 21

56 0.5 56 o [ou] point five; zero point five; nought point five

57 0.002 57 o [ou] point o [ou] o [ou] two; zero point zero zero two

59 0.0000001 59 o [ou] point six noughts one

9.1 Các ký hiệu công thức chung 7

61 15.505 61 fifteen point five o [ou] five

62 x2 62 x square; x squared; the square of x; the second power of

x; x to the second power; x raised to the second power

63 x3 63 x cube; x cubed; x raised to the third power

64 xn 64. x to the n-th power;

65 x−n 65. x to the minus n-th power

66 √α 66. the square root of alpha.

67 √3α = β 67. the cube root of alpha is beta.

68 √5

α2 68 the fifth root of alpha square

69 α =√

R2+ X2 69 alpha equals to the square root of (capital) R square plus x

square

70 r α1+ A

2xb00 70 the square root of alpha first plus capital A divided to xb

double prime

71 df

dx 71. df over dx; the first derivative of f with respect to x

72 d2f

dx2 72 the second derivative of f with respect to x d two f over d x

square

73 dnf

dxn 73. the n-th derivative of f with respect to x

74 ∂2

f

∂x2 +∂

2

f

∂y2 = 0 74 partial d two f over partial d x square plus partial d two f

over partial d y square equals zero

75 y = f (x) 75 y is a function of x

76 Rβ

α 76. the intergral from alpha to beta; integral between limits

alpha and beta

77 d

dx

Rx

x 0F dx 77 d over dx of the integral from x0to x of capital F dx

78 E =P 1

αβ 78. capital E is equal to the ratio of the product P1 to the

prod-uct alpha beta

79 α m

n

= √n

αm 79. alpha to the m by n-th power equals the n-th root of alpha

to the m-th power

80 R dx

pc2

− y2

80 the integral of dx divided by the square root of c square minus y square

81 α + β

α− β =

c + d

c− d 81. alpha plus beta over alpha minus beta is equal to c plus dover c minus d.

82 V =

upsin2α− cos2α

82 V equals u square root of sin square alpha minus cosine square alpha

83 tan α = tan β

l 83. tangent alpha equals tangent beta divided by l

84 α3= log d 84 alpha cubed is equal to the logarithm of d to the base c

9.2 Ký hiệu chuyên ngành 8

86 (D− r1)[(D− r2)y] 86 open round brackets capital D minus r first close the round

brackets open square and round brackets capital D minus r second close the round bracket by y close the square brack-ets

87 fv =

mω2

α2

[rp2m2+ R2(R1+ω

2α2

rp )]

87 f sub v is equal to m omega square alpha square divided by square brackets, r, p square m square plus capital R second round brackets opened capital R first plus omega square al-pha square divided by rp round and square brackets closed

88 |fj(t1)− fj(t2)| 88 the absolute value of the quantity f sub j of t one minus f

sub j of t two

89 max

j=1,n

Pn

i=1aij(t) 89 maximum over j of the sum from i equals one to i equaqls

n of the modulus of aij of (t), where j runs from one to n

9.2 Ký hiệu chuyên ngành

9.2.1 Logic

90 ∀xF (x) 90 for all x F(x) holds

91 ∃xF (x) 91 there exists an x such that F(x) holds

92 A∧ B 92 A and B (Conjunction)

93 A∨ B 93 A or B (Disjunction)

95 A =⇒ B 95 A implies B (Implication)

96 A⇐⇒ B 96 A and B are logically equivalent (Equivalence)

9.2.2 Set

97 x∈ X 97 element x is a member of the set X (element x belongs to

the set X)

98 A⊂ B 98 A is a subset of B

99 A6⊆ B 99 A is a proper subset of B

101.A∪ B 101.Union of sets A and B

102.A∩ B 102.Intersection of sets A and B

103.Ac 103.Complement of the set A

104.A/R 104.Set of equivalence classes of A with respect to an

equiva-lence relation R

105.A× B 105.Cartesian product of A and B

106.Q

λ

Aλ 106.Cartesian product of the A sub lambda

107.{x|p(x)} 107.Set of all element x with the property p(x)

108.{Aλ}λ∈Λ 108.Family with index set Lambda

109.f : X→ Y 109.mapping f from X to Y

110.f|A 110.restriction of a mapping f to A

9.2 Ký hiệu chuyên ngành 9

111.g◦ f 111.Composite of mapping f and g

112.lim sup An 112.Supperior limit of the sequence of sets A sub n

113.lim inf An 113.Inferior limit of the sequence of sets A sub n

114.lim

−→Aλ 114.Inductive limit of A sub lambda

115.lim

←−Aλ 115.Projective limit of A sub lambda

9.2.3 Order

116.(a, b) 116.open interval

117.[a, b] 117.closed interval

118.(a, b], [a, b) 118.half-open- interval

9.2.4 Algebra

123.a≡ b (mod n) 123.a and b are congruent modulo n

125.det A 125.Determinant of a square matrix A

126.trA 126.Trace of a square matrix A

127.AT 127.Transpose of a matrix A

128.In 128.Unit matrix of degree n

129.A⊗ B 129.Kronecker product of two matrix A and B

130.M ∼= N 130.Two algebraic systems M and N are isomorphic

131.M/N 131.Quotiont space of an algebraic system M by N

132.dim M 132.Dimension of a linear space M

134.ker f 134.Kernel of a mapping f

135.Coim f 135.Coimage of a mapping f

136.Coker f 136.Cokernel of a mapping f

137.(¯a, ¯b) 137.inner product of two vectors ¯a and ¯b

138.M⊗ N 138.tensor product of two modules M and N

139.hom(M, N ) 139.Set of all homomorphisms from M to N

140.ΛM 140.Exterior algebra of a linear space M

9.2.5 Topology

141.a → a 141.sequence a sub n converges to a

9.2 Ký hiệu chuyên ngành 10

143.lim an 143.limit of a sequence a sub n

144.lim sup an 144.superior limit of a sequence a sub n

145.lim inf an 145.inferior limit of a sequence a sub n

146.E, clE¯ 146.Closure of a set E

147.E◦, int E 147.Interior of a act E

148.d(x, y) 148.distance between two point x and y

9.2.6 Function

151.grad ϕ 151.gradient of a function varphi

152.∆ϕ 152.Laplacian of a function varphi

153.D(u1, u2, , un)

D(x1, x2, , xn) 153.Jacobian determinat of (u1, u2, , un) with respect to

(x1, x2, , xn)

154.|z| 154.absolute value of z

155.Re z 155.real part of a complex number z

156.Im z 156.Imaginary part of a complex number z

157.arg z 157.Argument of a complex number z

158.D(T ) 158.Domain of an operator T

159.R(T ) 159.Range of an operator T

160.Supp T 160.Support of a function f

9.2.7 Probability

161.P (E) 161.Probability of an event E

162.E(X) 162.Mean (expectation) of a random variable X

163.V (X)δ2

(X) 163.Variance of a random variable X

164.ρ(X, Y ) 164.Correlation coefficient of two random variables X and Y

165.E(X|Y ) 165.Conditional expectation of random variable X under the

condition Y