Arithmetic function

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Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Quantum Mechanics: Fundamentals

Introduces the fundamentals of quantum mechanics, covering wave functions and energy levels.

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Möbius inversion formula

Covers the Möbius inversion formula and its proof, including the change of variables in summation.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Integers: Sets, Maps, and Principles

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Inclusion-Exclusion Formula

Explores the inclusion-exclusion formula in discrete mathematics, demonstrating its applications through examples and probability scenarios.

The Pigeonhole Principle: Basics and Applications

Covers the Pigeonhole Principle, its applications, and examples of its guarantees.

Generating Functions: Advanced Counting

Covers the definition of generating functions and their application in solving recurrence relations.