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37 relations: Adrien-Marie Legendre, American Mathematical Monthly, Big O notation, Constructive proof, Dirichlet's theorem on arithmetic progressions, Divisibility rule, Euclid, Euclid's Elements, Euler product, Exponential growth, Factorial, Floor and ceiling functions, Fundamental theorem of arithmetic, General topology, Geometric series, Harmonic series (mathematics), Hillel Furstenberg, Inclusion–exclusion principle, Incompressibility method, Infinite set, Irrational number, Legendre's formula, Leibniz formula for π, Leonhard Euler, Number theory, Oxford University Press, Paul Erdős, Prime number, Prime number theorem, Pronic number, Proof by contradiction, Proof of the Euler product formula for the Riemann zeta function, Reductio ad absurdum, Square number, Stirling's approximation, The Mathematical Intelligencer, Theorem.
Adrien-Marie Legendre
Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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Big O notation
Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.
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Constructive proof
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object.
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Dirichlet's theorem on arithmetic progressions
In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is a non-negative integer.
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Divisibility rule
A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.
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Euclid
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
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Euclid's Elements
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
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Euler product
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers.
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Exponential growth
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
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Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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Floor and ceiling functions
In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).
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Fundamental theorem of arithmetic
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.
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General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
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Geometric series
In mathematics, a geometric series is a series with a constant ratio between successive terms.
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Harmonic series (mathematics)
In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.
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Hillel Furstenberg
Hillel (Harry) Furstenberg (הלל (הארי) פורסטנברג) (born September 29, 1935) is an American-Israeli mathematician, a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Wolf Prize in Mathematics.
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Inclusion–exclusion principle
In combinatorics (combinatorial mathematics), the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as where A and B are two finite sets and |S| indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite).
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Incompressibility method
In mathematics, the incompressibility method is a proof method like the probabilistic method, the counting method or the pigeonhole principle.
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Infinite set
In set theory, an infinite set is a set that is not a finite set.
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Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
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Legendre's formula
In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!.
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Leibniz formula for π
In mathematics, the Leibniz formula for pi, named after Gottfried Leibniz, states that It is also called Madhava–Leibniz series as it is a special case of a more general series expansion for the inverse tangent function, first discovered by the Indian mathematician Madhava of Sangamagrama in the 14th century, the specific case first published by Leibniz around 1676.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
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Paul Erdős
Paul Erdős (Erdős Pál; 26 March 1913 – 20 September 1996) was a Hungarian mathematician.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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Prime number theorem
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.
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Pronic number
A pronic number is a number which is the product of two consecutive integers, that is, a number of the form.
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Proof by contradiction
In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition.
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Proof of the Euler product formula for the Riemann zeta function
Leonhard Euler proved the Euler product formula for the Riemann zeta function in his thesis Variae observationes circa series infinitas (Various Observations about Infinite Series), published by St Petersburg Academy in 1737.
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Reductio ad absurdum
In logic, reductio ad absurdum ("reduction to absurdity"; also argumentum ad absurdum, "argument to absurdity") is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible.
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Square number
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.
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Stirling's approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials.
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The Mathematical Intelligencer
The Mathematical Intelligencer is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.
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Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.
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Euclid theorem, Euclid theorems, Euclid's Theorem, Euclid's theorems, Infinite primes, Infinitude of prime numbers, Infinitude of primes, Infinitude of the prime numbers, Infinitude of the primes.
References
[1] https://en.wikipedia.org/wiki/Euclid's_theorem
