Exponentiation by squaring

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Covers regular languages, encoding, alphabets, words, languages, concatenation, exponentiation, and iterative closure.

Explores defining arithmetic operations through counting, with insights on cardinal numbers, Cantor's work, and Sudoku.

Covers the basics of computer arithmetic, focusing on floating point numbers and their operations.

Covers operations with complex numbers and convergence of functions as x approaches 0.

Covers commutative groups and their significance in cryptography.

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.

Explains recursive algorithms for factorial, exponentiation, and search problems.

Explores quantum random number generation, discussing the challenges and implementations of generating good randomness using quantum devices.

Covers examples of modular exponentiation, complexities, Lame's Theorem, Collatz Conjecture, and prime numbers.

Covers Shor's factoring algorithm, which efficiently factors large numbers using quantum computers.