The Nonlinear Library LW - Math-to-English Cheat Sheet by nahoj
Apr 9, 2024
11:02
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Math-to-English Cheat Sheet, published by nahoj on April 9, 2024 on LessWrong.
Say you've learnt math in your native language which is not English. Since then you've also read math in English and you appreciate the near universality of mathematical notation. Then one day you want to discuss a formula in real life and you realize you don't know how to pronunce "an".
Status: I had little prior knowledge of the topic. This was mostly generated by ChatGPT4 and kindly reviewed by @TheManxLoiner.
General
Distinguishing case
F,δ
"Big F" or "capital F", "little delta"
Subscripts
an
"a sub n" or, in most cases, just "a n"
Calculus
Pythagorean Theorem
a2+b2=c2
"a squared plus b squared equals c squared."
Area of a Circle
A=πr2
"Area equals pi r squared."
Slope of a Line
m=y2y1x2x1
"m equals y 2 minus y 1 over x 2 minus x 1."
Quadratic Formula
x=bb24ac2a
"x equals minus b [or 'negative b'] plus or minus the square root of b squared minus four a c, all over two a."
Sum of an Arithmetic Series
S=n2(a1+an)
"S equals n over two times a 1 plus a n."
Euler's Formula
eiθ=cos(θ)+isin(θ)
"e to the i theta equals cos [pronounced 'coz'] theta plus i sine theta."
Law of Sines
sin(A)a=sin(B)b=sin(C)c
"Sine A over a equals sine B over b equals sine C over c."
Area of a Triangle (Heron's Formula)
A=s(sa)(sb)(sc), where s=a+b+c2
"Area equals the square root of s times s minus a times s minus b times s minus c, where s equals a plus b plus c over two."
Compound Interest Formula
A=P(1+rn)nt
"A equals P times one plus r over n to the power of n t."
Logarithm Properties
logb(xy)=logb(x)+logb(y)
Don't state the base if clear from context: "Log of x y equals log of x plus log of y."
Otherwise "Log to the base b of x y equals log to the base b of x plus log to the base b of y."
More advanced operations
Derivative of a Function
dfdx or ddxf(x) or f'(x)
"df by dx" or "d dx of f of x" or "f prime of x."
Second Derivative
d2dx2f(x) or f''(x)
"d squared dx squared of f of x" or "f double prime of x."
Partial Derivative (unreviewed)
xf(x,y)
"Partial with respect to x of f of x, y."
Definite Integral
baf(x)dx
"Integral from a to b of f of x dx."
Indefinite Integral (Antiderivative)
f(x)dx
"Integral of f of x dx."
Line Integral (unreviewed)
Cf(x,y)ds
"Line integral over C of f of x, y ds."
Double Integral
badcf(x,y)dxdy
"Double integral from a to b and c to d of f of x, y dx dy."
Gradient of a Function
f
"Nabla f" or "gradient of f" to distinguish from other uses such as divergence or curl.
Divergence of a Vector Field
F
"Nabla dot F."
Curl of a Vector Field
F
"Nabla cross F."
Laplace Operator (unreviewed)
Δf or 2f
"Delta f" or "Nabla squared f."
Limit of a Function
limxaf(x)
"Limit as x approaches a of f of x."
Linear Algebra (vectors and matrices)
Vector Addition
v+w
"v plus w."
Scalar Multiplication
cv
"c times v."
Dot Product
vw
"v dot w."
Cross Product
vw
"v cross w."
Matrix Multiplication
AB
"A B."
Matrix Transpose
AT
"A transpose."
Determinant of a Matrix
|A| or det(A)
"Determinant of A" or "det A".
Inverse of a Matrix
A1
"A inverse."
Eigenvalues and Eigenvectors
λ for eigenvalues, v for eigenvectors
"Lambda for eigenvalues; v for eigenvectors."
Rank of a Matrix
rank(A)
"Rank of A."
Trace of a Matrix
tr(A)
"Trace of A."
Vector Norm
v
"Norm of v" or "length of v".
Orthogonal Vectors
vw=0
"v dot w equals zero."
With numerical values
Matrix Multiplication with Numerical Values
Let A=(1234) and B=(5678), then AB=(19224350).
"A B equals nineteen, twenty-two; forty-three, fifty."
Vector Dot Product
Let v=(1,2,3) and w=(4,5,6), then vw=32.
"v dot w equals thirty-two."
Determinant of a Matrix
For A=(1234), |A|=2.
"Determinant of A equals minus two."
Eigenvalues and Eigenvectors with Numerical Values
Given A=(2112), it has eigenvalues λ1=3 and λ2=1, with corresponding eigenvectors v1=(11) and v2=(11).
"Lambda ...
Say you've learnt math in your native language which is not English. Since then you've also read math in English and you appreciate the near universality of mathematical notation. Then one day you want to discuss a formula in real life and you realize you don't know how to pronunce "an".
Status: I had little prior knowledge of the topic. This was mostly generated by ChatGPT4 and kindly reviewed by @TheManxLoiner.
General
Distinguishing case
F,δ
"Big F" or "capital F", "little delta"
Subscripts
an
"a sub n" or, in most cases, just "a n"
Calculus
Pythagorean Theorem
a2+b2=c2
"a squared plus b squared equals c squared."
Area of a Circle
A=πr2
"Area equals pi r squared."
Slope of a Line
m=y2y1x2x1
"m equals y 2 minus y 1 over x 2 minus x 1."
Quadratic Formula
x=bb24ac2a
"x equals minus b [or 'negative b'] plus or minus the square root of b squared minus four a c, all over two a."
Sum of an Arithmetic Series
S=n2(a1+an)
"S equals n over two times a 1 plus a n."
Euler's Formula
eiθ=cos(θ)+isin(θ)
"e to the i theta equals cos [pronounced 'coz'] theta plus i sine theta."
Law of Sines
sin(A)a=sin(B)b=sin(C)c
"Sine A over a equals sine B over b equals sine C over c."
Area of a Triangle (Heron's Formula)
A=s(sa)(sb)(sc), where s=a+b+c2
"Area equals the square root of s times s minus a times s minus b times s minus c, where s equals a plus b plus c over two."
Compound Interest Formula
A=P(1+rn)nt
"A equals P times one plus r over n to the power of n t."
Logarithm Properties
logb(xy)=logb(x)+logb(y)
Don't state the base if clear from context: "Log of x y equals log of x plus log of y."
Otherwise "Log to the base b of x y equals log to the base b of x plus log to the base b of y."
More advanced operations
Derivative of a Function
dfdx or ddxf(x) or f'(x)
"df by dx" or "d dx of f of x" or "f prime of x."
Second Derivative
d2dx2f(x) or f''(x)
"d squared dx squared of f of x" or "f double prime of x."
Partial Derivative (unreviewed)
xf(x,y)
"Partial with respect to x of f of x, y."
Definite Integral
baf(x)dx
"Integral from a to b of f of x dx."
Indefinite Integral (Antiderivative)
f(x)dx
"Integral of f of x dx."
Line Integral (unreviewed)
Cf(x,y)ds
"Line integral over C of f of x, y ds."
Double Integral
badcf(x,y)dxdy
"Double integral from a to b and c to d of f of x, y dx dy."
Gradient of a Function
f
"Nabla f" or "gradient of f" to distinguish from other uses such as divergence or curl.
Divergence of a Vector Field
F
"Nabla dot F."
Curl of a Vector Field
F
"Nabla cross F."
Laplace Operator (unreviewed)
Δf or 2f
"Delta f" or "Nabla squared f."
Limit of a Function
limxaf(x)
"Limit as x approaches a of f of x."
Linear Algebra (vectors and matrices)
Vector Addition
v+w
"v plus w."
Scalar Multiplication
cv
"c times v."
Dot Product
vw
"v dot w."
Cross Product
vw
"v cross w."
Matrix Multiplication
AB
"A B."
Matrix Transpose
AT
"A transpose."
Determinant of a Matrix
|A| or det(A)
"Determinant of A" or "det A".
Inverse of a Matrix
A1
"A inverse."
Eigenvalues and Eigenvectors
λ for eigenvalues, v for eigenvectors
"Lambda for eigenvalues; v for eigenvectors."
Rank of a Matrix
rank(A)
"Rank of A."
Trace of a Matrix
tr(A)
"Trace of A."
Vector Norm
v
"Norm of v" or "length of v".
Orthogonal Vectors
vw=0
"v dot w equals zero."
With numerical values
Matrix Multiplication with Numerical Values
Let A=(1234) and B=(5678), then AB=(19224350).
"A B equals nineteen, twenty-two; forty-three, fifty."
Vector Dot Product
Let v=(1,2,3) and w=(4,5,6), then vw=32.
"v dot w equals thirty-two."
Determinant of a Matrix
For A=(1234), |A|=2.
"Determinant of A equals minus two."
Eigenvalues and Eigenvectors with Numerical Values
Given A=(2112), it has eigenvalues λ1=3 and λ2=1, with corresponding eigenvectors v1=(11) and v2=(11).
"Lambda ...