In (KI1V13005), I explored the mathematical foundations crucial for AI, focusing on proofs, calculus, and linear algebra. Below is a breakdown of the topics covered:
I got introduced to key mathematical concepts and proof techniques essential for a broad range of computer related skills.
Proofs and Sets: Learned proof writing and set theory basics.
Vectors and Spaces: Studied vectors and vector space properties.
Matrices and Maps: Explored matrices and linear transformations.
Scalar Products: Covered lengths, angles, and their applications.
Systems and Inverses: Worked on solving equations with matrices.
Eigenvalues and Induction: Analyzed eigenvalues and induction proofs.
Calculus Basics: Introduced to functions, limits, and derivatives.
Advanced Calculus: Covered partial derivatives, gradients, and integration.
Proof Writing: Constructed mathematical proofs.
Vector Operations: Performed calculations with vectors.
Matrix Manipulation: Solved systems using matrices.
Derivative Calculation: Applied differentiation techniques.
Integration: Performing integrals for computing area and volume.
Induction: Used induction to prove statements.
Function Analysis: Explored properties like cardinality and limits.