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Sylvester's Theorem: Orthogonal Bases

Explores Sylvester's Theorem and the importance of orthogonal bases in linear algebra.

Modular Arithmetic: Foundations and Applications

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

Limits and Examples

Explores the concept of limits and provides examples of their existence and non-existence in various functions.

Matrix Multiplication and Inverses

Covers matrix product, inverses, and properties of invertible matrices.

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Matrix Inversion: Basics and Properties

Covers the basics of matrix inversion, properties of matrix multiplication, and the uniqueness of matrix inverses.

Differential Equations: Solutions and Uniqueness

Explores differentiability, continuity, solutions, and uniqueness in differential equations, emphasizing well-posed problems and real-world applications.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Local Invertibility: Vector Fields

Covers local invertibility of vector fields and the Inverse Function Theorem.

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