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0.0 – introduction

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0 – introduction

1 – Math and number theory introduction

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Lesson 0 : Math and number theory introduction

1.1 – Primes and Factors

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Lesson 1 : Factors and Factorization – Explanation With Code

Lesson 2 : prime factorization – Explanation with Code

Lesson 3 : The number of factors of a number n – Explanation With Code

Lesson 4 : The sum of factors of n – Explanation With Code

Lesson 5 : The product of factors of n – Explanation With Code

Lesson 6 : a perfect number

Lesson 7 : Number of primes

Lesson 8 : Density of primes

Lesson 9&10 : Check if a number is prime using sqrt or Factors – Explanation with Code

Problem 1 : CF 797 – k-Factorization

Problem 2 : CF 762A – k-th divisor

Problem 3: CF 1445C – Division

Problem 4 : CF 27E – Number With Given Divisors

Problem 5 : CF 1247D – Power Products

1.2 – The Sieve of Eratosthenes

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Lesson 11 : The Sieve of Eratosthenes – Checking if Numbers are Prime

Lesson 12 : Segmented Sieve of Eratosthenes – Checking if Numbers are Prime

Lesson 13 : Linear Sieve of Eratosthenes – Checking if Numbers are Prime

1.3 – Euclidean algorithm

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Lesson 14 : Euclidean algorithm – The greatest common divisor

Lesson 15 : Euclidean algorithm – The least common multiple

Lesson 16 : Extended Euclidean algorithm

1.4 – Euler’s totient function

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Lesson 17 : Euler’s totient function

1.5 – Modular Arithmetic

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Lesson 18 : Modular Arithmetic Explanation With Code

Lesson 19 : Modular exponentiation – ( Fast Power ) Explanation With Code

Lesson 20 : Modular Multiplicative inverse

1.6 – Conjectures

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Lesson 21 : Goldbach’s conjecture

Lesson 22 : Twin prime conjecture

Lesson 23 : Legendre’s conjecture

1.7 – Primality tests

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Lesson 24 : Fermat Primality testing

Lesson 25 : Miller Rabin Primality testing

1.8 – Solving equations

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Lesson 26 : Diophantine equations

Lesson 27 : Chinese remainder theorem

Lesson 28 : Lagrange’s theorem

Lesson 29 : Zeckendorf ’s theorem

Lesson 30 : Pythagorean triples

Lesson 31 : Wilson’s theorem

2 – Matrices

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Lesson 1 : matrix and vector

Lesson 2 : matrix Transpose

Lesson 3 : square matrix

2.1 – Matrix Operations

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Lesson 4 : Matrix multiplication – identity matrix

Lesson 5 : Matrix power

Lesson 6 : Determinant

2.2 – Linear recurrences

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Lesson 7 : linear recurrence

Lesson 8 : Fibonacci numbers

Lesson 9 : General case

3 – Probability

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Lesson 1 : Probability Calculation

Lesson 2 : Probability using sample spaces

Lesson 2 : Events

Lesson 2 : complement

Lesson 5 : union

Lesson 6 : intersection

Lesson 7 : Conditional probability

Lesson 8 : Random variables

Lesson 9 : Expected value

3.1- Distributions

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Lesson 10 : Distributions

Lesson 11 : uniform distribution

Lesson 12 : binomial distribution

Lesson 13 : geometric distribution

3.2- Markov chains

3.3- Randomized algorithms

المستوى الخامس Level 5 Math and number theory & Computational Geometry & Combinatorics

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