Mathematical Conventions Survey

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Everyone knows that 36 questions can lead to love. But can answering questions lead to hate? Research has shown that answering the following 100 questions with friends or potential lovers is a leading cause of murder among mathematicians in the United States. Terrence Tao credits the 100 questions for "... singlehandedly prevent[ing] the resolution of the Riemann Hypothesis", in a post-cage fight interview. His former colleague was unavailable for comment. Try the 100 questions today!

(Contact: thomas dot lam at cims.nyu.edu)

(Update: Results are OUT! https://cims.nyu.edu/~tjl8195/survey/results.html)

All questions are optional. You are encouraged to skip any question that you do not understand or otherwise cannot give an answer to for any reason.

1. The naturals start at

Clear selection

2. Settle the debate.

Clear selection

3. 0 to the power 0 is

indeterminate

undefined

Other:

Clear selection

4. Manifolds are

second countable

not necessarily second countable

Clear selection

5. Euler's totient function is denoted

𝜙

Other:

Clear selection

6. sqrt(-1) is

i, by definition

i, but not by definition

not defined

Other:

Clear selection

7. The empty set is

{}

∅

𝜙 (that's a phi)

Other:

Clear selection

m+n

n+m

Clear selection

m/n

n/m

Clear selection

10. The empty graph is

connected

not connected

Clear selection

11. The set of complex numbers is

\mathbb{C} i.e. ℂ

\mathbf{C} i.e. 𝗖

Other:

Clear selection

12.

Let V be a vector space.

Let E be a vector space.

Let V be a linear space.

Let E be a linear space.

Clear selection

13. f(x) = 3 is

increasing

not increasing

Clear selection

14. The inner product of v and w is

<v, w>

v · w

(v, w)

Other:

Clear selection

15. Fill in the blank: "E = {n ∈ ℤ ___ n is even}"

s.t.

such that

∋

Other:

Clear selection

16. ⊂ means

strict subset

not necessarily strict subset

I don't use this notation

Clear selection

17. The Laplace equation is

Δu = 0

-Δu = 0

Clear selection

18. The heat equation is

-Δu + u̇ = 0

-Δu + ∂ₜu = 0

-Δu + uₜ = 0

Clear selection

19. Let ___ be a category.

C ($C$)

ℂ ($\mathbb{C}$)

𝒞 ($\mathcal{C}$ or $\mathscr{C}$)

Other:

Clear selection

20. Numbers

exist (or can exist)

do not exist (or cannot exist)

Clear selection

21. The divergence of F is

div F

∇ · F

Clear selection

22. The curl of F is

curl F

∇×F

Clear selection

23. The 5th octant is

(+, -, -)

(-, +, -)

(-, -, +)

(-, +, +)

(+, -, +)

(+, +, -)

(-, -, -)

Clear selection

24. ℤₚ is

the integers mod p; the cyclic group of p elements

the ring of p-adic integers

the finite field of p elements

Other:

Clear selection

25. Up is

along the y axis

along the z axis

Clear selection

26. The existence and uniqueness theorem for ODEs is

Cauchy–Lipschitz

Picard–Lindelöf

Cauchy–Lipschitz–Picard–Lindelöf

Picard

Other:

Clear selection

27. Choose how many mathematicians you want to upset.

I accept the axiom of choice

I reject the axiom of choice, but accept the axiom of countable choice.

I reject the axiom of countable choice.

Clear selection

28. The set of the first n positive integers is

{1,2,3, …, n}

{1,2,3, ⋯, n} (those should be centered dots ala \cdots)

Clear selection

29. (Lowercase) epsilon is

Clear selection

30. My proof is done.

QED

Q.E.D.

white box

black box

Other:

Clear selection

31. Let R be a ring.

R is commutative

R need not be commutative

Clear selection

32. Let R be a ring.

R is unital

R need not be unital

Clear selection

33. The Fourier Transform of f is

Option 1

Option 2

Option 3

Option 4

Other:

Clear selection

34. The group of symmetries of a regular n-gon is

Dₙ ($D_n$)

D₂ₙ ($D_{2n}$)

Clear selection

35. T is a linear map on a vector space V. x is an element of V. T applied to x is

T(x)

<T, x>

Other:

Clear selection

36. The order of operations is

PEMDAS

BODMAS (or similar)

Other:

Clear selection

37. The mnemonic for the signs of trig functions is

ASTC ("All Students Take Calculus", e.g.)

CAST

Clear selection

38. The second tetration of x is

²x

x↑↑2

Clear selection

39. The Lebesgue measure is

𝓛

Other:

Clear selection

40. The Fibonacci sequence is

F₀ = 1, F₁ = 1, F₂ = 2, ...

F₁ = 1, F₂ = 1, F₃ = 2, ...

Clear selection

41. The Jacobian matrix of a function f: ℝⁿ → ℝᵐ

has dimensions m x n

has dimensions n x m

Clear selection

42. The Jacobian matrix of a function f: ℝⁿ → ℝᵐ

is Df

is Jf

is ∇f

Other:

Clear selection

43. The inverse function of sine is

sin¯¹(x)

arcsin(x)

asin(x)

Arcsin(x)

Asin(x)

Clear selection

44. a and x are elements of a group. The conjugation of x via a is

axa⁻¹

a⁻¹xa

Clear selection

45. What is a tensor?

A multilinear map of type Vᵐ × (V*)ⁿ → ℝ

A multilinear map of type Vᵐ × (V*)ⁿ → Vˢ × (V*)ᵗ

A smooth section of a vector bundle formed by objects of the first option's type

A smooth section of a vector bundle formed by objects of the second option's type

An element of a tensor product of vector spaces

A multidimensional array

An object that transforms like a tensor

Other:

Clear selection

46. The base of log is

Clear selection

47. x=0 for f(x) = -x^2 is a/an

global maximum

absolute maximum

Clear selection

48. x=0 for f(x) = cos(x) is a

local maximum

relative maximum

Clear selection

49. Three times four is

3×4

3 · 4

(3)(4)

Clear selection

50. In the Sleeping Beauty problem, the probability that the coin came up heads is

1/3

1/2

Other:

Clear selection

51. The set of all real x satisfying 1 < x < 2 is

(1, 2)

]1, 2[

Clear selection

52. x is an element of ℝⁿ. The norm of x is

|x|

||x||

Clear selection

53. The Lᵖ space of functions on the open interval (0,1) is

Lᵖ(0,1)

Lᵖ((0,1))

Lₚ(0,1)

Lₚ((0,1))

Other:

Clear selection

54. Let M be a smooth manifold. For a vector bundle E → M, we denote by Γ(E) the set of smooth sections of E. TM denotes the tangent bundle.

A connection ∇ on M has type

∇ : TM × Γ(TM) → TM

∇ : TM × Γ(E) → E, where E need not be TM

∇ : Γ(TM) × Γ(TM) → Γ(TM)

∇ : Γ(TM) × Γ(E) → Γ(E), where E need not be TM

Other:

Clear selection

55. Bounded and equicontinuous sequences of functions on a separable metric space admit a uniformly converging subsequence.

This is Arzelà–Ascoli.

This is Ascoli–Arzelà.

Clear selection

56. 3 and 5 are congruent modulo 2.

3 ≡ 5 (mod 2)

3 ≡ 5 mod 2

Other:

Clear selection

57. f : X → Y

The range of f is Y.

The range of f is f(X).

Clear selection

58. log²(x) is

The iterated log, log(log(x))

log(x), squared

Clear selection

59. A, B, C, and D are points in the real projective plane. The quantity (A, B; C, D) is a

cross ratio

double ratio

Clear selection

60. A straw has

one hole

two holes

Clear selection

61. The golden ratio is

approximately 1.618

approximately 0.618

Clear selection

62. The floor of x is

⌊x⌋

[x]

Clear selection

63. The set of limit points of {1} is

{}

{1}

Clear selection

64. f(x) = 3x is

one-to-one

injective

Clear selection

65. The three real numbers a, b, c are to be ordered without loss of generality.

a ≤ b ≤ c

a ≥ b ≥ c

Clear selection

66. The integral of the function x+1 over the interval (0,1) is

∫₀¹ x+1 dx

∫₀¹ (x+1) dx

Clear selection

67. A is a matrix over the field of complex numbers. The conjugate transpose of A is

Aᴴ

A†

Other:

Clear selection

68. A smooth map f: M → N induces a smooth map df(x) between the tangent space at x and the tangent space at f(x).

df is called a pushforward.

df is called a differential.

df is called a derivative.

df is called a total derivative.

Other:

Clear selection

69. My proof has arrived at a contradiction.

⊥

⨳

※

⇒⇐

↯

Opq

↮ (If displayed improperly: That's a slash in the middle of a double arrow)

I have no symbol for this.

Other:

Clear selection

70. The entire function f(z) = eᶻ is

conformal (because the derivative never vanishes)

not conformal (because it is not injective)

Clear selection

71. The expected value of a random variable X is

𝔼[X]

𝔼(X)

𝔼X

E[X]

E(X)

Other:

Clear selection

72. 1/x is

continuous

not continuous

Clear selection

73. The vector field F(x, y, z) = (yz, xz, xy) is

irrotational

curl-free

longitudinal

curl-less

Clear selection

74. The cardinality of a set S is

|S|

card S

Other:

Clear selection

75. These questions are all about

math

maths

Clear selection

76. Endow ℚ with the usual metric. Let E be the subset of ℚ consisting of all rationals in (0, 1).

E is precompact because for any r > 0, it can be covered with finitely many balls of radius r.

E is not precompact because its closure is not compact.

Clear selection

77. The indicator function is notated via the character

𝕀

𝟙

Other:

Clear selection

78. The (preferred) shorthand for the sequence a₁, a₂, a₃, ... is

{aₙ}ₙ

(aₙ)ₙ

Other:

Clear selection

79. The n-volume of the unit ball in n dimensions is

αₙ

ωₙ

Other:

Clear selection

80. When integrating, the d of dx should be

upright (like $\mathrm{d}x$)

not upright (like $dx$)

Clear selection

81. [n] is

{1, 2, ..., n}

{0, 1, ..., n-1}

Clear selection

82. A signed measure

is real-valued

can take values of ±∞ (but not both)

Clear selection

83. Brownian motion is

continuous

continuous almost surely

Clear selection

84. The complement of the set A is

Aᶜ

Other:

Clear selection

85. The notation for the differential when integrating over a 2-dimensional surface embedded in Euclidean space is

dσ

dΣ

d𝓗²

Other:

Clear selection

86. Partitions (of positive integers) are visually represented via

Young tableaux

Ferrers diagrams

Clear selection

87. The unit outward normal is

ν (that's a nu)

Other:

Clear selection

88. The Yoneda embedding is

𝒴

よ

Other:

Clear selection

89. Your go-to dimension for a Euclidean space is

Other:

Clear selection

90. Let m and n be relatively prime positive integers. I cannot procure exactly mn - m - n dollars using only m-dollar bills and n-dollar bills. But any larger integer quantity can be made.

This is the Frobenius Coin theorem.

This is the Chicken McNugget theorem.

Clear selection

91. The convolution of f and g is

f ∗ g

f ⋆ g

Other:

Clear selection

92. LaTeX is pronounced

lay-teks

lay-tek

lah-teks

lah-tek

luhtek

Other:

Clear selection

93. X and Y are independent.

X ⊥ Y

X ⫫ Y

Other:

Clear selection

94. The larger number among x and y is

max(x, y)

max{x, y}

Other:

Clear selection

95. The collection of morphisms from an object A to an object B is denoted

hom(A, B)

Hom(A, B)

Mor(A, B)

Other:

Clear selection

96. A and B are two distinct points in the Euclidean plane. The length of the segment that connects A and B is

|AB|

Other:

Clear selection

97. Let f(x, y) be a function in two variables. The function that sends y to f(x, y) for a fixed value of x is

f(x, ·)

f(x, –)

Other:

Clear selection

98. The function f(x) = 3x + 1 is

linear

not linear

Clear selection

99. The floor of exp(exp(exp(79)))

exists

does not exist

Clear selection

100. The value of 6÷2(1+2) is

f*** you

Clear selection

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