Lectures related to Catalan Numbers: Theory and Applications

Covers landmarks, coordinate systems, frames, and terminology in coordinates, emphasizing geometric angles and orthogonal vectors.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explores the scalar product of vectors, including properties and calculation methods.

Analyzes angular speed of rotation, internal forces, vectors, and system transformation in a solid.

Explores properties and interpretations of vectors in space, including mixed product and linear dependence.

Introduces the basics of analytical geometry, emphasizing vector representation, operations, and applications in geometry.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Covers prime numbers, vectors, 3D geometry, crystallography, and algebraic structures in materials science.