Lectures related to Advanced Analysis II: Methods of Calculus Composition

Delves into using polynomials for combinatorial computations and explores operations and identities with binomial coefficients.

Covers counting problems using generating functions to find solutions.

Explains permutations, binomial coefficients, and multinomial coefficients with practical examples.

Explores designing algorithms with recursion and dynamic programming, covering concepts like the Towers of Hanoi and efficient solutions.

Introduces derivatives, trigonometry, and motion principles through basic and trigonometric functions differentiation.

Covers commutative rings, fields, injective morphisms, characteristic, Frobenius, and binomial theorem.

Covers the definitions and elementary operations of real polynomials, including the binomial theorem and the Horner scheme.