Maths vocab in English
Maths vocab in English. Quelques détails importants : — math vs. maths : les deux sont corrects toutefois math relève de l'anglais américain et.
On a new limit theorem in probability theory (Translation ofSur un
15 ???. 2018 ?. (Sur un nouveau théor`eme-limite de la théorie des probabilités) ... no doubt that it is Cramér who initiated the mathematical.
Mathematical English (a brief summary)
Mathematical English (a brief summary). Jan Nekovár Basic arithmetic operations. Addition: ... probability probabilité die (pl. dice) dé.
Naming Infinity: A True Story of Religious Mysticism and
Mathematics—France—Philosophy. 6. Set theory. I. Kantor Jean-Michel. II. Title. QA27.R8G73 2009. 510.947?0904
en-lexique-math-juillet2015.pdf
Lexique de mathématiques – Mathematics Glossary / 1. ENGLISH. Notes: symbols abbreviations
The origins and legacy of Kolmogorovs Grundbegriffe
5 ????. 2018 ?. The British statisticians had little interest in mathematical probability theory and hence no puzzle to solve concerning how to link it to the ...
The Origins of the Word “Martingale”
Journ@l électronique d'Histoire des Probabilités et de la Statistique/ tingales” in Mathématiques & Sciences Humaines/Mathematical Social Sci-.
Recent Advances in Mathematical Statistics
(16) BOREL E. Une objection 'a la definition empirique de la probabilite. Sci. U.R.S.S.
AHAJIH3A
Functional Analysis Optimization and Mathematical Economics. Malliavin P. Intégration of Probabilités. Analyse de Fourier et.
Curriculum vitae Laure Marêché
2016-2019: PhD in Mathematics at the Laboratoire de Probabilités Statistique et Modélisation
Mathematical English (a brief summary)
Jan Nekov´ar
Universit´e Paris 6c
?Jan Nekov´ar 2011 1Arithmetic
Integers
0zero10ten20twenty
1one11eleven30thirty
2two12twelve40forty
3three13thirteen50fifty
4four14fourteen60sixty
5five15fifteen70seventy
6six16sixteen80eighty
7seven17seventeen90ninety
8eight18eighteen100one hundred
9nine19nineteen1000one thousand
-245minus two hundred and forty-five22 731twenty-two thousand seven hundred and thirty-one
1 000 000one million
56 000 000fifty-six million
1 000 000 000one billion [US usage, now universal]
7 000 000 000seven billion [US usage, now universal]
1 000 000 000 000one trillion [US usage, now universal]
3 000 000 000 000three trillion [US usage, now universal]
Fractions [= Rational Numbers]
12 one half38 three eighths 13 one third269 twenty-six ninths 14 one quarter [= one fourth]-534 minus five thirty-fourths 15 one fifth237 two and three sevenths 117minus one seventeenth
Real Numbers
-0.067minus nought point zero six seven81.59eighty-one point five nine
-2.3·106minus two point three times ten to the six [=-2 300 000minus two million three hundred thousand]4·10-3four times ten to the minus three
[= 0.004 = 4/1000four thousandths]π[= 3.14159...]pi [pronounced as 'pie"]
e[= 2.71828...]e [base of the natural logarithm] 2Complex Numbers
ii3 + 4ithree plus four i
1-2ione minus two i1-2i= 1 + 2ithe complex conjugate of one minus two i equals one plus two i
The real part and the imaginary part of 3 + 4iare equal, respectively, to 3 and 4.Basic arithmetic operations
Addition:3 + 5 = 8three plus five equals [= is equal to] eight Subtraction:3-5 =-2three minus five equals [=...] minus two Multiplication:3·5 = 15three times five equals [=...] fifteen Division:3/5 = 0.6three divided by five equals [=...] zero point six (2-3)·6 + 1 =-5two minus three in brackets times six plus one equals minus five1-32+4
=-1/3one minus three over two plus four equals minus one third4! [= 1·2·3·4]four factorial
Exponentiation, Roots
52[= 5·5 = 25]five squared
53[= 5·5·5 = 125]five cubed
54[= 5·5·5·5 = 625]five to the (power of) four
5 -1[= 1/5 = 0.2]five to the minus one 5 -2[= 1/52= 0.04]five to the minus two⎷3 [= 1.73205...]the square root of three3⎷64 [= 4]the cube root of sixty four
5⎷32 [= 2]the fifth root of thirty two
In the complex domain the notation
n⎷ais ambiguous, since any non-zero complex number hasndifferentn-th roots. For example,4⎷-4 has four possible values:±1±i(with all possible combinations of signs). (1 + 2)2+2one plus two, all to the power of two plus two
eπi=-1e to the (power of) pi i equals minus one
Divisibility
The multiples of a positive integeraare the numbersa,2a,3a,4a,.... Ifbis a multiple ofa, we also say thatadividesb, or thatais a divisor ofb(notation:a|b). This is equivalent to ba being an integer. 3Division with remainder
Ifa,bare arbitrary positive integers, we can dividebbya, in general, only with a remainder. For example, 7 lies between the following two consecutive multiples of 3:2·3 = 6<7<3·3 = 9,7 = 2·3 + 1?
??73 = 2 +13 In general, ifqais the largest multiple ofawhich is less than or equal tob, then b=qa+r, r= 0,1,...,a-1. The integerq(resp.,r) is thequotient(resp., theremainder) of the division ofbbya.Euclid"s algorithm
This algorithm computes thegreatest common divisor(notation: (a,b) = gcd(a,b)) of two positive integersa,b. of the division ofbbya. This procedure, which preserves the gcd, is repeated until we arrive atr= 0.Example.Compute gcd(12,44).
44 = 3·12 + 8
12 = 1·8 + 4
8 = 2·4 + 0gcd(12,44) = gcd(8,12) = gcd(4,8) = gcd(0,4) = 4.
This calculation allows us to write the fraction
4412in its lowest terms, and also as a continued fraction: 4412
=44/412/4=113 = 3 +11 + 12 If gcd(a,b) = 1, we say thataandbarerelatively prime. addadditionner algorithmalgorithme Euclid"s algorithmalgorithme de division euclidienne bracketparenth`ese left bracketparenth`ese `a gauche right bracketparenth`ese `a droite curly bracketaccolade denominatordenominateur 4 differencediff´erence dividediviser divisibilitydivisibilit´e divisordiviseur exponentexposant factorialfactoriel fractionfraction continued fractionfraction continue gcd [= greatest common divisor]pgcd [= plus grand commun diviseur] lcm [= least common multiple]ppcm [= plus petit commun multiple] infinityl"infini iterateit´erer iterationit´eration multiplemultiple multiplymultiplier numbernombre even numbernombre pair odd numbernombre impair numeratornumerateur paircouple pairwisedeux `a deux powerpuissance productproduit quotientquotient ratiorapport; raison rationalrationnel(le) irrationalirrationnel(le) relatively primepremiers entre eux remainderreste rootracine sumsomme subtractsoustraire 5
Algebra
Algebraic Expressions
A=a2capital a equals small a squared
a=x+ya equals x plus y b=x-yb equals x minus y c=x·y·zc equals x times y times z c=xyzc equals x y z (x+y)z+xyx plus y in brackets times z plus x y x2+y3+z5x squared plus y cubed plus z to the (power of) five
x n+yn=znx to the n plus y to the n equals z to the n (x-y)3mx minus y in brackets to the (power of) three m x minus y, all to the (power of) three m 2 x3ytwo to the x times three to the y ax2+bx+ca x squared plus b x plus c⎷x+3⎷ythe square root of x plus the cube root of y
n⎷x+ythe n-th root of x plus y a+bc-da plus b over c minus d?n m?(the binomial coefficient) n over mIndices
x0x zero; x nought
x1+yix one plus y i
R ij(capital) R (subscript) i j; (capital) R lower i j M kij(capital) M upper k lower i j; (capital) M superscript k subscript i j?n i=0aixisum of a i x to the i for i from nought [= zero] to n; sum over i (ranging) from zero to n of a i (times) x to the i?∞ m=1bmproduct of b m for m from one to infinity; product over m (ranging) from one to infinity of b m?n j=1aijbjksum of a i j times b j k for j from one to n; sum over j (ranging) from one to n of a i j times b j k?n i=0? n i?xiyn-isum of n over i x to the i y to the n minus i for i from nought [= zero] to n 6Matrices
columncolonne column vectorvecteur colonne determinantd´eterminant index (pl. indices)indice matrixmatrice matrix entry (pl. entries)coefficient d"une matrice m×nmatrix [mbynmatrix]matrice `amlignes etncolonnes multi-indexmultiindice rowligne row vectorvecteur ligne squarecarr´e square matrixmatrice carr´eeInequalities
x > yx is greater than y x≥yx is greater (than) or equal to y x < yx is smaller than y x >0x is positive x≥0x is positive or zero; x is non-negative x <0x is negative ?The French terminology is different! x > yx est strictement plus grand que y x≥yx est sup´erieur ou ´egal `a y x < yx est strictement plus petit que y x >0x est strictement positif x≥0x est positif ou nul x <0x est strictement n´egatifPolynomial equations
A polynomial equation of degreen≥1 with complex coefficients 7 f(x) =a0xn+a1xn-1+···+an= 0 (a0?= 0) hasncomplex solutions (= roots), provided that they are counted with multiplicities.For example, a quadratic equation
ax2+bx+c= 0 (a?= 0)
can be solved by completing the square,i.e., by rewriting the L.H.S. as a(x+ constant)2+ another constant.This leads to an equivalent equation
a x+b2a? 2 =b2-4ac4a, whose solutions are x1,2=-b±⎷Δ
2a, where Δ =b2-4ac(=a2(x1-x2)2) is the discriminant of the original equation. More precisely, ax2+bx+c=a(x-x1)(x-x2).
If all coefficientsa,b,care real, then the sign of Δ plays a crucial rˆole: if Δ = 0, thenx1=x2(=-b/2a) is a double root; if Δ>0, thenx1?=x2are both real; if Δ<0, thenx1=x2are complex conjugates of each other (and non-real).
coefficientcoefficient degreedegr´e discriminantdiscriminant equation´equationL.H.S. [= left hand side]terme de gauche
R.H.S. [= right hand side]terme de droite
polynomialadj.polynomial(e) polynomialn.polynˆome provided that`a condition que rootracine simple rootracine simple double rootracine double triple rootracine triple multiple rootracine multiple root of multiplicity mracine de multiplicit´e m 8 solutionsolution solver´esoudreCongruences
Two integersa,barecongruentmodulo a positive integermif they have the same remainder when divided bym(equivalently, if their differencea-bis a multiple ofm). a≡b(modm)a is congruent to b modulo m a≡b(m) ?Some people use the following, slightly horrible, notation:a=b[m]. Fermat"s Little Theorem.Ifpis a prime number andais an integer, then a p≡a(modp). In other words,ap-ais always divisible byp. Chinese Remainder Theorem.Ifm1,...,mkare pairwise relatively prime integers, then the system of congruences has a unique solution modulom1···mk, for any integersa1,...,ak. ?The definite article (and its absence) measure theoryth´eorie de la mesure number theoryth´eorie des nombresChapter onele chapitre un
Equation (7)l"´equation (7)
Harnack"s inequalityl"in´egalit´e de Harnack the Harnack inequality the Riemann hypothesisl"hypoth`ese de Riemann the Poincar´e conjecturela conjecture de Poincar´eMinkowski"s theoremle th´eor`eme de Minkowski
the Minkowski theorem the Dirac delta functionla fonction delta de DiracDirac"s delta function
the delta functionla fonction delta 9GeometryA BCD
ELetEbe the intersection of the diagonals of the rectangleABCD. The lines (AB) and (CD) are parallel to each other (and similarly for (BC) and (DA)). We can see on this picture severalacute angles:?EAD,?EAB,?EBA,?AED,?BEC ...;right angles: ?ABC,?BCD,?CDA,?DABandobtuse angles:?AEB,?CED. Pe Q R rLetPandQbe two points lying on an ellipsee. Denote byRthe intersection point of the respective tangent lines toeatPandQ. The linerpassing throughPandQis called the polar of the pointRw.r.t. the ellipsee. 10 Here we see three concentric circles with respective radii equal to 1, 2 and 3. If we draw a line through each vertex of a given triangle and the midpoint of the opposite side, we obtain three lines which intersect at the barycentre (= the centre of gravity) of the triangle.Above, three circles have a common tangent at their (unique) intersection point. 11Euler"s Formula
LetPbe a convex polyhedron. Euler"s formula asserts thatV-E+F= 2,
V= the number of vertices ofP,
E= the number of edges ofP,
F= the number of faces ofP.
Exercise.Use this formula to classify regular polyhedra (there are precisely five of them: tetrahedron, cube, octahedron, dodecahedron and icosahedron). For example, an icosahedron has 20 faces, 30 edges and 12 vertices. Each face is an isosceles triangle, each edge belongs to two faces and there are 5 faces meeting atquotesdbs_dbs47.pdfusesText_47[PDF] math informatique 1ère année cours
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