Lectures related to Lagrange Theorem: Applications and Proofs

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Explains the Intermediate Value Theorem for continuous functions on closed intervals.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Explores the proof of the Prime Number Theorem and its implications in number theory.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Covers examples of direct and indirect proofs in mathematics.

Explains compact sets, convergence, and absolute convergence in real analysis.

Covers group theory concepts like isomorphism and semi-direct product through examples and proofs.

Explores the concept of free abelian groups as an important left adjoint functor.