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 . 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. 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