Poincare Inequality: Young the Quality on the Night

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Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.

Monster Group Construction

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Quadratic Spaces and Quaternion Algebra

Explores quadratic spaces, norms, and quaternion algebra over fields.

Ring of Polynomials: Coefficients and Multiplication

Covers the ring of polynomials, focusing on coefficients and multiplication.

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Linear Algebra: Systems of Linear Equations

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

Modular Arithmetic: Foundations and Applications

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

Complex Numbers: Roots and Polynomials

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Approximations in Engineering: Leading Digits and Dominant Balance

Explores the significance of leading digits and dominant balance in engineering approximations, showcasing historical methods like slide rules and their relevance in solving challenging problems.

Linear Transformations: Matrices and Applications

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