Lectures related to Modular Arithmetic: Exponentiation Optimization

Covers prime numbers, primality testing algorithms, modular arithmetic, and efficient exponentiation methods.

Covers the fast exponentiation algorithm and its time complexity, prime number properties, and the El-Gamal encryption scheme.

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

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

Covers optimization algorithms, convergence properties, and time complexity of sequences and functions.

Explores prime numbers, modular arithmetic, Wilson's theorem, and complexity analysis.

Covers the analysis of algorithm efficiency and optimizing code for faster execution.

Explores algorithmic challenges, time complexity, optimization, recursion, and probability calculations.

Explores dynamic programming for efficient problem-solving, illustrated with binomial coefficients and Pascal's triangle.

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Covers algorithmic complexity and travel time analysis, focusing on measuring the time taken by algorithms and evaluating their performance.

Explores dynamic programming for the Knapsack problem, discussing strategies, algorithms, NP-hardness, and time complexity analysis.

Introduces greedy algorithms and matroids, highlighting their efficiency in solving optimization problems.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores the knapsack problem and the traveling salesman problem with a focus on optimization algorithms.

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Covers classical and quantum computational complexity concepts and implications.

Delves into the complexity of factoring polynomials and the implications for security.

Covers number theory, division, remainder, congruence, prime numbers, integer representation, and the Euclidean algorithm.

Explores linear programming optimization with constraints, Dijkstra's algorithm, and LP formulations for finding feasible solutions.