Discrete Math Calculators: (39) lessons

[+] Affine Cipher
Builds the Affine Cipher Translation Algorithm from a string given an a and b value

Features: Calculator | Practice Problem Generator
[+] Boolean Algebra Multiplication
Determines the product of two expressions using boolean algebra.

Features: Calculator | Watch the VideoTags: algebra, boolean, multiplication
[+] Chinese Remainder Theorem
Given 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 Subsitution

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Examples (1): x = 1 mod 2,x = 2 mod 3,x = 3 mod 5,x = 4 mod 11Tags: equation, modulus, theorem
[+] Collatz Conjecture
Takes any natural number using the Collatz Conjecture and reduces it down to 1.

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Examples (1): Collatz for 50Tags: algorithm, collatz
[+] Congruence Modulo n
Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n).

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Examples (2): 3 = 4 mod 7, 20 = 5 (mod 2)Tags: congruent, modulo
[+] Cross Partitions
Given a set of partitions, this determines the cross partitions.

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[+] Derangements - Subfactorials
Calculates the number of derangements/subfactorial !n.

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Examples (3): !5, 6 derangements, 8 subfactorialTags: derangement, factorial, permutation, subfactorial
[+] Digit Problems
Determines how many (n) digit numbers can be formed based on a variety of criteria.

Features: Calculator | Watch the VideoTags: combination, digit
[+] Diophantine Equations
Solves for ax + by = c using integer solutions if they exist

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Examples (1): 87x - 64y = 3Tags: equation, euclid, solution
[+] Euclids Algorithm and Euclids Extended Algorithm
Given 2 numbers a and b, this calculates the following
1) The Greatest Common Divisor (GCD) using Euclids Algorithm
2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm

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Examples (2): Euclids Algo for 5 and 90, Euclids Extended Algorithm for 15 and 65Tags: algorithm, euclid, greatest common factor
[+] Eulers Totient (φ)
[+] Fermats Little Theorem
For any integer a and a prime number p, this demonstrates Fermats Little Theorem.

Features: CalculatorTags: modulus, prime
[+] Finite Field
Demonstrates the addition table and multiplication table for a finite field (Galois Field) of n denoted GF(n).

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Examples (1): GF(7)Tags: addition, finite, modulus, multiplication
[+] Gamma Constant γ
This calculator generates 5000 iterations for the development of the gamma constant γ

Features: Calculator

Examples (2): gamma, gamma constantTags: constant, gamma
[+] Group Combinations
Given 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 Number
This calculator determines the nth heptagonal number

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Examples (2): 30th Heptagonal number, 45th Heptagonal numberTags: heptagon, number
[+] Hexagonal Number
This calculator determines the nth hexagonal number

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Examples (2): 30th Hexagonal number, 45th Hexagonal numberTags: hexagon, number
[+] Hyperbolic Function
Calculates hyperbolic function values: sinh, cosh, tanh, csch, sech, coth

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Examples (2): sinh(1), cosh(2)Tags: euler, function
[+] Hyperbolic Inverse
Calculates hyperbolic function values: arcsinh, arccosh, arctanh, arccsch, arcsech, arccoth

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Examples (2): arcsinh(1), arccosh(2)Tags: euler, function
[+] Interpolation
Given a set of data, this interpolates using the following methods:
* Linear Interpolation
* Nearest Neighbor (Piecewise Constant)
* Polynomial Interpolation

Features: Calculator | Quiz Generator | Practice Problem GeneratorTags: estimation, interpolation
[+] Interval Partition
Given a partitioned interval, this evaluates the norm (mesh) by calculating each subinterval

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Examples (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.

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Examples (2): lagrange for 454, bachet conjecture for 300Tags: lagrange, natural, square
[+] Letter Arrangements in a Word
Given a word, this determines the number of unique arrangements of letters in the word.

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Examples (2): word arrangments of ANIMAL, word arrangements for calculusTags: arrangements, factorial, permutation
[+] Linear Congruence
Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists

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Examples (3): 3x = 7 mod 4, 5y = 8 modulo 3, 2x is congruent to 7 mod 17Tags: congruence, equation, modulus
[+] Linear Congruential Generator
Using the linear congruential generator algorithm, this generates a list of random numbers based on your inputs

Features: Calculator | Quiz Generator | Practice Problem GeneratorTags: algorithm, encryption, seed
[+] Modular Exponentiation and Successive Squaring
Solves xn mod p using the following methods:
* Modular Exponentiation
* Successive Squaring

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Examples (2): 11^13 mod 53, 2^8633 modulo 8633Tags: exponent, modulus, square
[+] Modulus
Given 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 5

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Examples (5): 120 mod 7, 65MOD3, 145 MODULUS 8, 190 % 6, 7 mod 3+5 mod 8 - 32 mod 5Tags: modulus, remainder
[+] Multifactorials
Calculates the multifactorial n!(m)

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Examples (2): 16!!!, 30!(4)Tags: factorial, permutation
[+] Nonagonal Number
This calculator determines the nth nonagonal number

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Examples (2): 30th Nonagonal number, 45th Nonagonal numberTags: nonagon, number
[+] Number Property
This 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
* Repunit

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Examples (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 Number
This calculator determines the nth octagonal number

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Examples (2): 30th Octagonal number, 45th Octagonal numberTags: number, octagon
[+] Ordered and Unordered Partitions
Given 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)

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Examples (3): 10 partitions of 5, 18 ordered partitions of 6, 50 unordered partitions of 10Tags: factorial, partition
[+] Pentagonal Number
This calculator determines the nth pentagonal number

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Examples (2): 30th Pentagonal number, 45th Pentagonal numberTags: number, pentagon
[+] Primitive Root
Given a prime number p and a potential root of b, this determines if b is a primitive root of p.

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Examples (1): Is 3 a primitive root of 7Tags: modulus, prime number, primitive, root
[+] Quotient-Remainder Theorem
Given 2 positive integers n and d, this displays the quotient remainder theorem.

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Examples (1): 50 div 3
[+] Rectangular Number
This calculator determines the nth rectangular number

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Examples (2): 30th rectangular number, 45th rectangular numberTags: number, rectangular
[+] Sieve of Eratosthenes
Using the Sieve of Eratosthenes algorithm, this will show how many prime numbers are less than a number (n).

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Examples (2): sieve of Eratosthenes less than 40, prime numbers less than 50Tags: algorithm, prime
[+] Triangular Number
This calculator determines the nth triangular number

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Examples (2): 30th triangular number, 45th triangular numberTags: number, triangular
[+] Truth Tables
Sets up a truth table based on a logical statement of 1, 2 or 3 letters with statements such as propositions, equivalence, conjunction, disjunction, negation.

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Examples (5): P && Q, p || q, P && Q && R, P || (Q && R), !p && qTags: conjunction, disjunction, equivalence, negation, proposition