### Discrete Math Calculators: (39) lessons

 [+] Affine CipherBuilds the Affine Cipher Translation Algorithm from a string given an a and b valueFeatures: Calculator | Practice Problem Generator [+] Boolean Algebra MultiplicationDetermines the product of two expressions using boolean algebra.Features: Calculator | Watch the VideoTags: algebra, boolean, multiplication [+] Chinese Remainder TheoremGiven a set of modulo equations in the form: x ≡ a mod b x ≡ c mod d x ≡ e mod f the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.Given that the ni portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive SubsitutionFeatures: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (1): x = 1 mod 2,x = 2 mod 3,x = 3 mod 5,x = 4 mod 11Tags: equation, modulus, theorem [+] Collatz ConjectureTakes any natural number using the Collatz Conjecture and reduces it down to 1.Features: Calculator | Practice Problem Generator | Watch the VideoExamples (1): Collatz for 50Tags: algorithm, collatz [+] Congruence Modulo nGiven a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n).Features: Calculator | Practice Problem Generator | Watch the VideoExamples (2): 3 = 4 mod 7, 20 = 5 (mod 2)Tags: congruent, modulo [+] Cross PartitionsGiven a set of partitions, this determines the cross partitions.Features: Calculator | Practice Problem Generator | Watch the VideoTags: partition, set, subset [+] Derangements - SubfactorialsCalculates the number of derangements/subfactorial !n.Features: Calculator | Practice Problem Generator | Watch the VideoExamples (3): !5, 6 derangements, 8 subfactorialTags: derangement, factorial, permutation, subfactorial [+] Digit ProblemsDetermines how many (n) digit numbers can be formed based on a variety of criteria.Features: Calculator | Watch the VideoTags: combination, digit [+] Diophantine EquationsSolves for ax + by = c using integer solutions if they existFeatures: Calculator | Practice Problem GeneratorExamples (1): 87x - 64y = 3Tags: equation, euclid, solution [+] Euclids Algorithm and Euclids Extended AlgorithmGiven 2 numbers a and b, this calculates the following1) The Greatest Common Divisor (GCD) using Euclids Algorithm2) x and y in Bézouts Identity ax + by = d using Euclids Extended AlgorithmFeatures: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (2): Euclids Algo for 5 and 90, Euclids Extended Algorithm for 15 and 65Tags: algorithm, euclid, greatest common factor [+] Eulers Totient (φ)Given a positive integer (n), this calculates Euler's totient, also known as φFeatures: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (28): totient of 2!, phi(2), totient of 3!, phi(3), totient of 4!, phi(4), totient of 5!, phi(5), totient of 6!, phi(6), totient of 7!, phi(7), totient of 8!, phi(8), totient of 9!, phi(9), totient of 10!, phi(10), totient of 11!, phi(11), totient of 12!, phi(12), totient of 13!, phi(13), totient of 14!, phi(14), totient of 15!, phi(15)Tags: euler, phi, totient [+] Fermats Little TheoremFor any integer a and a prime number p, this demonstrates Fermats Little Theorem.Features: CalculatorTags: modulus, prime [+] Finite FieldDemonstrates the addition table and multiplication table for a finite field (Galois Field) of n denoted GF(n).Features: Calculator | Practice Problem Generator | Watch the VideoExamples (1): GF(7)Tags: addition, finite, modulus, multiplication [+] Gamma Constant γThis calculator generates 5000 iterations for the development of the gamma constant γFeatures: CalculatorExamples (2): gamma, gamma constantTags: constant, gamma [+] Group CombinationsGiven an original group of certain types of member, this determines how many groups/teams can be formed using a certain condition.Features: Calculator | Watch the VideoTags: combination, group [+] Heptagonal NumberThis calculator determines the nth heptagonal numberFeatures: Calculator | Practice Problem GeneratorExamples (2): 30th Heptagonal number, 45th Heptagonal numberTags: heptagon, number [+] Hexagonal NumberThis calculator determines the nth hexagonal numberFeatures: Calculator | Practice Problem GeneratorExamples (2): 30th Hexagonal number, 45th Hexagonal numberTags: hexagon, number [+] Hyperbolic FunctionCalculates hyperbolic function values: sinh, cosh, tanh, csch, sech, cothFeatures: Calculator | Practice Problem GeneratorExamples (2): sinh(1), cosh(2)Tags: euler, function [+] Hyperbolic InverseCalculates hyperbolic function values: arcsinh, arccosh, arctanh, arccsch, arcsech, arccothFeatures: Calculator | Practice Problem GeneratorExamples (2): arcsinh(1), arccosh(2)Tags: euler, function [+] InterpolationGiven a set of data, this interpolates using the following methods: * Linear Interpolation * Nearest Neighbor (Piecewise Constant) * Polynomial InterpolationFeatures: Calculator | Quiz Generator | Practice Problem GeneratorTags: estimation, interpolation [+] Interval PartitionGiven a partitioned interval, this evaluates the norm (mesh) by calculating each subintervalFeatures: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (1): 1,3,5,8,12Tags: interval, mesh, partition [+] Lagrange Four Square Theorem (Bachet Conjecture)Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.Features: Calculator | Practice Problem Generator | Watch the VideoExamples (2): lagrange for 454, bachet conjecture for 300Tags: lagrange, natural, square [+] Letter Arrangements in a WordGiven a word, this determines the number of unique arrangements of letters in the word.Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (2): word arrangments of ANIMAL, word arrangements for calculusTags: arrangements, factorial, permutation [+] Linear CongruenceGiven an modular equation ax ≡ b (mod m), this solves for x if a solution existsFeatures: Calculator | Practice Problem Generator | Watch the VideoExamples (3): 3x = 7 mod 4, 5y = 8 modulo 3, 2x is congruent to 7 mod 17Tags: congruence, equation, modulus [+] Linear Congruential GeneratorUsing the linear congruential generator algorithm, this generates a list of random numbers based on your inputsFeatures: Calculator | Quiz Generator | Practice Problem GeneratorTags: algorithm, encryption, seed [+] Modular Exponentiation and Successive SquaringSolves xn mod p using the following methods: * Modular Exponentiation * Successive SquaringFeatures: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (2): 11^13 mod 53, 2^8633 modulo 8633Tags: exponent, modulus, square [+] ModulusGiven 2 integers a and b, this modulo calculator determines a mod b or simplifies modular arithmetic such as 7 mod 3 + 5 mod 8 - 32 mod 5Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (5): 120 mod 7, 65MOD3, 145 MODULUS 8, 190 % 6, 7 mod 3+5 mod 8 - 32 mod 5Tags: modulus, remainder [+] MultifactorialsCalculates the multifactorial n!(m)Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (2): 16!!!, 30!(4)Tags: factorial, permutation [+] Nonagonal NumberThis calculator determines the nth nonagonal numberFeatures: Calculator | Practice Problem GeneratorExamples (2): 30th Nonagonal number, 45th Nonagonal numberTags: nonagon, number [+] Number PropertyThis calculator determines if an integer you entered has any of the following properties: * Even Numbers or Odd Numbers (Parity Function or even-odd numbers) * Evil Numbers or Odious Numbers * Perfect Numbers, Abundant Numbers, or Deficient Numbers * Triangular Numbers * Prime Numbers or Composite Numbers * Automorphic (Curious) * Undulating Numbers * Square Numbers * Cube Numbers * Palindrome Numbers * Repunit Numbers * Apocalyptic Power * Pentagonal * Tetrahedral (Pyramidal) * Narcissistic (Plus Perfect) * Catalan * RepunitFeatures: Calculator | Practice Problem Generator | Watch the VideoExamples (6): 30 as a unique number, 45 as a composite number, numerical properties of 100, properties of 35, tell me about 72, A(4)Tags: cube, divisor, even, number, odd, palindrome, pentagon, perfect, property, pyramid, square [+] Octagonal NumberThis calculator determines the nth octagonal numberFeatures: Calculator | Practice Problem GeneratorExamples (2): 30th Octagonal number, 45th Octagonal numberTags: number, octagon [+] Ordered and Unordered PartitionsGiven a population size (n) and a group population of (m), this calculator determines how many ordered or unordered groups of (m) can be formed from (n)Features: Calculator | Quiz Generator | Practice Problem Generator | Watch the VideoExamples (3): 10 partitions of 5, 18 ordered partitions of 6, 50 unordered partitions of 10Tags: factorial, partition [+] Pentagonal NumberThis calculator determines the nth pentagonal numberFeatures: Calculator | Practice Problem GeneratorExamples (2): 30th Pentagonal number, 45th Pentagonal numberTags: number, pentagon [+] Primitive RootGiven a prime number p and a potential root of b, this determines if b is a primitive root of p.Features: Calculator | Practice Problem Generator | Watch the VideoExamples (1): Is 3 a primitive root of 7Tags: modulus, prime number, primitive, root [+] Quotient-Remainder TheoremGiven 2 positive integers n and d, this displays the quotient remainder theorem.Features: Calculator | Practice Problem GeneratorExamples (1): 50 div 3 [+] Rectangular NumberThis calculator determines the nth rectangular numberFeatures: Calculator | Practice Problem GeneratorExamples (2): 30th rectangular number, 45th rectangular numberTags: number, rectangular [+] Sieve of EratosthenesUsing the Sieve of Eratosthenes algorithm, this will show how many prime numbers are less than a number (n).Features: Calculator | Practice Problem Generator | Watch the VideoExamples (2): sieve of Eratosthenes less than 40, prime numbers less than 50Tags: algorithm, prime [+] Triangular NumberThis calculator determines the nth triangular numberFeatures: Calculator | Practice Problem GeneratorExamples (2): 30th triangular number, 45th triangular numberTags: number, triangular [+] Truth TablesSets up a truth table based on a logical statement of 1, 2 or 3 letters with statements such as propositions, equivalence, conjunction, disjunction, negation.Features: Calculator | Practice Problem Generator | Watch the VideoExamples (5): P && Q, p || q, P && Q && R, P || (Q && R), !p && qTags: conjunction, disjunction, equivalence, negation, proposition