Hello guys,
I am writing about most of the mathematics topics involved in competitive Programming.
GCD (Greatest Common Divisor)
→ Properties of GCD
→ Brute Force and Euclidean algorithm to compute GCD
→ Analysis of Euclidean algorithm
Modular Arithmetic
→ Basic properties of modulo
→ proof of condition for inverse modulo to exist
->Modulo inverse using extended euclidean algorithm with proof
→ Modulo inverse using Fermat’s theorem
→ Solution of Modulo inverse of all integers less than m
Prime Numbers
→ Properties of prime
→ Wilson’s theorem
→ School method for primality testing
→ Fermat’s theorem and its drawbacks
→ Miller-Rabin test with proof
→ Why Miller-Rabin is better
→ Deterministic version of Miller-Rabin
→ Seive of Eratosthenes
Prime Factors
→ Properties of Prime Factors
→ Proof of Number of divisors
→ Trial Division Method for Prime Factors
→ Optimization for trial Division method
→ O(N^{1/3}) algorithm for calculating number of divisors
→ Logarithmic Prime Factorisation Using Seive
Star and Bars - Combinatorics(Latest Post)
→ Star and Bars theorem with proof
→ Number of non-negative integer sum
→ Number of lower bound integer sum
→ Coefficient of x^n in (1-x)^{-k}
Combinatorics (coming soon)
Probability (coming soon)
Geometry (coming soon)
Miscellaneous topics (coming soon)
Please tell me if something is wrong or you would like me to add some more information.
Thank you and Happy Coding