Prime Gaps and Multiplicative Sieve Inequalities

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Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Explores the existence of primes in arithmetic progressions and the properties of the Euler gamma function.

Explores the analytic and algebraic properties of Dirichlet series associated with arithmetic functions.

Explores modular arithmetic and its role in the RSA cryptosystem for error detection.

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Covers binary addition, prime numbers, and the sieve of Eratosthenes in number theory.

Covers stochastic models for communication systems, including concepts like stochastic processes and Markov chains.

Covers the calculation of the length of curves and the properties of tangent vectors.