mẫu câu toán học anh-việt

Nguyễn Hữu Điển
MẪU CÂU TOÁN HỌC
ANH - VIỆT
Bản 1.0
NHÀ XUẤT BẢN GIÁO DỤC
51
GD-05
89/176-05 Mã số: 8I092M5
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.
Hà Nội, ngày 5 tháng 8 năm 2009
Nguyễn Hữu Điển
Mục lục
Lời nói đầu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Mục lục . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chương 9. Một số quy tắc đọc k ý 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
2. − 2. minus
3. ± 3. plus or minus
4. × 4. multiplication sign (sign of multiplication)
5. : 5. division sign (sign of division)
6. ( ) 6. round brackets (parentheses)
7. [ ] 7. square brackets (br ackets)
8. { } 8. curly brackets (braces)
9. ∼ 9. equivalent, similar
10.  10. congruent to , is isomorphic to
11. α = β 11. alpha equals beta, alpha is equal to beta
12. α = 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. α
2
> α
n
19. alpha second is greater than alpha n-th
20. x −→ ∞ 20. x lends to infinity
21. x = ∞ 21. x approaches infinity

22. n! 22. n factorial
23. α

23. alpha prime
24. α

24. alpha double prime, alpha second prime
25. α

25. alpha triple prime
26.
α
26. alpha vector, the mean value of alpha
27. ˙x 27. the first derivative
28. ¨x 28. the second derivative
29.

x
29. the third derivative
9.1. Các ký hiệu công thức chung 6
30. α
1
30. alpha first, alpha sub one, alpha suffix one
31. α
n
31. alpha n-th, alpha sub n, alpha suffix n
32. f

c
32. f prime sub c, f prime suffix c, f suffix c prime

33. α

2
33. alpha second double prime, alpha double prime second
34. 90
◦
34. ninely degree
35. 6

35. six minute
36. 10

36. ten seconds (ten inches)
37. α + β = γ 37. alpha plus beta is gamma, alpha plus be ta 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 bet a 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 twe nt y 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.
αβ
2
β
= αβ 46. alpha beta square (divided) by b eta 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 ±

x
2
− y
2
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
2
51. a half (a one half)
52.
1
3
52. a third (a one third)
53.
1
4
53. a forth; a squarter
54.
3
4
54. three fourths; three squarters
55. 2
1
2
55. two and a half
56. 0.5 56. o [ou] point five; zero po int five; nought point five.
57. 0.002 57. o [ou] point o [ou] o [ou] two; zero point zero zero two.

58. .002 58. point two noughts two.
59. 0.0000001 59. o [ou] point six noughts one .
9.1. Các ký hiệu công thức chung 7
60. 1.12 60. one point one two.
61. 15.505 61. fifteen point five o [ou] five
62. x
2
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. x
3
63. x cube; x cubed; x r aised to the third power.
64. x
n
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.
3
√
α = β 67. the cube root of alpha is beta.
68.
5
√
α
2

68. the fifth root of alpha square.
69. α =
√
R
2
+ X
2
69. alpha equals to the square root of (capital) R square plus x
square.
70.

α
1
+ A
2xb

70. the square root of alpha first plus cap ital A divided to xb
double prime.
71.
df
dx
71. df over dx; the first de rivative of f with respect to x.
72.
d
2
f
dx
2
72. the second derivative of f with respect to x d two f over d x
square.

73.
d
n
f
dx
n
73. the n-th derivative of f with respect to x.
74.
∂
2
f
∂x
2
+
∂
2
f
∂y
2
= 0 74. partial d two f over partial d x square plus part ial d two f
over partial d y square equals zero.
75. y = f(x) 75. y is a function of x.
76.

β
α
76. the intergral from alpha to beta; integral between limits
alpha and beta.
77.
d

dx

x
x
0
F dx 77. d over dx of the inte gral from x
0
to 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
√
α
m
79. alpha to the m by n-th power equals the n-th root of alpha
to the m-th power.
80.

dx

c
2
− y

2
80. the inte gral of dx divided by the square roo t 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 d
over c minus d.
82. V =
u

sin
2
α −cos
2
α
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. α
3
= log
c
d 84. alpha cubed is equal to the logarithm of d to the base c.

85. [(x + a)
p
−
r
√
x]
−q
85. x+a in round brackets t o the power p minus the r-th root
of x all (in square brackets) to the minus q-th power.
9.2. Ký hiệu chuyên ngành 8
86. (D − r
1
)[(D − r
2
)y] 86. open round brackets capital D minus r first close t he round
brackets open square and round brackets capital D minus r
second close the round bracket by y close the square brack-
ets.
87. f
v
=
mω
2
α
2
[rp
2
m
2
+ R

2
(R
1
+
ω
2
α
2
rp
)]
87. f sub v is equal t o m omega square alpha square divided by
square brackets, r, p square m square plus capital R second
round b rackets opened capital R first plus o mega square al-
pha square divided by rp round and square brackets closed.
88. |f
j
(t
1
) −f
j
(t
2
)| 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

n
i=1

a
ij
(t) 89. maximum over j of the sum from i equals one to i equaqls
n of the modulus of a
ij
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)
94. ¬A 94. not A (negation)
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 me mber of the set X (element x belongs to
the set X)
98. A ⊂ B 98. A is a subset of B
99. A ⊆ B 99. A is a proper subset of B
100. ∅ 100. Empty set
101. A ∪B 101. Union of sets A and B
102. A ∩B 102. Int ersection of sets A and B
103. A
c
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.


λ
A
λ
106. Cartesian product of t he A sub lambda
107. {x|p(x)} 107. Set of all element x with the property p(x)
108. {A
λ
}
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 A
n
112. Supperior limit of the sequence of sets A sub n
113. lim inf A
n
113. Inferior limit of the sequence of sets A sub n
114. lim
−→
A
λ
114. Inductive limit of A sub lambda
115. lim
←−

A
λ
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
119. max A 119. Maximum of A
120. min A 120. Minimum of A
121. sup A 121. Supremum of A
122. inf A 122. infimum of A
9.2.4. Algebra
123. a ≡ b (mod n) 123. a and b are congruent modulo n
124. a|b 124. a dividies b
125. det A 125. Determinant of a square matrix A
126. trA 126. Trace of a square matrix A
127. A
T
127. Transpose of a matrix A
128. I
n
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
133. f 133. Image of a mapping f

134. ker f 134. Kernel of a mapp ing 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. Λ
M
140. Exterior algebra of a linear space M
9.2.5. Topology
141. a
n
→ a 141. sequence a sub n converges to a
142. a
n
↓ a(a
n
↑ a) 142. sequence a sub n converges monotically decreasingly (in-
creasingly) to a
9.2. Ký hiệu chuyên ngành 10
143. lim a
n
143. limit of a sequence a sub n
144. lim sup a
n
144. superior limit of a sequence a sub n

145. lim inf a
n
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
149. ∂C 149. Boundary of C
150. ||x|| 150. Norm of x
9.2.6. Function
151. grad ϕ 151. gradient of a function varphi
152. ∆
ϕ
152. Laplacian of a function varphi
153.
D(u
1
, u
2
, , u
n
)
D(x
1
, x
2

, , x
n
)
153. Jacobian determinat of (u
1
, u
2
, , u
n
) with respect to
(x
1
, x
2
, , x
n
)
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 r ando m variable X
163. V (X)δ
2
(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