Lectures related to Liouville number

Algebraic Fields: Transcendence Degree

Explores transcendence degree in algebraic fields and classical analytic functions.

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.

Intersection: Sets and Properties

Explores the intersection of sets, defining it and discussing its properties.

Diophantine Approximation: Minbowski's Theorem

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

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Mixing Time Changes of Nilflows

Delves into mixing time changes in nilflows, emphasizing the delicate nature of mixing and its dependence on singularities.

Approximation and Compound Interest

Explores evaluation methods, raising numbers to a power, chess game origins, and compound interest calculations.

Real Numbers: Properties and Operations

Covers the properties and operations of real numbers, including divisibility rules and the concept of irreducible fractions.

Square Roots and Irrationality

Explores even squares, irrationality of √2, gaps in rational numbers, and minorants in Q.

Continuity of a Function

Explores the conditions for continuity of a function on real numbers.

Real Numbers: sqrt(2)

Explores real numbers, focusing on the square root of 2 and the implications of its irrationality.

Power Functions: Examples

Covers examples of solving equations with power functions and irrational exponents, emphasizing the importance of considering the domain of functions involved.

Real Numbers: Structure and Properties

Covers the structure and properties of real numbers, including the introduction to the axiomatic system and the implications of Archimedean property.

Infimum and Supremum: Understanding Bounded Sets

Explains infimum, supremum, Archimedes' properties, rational numbers density, and exercises on irrational numbers and minimum values.

Real Numbers: Absolute Value and Density

Covers absolute value, density of rationals, and real line topology.

Newton's Binomial Theorem

Explores Newton's Binomial Theorem, real positive non-integer exponents, and proof methods using contrapositive and absurd reasoning.

Real Numbers: Definitions and Properties

Explores real numbers, bounds, supremum, infimum, and Archimedean property with practical examples.

Decimal Development

Delves into infinite decimal numbers, exploring convergence and divergence, and showcasing examples of rational and irrational numbers.

Diophantine Approximation on Manifolds: Lower Bounds

Covers Diophantine approximation on manifolds with a focus on lower bounds.

Properties of Real Numbers: Bounds, Density, Absolute Value

Covers the properties of real numbers, including bounds, density, and absolute value.